Travel Behaviour Research: Updating the State of Play

TRAVEL BEHAVIOUR RESEARCH: UPDATING THE STATE OF PLAY

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TRAVEL BEHAVIOUR RESEARCH: UPDATING THE STATE OF PLAY

Edited by JUAN DE DIGS ORTUZAR Pontificia Universidad Catolica de Chile DAVID HENSHER University of Sydney and

SERGIO JARA-DIAZ Universidad de Chile

1998 ELSEVIER Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo

ELSEVIER SCIENCE Ltd The Boulevard, Langford Lane Kidlington, Oxford, OX5 1GB, UK

Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for. British Library Cataloguing in Publication Data A catalogue record from the British Library has been applied for.

First edition 1998

ISBN: 0-08-043360-X

© 1998 Elsevier Science Ltd All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. (=c) The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.

CONTENTS

Foreword

ix

Part I

Underpinnings of Travel Behaviour

Chapter 1

Behavioural Assumptions Overlooked in Travel Choice Modelling Tommy Gdrling

Chapter 2

Chapter 3

Chapter 4

Chapter 5

A General Micro-Model of Users' Behaviour: The Basic Issues Sergio R. Jam-Diaz

19

Causal Analysis in Travel Behaviour Research: A Cautionary Note Ram M. Pendyala

35

Driver Information Processing Failures in Road Accidents: From Description to Interpretation Pierre Van Elslande and Daniele Dubois

49

The Simulation of Behaviour in a Non-Experienced Future: The Case of Urban Road Pricing Charles Raux, Odile Andan and Cecile Godinot

67

Part II

Stated Preference

Chapter 6

Reflections on Stated Preference: Theory and Practice John Bates

Chapter 7

3

Stated Preference Studies: The Design Affects the Results Staffan Widlert

89

105

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Travel Behaviour Research: Updating the State of Play

Chapter 8

Chapter 9

Own Account or Hire Freight: A Stated Preference Analysis Lasse Fridstr0m and Anne Madslien

123

Behavioural Models of Airport Choice and Air Route Choice Mark A. Bradley

141

Chapter 10 A Model of Employee Participation in Telecommuting Programs Based on Stated Preference Data Jin-Ru Yen, Hani S. Mahmassani and Robert Hermann

161

Chapter 11 Discrete Logit Modelling Based on SP Data of the Analytic Hierarchy Process for Parking Choice Shoji Matsumoto and Luperfina E. Rajas

181

Part III

Travel Patterns

Chapter 12 Estimation of Origin-Destination Matrices Using Traffic Counts: An Application to Stockholm, Sweden Torgil Abrahamsson

199

Chapter 13 Two New Methods for Estimating Trip Matrices from Traffic Counts Otto Anker Nielsen

221

Chapter 14 Simple Models of Highway Reliability—Supply Effects Luis G. Willumsen and Nick B. Hounsell

251

Chapter 15 Detecting Long-Term Trends in Travel Behaviour: Problems Associated with Repeated National Personal Travel Surveys Uwe Kunert

263

Contents

vii

Chapter 16 Mobility Surveys in Lisbon and Porto: A Comparative Analysis of Results Jose Manuel Viegas and Faustina Guedes Gomes

279

Chapter 17 Changes in Urban Travel Behaviour of Elderly People Pascal Pocket

299

Chapter 18 Potential Estimate for the Acceptance of a New Motorised Bicycle in Urban Traffic: Methodic Aspects and Results Gerd Sammer, Kurt Fallast and Fritz Wernsperger

317

Chapter 19

Configurational Modelling of Urban Movement Networks Alan Penn, Bill Hillier, David Banister and Jianming Xu

339

Part IV

Dynamics of Route Choice

Chapter 20

Day-To-Day Dynamics of Urban Commuter Departure Time and Route Switching Decisions: Joint Model Estimation Rong-Chang Jou and Hani S. Mahmassani

365

Departure Time and Path Choice Models for Intercity Transit Assignment Agostino Nuzzolo and Francesco Russo

385

The Impact of Dynamic Traffic Information: Modelling Approach and Empirical Results Eric C. van Berkum and Peter H.J. van der Mede

401

Chapter 21

Chapter 22

Part V

Methodological Advancements

Chapter 23

Bayesian Reliability of Discrete Choice Models Rodrigo A. Garrido

425

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Travel Behaviour Research: Updating the State of Play

Chapter 24

Discrete Choice Models with Latent Variables using Subjective Data Takayuki Morikawa and Kuniaki Sasaki

435

Chapter 25 The Stability of Parameter Estimates in Household Based Structured Logit Models for Travel-to-Work Decisions Terje Tretvik and Staff an Widlert

457

Chapter 26 The Dependent Availability Logit Model and its Applications Wafaa Saleh and Michael G.H. Bell

473

Chapter 27

The Timing of Change for Automobile Transactions: Competing Risk Multispell Specification David A. Hensher

Chapter 28 Forecasting Car-Occupancy: Literature Review and Model Development Gerard De Jong, Andrew Daly, Hugh Gunn and Ursula Blom Chapter 29

Co-Ordination of Road Pricing Policies in Hong Kong William H.K. Lam and Rui J. Ye

487

507

527

List of Participants

541

Index

545

FOREWORD The Seventh International Conference on Travel Behaviour held in Valle Nevado, Santiago, Chile from 13-16 June 1994, hosted by the International Association of Travel Behaviour Research (IATBR), continued the commitment through the assembly of papers and participants to review the state of the art and practice in travel behaviour research. Previous conferences have been held since 1973 in South Berwick, Maine; Asheville, North Carolina; Tanunda, South Australia; Eibsee, Germany; Aixen-Provence, France; and Quebec, Canada. A total of 90 papers under 23 themes were presented in general sessions and workshops. Themes included estimation of OD matrices, car use modelling, freight modelling, stated preference methods, allocation and valuation of travel time savings, activity-based analysis, travel surveys, departure time and route choice, dynamic traffic information, behavioural policy issues such as road pricing, developments in land use and transport modelling, parking choice models, model estimation, longitudinal data and timing of change, and a range of applications in urban and interurban contexts in passenger and freight markets. Twenty-nine papers from the conference have been accepted after refereeing and revision for this book. In selecting papers the single criterion was excellence. The themes herein represent the latest published update by IATBR of the map of travel behaviour research, which in time will be updated by the proceedings of the Texas Conference held in September 1997. The book is organised into five sections, reflecting the mix of accepted papers and the predominant themes of the broader literature. As we approach the end of the 20th century we see a very strong intellectual support for the importance of research designed to improve our understanding of the behavioural responses of individuals in diverse contexts such as household decision making, organisation decisions and self-centred behavioural choice. The simplifications made historically about the formation of preferences and the stability of such preferences over time have been shown to be a primary candidate for error in predicting travel behaviour responses. While we cannot claim to have gained enough insights to totally reject historical predictions, we nevertheless are accumulating knowledge to enable researchers to distinguish between the necessity for further detail, because it does represent a significant contribution to im-

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proved understanding of traveller behaviour, and where additional detail adds little insight. The challenge will always remain to pursue further insights about behaviour, but to be able to incrementally select new inputs for the state of practice. A very good example is stated preference methods, which have a history of 20 years in transportation, where the first 10 years might be best described as speculative and suspicious by most; however, a breakthrough came in the mid-eighties when it was recognised that such tools provide an appealing way of evaluating the role of new alternatives, which are sufficiently different from currently experienced alternatives. By the early nineties, the recognition of the power of information sourced from combining revealed and stated preference data placed stated preference methods firmly at the centre of state of the art studies of traveller behaviour. As we end the 20th century we see a strong promotion of stated preference methods as enrichment tools for a market-based approach to travel demand modelling. The book is organised into five parts. The first, Underpinnings of Travel Behaviour, contains both challenges and proposals. Garling criticises micro-economic theory as an adequate theoretical basis for travel choice modelling, Jara-Diaz proposes an expanded micro-economic framework defining travel decisions as part of activity assignment, Pendyala discusses causal analysis when multiple interrelated decisions are made, and Van Elslande and Dubois look at driver's information processing failures and their incidence on accidents. The article by Raux et al. tries to rescue the simulation of behaviour as a tool for travel analysis, given the willingness to deal with a road pricing experiment by individuals, in spite of their attitude against it. This is a good interface with the contents of the second part of the book. Six papers are included in the Stated Preference section. Two of them deal with questions and expectations. On the one hand, Bates shows the difficulties inherent in SP, not to dismiss the method but to be aware of them and to overcome problems cleverly. On the other hand, Widlert's claim of wide variability in valuation results from SP studies (the design affects the results) raises important questions about the design effects of SP experiments. Four interesting applications follow. Fridstrom and Madslien analyse freight choices for the Norwegian wholesale industry, Bradley deals with airport and air route choice, and Yen et al. study telecommuting behaviour. Finally, Matsumoto and Rojas use new techniques to generate stated preferences for their analysis of parking choices, with promising results.

Foreword

xi

The section on Travel Patterns contains two papers on trip matrix estimation from traffic counts, applied to different Scandinavian regions. Both contain methodological improvements (Abrahamson, and Nielsen), and Willumsen and Hounsell look at the effects of supply on highway travel time reliability. On mobility surveys, Kunert (using German data) shows the need to supplement information on individuals and households with information on the data collection process and Viegas and Gomes report and compare two large surveys undertaken in Portugal. On a different line, Pochet concludes that car ownership is the key variable to explain changes in travel patterns of elderly people in France. Sammer et al. predict from 7 to 9 percent share of trips for a new motorised bicycle in a small size city and the findings of Penn et al. suggest the possibility of using urban design parameters (such as grid configuration, height and width of streets) to arrive at better relations between pedestrians and vehicles in urban areas. The Dynamics of Route Choice is analysed from different perspectives in three papers. A dynamic switching model with state dependence and serial correlation is calibrated to represent departure time and route choice in Dallas, by Jou and Mahmassani. The same problem is studied by Nuzzolo and Russo, but in a different context with a different method; inter-city traffic assignment using penalty functions for deviations regarding target times. Lastly, van Berkum and van deer Mede present a successful application of a route choice model that includes information processing from a variable message sign. The concluding part on Methodological Advancements includes a collection of seven papers containing theoretical developments and applications. Three are related to discrete choice modelling theory (articles by Garrido, Morikawa and Sasaki, and Saleh and Bell). Tretvik and Wiedlert present a successful experiment on transferability of travel-to-work from Stockholm to Trondheim (one tenth of the population). Two deal with car use and duration modelling with extensions to competing risks (papers by Hensher and De Jong et al.), and one expands the scope of the book by looking at road issues (Lam et al.). We cannot conclude this presentation without mentioning that the book includes one of the last joint papers by the late Robert Herman, whose example as a true researcher and guide for many generations of students and colleagues, was with us during the meeting in Austin, Texas, where he lived and taught for many years to the benefit of our profession. The editors are indebted to Chris Pringle of Elsevier Science Ltd, Oxford, for his advice and encouragement in bringing this book to fruition,

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and encouraging the editors to deliver on time. We are also grateful to Stephen Bradley at Elsevier, Oxford, for his dedicated work as Language Editor and to Sabine Plantevin at Elsevier, Amsterdam, our Production Editor, who ensured that everything was done swiftly and efficiently. Finally, thanks are also due to Joe Finegan and his team at Scanway Graphics International, Dublin, for a job truly well done. Although the Chile conference took place three years prior to the final production of this book, we are confident that its contents contribute to the currency of the state of the art and practice in travel behaviour research. Juan de Dios Ortuzar David Hensher Sergio Jara-Diaz

Part I Underpinnings of Travel Behaviour

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1

Behavioural Assumptions Overlooked in Travel-Choice Modelling Tommy Garling

Abstract The substantial theoretical basis of travel-choice modelling is criticised for being an inaccurate description of how people make choices. Drawing on research in the behavioural sciences in general, and psychology in particular, several alternative behavioural assumptions are proposed. These include problem solving in connection with interdependent choices; information acquisition, representation, and use preceding choices; accuracy-effort trade-offs in the application of decision rules for making isolated choices; the constraining influence of social factors on selfish motives; and planning and automatisation in the implementation of choices. Although less simple and elegant than the current theory, such a set of more valid behavioural assumptions is in particular needed in a field concerned with applications.

Introduction In travel-choice modelling a clear distinction is not always made between the statistical theory, on the basis of which techniques for estimating model parameters are derived, and the substantial theory which must guide any modelling of a real-world process (such as making choices). It is unfortunate for the field that the former seems to have received much more attention than the latter. In this chapter, I will focus exclusively on the substantial theory. The point I am trying to make is that this theory overlooks several important behavioural assumptions. In reviewing the proceedings of two previous travel-behaviour conferences (Garling, 1993), I made the observation that behavioural assump-

4

Travel Behaviour Research: Updating the State of Play

tions are almost always made without reference to existing theories in the behavioural sciences. To some extent, I feel this is so because of ignorance. Another important reason is that behavioural-science theories are seldom quantitative. The first reason should be relatively easy to do something about. However, with regard to the second reason, travel-choice modellers may need to realise that quantitative behavioural theories may be unattainable. At least this is the point Simon (1990) makes in a major paper. He argues that we may be unjustified in believing that it will ever be possible to discover quantitative laws that apply to human behaviour. If this statement is taken seriously, quantitative forecasting of travel demand, for instance, may never be feasible. Therefore, new ways of approaching forecasting problems are called for. Following my criticism in the next section, I will attempt to provide alternative behavioural assumptions based on current research in the behavioural sciences (in particular psychology). These assumptions have guided my own work in the field (e.g., Garling et al., 1989, 1997a, 1997b; Golledge et al., 1994). However, a full-fledged alternative theory does not exist. My suggestions are meant to indicate directions I believe future developments need to take.

Criticism of the Theoretical Basis of Travel Choice Modelling Current travel-choice modelling is based on microeconomic theory (BenAkiva and Lerman, 1985). However, for more than 30 years behavioural scientists (e.g., Camerer, 1989; Edwards, 1954; Simon, 1982; Kahneman and Tversky, 1979; see Abelson and Levy, 1985, for a review) have been arguing, and occasionally economists themselves have been arguing (March, 1978; Thaler, 1992), that this theory is not an accurate description of how people make decisions.a Contrary to a basic assumption of the theory, people's preferences have been shown to be inconsistent. For instance, there is evidence that preferences are intransitive (e.g., Tversky, 1969), that they change over time (e.g., Loewenstein and Prelec, 1993; a

Implied by this sentence is that one, or more, deliberate decisions are first made to choose something, then the choice is (observed to be) executed. Subsequently, the term decision is used interchangeably with choice. It should be clear from the context when it is assumed that choice (or behaviour) is not preceded by decisions.

Behavioural Assumptions Overlooked in Travel-Choice Modelling

5

Stevenson, 1986), and that they are influenced by the elicitation procedure (e.g., Fischhoff, 1991). I am aware of two counter arguments. One is that people's preferences are only inconsistent if they are stated, and not if they are revealed in "real behaviour". It is true that personal involvement, requirement to justify a choice to others, and real consequences of decisions occasionally have been shown to affect choices empirically (Payne et al., 1992). However, it is not always the case that such effects can be interpreted as support for microeconomic theory (Grether and Plott, 1979; Slovic and Lichtenstein, 1983). In fact, inconsistencies may sometimes increase rather than decrease. The other counter argument, formalised in random utility theory (BenAkiva and Lerman, 1985), is that inconsistencies ("taste variation") cancel at an aggregate level. Unfortunately, techniques for estimating parameters in models (such as the logit) do not seem to provide sensitive tests of systematic deviations. In fact, as shown by Camerer (1987, 1992), in markets many known systematic biases people are susceptible to, demonstrated for years in psychological research (e.g., Kahneman et al., 1982), do not cancel. On the contrary, they may contribute significantly to market dysfunction. Microeconomic theory is also incomplete. Neither does it specify what utility is (apart from a hypothetical variable lacking any other theoretical meaning), nor how it is maximised by a decision maker. The first incompleteness leads to the following circularity (McNulty, 1990): A person chooses an alternative A over B because he or she prefers it; A is preferred over B because the person chooses it. The vagueness of the concept of utility was recently noted by Kahneman and Snell (1990) who argue that a distinction should be made between experienced utility (satisfaction from consuming a good) predicted utility (anticipating satisfaction from consuming a good), and decision utility (the weight assigned to the outcome consuming the good when making a decision). In a similar vein, Garling et al. (1996) suggested a classification of utility with reference to a temporal and an experience dimension. In other research, carried out in collaboration with different colleagues (Lindberg et al., 1989, 1992), we have successfully, in some cases, attempted to find a relation between utility maximised in choices (for example of residential location) and psychologically meaningful motivational concepts such as, "happiness", "an interesting life", "inner harmony", and "moral obligation". Another related target of criticism is the underlying assumption that utility refers

6

Travel Behaviour Research: Updating the State of Play

to the selfishness motive. As discussed in Biel and Garling (1995) and, related to travel behaviour, in Garling and Sandberg (1997), research in social psychology has documented that social motives may sometimes be as equally important as selfishness for people's choices. There is also a second form of incompleteness. At best microeconomic theory specifies the variables affecting choices, tacitly assuming that information about these variables are available to the decision maker. Such assumptions are, however, frequently unjustified. They may be relaxed if it can be assumed instead that people are simply not completely informed, not that they are systematically misinformed. However, underlying the notion of bounded rationality (Simon, 1982), errors people make in acquiring and processing information before making choices are often systematic. Such findings suggest that alternative theories are both needed and feasible. Some years ago, my colleagues and I published a conceptual paper (Garling et al., 1984) where we argued that travel is guided by plans. As noted by Walmsley (1988), this is neither a new insight, nor is it hardly more than a trivial statement. However, our main point was not so much that travel is guided by plans but that information acquisition is. Our goal was to understand why people acquire cognitive maps of their environments with the properties they appear to have. Somewhat naively, we thought at that time that travel behaviour researchers would be interested in our ideas. However, with few exceptions (see, Axhausen and Garling, 1992) conceptualisations of travel choices as plans do not exist. There are also few, if any, accurate conceptualisations of information acquisition, representation and use. Once, I even heard the argument that cognitively represented information plays no role, because "objective" information about destinations is a better predictor of choices of destinations than peoples responses to questions aimed at measuring knowledge of destinations. This finding is, of course, not surprising, if reliable measures are lacking cognitive information. On what other information than a cognitive map could a choice of (for instance, a destination) be based? As we discussed (Garling et al., 1984), there are external sources of information (e.g., actual maps) that people may access. Choices are sometimes also made when people are in the place, in which case they can rely on perceptual information. A third possibility is that people are able to make educated guesses on the basis of other knowledge which they have. Yet, it cannot be denied that people acquire information which they later retrieve and use. Research shows that people acquire cognitive maps witness this (Garling and Golledge,

Behavioural Assumptions Overlooked in Travel-Choice Modelling

7

1989). Why then should people not use the information they acquire? If it is used, inaccuracies in this information will, however, affect choices. Such systematic inaccuracies are likely to apply to most people. An example is the systematic errors people seem to make in judging spatial relations (e.g., Tversky, 1981). Another example is the many systematic errors people make in forecasting events (e.g., Kahneman et al., 1982). Still another issue concerns the implementation of a choice. Since microeconomic theory does not specify the process preceding an observed choice (behaviour), this important problem has been overlooked. A few economists (Hoch and Loewenstein, 1991; Thaler and Shefrin, 1981), have been more insightful. They discussed the use of self-control techniques in the implementation of choices. Repeated successful implementation often entails developing habits. Theorising about how habits are acquired has a long tradition in behavioural research (e.g., Garling and Garvill, 1993; Roniset al., 1989). In summary, microeconomic theory is both an invalid and incomplete description of how people make choices. Therefore, it is not an appropriate theoretical basis of travel-choice modelling. In particular, the theory fails to account for (1) that choices are often part of plans; (2) that people show systematic biases in acquiring, representing and using information on which choices are based; (3) that choices, or preferences, are inconsistent; (4) that the concept of utility refers to many different entities, not all of which are related to a selfish motive; and (5) that choices are implemented through a process which sometimes entails developing habits.

Some Suggestions of Alternative Behavioural Assumptions Interdependent decisions It has been recognised that choices are frequently interdependent. In such cases, the interdependent choices are simply modelled by expanding the choice set to include all possible combinations of options. However, interdependencies go further than this. Like many other activities, making a trip requires the formation of a plan (Garling et al., 1984; Miller et al., 1960). Formation of a plan entails problem solving as it has been studied in psychological laboratories: Alternatives are generated after heuristic search in a solution space, evaluated according to designated criteria, selected and implemented. Starting with the work of Newell and Simon

8

Travel Behaviour Research: Updating the State of Play

(1972), production systems have proved to be a useful means of modelling problem solving. A production system is a set of instructions specifying the conditions under which actions should be undertaken. A review of production-system models, relevant to travel-choice modelling, is found in Garling et al. (1994). Current research on human problem solving is reviewed in many sources (e.g., Lesgold, 1988). An example of what may be called a problem-solving theory of decision making is given in Hayes-Roth and Hayes-Roth (1979). In their production-system model of how people "plan a day's errands" implemented in a computer program, planning is not a linear sequence of decisions. Rather than proceeding hierarchically from a global schematic plan, to a more refined plan, people are modelled as opportunistic in their planning. For instance, tentative decisions to perform some initial activities may highlight constraints on the planning of later activities and cause a refocusing on their planning. Furthermore, a person may decide that there is insufficient time to plan ahead, do only some rudimentary planning, or to plan meticulously. Such meta-decisions of how much to plan are also integral parts of the planning process. Other meta-decisions concern the criteria to evaluate the plan, what types of decisions to make and by what heuristics to make the decisions. In planning people change forth and back between the different levels of abstraction, rather than always proceeding orderly from the more to the less abstract. In addition to outlining the properties of planning, Hayes-Roth and Hayes-Roth (1979) attempted to specify underlying mechanisms of problem solving. This was done on the basis of data collected from subjects by means of think-aloud protocols (Ericson and Simon, 1984), as well as other conventional techniques in psychological experimentation, such as chronometry and error analyses (Ericson and Oliver, 1988). The assumption is made that planning comprises the independent actions of many "cognitive specialists", who record their decisions in a common data structure. On the basis of this available information, each specialist makes tentative decisions to be incorporated into the plan. These decisions concern the plan itself, what data are useful in developing the plan, desirable attributes of plan decisions and how to approach the planning problem. Some of the specialists suggest high-level, abstract additions to the plan, while others suggest detailed sequences of specific operations. An executive makes decisions about how to allocate cognitive resources, what types of decisions to make at certain points in time, and how to resolve conflicts when there are competing decisions. My example has two implications for the current practice of travel-

Behavioural Assumptions Overlooked in Travel-Choice Modelling

9

choice modelling. (1) The interdependence of travel choices is more conditional on the external circumstances than is usually believed; and (2) how interdependent travel decisions are made depends to a larger extent on meta-decisions than is usually believed.

Information acquisition, representation and use It is apparent that acquisition, representation and use of information, play an important role for travel choices. Unknown alternatives are not chosen. If the consequences of choosing an alternative are unknown, or misrepresented, they will also affect the choice. Thus, it is obvious that risk and uncertainty are invariably associated with consequences, although almost never considered in travel-choice modelling. A first step is to specify what information is relevant. Such a specification must take as its starting point an analysis of the information possessed by the decision maker rather than what information ought to be relevant. In particular environments, people know how far away destinations are, how they can get there, how places look so that they can be recognised from different angles, and how useful different places are in relation to the current purpose (Garling and Golledge, 1989). However, such information is never complete. Usually it is also in some ways systematically distorted (e.g., Tversky, 1981). There are several attempts at production-system modelling of the acquisition, representation and use of information about the environment (e.g., Gopal et al., 1989). The availability of geographical information systems may make further such efforts feasible (Golledge et al., 1994). Several questions remain to be answered, such as how distortions are produced, the role of affective components in the process, and how decisions depend on how the information is acquired and represented. With respect to the last question it has been shown, for instance, that a map-like spatial representation is more easily acquired if people have access to a map (Thorndyke and Hayes-Roth, 1982). In a series of studies (e.g., Garling, 1989; Garling and Garling, 1988), my collaborators and I showed that whether, or not, a spatial representation is cognitively available affects choices. It is never the case that travellers choosing among alternatives are informed about probabilities of the outcomes. However, this does not mean that they assume that the outcomes are certain. Instead, the travellers are likely to supply their own probabilities in evaluating the different alternatives. Choices will be affected since the judgements of probability

10

Travel Behaviour Research: Updating the State of Play

are probably used to weight the consequences (Tversky and Kahneman, 1992). How judgements of uncertainty are made have been extensively studied. In general they are based on heuristics which sometimes are biased relative to base rates (Kahneman et al., 1982). For instance, if a fatal accident becomes known through the mass media, many people will judge the probability of an accident to be higher. Another bias is a tendency to be overoptimistic (Zakay, 1983), at least about one's own future (Sjoberg and Biel, 1983). In making choices people who do not know the objective probability of consequences may distort them in a way consistent with such overoptimism (Hogarth and Einhorn, 1990). My examples in this subsection suggest, (1) that choice sets should be modelled more accurately with regard to how people actually acquire and represent information about environments; and (2) that the influence of risk and uncertainty on choices cannot be overlooked.

Decision rules In a major behavioural theory of how people make single, isolated choices among multiattribute alternatives, Payne et al. (1993) proposed a constructive view of decision making which captures much of the accumulated knowledge of contemporary research in the area. According to this theory, people use different heuristic decision rules in adjusting to demands such as time pressure, information overload and accuracy standards. The theory may be seen as a special case of the model proposed by Hayes-Roth and Hayes-Roth (1979), although Payne et al. (1993) argue that "top-down" processes play a more decisive role than Hayes-Roth and Hayes-Roth conjectured. Yet, instead of using the expected utility/value, additive utility or weighted additive utility decision rules, the cornerstones of utility maximisation, people use many other decision rules in response to task demands. The same single choice may even be preceded by the sequential application of several decision rules (Tversky, 1972). For instance, the number of alternatives may first be screened by means of an eliminationby-aspects, disjunctive or conjunctive decision rule, then a weighted additive decision rule used to select one of the remaining alternatives. On the basis of a computer simulation, Payne et al. (1993) were able to define how much effort each of several decision rules required. For instance, the lexicographic decision rule (choosing on the basis of the most important attribute differentiating between the alternatives) was found to require much less effort than the weighted additive decision rule (choosing

Behavioural Assumptions Overlooked in Travel-Choice Modelling

11

the alternative with the highest weighted sum of utility across all attributes). It was also found that the former rule often picked the same alternative as the latter. When introducing time pressure, the lexicographic rule actually picked this alternative much more frequently. Empirically it was shown that people tended to achieve an optimal accuracy-effort tradeoff. Another reason why people prefer decision rules other than additive utility is that these alternative rules impose less requirements on tradeoffs which presuppose an interval-scale representation of utility (Svenson, 1979). If an alternative can be found that dominates all other alternatives (i.e., an alternative that is better on at least one attribute and not worse on any), a trade-off is unnecessary. In this vein, it has been suggested that decision makers attempt to find alternatives which dominates others (Montgomery, 1989). The lexicographic decision rule is an example of that. Its application requires that people are willing to place more weight on one attribute. Another example is the conjunctive decision rule reflecting the satisficing principle (Simon, 1982): Alternatives are processed sequentially and the first one fulfilling specified criteria is chosen. As a consequence, trade-offs representing conflicts are avoided. The inconsistencies of preferences which microeconomic theory has difficulty in accommodating simply reflect the use of heuristic decision rules. Several empirically supported rationales for using such decision rules have been given. It would certainly be a mistake to conclude that observations that people use heuristic decision rules are inaccurate. It is not the observations that are in error but the theory that fails to predict them.

Selfish versus social motives In economics, selfishness is assumed to explain much individual behaviour (Samuelson, 1983). However, the picture is less simple. When there is a conflict between self-interest and what is good for the society at large, people do not always act in self-interest. In research on social dilemmas (Caporael et al., 1989; Liebrand et al., 1992) where the outcome of the self-interest choice becomes the worse alternative if a majority makes this choice, it has been found that some people restrain themselves and cooperate, even though they are anonymous and do not know how others choose. These people are assumed to have a pro-social value orientation (Liebrand and McClintock, 1988). In contrast, a pro-self value orientation

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Travel Behaviour Research: Updating the State of Play

predisposes people to act in self-interest. This, however, may be constrained. Social factors (communication, personal responsibility, group identification) are known to constrain selfishness. The dilemma structure (payoff, information feedback) is also known to do this. Biel and Garling (1995) assumed that differences depending on social value orientation remain even though self-interest is constrained. Social dilemmas have individual and collective consequences. For instance, positive consequences of choosing the automobile may be travel time, flexibility and comfort. These are consequences of a single-trip experienced by each individual. Negative consequences are noise, congestion, air pollution, energy depletion and traffic accidents. These collective consequences depend on the number of people who make the choice. They also have consequences for the individuals who in varying degrees, are exposed to noise, congestion, etc. When making the choice people may consider the individual consequences, collective consequences or individual outcomes of the collective consequences. We assume that the collective consequences are always salient to pro-social individuals. Furthermore, the individuals ignore the uncertainty associated with such consequences. To pro-self persons, the individual consequences are salient. If their selfinterest is constrained, they still focus on the individual outcomes of the collective consequences. Furthermore, they are more strongly affected by uncertainty. There are reasons to question that selfish motives always underlie choices people make. Even if they do, other motives may be prevalent if the social situation constrains self-interest. An alternative theory must accommodate such observations.

Implementing choices A decision is only an intention or commitment to behave. Reflecting that preferences may be inconsistent over time, the decision maker sometimes changes his mind and chooses not to carry out the behaviour. Under what circumstances does this occur? In other words, when are people's behaviour possible to predict from their stated choices? The latter issue has been an important topic in attitude research (Dawes and Smith, 1985). If the behaviour is carefully planned, it is more likely to be carried out due to a higher degree of commitment. Alternative behaviours may also appear less attractive than they would otherwise do (Svenson, 1992). In the case where an individual exerts control, careful planning should be

Behavioural Assumptions Overlooked in Travel-Choice Modelling

13

furthermore effective in preventing obstacles from interfering with a chosen action. The determinants of initiating a behaviour are frequently not the same as those factors which determine persistence (Ronis et al., 1989). A frequently repeated behaviour (such as commuting by automobile) is not necessarily preceded by deliberate decisions. Such behaviours are performed automatically. Several theories of automatisation have been proposed (e.g., Anderson 1982). One important consequence of automatisation is that the behaviour may be inconsistent with attitudes (Chaiken and Yates, 1985). Breaking a habit, which is not preferred, presupposes that there are alternatives which people become aware of, that the alternatives look better, the alternatives are not forgotten and the alternatives are eventually experienced as better. Implementing a choice is an important neglected phase. Time-inconsistent preferences are one reason why choices are sometimes not implemented. Automatisation explains why, in other cases, nonpreferred behaviours are performed.

Conclusions Taking my point of departure, a critical assessment of microeconomic theory (Ben-Akiva and Lerman, 1985) for being an inappropriate substantial theory for travel-choice modelling, I suggested several psychological theories that entail behavioural assumptions which are more plausible. Unfortunately, far from anything as simple and elegant as microeconomic theory has been possible to suggest. I think it must be realised that, at least at this time, there is an unavoidable trade-off between simplicity and elegance on the one hand, and accuracy on the other. In travel behaviour research, with its strong emphasis on applications, the latter should clearly be preferable if the contributions of the research are judged with regard to their relevance to real-world problems.

Acknowledgements The ideas discussed in this paper were developed in connection with a research project which was financially supported by grant No. 91-238-63 from the Swedish Transportation and Communications Research Board.

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Travel Behaviour Research: Updating the State of Play

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Liebrand, W.B.G., Messick, D.M. and Wilke, H.A.M. (eds.) (1992) Social Dilemmas. Pergamon Press, Oxford. Lindberg, E., Garling, T. and Montgomery, H. (1989) Belief-value structures as determinants of consumer behaviour: a study of housing preferences and choices. Journal of Consumer Policy 12, 119-137. Lindberg, E., Hartig, T., Garvill, J. and Garling, T. (1992) Residentiallocation preferences across the life span. Journal of Environmental Psychology 12, 187-198. Loewenstein, G. and Prelec, D. (1993) Preferences for sequences of outcomes. Psychological Review 100, 91-108. March, J.G. (1978) Bounded rationality, ambiguity, and the engineering of choice. Bell Journal of Economics 9, 587-608. McNully, T.M. (1990) Economic theory and human behaviour. The Journal of Value Inquiry 24, 325-333. Miller, G.A., Galanter, E. and Pribram, K.H. (1960) Plans and the Structure of Behaviour. Holt, Rinehart and Winston, New York. Montgomery, H. (1989) From cognition to action: the search for dominance in decision making. In H. Montgomery and O. Svenson (eds.), Process and Structure in Human Decision Making. John Wiley & Sons, New York. Newell, A. and Simon, H.A. (1972) Human Problem Solving. PrenticeHall, Englewood Cliffs. Payne, J.W., Bettman, J.R. and Johnson, EJ. (1992) Behavioural decision research: a constructive processing perspective. Annual Review of Psychology 43, 87-131. Payne, J.W., Bettman, J.R. and Johnson, E.J. (1993) The Adaptive Decision Maker. Cambridge University Press, Cambridge. Ronis, D.L., Yates, J.F., and Kirscht, J.P. (1989) Attitudes, decision, and habits as determinants of repeated behaviour. In A.R. Pratkanis, S.J. Breckler and A.J. Greenwald (eds.), Attitude Structure and Function. Erlbaum, Hillsdale, NJ. Samuelson, P.A. (1983) Foundations of Economic Analysis. Harvard University Press, Cambridge, MA. Simon, H.A. (1982) Models of Bounded Rationality. Volume 2: Behavioural Economics and Business Organisation. The MIT Press, Cambridge, Mass.

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Simon, H.A. (1990) Invariants of human behaviour. Annual Review of Psychology 41, 1-19. Sjoberg, L. and Biel, A. (1983) Mood and belief-value correlation. Acta Psychologica 53, 253-270. Slovic, P. and Lichtenstein, S. (1983) Preference reversals: a broader perspective. American Economic Review 73, 596-605. Stevenson, M.K. (1986) A discounting model for decisions with delayed positive or negative outcomes. Journal of Experimental Psychology: General 115, 131-154. Svenson, O. (1979) Process descriptions of decision making. Organisational Behaviour and Human Performance 23, 86-112. Svenson, O. (1992) Differentiation and consolidation theory of human decision making: a frame of reference for the study of pre- and postdecision processes. Acta Psychologica 80, 143-148. Thaler, R.H. (1992) The Winner's Curse: Paradoxes and Anomalies of Economic Life. Free Press, New York. Thaler, R.H. and Shefrin, H.M. (1981) An economic theory of selfcontrol. Journal of Political Economy 89, 392-410. Thorndyke, P.W. and Hayes-Roth, B. (1982) Differences in spatial knowledge acquired from maps and navigation. Cognitive Psychology 14, 560589. Tversky, A. (1969) Intransitivity of preferences. Psychological Review 76, 31-48. Tversky, A. (1972) Elimination by aspects: a theory of choice. Psychological Review 79, 281-299. Tversky, A. and Kahneman, D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5, 297-323. Tversky, B. (1981) Distortions in memory for maps. Cognitive Psychology 13, 407-433. Walmsley, D.J. (1988) Urban Living. John Wiley & Sons, New York. Zakay, D. (1983) The relationship between the probability assessor and the outcomes of an event as a determiner of subjective probability. Acta Psychologica 53, 271-280.

2

A General Micromodel of Users' Behaviour: Basic Issues Sergio R. Jam-Diaz

Abstract From a microeconomic viewpoint, the so-called modal utility in discrete choice models is a conditional indirect utility function, which represents the maximum level of satisfaction that can be reached at given prices and income if a particular mode was chosen. Therefore, its functional form represents implicitly, or explicitly, the analytical solution of an optimisation problem, thus, both the specification of direct utility (variables and form) and the type of constraints considered determine the specification of modal utility. In this chapter, the main issues behind the formulation of a general microeconomic model of users' behaviour are discussed. The model is motivated by, and contrasted against, other forms of representing the primal problem of individual behaviour, coming either from the microeconomic literature on the role of time in consumer's behaviour (Becker, 1965; DeSerpa, 1971; Evans, 1972), or from the approaches that yield, or discuss mode choice models with a microeconomic perspective (McFadden, 1981; Train and McFadden, 1978; Viton, 1985; Truong and Hensher, 1985; Bates, 1987; Jara-Diaz and Farah, 1987). The implications of the new formulation on actual modelling under different assumptions are presented and discussed.

Introduction In discrete mode choice modelling, utility is, in fact, a truncated conditional indirect utility function. Therefore, it corresponds to the solution of an optimisation problem representing consumer behaviour. The functional form, and the arguments of modal utility, are thus determined by the analytical properties of direct utility, by the variables that are assumed to influence this latter and by the type of constraints considered.

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Travel Behaviour Research: Updating the State of Play

The aim of this chapter is to detect and discuss the issues behind the formulation of a model for consumer behaviour, in order to justify a new framework to understand users' choices. In the next section, I review the foundations of consumer models that include time in the analysis; in the third section, the microeconomics of mode choice are critically synthesised. Then I formulate a model for users' behaviour, discussing the issues raised in the previous analysis. Additional comments are given in the final section.

Transport Related Microeconomic Individual Behaviour Models The introduction of time in the models of individual behaviour was a major step towards the understanding of transport within the context of human activities. These microeconomic models have had a great influence in the subsequent generation of theoretical approaches that have provided the foundations for the presently used specifications of (discrete) mode choice models. The particular form in which each author formulates the basic problem of utility maximisation subject to different type of constraints, has an impact on the interpretation of behaviour. And there are important differences among the most relevant of the articles in this area of literature. It is well known that the basic consumer model postulates that utility depends upon the level of consumption of market goods (X), which is maximised subject to a budget constraint. In his pioneering article, Becker (1965) presents a formulation in which utility depends on the consumption of "basic commodities" (Z), which require both market goods and time to be prepared (T); he then introduces income and time constraints, including working hours as a variable (W}. So his basic model is

subject to

where r is total time available, IF is other (fixed) income and w is the wage rate. As Becker (1965, pp. 496-497) points out, the constraints are

A General Micromodel of Users' Behaviour

21

not independent "because time can be converted into goods by using less time at consumption and more at work". In fact, if one solves for W in equation (3) and replaces the result in equation (2), then

where bt and tt are the market goods and time requirement per unit of Z,. Becker names the righthand side of equation (4) "full income", and represents the maximum amount of money the individual could make working the whole period. Under this setting, the term that multiplies Z/ represents the full price of consumption, including the expenditure on the necessary market goods plus foregone income. The main contribution of Becker is to analyse all properties of demand in terms of this "full price", that has a time component. It is fairly evident that Becker's assertion of "time can be converted into goods" is possible because of two apparently innocent features of the model: first, working hours can be chosen freely, and second, they do not appear as arguments in the utility function. This, indeed, has an impact in terms of the interpretation of the results. Besides some other problems in the model, these are important limitations which are taken into account in subsequent influential pieces by DeSerpa (1971) and Evans (1972). However, Becker's work remain an important reference.3 A few years later, DeSerpa (1971) proposed a model in which the time necessary to consume market good i affects utility, together with the amount consumed. He includes both income and time constraints, and added what can be identified as the first set of "technical" constraints, in the form of minimum time requirements to consume a given market good. Thus, his model looks like

subject to

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Travel Behaviour Research: Updating the State of Play

where T now includes all activities. Note that, although utility has the same arguments as Becker's model, this is justified in a different direction, as the time devoted to consumption has a direct effect on the individual's level of satisfaction. Within this context, it is important to note that DeSerpa calls the consumption of Xt an "activity". Also, he explains that the model can be generalised to include a work commodity, "pure time" commodities and negative prices. He is the first to point out that the value of saving time in the activity is positive only when the corresponding time consumption constraint is active (i.e. the individual would have liked to spend less time than required). DeSerpa's framework helps to clarify important conceptual aspects regarding the value of time, and his article is a valuable source for further discussion. Key points and views regarding utility and constraints were neatly exposed by Evans (1972). He made a strong remark regarding Becker's synthesis of constraints (2) and (3), recalling that working time should also be included as an argument in utility (previously mentioned by Johnson, 1966; Oort, 1969), which would prevent W from being used as a "pivot" variable in the constraints. After this, Evans proposes a model in which the only source of direct utility is the time devoted to the different activities; market goods enter the picture as inputs that are necessary to develop each activity, and they are the source of the activity cost. Pure time activities are allowed to exist simply as a particular case, and their cost can be either positive (the individuals pays), or negative (the individual is paid). Besides, Evans introduces a set of constraints representing relations among activities, which means that time devoted to activity / can be technically related with time spent on activity;. Formally (in our notation) Evans model is

subject to

A General Micromodel of Users' Behaviour

23

where Q is a matrix containing the input of goods at a certain rate per unit of time, which are required for each activity, and B is a matrix that links activity times. As T includes all activities, equation (10) is the budget constraint with a negative wage rate as one component of P. If the three basic articles are viewed from a positive perspective, we can see similarities and differences. All three are extensions of the basic consumer approach to encompass time requirements for consumption, which induces the need for a time availability constraint. The arguments in (direct) utility are the basic commodities Z (Becker, 1965), goods X and consumption time T (DeSerpa, 1971), and activity time T (Evans, 1972). Although these three views of utility might appear as an issue to be discussed regardless of the role of the constraints, it is more rewarding to look at the whole formulation in each case. In my view, one of the most important aspects in these models that include goods and time, is precisely the relation between them; and this is only present in Evans' framework. This is evident when one sees that, in order to get equation (10), the relation

has to hold. Equation (14) is an explicit transformation function with fixed coefficients, which gives the combination of outputs needed to perform a set T of activities. This does not appear in DeSerpa's framework, because TI is directly linked to Xt. In my view, the physical link between goods and time is a key aspect in the formulation of a general model of consumer behaviour. Before discussing the approaches that are specifically designed to understand transportation decisions (mode choice, in fact), let me point out three aspects that are very much related to these important articles. First, note that the very existence of a transformation function between goods and time would make a U(X, T) type utility function a U(T) one, but that this would not be neutral regarding the budget constraint, because X is postulated as a direct source of utility. Second, only Evans introduces an explicit set of relations among activities (time) which goes beyond the fact that similar (or the same) goods can be involved in two different activities; one can claim, however, that if two activities are closely related functionally, then a single (aggregate) activity could always be defined. Finally, note that commodity consumption is still the central point in both Becker's and DeSerpa's frameworks; as for Becker, T is a factor to produce final goods Z, and for DeSerpa T is part of the description of X;

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Travel Behaviour Research: Updating the State of Play

in Evans, however, it is X that plays a "secondary" role, as buying goods is a means to enjoy T, and this is conceptually neat and reasonable.

Microeconomic Foundations of Discrete Mode Choice Models The literature on the microeconomics of mode choice is not as numerous as one could have imagined. And, still today, the most influential pieces are the Train and McFadden (1978) goods-leisure trade off framework, and McFadden's (1981) ambitious piece. For the purposes of this chapter, the article by Truong and Hensher (1985), Bates' (1987) sharp comment, and the interpretative synthesis by Bates and Roberts (1986), are valuable sources of discussion, although all three were meant to be contributions to the discussion on the value of time. For different reasons, the articles by Viton (1985) and Jara-Diaz and Farah (1987) have some relevance in our discussion because of the analysis of the role of income. The goods-leisure trade off framework for mode choice models (Train and McFadden, 1978) postulates that the basic sources of utility are the consumption of goods and the time devoted to leisure. In the original formulation, the conflict between both sources is due to the choice of working hours, paid at a fixed (exogenous) rate: the more the individual works, the more s/he can consume and the less leisure time is available. The two constraints are income and time related, respectively; in both, working hours is the key adjustable variable, and mode choice appears as a (discrete) decision among feasible pairs (c/, ?/), where ct and r, are travel cost and time (for mode /), respectively. Letting working hours play the central role in the constraints makes this approach a Becker-type one, as the opportunity cost of any activity (leisure or travel) will always be the wage rate. And this happens in spite of the seemingly different utility formulations. In our restatement of the goods-leisure framework (Jara-Diaz and Farah, 1987), we imposed an exogenous working schedule to the individual (we have called this the "public servant" framework), such that both income and working time are fixed and given. Under this setting, mode choice (i.e. the choice of ct and tf from a discrete set) is the only source of conflict between consumption and leisure, induced by the existence of fast-expensive modes and slow-cheap ones. We have shown that, in this case, what matters is the time available to spend the given income, which originates our expenditure rate models (Jara-Diaz and Ortuzar, 1989).

A General Micromodel of Users' Behaviour

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A general formulation of the goods-leisure approach can be synthesised as follows:

subject to

where G is goods expenditure, and L leisure time (v and /implies variable and fixed, respectively). The variable working time Wv is now a choice. If this is compared against Becker's equations (1), (2) and (3), G is 2) PfXi, Wv + WF = W, and L = S Tt. Note, that again working time does not appear in the direct utility function. Replacing both G and L in U by the corresponding functions of Wv from the constraints, problem (15)(18) turns into an unconstrained one which can be written as

mode choice set. The solution of problem (19) for i e M,

WV^Q

where M is the mode choice set. The solution of equation (19) for a given pair (c(, tf) yields a conditional optimum for Wv, which is, in fact, W*(IF- c{, T - WF— ?,-). Replacing this function in the original utility expression, a conditional indirect utility function is obtained. This analytical procedure works well if we end up with a positive value for Wv. However, if the case is one in which the individual is working more than desired (i.e. s/he would reduce WF if possible), then Wv will be zero and the only source of trade-off between goods and leisure is mode choice; equations (15)-(18) encompasses both cases. If Wv happens to be positive (which is something truly observable), then the value of leisure is the wage rate under this framework. Therefore, although they look different and their utilities have different foundations, Train and McFadden (1978) and Becker (1965) are in fact the same model. Let me recall, however, that X and T in Becker are the

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Travel Behaviour Research: Updating the State of Play

inputs to obtain the basic commodities Z, and they are treated as a vector, as opposed to G and L, which are aggregates. The framework proposed by Truong and Hensher (1985), cleverly corrected and enhanced by Bates (1987), is useful to highlight a couple of points that are very important for the purpose of this chapter. Truong, Hensher and Bates (THE) tried to translate both Becker's and DeSerpa's general frameworks into (discrete) mode choice formulations. Due to the presence of DeSerpa's technical constraints regarding minimum time requirements (see equation (8)), they show that the conditional indirect (modal) utility should have a mode-specific time coefficient; this coefficient should be generic if mode choice was derived from Becker's framework. This difference is also influenced by the fact that travel time does not enter direct utility in the so-called Becker type model, while it does not appear explicitly in DeSerpa's counterpart. In both cases, the THE formulation follows the goods-leisure approach which, as we have seen, is in fact Becker's. However, since goods and "activities" in DeSerpa's are also vectors explicitly written as such, also since working time is not adjustable, and since additional time constraints appear, interpreting DeSerpa's utility arguments X and T as goods and leisure is a misuse. Thus, what to use as an argument in direct utility, what constraints should be considered, and what is fixed or what is variable, are key decisions in proposing a framework for the modelling and understanding of travel decisions. As Viton (1985) pointed out, the modeller should also be careful with the way income is treated in modal utility, a point that later we have hopefully contributed to solve more precisely as part of an approach to detect income effect in mode choice (Jara-Diaz and Videla, 1989).

A General Model for Travel Behaviour As we have seen, there are basic questions that must be answered in order to formulate a model for travellers. From the literature, each one can be formulated as a particular problem and given a general interpretation. First, an explicitly relevant one: should working time enter direct utility as an argument? (both Evans and Bates highlight the importance of this). My position coincides with Evans: that the basic source of utility is the time devoted to the different activities, to all activities, including work, travel, sleep, chat and so on. In fact, this view has received some attention within the last decade, as in Winston (1987), who emphasises activity

A General Micromodel of Users' Behaviour

27

scheduling, and luster (1990), who sees "process benefits from time uses" as the main source of satisfaction (surprisingly, neither mention Evans paper). And then comes the second question: how do goods enter the picture? In a twofold manner, I propose: as necessary items to perform the different activities, and as the basic source of expenses. Third, should we account for time constraints on each activity? In my view, the time period devoted to each activity is potentially related to all other activities in two ways: direct time dependency (i.e. the duration of one activity affecting the duration of other activities), and through the use of common (or interrelated) goods. According to the preceding discussion on the relevant approaches and theories, a model of travel choices can be looked at as a time allocation problem, recognising that utility is directly derived from what the individual does (activities), which requires goods that are costly. Therefore, I propose the following model:

T

s

u

b

j

e

c

t

t

o

where W/ is working time in period T (i = F, fixed; i = v, variable); T is a vector of activity times Tt in period T; r is a vector of travel times ?,, in period r; B is the number of trips in period r; 8r; = 1 if mode / is used in trip / (0 otherwise); F is a technical transformation function that converts T into X and vice versa; Xid is the amount of good / bought in zone d in period r; Pid is the price of good / in zone d; MJ is the set of modes available for trip /. Thus, all activities have a direct impact on utility, in spite of the fact that some of them are sought out (pleasurable activities) and some are required or unavoidable, but ideally would not be performed. The sum of all activity times includes work, travel and pure idle time in addition

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Travel Behaviour Research: Updating the State of Play

to sleeping, eating, talking, shopping, watching TV and so on. But, as justified earlier, activities are interrelated by themselves and through goods requirement. Therefore, one cannot view equations (20) and (21) as an independent optimisation subproblem, because it requires the set of relations represented by the transformation function (22), which in turn, makes the optimal solution dependent on goods consumption. In this model, goods can be bought in different locations and, at potentially different prices. As residence and work places are given, the number of trips is only sensitive to the choice of X, a relation which appears as equation (24); this can be viewed as the result of a network related subproblem (e.g. optimal number of trips given X). Under this view, the known (given) variables are WF, IF, ?,;-> c,7, r, Pid and w, while the decision variables are {Tf}, {§,7}, {Xid}, Wv and B. The solution for B is the generation model, the solution for X is the distribution model and the solution for d is the mode choice model. This formulation is not compatible with the goods-leisure framework, though. As discussed earlier, ^Tt = L and *2PidXid=G; because of the technical relation between X and T, there is an implicit relation between G and L, which has a straightforward interpretation: goods consumption requires L and vice versa, which is a missing fact in both the Becker and Train-McFadden models. In order to explore some implications of this model, let us see how it develops when analysing mode choice in the case of one trip k. This is a useful exercise, as it is the prevailing modelling practice in the field. All other trip decisions will be assumed as given, i.e. number of trips B, destinations (which are one of the dimensions in X), and all other mode choices. Then we can write

subject to

plus the non-negativity constraints. For simplicity only, relation (24) be-

A General Micromodel of Users' Behaviour

29

tween B and X has been dropped, which means that the amount of goods does not affect the number of trips. As usual in the discrete choice approach, problem (25)-(28) can be solved conditional on mode choice, which yields conditional solutions for T, T±X and W. Formally,

where t and c are obviously defined, and tp is the vector of travel times except tik. Then the conditional indirect utility function corresponds to

In spite of its generality, equation (32) is very helpful in explicitly showing some key aspects in the specification of modal utility. First, unlike modal cost, travel time plays a dual role in the indirect utility: it provides direct (dis)satisfaction, as a survivor from U in equation (25), and it affects available time to do other activities, as a consequence of constraint (26). This second role of travel time deals with the trade-off with pleasurable activities, e.g. sleeping until late or playing guitar with your children at night (or working more). The thing is, and this is part of the second key aspect, that both roles can not be distinguished if Vin (32) is approximated linearly; if this was accepted as a reasonable representation of (indirect) utility, the conditional comparisons would be based upon an expression like:

and the only terms that would influence mode choice would be

30

Travel Behaviour Research: Updating the State of Play

from which one can only estimate (g-a) and d, but neither g nor a can be obtained. Note also that a first-order approximation like equation (33) would make all variables except travel time and cost, irrelevant (e.g. no income effect). This would not happen if a second-order expansion was considered a better model than this. In fact, our test for the detection of income effect in mode choice rests ultimately on the significance of a second order term (Jara-Diaz and Videla, 1989); a similar approach is used to theoretically justify a segmentation by distance travelled (JaraDiaz, 1990). The third point that I would like to highlight is the role of the wage rate w. In this framework, the relevant value of w is the hourly payment the individual is offered to do extra work; it is true that this might have a relation with IF/WFbut, under the "public servant" scheme, w represents the real opportunity cost of activities performed outside the (fixed) working schedule. According to this, individuals in a sample should be asked about their work arrangement; if the individual has a fixed salary and fixed working time, s/he should be asked the value of the wage rate for additional work, as this is the value that should enter modal utility. Unlike direct utility, the conditional indirect modal utility in equation (32) can be interpreted in terms of "goods and leisure", as the first argument is, in fact, the total time available to perform T (which I have associated to L), or to keep on working, and the last argument is the time equivalent to buy X, i.e. G/w, minus the actual extra time worked. Formally,

which explicitly shows the difference with the U(G, L) approach.

Final Comments From a critical but constructive analysis of the microeconomic foundations of models related to trip decisions, some issues have been clearly established. First is the question of the sources of direct utility; starting from goods consumed and going through the concept of basic commodities, consumption time appeared as a necessary item to realise utility. After this shy beginning, time devoted to activities emerged as the basic source

A General Micromodel of Users' Behaviour

31

of satisfaction, and it is the goods that should be seen as the means to an end. Once this is accepted, every single minute in a period should be considered. The preceding analysis makes both work and travel times, variables that enter utility with the same rights and duties as all other activities. Thus, time can not be converted into money (through more work) without altering utility, which makes the fusion of income and time constraints a mistake. Second, the traditional time and income budget constraints are not enough to complete the picture of individual behaviour, as market goods and consumption time are related (as well as activities themselves). Just as the previous point, this also weakens the conceptual foundations of the goods-leisure framework. The addition of a set of technical constraints induces the need to perform certain activities which would be omitted otherwise. This is a point raised originally by DeSerpa and Evans, introduced later in the discrete choice literature by Hensher and Bates. It is surprising, though, that no explicit reference to a transformation function has been made within the context of mode choice, or that goods and leisure are still kept as the basic sources of utility. In my view, this needs revision and discussions; Evans contribution seems to be the best departure point. I hope this chapter will encourage further work in this direction. Finally, in agreement with Juster (1990), let me add that the vector of goods, X, should be rescued as a direct source of utility in addition to the time devoted to each activity. The main reason is that one should expect the marginal utility derived from a given activity to be dependent on the type and amount of goods involved. Thus, a U(X, T) utility function might well be justifiable through an activity approach, but emphasis would be on T rather than on X.

Acknowledgement This research was partially funded by FONDECYT, Chile.

References Bates, J.J. (1987) Measuring travel time values with a discrete choice model: a note. The Economic Journal 97, 493-498.

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Travel Behaviour Research: Updating the State of Play

Bates, J.J. and Roberts, M. (1986) Value of time research: summary of methodology and findings. Proceedings 14th PTRC Summer Annual Meeting, University of Sussex, July 1986, UK. Becker, G. (1965) A theory of the allocation of time. The Economic Journal 75, 493-517. DeSerpa, A. (1971) A theory of the economics of time. The Economic Journal 81, 828-846. Evans, A. (1972) On the theory of the valuation and allocation of time. Scottish Journal of Political Economy 19, 1-17. Gaudry, M.J.I., Jara-Diaz, S.R. and Ortuzar, J. de D. (1989) Value of time sensitivity to model specification. Transportation Research 23B, 151-158. Gronau, R. (1986) Home production: a survey. In O. Ashenfelter and R. Layard (eds.), Handbook of Labour Economics, Vol. 1. North Holland, Amsterdam. Jara-Diaz, S.R. (1990) Valor subjetivo del tiempo y utilidad marginal del ingreso en modelos de partition modal. Apuntes de Ingenieria 39, 4150. Jara-Diaz, S.R. and Farah, M. (1987) Transport demand and user's benefits with fixed income: the goods/leisure trade-off revisited. Transportation Research 21B, 165-170. Jara-Diaz, S.R, and Ortuzar, J. de D. (1989) Introducing the expenditure rate in the estimation of mode choice models. Journal of Transport Economics and Policy XXIII, 293-308. Jara-Diaz, S.R. and Videla, J. (1989) Detection of income effect in mode choice: theory and application. Transportation Research 23B, 393-400. Johnson, B. (1966) Travel time and the price of leisure. Western Economic Journal 8, 135-145. Juster, F.T. (1990) Rethinking utility theory. The Journal of Behavioural Economics 19, 155-179. McFadden, D. (1981) Econometric models of probabilistic choice. In C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data: With Econometric Applications. The MIT Press, Cambridge, Mass. Oort, C. (1969) The evaluation of travelling time. Journal of Transport Economics and Policy HI, 279-286. Train, K. and McFadden, D. (1978) The goods/leisure trade-off and disag-

A General Micromodel of Users' Behaviour

33

gregate work trip mode choice models. Transportation Research 12, 349-353. Truong, P. and Hensher, D.A. (1985) Measurement of travel time values and opportunity cost from a discrete-choice model. The Economic Journal 95, 438-451. Viton, P. (1985) On the interpretation of income variables in discrete choice models. Economic Letters 17, 203-206. Winston, G.C. (1987) Activity choice: a new approach to economic behaviour. Journal of Economic Behaviour and Organisation 8, 567-585.

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3

Causal Analysis in Travel Behaviour Research: A Cautionary Note Ram M. Pendyala

Abstract Causal models are increasingly being used in travel demand analysis as they offer greater insights into cause-and-effect relationships underlying travel behaviour. However, these modelling efforts usually assign the same causal relationships to the entire population under study. The inherent assumption that the same causal structure governs the behaviour of the entire population may be incorrect, as human behaviour is known to exhibit considerable variation both within and between behavioural units. This chapter investigates the extent to which such structural heterogeneity can be captured by models. The study involves an experiment in which model estimation is performed on simulated structurally heterogeneous data sets. The effect of structural heterogeneity on properties of parameter estimates is examined in detail. Based on the results of the experiment, the chapter concludes with a cautionary note on the estimation of causal models in travel behaviour research.

Introduction The development and implementation of effective transportation planning measures requires the ability to accurately model and forecast travel demand as it evolves over time. In particular, a planner needs to model cause-and-effect relationships governing travel behaviour to be able to answer "what-if" scenario based questions for alternative transportation policies. This need is being increasingly felt by transportation planners around the world as the focus of planning has shifted from facility expansion to the application of effective travel demand management strategies. An understanding of causal relationships underlying travel behaviour

36

Travel Behaviour Research: Updating the State of Play

would potentially better facilitate the evaluation of planning projects, trip reduction measures, alternative fuel vehicles, and advanced technologies. For this reason, causal analysis has been gaining increasing attention in travel behaviour research. Causal analysis has interested researchers in various fields of science and engineering for several reasons. Causal relationships may be considered to represent the most fundamental understanding of a phenomenon under study. Potentially, knowledge of causal relationships allows one to formulate policies and influence behaviour in an effective and more predictable way (Bagozzi, 1982; Blalock, 1985). Causal modelling efforts were first employed in biological (e.g. Wright, 1934) and psychosocial sciences (e.g. Greenwood, 1945). Due to the evident attractiveness of causal modelling, these initial efforts were soon followed by extensive applications in numerous other fields of research. The widespread application of causal models was further facilitated through advances in statistical and econometric estimation techniques coupled with improvements in computational resources. For example, causal models have been applied in sociology to study causes of crime (Ahn, 1985), in economics to study national income and expenditures (Sahni and Singh, 1984), in marketing to study consumer purchasing behaviour (Bagozzi, 1982), and in psychology to track causes of juvenile delinquency (Belson, 1985). Applications of causal models in the pure sciences include investigations into causes of various diseases in medical research (Elwood, 1988), factors contributing to plant and animal growth in botany and zoology (Braakhekke, 1980), and determinants of manufacturing system productivity in engineering (Horn, 1990). Causal modelling soon found application in transportation engineering and planning. In travel behaviour research, causal models have been applied to study various aspects of travel behaviour. Goodwin (1987) studied relationships between changes in family structure and public transport use. Kitamura (1987) analysed causal relationships between car ownership levels and car utilisation. Kitamura (1989) used the log-linear modelling method to estimate causal linkages between car ownership and transit use. Lyon (1984), Golob (1989), Golob and Meurs (1987) and van Wissen and Golob (1990) have used various econometric and sociometric methods to analyse causal relationships among trip generation, mode choice, attitudes and perceptions, travel time expenditures, and travel distances. These represent but a small fraction of the applications of causal modelling in travel behaviour research. A more extensive and thorough review can be found in Pendyala (1992).

Causal Analysis in Travel Behaviour Research

37

This paper addresses an important issue concerned with the specification and estimation of causal models. This issue is related to the behavioural paradigm that different behavioural units within the same population may be driven by differing causal mechanisms. More often than not, especially when dealing with human behaviour, the same data set may have several causal structures governing relationships among variables. However, causal modelling efforts assign the same set of causal relationships to all behavioural units in the study population. In other words, a strong assumption that all behavioural units are driven by the same causal mechanism is inherent in causal modelling. This assumption is questionable considering that human behaviour tends to show considerable variation both within and between behavioural units (Middlebrook, 1974). In this paper, the variation in causal relationships between behavioural units will be termed "structural heterogeneity". Examples of such structural heterogeneity can be found in numerous areas of behavioural research. In travel behaviour research, household car ownership may be driven by trip generation for a portion of the population, while trip generation may be driven by car ownership for another portion of the population. These represent causally opposite decision-making mechanisms. In addition, there may be a third portion of the population for whom there is no causal relationship between trip generation and car ownership at all. If all three possible sets of relationships are embedded in a data set, can model systems represent such structurally heterogeneous populations and if so, to what degree of accuracy? What is the effect of the presence of structural heterogeneity on the statistical properties of parameter estimates? The fundamental questions raised above need to be answered before causal models can be applied effectively in behavioural research. This paper investigates the impacts of structural heterogeneity on causal model estimability and statistical properties of parameter estimates. An experimental approach is adopted to make this assessment. Model systems are estimated on structurally heterogeneous data sets that are simulated (generated) based on known relationships. Model estimates are compared against true parameter values to assess the effects of structural heterogeneity on model estimation. In the next section, the problem statement is described and illustrated in greater detail. This is followed by a description of the simulation experiment. The fourth section presents the results of the simulation experiment while the fifth and final section provides concluding remarks.

38

Travel Behaviour Research: Updating the State of Play

Structural Heterogeneity in Travel Behaviour Human travel behaviour is very complex and is characterised by a substantial amount of randomness. (Hanson and Huff, 1982). It is very likely that different behavioural units are driven by different causal mechanisms. In fact, the causal mechanism underlying behaviour may vary for the same behavioural unit depending on the circumstances in which a travel decision has to be made. However, models tend to assign the same causal relationships to all behavioural units. This may not be appropriate given that decision-making rules differ across behavioural units and over time (Middlebrook, 1974). There are several examples of such possible structural heterogeneity in travel behaviour. For example, mode choice and destination choice are inter-related travel characteristics and the direction of causation between them may be different for different people. For some population units, mode choice may be driven by destination choice. As an example, consider a shopping trip. Choosing to shop at a place close to home may make the person opt to use the bicycle or walk, while choosing to shop at a store far away from home may entail using the car. In this case, it is clear that destination choice preceded and lead to a choice of mode. In contrast, some other population units of the study area may be driven by mode choice. Suppose a person chooses to drive because a car is available, it is night and unsafe to walk, or needs to trip chain with other trip purposes. Then, this person may choose to shop at a location farther from home because the car is being used anyway. On the other hand, if the person is taking an evening stroll, the shop close to home will be chosen. In this case, choice of destination is driven by the choice of transport mode. Two more types of relationships are possible. The first would be one in which mode and destination are chosen simultaneously. In this case, the person would make the decisions to go to a store far away and use the car simultaneously. Finally, mode choice and destination choice may not be related at all for some people. A person who is handicapped may choose to drive for reasons of safety and convenience. However, this person may choose to shop at a place closer to home because it would be cumbersome to drive long distances. In this case, clearly mode choice and destination choice are not related in reality, and any relation that does exist between them is purely spurious because the choices were actually influenced by the common variable "being handicapped". Similarly, other examples of relationships that may differ across behavioural units and over time may be conjectured. Car ownership, mode

Causal Analysis in Travel Behaviour Research

39

choice, travel destination choice, route choice, and trip frequency are all aspects of travel behaviour, the relationships among which may be different for different people. This may have serious implications for forecasting and impact assessment of travel demand management strategies. Assuming a certain causal relationship for all behavioural units, when in fact, only a certain segment follows that relationship, may lead to highly erroneous forecasts. Impact assessments performed on the basis of such strong assumptions may be inaccurate and implementation of a travel demand strategy on a large scale may yield results that are very different from what it was originally intended to provide. Considering the importance of this issue, the question that merits immediate attention is whether models can reveal true causal relationships in the presence of structurally heterogeneous population segments. Also, the impact of structural heterogeneity on statistical properties of parameter estimates needs to be assessed. In the next section, a simulation experiment aimed at addressing these questions is described in detail.

Experimental Design and Procedure This section describes a simulation experiment aimed at assessing the extent to which models can replicate causal relationships in structurally heterogeneous samples. Such an assessment would be best accomplished by comparing model estimates against true parameter values. However, as true parameter values are never known a priori in real-world data sets, it was considered most appropriate to adopt an experimental approach. In the experiment, two model systems representing causally opposite structures are developed. Data sets generated using each structure are then pooled to form a structurally heterogeneous sample, such that the unified data set has two completely different underlying causal relationships. One of the two underlying model systems is estimated on the pooled data set to assess the accuracy with which models can capture causal relationships in the presence of structural heterogeneity.

Specification of Causal Structures Quite often, behavioural phenomena are characterised by several variables interacting among each other simultaneously (Maddala, 1983). In travel demand analysis, car ownership, mode choice, trip generation, vehicle

40

Travel Behaviour Research: Updating the State of Play

miles travelled, and travel times are all interdependent variables describing travel behaviour. For this reason, analysis of travel behaviour has increasingly involved the specification and estimation of simultaneous equations model systems. In a simultaneous equation model system, relationships among several endogenous (dependent) and exogenous (explanatory) variables can be explicitly incorporated. This allows the analyst to model behavioural phenomena in a unified and coherent framework. Recent advances in econometric and statistical methods coupled with improvements in computational resources have further contributed to the widespread application of simultaneous equations models in travel behaviour research. In this paper, two simultaneous equations model systems are used to generate the different causal structures. Each model system consists of two equations, having two endogenous variables and two exogenous variables. For ease of estimation, a linear system is considered. However, the results of this paper can be extended to non-linear systems as endogenous variables may be regarded as latent variables (to allow for discrete choice, censored, or truncated distributions). Consider two endogenous variables describing travel behaviour, say, car ownership and residential location choice. Also consider two exogenous variables, household size and household income. There are two plausible sets of relationships that may apply to different households: (A) Car ownership is predetermined. Residential location choice is dependent upon car ownership (say, a household decides to live in a neighbourhood well served by transit if its car ownership is low). (B) Residential location choice is predetermined. Car ownership is then determined based on the type of residential location (say, if the neighbourhood is not well served by transit, the household may choose to acquire additional cars). Both of the above are quite plausible relationships. It is very possible that some households follow structure (A) while other households follow structure (B). In addition, two other sets of plausible relationships exist. First, car ownership and residential location may be determined simultaneously, and second, car ownership and residential location may not be related at all. As the objective of this paper can be accomplished by just considering two different causal structures, only structures (A) and (B)

Causal Analysis in Travel Behaviour Research

41

described above are used to produce a structurally heterogeneous data set. Causal structures (A) and (B) may be represented using systems of simultaneous equations. Let the endogenous variables be represented as, YI = Car ownership Y2 = Residential location choice and the exogenous variables as, Xi = Household size X2 = Household income. Then, causal structure (A) can be mathematically represented as,

where yl5 S1? /32 and 52 are structural model coefficients; e\ and e2 are random structural error terms distributed as bivariate normal (0, Se) with covariance matrix as follows:

Let causal structure (A) depicted above represent the true causal relationships underlying travel behaviour for a portion of the sample. The following values are assigned to various parameters noted above (these represent true values against which model estimates are to be compared): yt = 2.0 o-ei = l

5! = 0.3 0-^ = 1.2

& =-1.5 o- 61€2 =1.08

52 = 0.25

Similarly, causal structure B may be mathematically represented as,

where 01, 5t, y2, and 52 are structural model coefficients; €i and e2 are

42

Travel Behaviour Research: Updating the State of Play

random structural error terms distributed as bivariate normal (0, Se) with covariance matrix as specified previously. Let causal structure (B) depicted above represent the true causal relationships underlying travel behaviour for the remaining portion of the sample under study. The following values are assigned to various parameters for data generation purposes: )8i=-1.5 a€l = 1

72 = 2.0 o-C2 = 1.2

Si = 0.25 o-ei£2 = 1.08

^ = 0.25

A close similarity is maintained in specifying the true parameter values for structures (A) and (B). This helps in achieving efficiency in the data generation process and allows a more meaningful comparison between estimated and true values. The only difference between the two structures lies in the direction of the causal link between the endogenous variables, YI (car ownership) and Y2 (residential location). Also, for purposes of data generation, it is assumed that the exogenous variables, Xi and X2, are distributed as bivariate normal with the following parameterisation: /**! = 3

fiX2 = 38

axi = 2.5

crX2 = 6

pxlX2 = 0.7

The model specification and parameterisation described in this section allows the generation of structurally heterogeneous data sets on which model systems can be estimated. The experimental procedure is briefly outlined in the next section.

Experimental procedure The procedure followed in performing the simulation experiment can be outlined as follows: (i)

A bivariate normal random vector of exogenous variables (Xi,X2) is generated using the parameters specified in the previous section. This is repeated 500 times to get a sample size of 500.

(ii)

A realisation of a bivariate normal random vector of error terms (e l5 e2) is generated using the specified parameter values. This is done for each of the 500 cases.

Causal Analysis in Travel Behaviour Research (iii)

43

Using the model specification in equation (1), endogenous variables YI and Y2 are computed and generated for each of the 500 cases. In this way, a complete data set with causal structure (A) as its underlying basis is obtained. 100 such data sets are generated.

(iv) Model structure (A) is estimated (using full-information maximum likelihood techniques) on each of the 100 data sets. Arithmetic means of parameter estimates are computed, tabulated, and compared against the true values. (v)

Steps (i) through (iii) are repeated for structure (B).

(vi)

From each of the 100 data sets of causal structure (A), a random sample of 250 is drawn. Similarly, from each of the 100 data sets of causal structure (B), a random sample of 250 is drawn.

(vii) The samples are pooled such that 100 data sets of sample size 500 each are generated. All data sets have 250 sample units drawn from causal structure (A) and 250 sample units drawn from structure (B). This yields 100 structurally heterogeneous data sets. (viii) Model structure (A) is estimated on each of the 100 structurally heterogeneous data sets. Arithmetic means of parameter estimates are compared against true values to assess the degree of accuracy with which models can capture structurally heterogeneous causal relationships.

Results of Simulation Experiment Full-information maximum likelihood (FIML) methods, implemented via LISREL structural equations software (Joreskog and Sorbom, 1987), were used for model estimation. A review of these methods can be found in Greene (1990). This section provides results of the model estimation efforts on structurally homogeneous and structurally heterogeneous data sets. First, the model system describing structure (A) was estimated on the 100 data sets generated purely based on structure (A). These may be considered structurally homogeneous data sets. One would expect models

44

Travel Behaviour Research: Updating the State of Play

to provide accurate parameter estimates under these conditions. Table 1 provides results of this effort. It can be seen that, in the case of structural homogeneity, models do capture and replicate true relationships among variables. Percentage errors in parameter estimates are extremely small. Table 1 Estimation of causal structure (A) on homogeneous data set: comparison of true and estimated parameter values Parameter

True value

Estimated value

Error in estimate (%)

True standard error

Estimated standard error

Error in standard error

jSz 7! 8j §2

-1.50 2.00 0.30 0.25

-1.499 2.000 0.298 0.248 1.004 1.438 1.084

0.0 0.0 -0.6 -1.0 0.4 -0.1 0.4

0.0156 0.0241 0.0105 0.0164 0.0645 0.1086 0.0822

0.0154 0.0256 0.0111 0.0169 0.0639 0.0970 0.0742

-1.8 6.3 6.4 3.0 -1.0 -10.7 -9.8


al2 o-ei€2

1.00

1.44 1.08

Note: Causal structure (A) = 500 observations; causal structure (B) = 0 observations.

The estimated values of parameter standard errors very closely replicate the true standard errors over 100 simulations. It should be noted that the larger percentage errors obtained for these estimates merely reflect the small quantities being dealt with. Next, the model system describing structure (A) was estimated on the 100 structurally heterogeneous data sets. The results of this estimation effort are shown in Table 2. In this case, there is absolutely no resemblance between true parameter values and model estimates. The model estimate of coefficient /32 has a positive sign, while the true value is —1.5. Similarly, ji shows a reversal in sign. Estimates of variances of error terms are quite large reflecting the poor predictive accuracy of the model. The error covariance estimate also reversed sign and the estimated correlation coefficient between e± and e2 is —1.0, while the true value is 0.9. Similar results can be expected if one were to estimate model structure (B) on structurally homogeneous and heterogeneous data sets. Indeed, when model structure (B) was estimated on the structurally heterogeneous data sets, model indications were found to be very poor and similar to those of Table 2 (Pendyala, 1992). The simulation experiment clearly shows that estimated values of model parameters provide very poor indications under structural heterogeneity.

Causal Analysis in Travel Behaviour Research

45

Table 2 Estimation of causal structure (A) on heterogeneous data set: comparison of true and estimated parameter values Parameter

True value

Estimated value

Error in estimate (%)

True standard error

Estimated standard error

Error in standard error

02 7! 5! 62
-1.50 2.00 0.30 0.25 1.00 1.44 1.08

1.347 -0.428 0.012 0.072 3.545 19.567 -8.329

-189.8 -121.4 -95.9 -71.1 254.5 1258.8 -871.2

0.122 0.025 0.011 0.021 1.602 2.026 4.344

2.761 0.500 0.206 0.461 2.244 4.677 9.802

2167.1 1862.7 1760.4 2079.3 40.1 130.8 125.6

Note: Causal structure (A) = 250 observations; causal structure (B) = 250 observations.

Parameters are highly biased and inefficient, which would in turn yield both inaccurate and unreliable forecasts. In addition, one notes that the values of true standard errors themselves increase, indicating that the reliability of parameters decreases in the presence of structural heterogeneity.

Discussion and Conclusions This research stems from the growing recognition in travel behaviour research that a deeper understanding of cause-and-effect relationships is required to accurately predict the impacts of travel demand management strategies, transportation and energy policies, and advanced technologies. Indeed travel demand models are increasingly being used to unravel causal relationships underlying travel behaviour. This paper critically examines such modelling efforts in light of the fact that there may be several causal mechanisms embedded within the same data set. In behavioural research, structural heterogeneity can be expected to be the norm rather than the exception. The simulation experiment performed in this paper clearly shows that models perform very poorly in the presence of structural heterogeneity. Model estimates are biased and inefficient. The use of such model estimates for planning purposes will yield highly erroneous forecasts and impact assessments. Travel demand management strategies implemented on the assumption that there is one unique causal mechanism

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Travel Behaviour Research: Updating the State of Play

driving travel behaviour of the entire population may not yield the expected results. This problem is further exacerbated by the lack of a priori knowledge, or established causal theories, in travel behaviour research. If one had prior knowledge about the causal decision-making processes driving various segments of the population, then one could potentially stratify the population into homogeneous segments (in market research and economics, this is called market segmentation) and estimate suitable model systems for each segment. However, in travel behaviour research, one deals with unobserved individual factors, randomness of human behaviour and choices, and lack of sufficient information to identify behaviourally homogeneous groups. This is not to say that causal modelling does not have merit. Causal relationships represent the most fundamental understanding of a behavioural phenomenon and can help planners accurately predict policy impacts before actual large-scale implementation. This research points to the need to exercise caution in the specification and estimation of causal models as one may be dealing with multiple decision-making processes driving travel behaviour. For example, the presence of structural heterogeneity may warrant the use of conservative estimates of impact predictions derived from travel demand models. In addition, consideration should be given to the application of exploratory and qualitative research methods to better understand and unravel the complex behavioural mechanisms underlying the phenomenon under study before undertaking quantitative modelling efforts. Exploratory research methods may include the analysis of various demographic, socioeconomic, and travel segments of the population to examine whether certain groups within the population exhibit similar behaviour. Qualitative research methods such as those involving in-depth interviews and focus groups may also offer additional insights into the cause-and-effect relationships underlying human behaviour. These techniques have been and continue to be used in social and psychological sciences with considerable success and certainly merit increased use in the travel behaviour arena. Further research is needed to understand the full implications of structural heterogeneity on travel demand modelling practice. For example, an issue that merits further attention is with regard to the sensitivity of model estimates to various degrees of structural heterogeneity. In this paper, the structurally heterogeneous data set had an equal split between two causal structures. If, on the other hand, one causal structure domin-

Causal Analysis in Travel Behaviour Research

47

ated the other, then would model estimates replicate the dominant causal structure? What is the degree of structural heterogeneity up to which models provide statistically acceptable parameter estimates? Answers to these questions may provide further insights into our ability to model structurally heterogeneous causal processes.

Acknowledgements This research was undertaken as part of the author's Ph.D. Dissertation under the guidance of Prof. Ryuichi Kitamura at the University of California, Davis. Partial funding was obtained through a dissertation grant awarded by the Region 9 Transportation Center of the U.S. Department of Transportation at the University of California, Berkeley, U.S.A.

References Ahn, C. (1985) Social Development and Political Violence: A CrossNational Causal Analysis. Seoul National University Press, Seoul. Bagozzi, R.P. (1982) A field investigation of causal relations among cognitions, affect, intentions, and behaviour. Journal of Marketing Research 19, 562-584. Belson, W.A. (1985) Juvenile Theft: The Causal Factors. Harper and Row, New York. Blalock, H.M., Jr. (ed.) (1985) Causal Models in Panel and Experimental Designs. Aldine Publishing, New York. Braakhekke, W.G. (1980) On coexistence: a causal approach to diversity and stability in grassland vegetation. Agricultural Research Report 902. Centre for Agricultural Publishing and Documentation, Wageningen, The Netherlands. Elwood, J.M. (1988) Causal Relationships in Medicine: A Practical System for Critical Appraisal. Oxford University Press, Oxford. Golob, T.F. (1989) The causal influence of income and car ownership on trip generation by mode. Journal of Transport Economics and Policy XXIII, 141-162. Golob, T.F. and Meurs, Ff. (1987) A structural model of temporal change in multimodal travel demand. Transportation Research 21A, 391-400.

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Travel Behaviour Research: Updating the State of Play

Goodwin, P.B. (1987) Family changes and public transport use 1984-1987: A dynamic analysis using panel data. Report Code IVV/271/16/Mr, submitted to the Project Bureau of The Netherlands Ministry of Transport. Bureau Goudappel Coffeng bv, Deventer. Greene, W.H. (1990) Econometric Analysis. Macmillan, New York. Greenwood, E. (1945) Experimental Sociology: A Study in Method. Kings Crown Press, New York. Hanson, S. and Huff, J.O. (1982) Assessing day to day variability in complex travel patterns. Transportation Research Record 891, 18-24. Horn, W. (ed.) (1990) Causal AI Models: Steps Toward Applications. Hemisphere Publishing Corporation, New York. Joreskog, K. and Sorbom, D. (1987) New developments in LISREL. Data Analyst 4, 1-22. Kitamura, R. (1987) A panel analysis of household car ownership and mobility. Journal of Infrastructure Planning and Management of the JSCE 338IF/-7, 13-27. Kitamura, R. (1989) A causal analysis of car ownership and transit use. Transportation 16, 155-173. Lyon, P.K. (1984) Time-dependent structural equations modelling: a methodology for analysing the dynamic attitude-behaviour relationship. Transportation Science 18, 395-414. Maddala, G.S. (1983) Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press, Cambridge. Middlebrook, P.N. (1974) Social Psychology and Modern Life. Alfred A. Knopf, New York. Pendyala, R.M. (1992) Causal Models of Travel Behaviour Using Simultaneous Equations Systems: A Critical Examination. PhD Thesis, Department of Civil Engineering, University of California at Davis. Sahni, B.S. and Singh, B. (1984) On the causal directions between national income and government expenditure in Canada. Public Finance 39, 234-248. Van Wissen, L.J.G. and Golob, T.F. (1990) Simultaneous equations systems involving binary choice variables. Geographical Analysis 22, 224243. Wright, S. (1934) The method of path coefficients. Annals of Mathematical Statistics 5, 161-215.

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Driver Information Processing Failures in Road Accidents: From Description to Interpretation Pierre Van Elslande and Daniele Dubois

Abstract The purpose of this chapter is to describe a line of research designed to reveal knowledge and representations used by drivers to manage the difficulties they encounter when travelling by road. It presents on-going work aimed at classifying road accidents according to the failures that can be identified during the various functional stages involved in driving activity, and the processes that produce these failures. We put forward a theoretical explanation for some of these failures which correspond globally to a problem of "representation", as seen through the concept of scene and situation categorisation. This concept results from the work conducted in the field of cognitive psychology aimed at determining the principles governing the organisation of human knowledge. A comparison of this type of conceptualisation, together with the results of empirical studies on driver road-journey management, leads us to question the standard modelling used to describe an essentially taxonomic structuring of the subject's knowledge. More specifically, accident scenario analysis provides a means of indicating a plurality and heterogeneity in the operator's knowledge structures in relation to the type of "object" they involve, the underlying finalities and the periods of activity. It also reveals the need to weigh their hierarchical content by drawing up dynamic models integrating the temporality and sequentiality of the situations.

Introduction Most empirical studies produced in the traditional field of road studies (Fell, 1976; Treat et al., 1979; OECD, 1988), and more generally in the human reliability field (Leplat and Rasmussen, 1984), reveal a marked

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tendency to focus analysis more on the identification of the various accident-producing factors and the set of determining causes, rather than on an analytic description of the processes specific to these accidents. This trend is even more systematised when we come to statistical analyses and their epidemiological objectives. The phenomena involved in accidentproduction are complex. This complexity is found in the multiplicity of variables involved at any one time, in the temporal decline of their influence and in the exceptional nature of the accident. In view of this, it is easy to explain the difficulties encountered when seeking a level of data aggregation that allows production of a case classification that integrates sequentiality and the logic of articulation for the relevant mechanisms. This difficulty is even more pronounced when the psychological processes involved are considered.

Towards a Scenario-Based Accident Classification Objectives The purpose of this section is to use some relevant data from in-depth accident analysis to elucidate the knowledge processes implied in accidentgenerating behaviour. With this aim in mind, we tried to define a level of description for the accident phenomena that lies somewhere between the case study and statistical analysis. Case studies such as monographs have, indeed, the advantage of fully describing the specificity of each accident "history", by integrating essential dimensions such as dynamics, sequentiality and multicausality. But one of the pitfalls lies in a lack of their ability to generalise empirical data which conforms too closely to "natural conditions", to the point of turning each accident into a specific case, "accidental", not comparable with another. In contrast, the advantage of a statistical analysis of accident data is that it provides a means of quantifying the significance of problems on a priori dimensions, such as descriptive driver properties (age, level of alcohol intake, etc.), and environmental variables (infrastructure characteristics, weather conditions, etc.). In terms of implications, they also define the measures to be taken to improve road safety. However, the major drawback of this type of use stems from the difficulty of describing the complexity of accident mechanisms using data, which is both general and detached from any temporality.

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Between monographs (case studies) and causal chains (statistical analysis), we tried to account for the accident phenomena in the form of typical scenarios describing the driver functional failure-generating process. These failures are identified at the critical moment which marks the transition between a normal course situation and an impaired course situation, when a driver is confronted by an unexpected event in his journey. They are analysed using the classical models of Rasmussen (1986, 1990) and Reason (1990), adapted to the specificity of driving task. To shift the analysis from the situation to driver functioning in no way neglects the multicausal nature of the accident. It simply involves breaking down this multicausality to reveal one particular aspect; namely, that of the cognitive processing which allowed the accident to occur. The option taken to analyse the difficulties encountered by the driver can be justified by the central position occupied by the operator in terms of microregulation of the road system. It is, in fact, through the operator that all the system inputs and outputs will transit. The driver is the component which drives the system. He has to adjust his activity to comply with the system's malfunctions. To realise this adjustment, the driver will rely on a certain number of functions and operations, from information gathering to action taking, going through cognitive functions such as understanding, anticipating and decision making. But in certain situations, where the driver is confronted with major problems resulting from the system, these problems will impede one of the functions, which usually allow him to adapt his activity to the difficulties encountered. And this, in turn, generates a functional failure, which is often referred to as "human error". So, in the case of accidents, the driver is the component to which most causalities tend to be attributed. In fact, the human operator, seen as the weak point of the system, is often considered to be at the origin of approximately 8090 percent of all accidents. However, revealing "human errors" is not the same as burdening drivers by attributing sole responsibility to them. It can be argued, in fact, that all error is human, whether it arises primarily from the designer, or later from the operator, but it is never only human because it occurs in sociotechnical conditions that facilitate its production (Cellier, 1990). It is more a question of determining the way in which system malfunctions will become a reality, and produce the functional failures for the operator when faced with the different conditions in which to perform his activity. Here, the purpose is to identify the level of this failure in relation to the various functional stages undertaken in this activity, and to better understand the processes that lead to its production.

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Method Because an accident is the result of a process involving the various, more or less complex, malfunctions that occur in different driving situations, we thought it productive to build up an intermediate level of phenomena by structuring the processes noted in an in-depth accident analysis. This took the form of both a typology of driver function failures and typical accident-causing malfunction scenarios. The development of these scenarios is based on the analysis of accident cases from the INRETS-MA databank which, at present, contains some 700 files involving more than 900 users. Each of these files stems from an in-depth investigation based on data collected by a multidisciplinary team on the scene of the accident (FERSI, 1994). At this stage of research, 392 accident-involved users were selected from this database in order to cover a wide range of critical driving situations and their relevant malfunctions. These accidents occurred while performing essential driving activity manoeuvres (overtaking, driving in line, intersections, negotiating a bend, etc.) on different road infrastructures (straight stretches, intersections, main roads, minor roads, open country, builtup areas, etc.), and involve functional failures at different levels of driving activity (information acquisition, information processing, decision and action). The first stage of analysis consisted of using each case individually. All the information contained in each file was used to identify the basic malfunction process involved in the accident and all the relevant parameters. On the basis of this in-depth analysis, we selected all the generic parameters that made up the pattern of the event, and enabled the accidents to be aggregated into typical scenarios. Those that were too specific to each case and hindered this aggregation were eliminated. The consolidating parameters used to determine the typical scenarios were as follows: • The road situation to be managed, describing the user's driving task where the malfunction process occurred, and its specific requirements. This "pre-accident" situation indicates the individual manoeuvre carried out, or intended, by the driver just as he encountered an interaction with another system component (another user, a specific layout, etc.). • Initiating factors. These correspond to the main driving context parameters (road, driver, other users, task, etc.) that served to trigger the

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driver functional failure when faced with the situation to be managed and its specific demands. These explanatory failure factors are differentiated in terms of whether they refer to external task performance conditions, or internal operator conditions. It should be noted, however, that failures are essentially the result of a combination of internal and external factors (Fig. 1), which shows how difficult it is to analyse the accident phenomena from a monocausal approach. The functional failure of the user where a previously stable driving situation develops into an accident situation. This parameter corresponds to the different errors, or specific difficulties, that drivers may have created or experienced. These errors or difficulties are related, within the framework of a driver functioning psychological model, to one or another of the stages of their situation management activity: stages involving information acquisition, information processing, decision or action. The critical event resulting from a functional failure corresponding to the critical actions taken or pursued by drivers, and inconsistent with the interaction to be managed, the result of this being the accident.

Figure 1 Explanation of failure according to factor type

The second stage was to group together cases with similar overall unifying parameters, and so build up typical scenarios. The basic structure for these scenarios is set out in Fig. 2. The last stage was to classify these

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Travel Behaviour Research: Updating the State of Play Road situation to be managed To cross an intersection with loss of right of way

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1

Initiating factors

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Endogeneous

Exogeneous

1* Insufficient knowledge of site j • Does not drive regularly I • Elderly driver (overwhelmed) I

^ f • Signposting default • Bounded visibility I • Layout default (complex, atypical)) is

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Erroneous categorization of the encountered place type => bad information seeking sequence \=> no detection of a vehicle J

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the course of a priority holder Vuser J (

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( ^ ) Figure 2 The basic scenario structure

scenarios into categories and subcategories according to their functional failure phase, and the more specific type of driver functional failure. 3

Typology The typology thus obtained leads to five generic "categories" found in sequence in the different stages of activity that can be analysed within a standard information processing model (Fig. 3). These categories are divided into 20 "types" of failure, which correspond, more specifically, to driving activity malfunctions. These types of failure illustrate some 60 typical malfunction scenarios. It is worth noting the significant proportion of perceptive failures, which correspond to both visibility and information a

The model which illustrates this failure classification can be found in Van Elslande (1997).

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Figure 3 Functional failure distribution according to category

gathering problems, and the even more significant proportion of cognitive failures, for a task domain which is often considered as implying essentially sensory-motor and handling abilities.

Failure in the detection phase Performing a task safely, in a given driving situation, is initially conditioned by the prior detection of all the data required for the task to be performed. This prior detection is essential if the user is to carry out the other functional sequences that comprise the driving activity in good time: information processing, selecting appropriate procedures and performing the relevant action. For drivers in this category, the accident can be attributed to not detecting (or failing to detect in time) certain essential situational parameters, such as a change in location layout, or the presence of another user on a potential collision course. Three malfunction subcategories are revealed and correspond to the type of perceptive problems identified by analysis: • A temporary interruption in the information search activity, combined with the performance of an additional task (e.g. discussing with a passenger, adjusting a radio, etc.). • Poor organisation of the search for information. This refers to faulty procedures such as untimely collection of cues, a cursory glance or, on the contrary, overfocusing on another part of the visual scene. • Encountering detection constraints, namely, obstacles that impede visi-

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Travel Behaviour Research: Updating the State of Play bility in the task environment, or inadequate pre-signposting, preventing drivers from obtaining the relevant information in good time.

Failure in the processing phase The second functional stage of the driving activity involves processing the information perceived in the situations encountered. This processing activity should essentially enable the driver to understand the type of situation confronted, anticipate its probable development, predict any unexpected event in a given situation, evaluate the scope for manoeuvre or a speed compatible with situational demands. This functional sequence will affect the decision made regarding the procedures to be applied to meet the situation, and the corresponding actions to be taken. Five categories of accident-causing failures were identified in this phase: • Failure to understand the interaction involved in the situation in hand. This event corresponds to a specific road configuration or a manoeuvre undertaken by another user and results in the driver failing to identify a hazard. • Failure to evaluate a danger specific to a particular situation that results in the operator failing to apply the necessary adjustments, although the event has been correctly identified. • Failure to anticipate, which corresponds to expectations formulated with regard to how a previously identified situation involving interaction with another road user will evolve. • Failure to predict the occurrence of a possible event that may result, for example, in adopting a speed incompatible with sight distance, as no interference is expected. • Encountering processing constraints as defined by an inability of the available information to fully describe the type of interaction encountered, its difficulties and its progression. The ambiguity and polysemy of this information lead to an erroneous categorisation of a type of location, or poor interpretation of a manoeuvre performed by another user.

Failures in the dedsional phase Once the road event in question has been detected and processed, the final processing stage to be considered is the appraisal and decisional process: the driver must "select", from the driving strategies that can feasibly be performed in the situation in question, the strategy that seems to him best suited to the event and its safety requirements. The following

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failures refer to two types of problem that have been identified to date in road accidents and which correspond to this decisional phase. • Obvious risk-taking. This refers more to the notion of "violation", defined by Reason (1990) as being a deliberate deviation from required practices (either considered as such by legislation or just simply obvious), to ensure that a potentially dangerous system operates safely, than to the notion of "error" in terms of information processing. The origin of this failure can be attributed, in general, to the preference drivers give to specific objectives (e.g. making up time, increased performance), to the detriment of safety itself. • Encountering decisional constraints. These comprise the situations that result in necessary risk-taking and can be also a cause of accidents. In the cases in question, drivers decided to perform a manoeuvre that had, because of inadequacies in layout, become hazardous and, although they sought to take as many precautions as possible, found themselves on the same course as another vehicle. Failure when taking action The final link in the functional chain involved in the driving activity, is the activation of vehicle controls by the driver, if he is to perform the manoeuvres specific to the strategy selected in the decisional stage. Problems may still arise at this stage, inasmuch as the action intended may be performed incorrectly and the regulating objective not achieved. Contrary to general opinion, few of the accidents studied were a direct result of this type of failure (which occur more frequently when performing an emergency manoeuvre, namely, when attempting to rectify an already impaired situation). A distinction can be made depending on whether performance failures are due to the driver encountering an external factor which makes the vehicle difficult to control, or simply the conditions regarding the attention given to the course control task: • Difficult vehicle controllability, when faced with an external factor: gust of wind, aquaplaning, etc. • Control defect, linked to attention being diverted to a secondary task, or a lack of attention due to fatigue and alcohol. Overall failure The last category differs from those indicated previously in that the case analyses it contains do not involve a specific functional phase that can, in

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turn, influence the other phases. For these accidents, the problem is related more to the driver's basic ability to act effectively when performing the task in question. This refers to detection, processing and decision making, as well as to the action itself, bearing in mind the inadequate psychophysiological abilities involved. For these cases, we will refer to overall failure insofar as several links, or even the entire functional chain, are involved in the activity that appears to have been influenced. This rather specific category applies to drivers who fall asleep, or lose consciousness at the wheel (loss of psychophysiological abilities}, or drivers with a high alcohol intake (impairment of sensory-motor and cognitive abilities). It also applies to some elderly drivers, whose processing and action skills prove inadequate in certain situations that are somewhat different from those normally encountered in routine driving (exceeding cognitive abilities).

Discussion The standard information processing model is of considerable use in that it provides a means of defining a functional breakdown of the activity, and, therefore, locating the stage at which a malfunction occurs. By using such a model, we were able to distribute the failures observed in drivers when processing the road situations facing them, in terms of the psychological function involved. However, once the level of malfunction (the functional category to which it refers), and the specific nature of the failure in relation to the task in question (its type), have been identified, and the process containing the failure (the malfunction scenario) described. We still have, for explanatory purposes, to put forward the psychological bases that allow them to develop. Among the failures identified, some show the need for more in-depth investigation regarding the organisation of the knowledge used by the driver to further his activity, which requires the use of recent models developed in the field of cognitive psychology. This, of course, applies to all the "errors" listed in the road situation "processing" stage, but also certain "perceptive errors", in that acquiring visual information can be considered as a product of the subject's hypotheses (Neboit, 1980).

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A Theoretical Background

Driving, cognition and road accidents As in most "situated" human behaviour, driving can be described in terms of its complexity, in that the situations considered by the driver comprise a considerable number of interacting variables, temporal dynamics, objectives that are ill-defined and sometimes conflicting, and contain a high level of risk in certain cases (De Keyser, 1988).

A considerable number of interacting variables One of the basic components of the road system is, in general, its great diversity (Saad and Mazet, 1991). This can be seen in terms of the environments through which it occurs, the vehicles encountered with their different, and often extremely diversified, dynamic features, together with the operators and their varying levels of experience and familiarity with a number of very contrasting locations. The result is a wide range of behaviour. For drivers, this diversity requires a highly organised ability to adapt, enabling them to select an appropriate response to fluctuations in the situations they encounter.

A temporal dynamics The essentially dynamic characteristic of driving imposes very severe constraints on the regulation modes applied. To manage a difficult situation, a driver will, at best, have only a few seconds to collect the relevant information, analyse it correctly, make the appropriate decision and carry out the appropriate regulating actions. This temporal decline reveals the need for drivers to develop anticipatory and predictive procedures to better control the situation. "It can be said that driving is anticipating whilst being aware that almost anything can happen and that safety is first and foremost managing the unpredictable" (Malaterre, 1987).

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Ill-defined and occasionally conflicting objectives In contrast to much other work, or even isomorphic activities such as piloting sea-going vessels or aircraft, the driving task is relatively unstructured (Saad and Mazet, 1991), in terms of the normative pre-organisation of objectives, the means and the procedures corresponding to what in work psychology is termed "the prescribed task" (Leplat and Hoc, 1983). In this respect, the Highway Code is more a collection of instructions of a general indicative nature, normative or even penal, and rarely provides an explicit and operative definition of the adjustment procedures for the different situations a driver may require when performing his activity. This poor structuring requires drivers to develop, on an individual basis and with experience, a collection of processing strategies and procedural skills that provide the expertise based on a gradual integration of the conditions in which they perform their activity. Moreover, in terms of "effective task", as described by Leplat (1990) (i.e. the internal model that guides the subject's activity effectively and not normatively), all drivers must repeatedly compromise between two often-contradictory objectives. One is a need for rapidity which frequently influences the use of this mode of transport, and the other is the safety requirements which more specifically demand, that speed is controlled within desirable limits. These controls can only operate within certain ranges permitted by the surrounding traffic (cf. the definition of driving as an activity that is both "forced" and "self-paced", Malaterre, 1987). This concept of compromise had led to homeostatic-type models showing a fluctuation in risk levels in relation to driver objectives and motivations (Wilde, 1988).

The high risk factor involved in certain cases This leads on from the three previous points. Risk is a component inherent in many driving situations, and plays a vital role in regulating driver activity (Saad, 1989). The models developed around this concept compare the "objective" risk, that represents a given situation, and the "subjective" risk that corresponds to the evaluation of danger by a driver at a given time and results from perceptive, cognitive and motivational data. The day-to-day encounter of "hazardous" situations involves a crucial aspect for drivers. Specifically, that of developing knowledge regarding the probability of certain events occurring, which enables drivers to put into effect the essential predictions with regard to their occurrence and the behaviour of other users (Lovegrove, 1978, quoted by Saad, 1989).

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Driving: An activity backed up by specific and categorical knowledge We will assume that the specifications of the driving task, as defined above, will impose direct constraints on the processing procedures implemented by the operator. The driver's interaction with the temporal dynamic of the situation will result, more specifically, in the determining nature of the use of knowledge organised to enable him to control the scenario in which he is involved, both effectively and in due time. The driver will base himself on this knowledge acquired through experience and will, therefore, develop detailed representations for the environments encountered and the rules governing their use. Depending on the clues collected, these representations will enable the driver to classify the driving situations encountered by using previously built-up knowledge and so develop anticipation and predictions with regard to the probable progression of these situations (Saad et al., 1990). Expectations based on "longterm" experience (expressed in terms of relatively stable knowledge) and "short-term" experience (corresponding to the few previous instants), also have a fundamental effect on the way a driver perceives and interprets a visual scene, particularly when identifying a danger or potential problem (Hills, 1980; Alexander and Lunenfeld, 1986). Thus, the temporal constraints imposed on the driver by the nature of the task itself usually imply that the problems encountered are solved directly after a comprehension activity: the driver comparing the problem in hand to a situation/problem category for which he has memorised the identifiable characteristics, together with the possible progression and solutions (Van Elslande, 1992).

An examination of cognitive psychology: Which structures? The overall aim of cognitive psychology is to establish a suitable representation of human knowledge and explain how knowledge is structured and used to resolve ordinary, everyday problems. The categorical organisation of human knowledge Inspired by the work carried out by Rosch (1975, 1978), the model for the categorical organisation of knowledge accounts for the two-fold ability of humans to discriminate the different items of information found in the environment, and to generalise them in such a way as to consider the different items of information as being cognitively equivalent. The charac-

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teristics and organising principles of the psychological categories, based essentially on simple objects, have made it possible to conclude that: • "natural" categories, i.e. "the semantic representation of objects in the real world" are organised in graded taxonomic-type structures; • one level is prioritised "the basic level", which is used to obtain a maximum of information with a minimum of cognitive effort. Therefore, this provides a good compromise when adjusting behaviour; • the objects contained in these categories are grouped together on the basis of common attributes, with perceptive or functional similarities, rather than on items which are independent from one another; • within a single category, all the exemplars are not equivalent, but distributed according to a certain degree of typicality around the best organising item, representative of the category, which is referred to as the prototype. Clearly, this type of knowledge organisation is closely linked to the type of cognitive processing undertaken, which within the theoretical frame of reference (Rosch, 1978), is restricted to a cognitive type of activity (knowledge oriented towards truth values) regarding natural objects. This categorical structure has an influence on cognitive processing with a significant correlation between the typicality of exemplars, response times and performances (Dubois and Denis, 1988). Typically, this can be assumed to be a decisive factor in information processing mechanisms. However, one criticism that can be made of most of the research work that helped to develop categorical concepts, is that it has focused essentially on perception in its contemplative dimension in relation to simple objects, out of context and removed from temporal applications (Van Elslande, 1991). By prioritising the "cognitive" function of these categories (in that they refer only to knowledge), their "operative" function (in that they refer to the performance of one's action) has been neglected. Road categories: Driving and accident situations Previous work in the field of driving activity (Dubois et al., 1993) showed the psychological relevance and valuable contribution of categorical concepts, when applied to the analysis of the mental organisation of the road environment. Thus, they revealed that the organisational principles based on perception of the environment are essential on an overall (macroscopic) level of categorisation of the sites in which driving activity is performed (e.g. types of builtup area). However, on a more local level (e.g. inter-

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section), we consider the operating dimension of the categories that have been formed: the categorical representation of the intersection includes not only the figurative properties derived from perception, but also the response categories involved in the driving task (Mazet, 1991). To focus the analysis of categorical representations on "objects" that are complex, in context and involved in the performance of a "natural" activity, includes a specific adaptive finality. Therefore, this brings us to develop Rosch's initial conceptions even further, by reintroducing functionality as the organising principle of the categories. In-depth accident analysis, however, also enables us to determine the categorisation process more accurately. The situation is interpreted on the basis of decisions regarding the categorical relationship to a problematic situational category. It was possible, therefore, to reveal accident categories based on the types of "error". Thus, by moving closer to the microregulating dimension of the activity, we had to consider the restraints imposed on the operator by task demands and, above all, reintroduce a temporal dynamic into the categorisation theory. Hence, this type of categorisation activity influences not only the forming of "objects", but also the units of knowledge directed towards anticipating problem categories that may be encountered, and by predicting ways of solving them. To consider the difficulties facing drivers in this way, requires a large corpus of experimentation, under laboratory conditions, to control the influence of the variables identified by accident analysis and formalised in the light of recent cognitive psychology models. It is in these terms that in situ investigations, together with laboratory and theoretical considerations may form the three phases of the situated research work agenda.

Conclusion Analysis of the underlying performance components of an activity, such as driving seen in terms of the concepts that have originated from the field of cognitive psychology, may provide many varied applications. In terms of a driver understanding what he is driving through, the operational advantage of hypotheses on human categorisation lies in a search for prototypical representations that best represent a category (in this case: "road scenes"), and which group together all the relevant characteristics for the individual. Once they have been identified, it is then possible to improve road and environment designs to render them more

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easily recognisable and more rapidly identifiable by the user when driving (Fleury et al., 1991). Dealing with the interpretation process that drivers use to manage the interaction situations facing them, identifying the problem categories they encounter, and revealing the failures to which they may be subjected, also provides a means of better determining the specificity of the knowledge required to identify and understand the problematic situations ahead of time. This identification of driving performance difficulties, and the contexts in which they occur, should provide a basis for training measures to encourage drivers to build situational mental categories. Hence, this should enable drivers to attribute appropriate significance to the situational cues that lead to expectations adapted to their probable development. Furthermore, by revealing the knowledge actually used by drivers, it should be possible to better identify the type of useful information transmitted to them by driving aids aimed at improving safety.

References Alexander, G.J. and Lunenfeld, H. (1986) Driver expectancy in highway design and traffic operations. Report No. FHWA-TO-86-1, US Department of Transportation, Washington, DC. Cellier, J.M. (1990) L'erreur humaine dans le travail. In J. Leplat and G. de Terssac (eds.), Les Facteurs Humains de la Fiabilite dans les Systemes Complexes, Octares, Marseille. De Keyser, V. (1988) De la contingence a la complexite: 1'evolution des idees dans 1'etude des processus continus. Le Travail Humain 51, 1-18. Dubois, D. and Denis, M. (1988) Knowledge organisation and instantiation of generals terms in sentence comprehension. Journal of Experimental Psychology 14, 604-611. Dubois, D., Fleury, D. and Mazet, C. (1993) Representations categorielles: perception et/ou action? Contribution a partir d'une analyse des situations routieres. In A. Weill-Fassina, P. Rabardel and D. Dubois (eds.), Representations pour VAction, Octares, Toulouse. Fell, J.C. (1976) A motor vehicle accident causal system: the human element. Human Factors 18, 85-94. FERSI (1994) In-depth investigation. FERSI Group Report, INRETS, Salon-de-Provence. Fleury, D., Dubois, D., Fline, C. and Peytavin, J.F. (1991) Categorisation

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mentale et securite des reseaux. Research Report 146, INRETS, Salonde-Provence. Hills, B.L. (1980) Vision, visibility and perception in driving. Perception 9, 183-216. Leplat, J. (1990) Relations between task and activity: elements for elaborating a framework for error analysis. Ergonomics 33, 1389-1402. Leplat, J. and Hoc, J.M. (1983) Tache et activite dans 1'analyse psychologique des situations. Cahiers de Psychologic Cognitive 3, 49-63. Leplat, J. and Rasmussen, J. (1984) Analysis of human errors in industrial incidents and accidents for improvement of work safety. Accident Analysis and Prevention 16, 77-88. Malaterre, G. (1987) Les Activites Sous Contrainte de Temps: Le Cas des Manoeuvres d'Urgence en Conduite Automobile. Ph.D. Thesis, Universite Paris V. Mazet, C. (1991) Perception et Action dans la Categorisation: Le Cas de rEnvironnement Urbain et Routier. Ph.D. Thesis, Universite Paris V. Neboit, M. (1980) L'analyse de 1'exploration visuelle comme moyen d'etude des activites perceptives du conducteur. Bulletin de Psychologic 344, 323-329. OCDE (1988) Road accidents: on-site investigations. OCDE Report, Paris. Rasmussen, J. (1986) A framework for cognitive task analysis in systems design. In E. Hollnagel, G. Mancini and D.D. Woods (eds.), Intelligent Decision Support in Process Environments, Springer-Verlag, Berlin. Rasmussen, J. (1990) The role of error in organising behaviour. Ergonomics 33, 1185-1200. Reason, J. (1990) Human Error. Cambridge University Press, Cambridge. Rosch, E. (1975) Cognitive representation of semantic categories. Journal of Experimental Psychology 104, 192-233. Rosch, E. (1978) Human categorisation. In N. Warren (ed.), Advances in Cross Cultural Psychology, Academic Press, London. Saad, F. (1989) Risk taking or danger mis-perception? Recherche-Transport-Securite 4, 51-58. Saad, F., Delhomme, P. and Van Elslande, P. (1990) Drivers' speed regulation when negotiating intersections. In M. Koshi (ed.), Transportation and Traffic Theory, Elsevier, New York. Saad, F. and Mazet, C. (1991) Analysis of road situations and driver's activity in a perspective of cognitive ergonomics. In Y. Queinnec and F. Daniellou (eds.), Designing for Everyone, Taylor & Francis, London. Treat, J.R., Tumbas, N.S., Shinar, D. and Hume, R.D. (1979) Tri-Level

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Study of Traffic Accidents: Causal Factors, Tabulation and Assessments. Final Report, Institute for Research in Public Safety, Indiana University. Van Elslande, P. (1991) Influence d'un schema de traitement sur 1'interpretation d'une situation routiere ambigue, Preprints 6th International Conference on Travel Behaviour, Quebec, May 1991, Canada. Van Elslande, P. (1992) Les erreurs d'interpretation en conduite automobile: mauvaise categorisation ou activation erronee de schemas? Intellectica 15, 125-149. Van Elslande, P. (1997) Classifying "human errors" in road accidents. In T. Seppala, T. Luopajarvi, C. Nygard and M. Mattila (eds.), From Experience to Innovation, Finish Institute of Occupational Health, Helsinki. Wilde, G.J.S. (1988) Risk homeostasis theory and traffic accidents: propositions, deduction and discussion of dissension in recent reactions. Ergonomics 31, 441-468.

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The Simulation of Behaviour in a Nonexperienced Future: The Case of Urban Road Pricing Charles Raux, Odile Andan and Cecile Godinot

Abstract Is it possible to simulate in a realistic manner behavioural reactions to a nonexperienced and a priori nonaccepted travel situation such as urban road pricing? We base our methodological answer on a series of gaming-simulation interviews of a small group of drivers. On the basis of one of their previous driving days, respondents had to adapt their behaviour to traffic congestion and driving bans and then, after the introduction of a new public transport supply, to scenarios of pay parking and finally of urban road pricing. As congestion is a phenomenon which the respondents know well and have often lived through, even if it has never been too serious in their own experience, the analysis of how the simulation operates suggests that this method of simulation could be relevant. This is how the application of this method is made possible for urban road pricing scenarios, which have not been experienced, nor initially accepted. The pertinence of the adaptations carried out and the implication of the respondents do not contradict the ability of this simulation method to elicit reactions. The stated adaptations—search for space and time modifications, resistance to congestion, apparent absence of costs calculation and partial transfer to public transport—suggest particular behavioural decision processes which need further validation. Methodological issues are also discussed, which help to point at the limits of application of this method. Apart from helping the construction of questionnaires for conventional stated preferences surveys, the main advantages are the exploration of choice processes, rather than elaborating the actual future adaptations themselves, and the working out of behavioural hypotheses.

Introduction The inclusion of road pricing scenarios in urban transport policies would seem inevitable in the not-too-distant future. However, if we judge by the

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debates and experiments in various places all over the world, public opinion is generally totally opposed to this idea. Analysis of attempts to introduce urban road pricing and opinion polls show that a considerable amount of "social engineering" is necessary, quite apart from the technical and economic considerations, in order to work out scenarios which are viable policy-wise (Jones and Harvey, 1992). The main problems to overcome concerns the preservation of private life within electronic collection systems, the equity of urban road pricing, and the use of the taxes which have thus been levied. As Jones and Harvey (1992) pointed out, with reference to British public opinion, if it can be shown that these funds are actually used for the improvement of travel conditions in the city, people are liable to agree to the idea of urban road pricing. Goodwin (1989) and Small (1992) suggested a pragmatic approach for dividing the funds obtained among the various users of urban areas. The experience of cordon tolls in Norway shows that the introduction of urban road pricing to finance the development of urban transport supply is possible. Furthermore, the considerable change which road pricing would bring about, lead us to consider methods of forecasting demand. Such a change in the conditions of travel would probably lead to a change in the levels of travel characteristics (e.g. price, time), but also in their role in the choice process of travellers. This is why stated preference (SP) methods are better candidate for forecasting reactions than the revealed preference (RP) methods, which apply the observations of past behaviour (Kroes and Sheldon, 1988). After more than twenty years of SP studies, it is now recognised that SP methods can usefully complement RP ones to improve forecasting ability of behavioural travel demand models (Polak and Jones, 1997). However, certain precautions have to be taken with the use of stated preference methods, especially in the context of unfavourable public opinion, otherwise these methods are liable to lead to reactions of rejection, or confusion, between opinions on the one hand and stated behaviour on the other (Leblanc, 1992). Therefore, it is important to adopt an exploratory approach before using stated preference methods. The aim of this approach is to design scenarios that are acceptable from the transport user point of view, to work out a setting for these scenarios in order to get the respondent to really take part in the simulation and, finally, to identify the characteristics of the alternatives as well as the relative importance of these characteristics in the choice process which the person undertakes. The method used here can be seen as a SP approach, if we consider SP

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as methods which "seek conclusions regarding individuals' preferences, or behaviour, based on the study of responses elicited under experimental or quasiexperimental conditions" (Polak and Jones, 1997). However, the method presented here is closer to gaming-simulation methods, such as those developed first by Jones (1979), and then applied in other contexts (Lee-Gosselin, 1990; Ampt and Jones, 1992; Kurani et al., 1994), than from conventional SP methods. We prefer to call it a 'stated adaptation' (SA) survey, following the taxonomy of Stated Responses surveys proposed by Lee-Gosselin (1997). The latter included SP surveys as a specific category: SA surveys differ from conventional SP exercises in that the respondent is fully free to state which behavioural responses s/he can imagine when faced with several hypothetical situations. Therefore, the first question to be asked is about the validity of such a simulation for the anticipation of realistic reactions in a nonexperienced and, presumably, nonaccepted situation, such as urban road pricing. This is mainly why we will try to answer this question by analysing and comparing the results of the simulation of urban road pricing with those of the simulation of congestion. The congestion being a phenomenon which the respondents know well, even if the level of congestion is not very high in the context of the survey. In the first section, we will describe the local French context in which the survey was carried out. In the second section, we will describe the make-up of the simulation, and the third and fourth sections will deal with the running of the simulation on the two categories of scenarios—congestion and urban road pricing. In conclusion, the fifth section will deal with the evaluation of the aptitudes of this simulation method.

The French Context In France, although the idea of the introduction of generalised road pricing in urban areas is energetically rejected by both elected representatives and public opinion, there are a certain number of examples of tolling specific roads. Since the seventies, France has called on companies under semiprivate management to build and run its interurban trunk motorways and the companies are reinbursed through levied tolls. In urban areas, on the other hand, the rule is that the motorway network should be free of charge. As a result of present restrictions on public funding, a few local authorities have decided to call on private companies to finance new urban highways. Nevertheless, because of the specific legislative context in this

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domain, the introduction of new urban toll highways requires a long and complex procedure. This explains why there are only few urban toll infrastructures at present. Moreover, there is currently no project of generalised urban area road pricing as tested in our survey. The Lyon conurbation, where the survey was carried out has 1,200,000 inhabitants within a radius of 15 to 20 km around the city centre made up of the two cities of Lyon and Villeurbanne (500,000 inhabitants). At the end of 1992, the public transport system consisted of 25 km of subways (four lines), and 91 regular bus lines representing an aggregate covering of 1,200km, 63km of which are bus lanes. An ambitious development plan for public transport was published at the beginning of the nineties, but abandoned for lack of available funding. In the course of 1993, the East bypass was brought into service. This allows through-traffic to go around the centre of the conurbation and has also improved access to, and from, the whole Eastern side of the conurbation. This major improvement in the supply of motorways, taken in conjunction with the economic recession at the time of the survey, has resulted in little congestion in the Lyon region. This is the reasonably car-friendly context in which the surveys on urban road pricing were carried out.

The Methodological Design of the Survey We decided to adopt a prudent approach because of the relatively massive French opposition to the idea of urban road pricing. Before simulating urban road pricing scenarios, we carried out approximately 20 open interviews of drivers who used to travel around the Lyon conurbation. These interviews showed that coercive measures were expected in the future but that the idea of an urban road pricing scheme is far from welcome. If a small minority spontaneously agree to the idea, the majority do not reject it out of hand, but automatically suggest amendments to improve it. What is patently obvious in every case is that: • the problem of the use of the funds obtained from levied tolls must be solved and their use for the improvement of travel conditions would make the measure more tolerable; • the availability of a "real" supply of public transportation is a prerequisite for the introduction of any coercive policy for the use of the private car.

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The lessons obtained from this preliminary survey then enabled us to design the scenarios to be tested in the simulation phase. In order to attain the objectives of effective implication of the respondent and evaluation of the role of the alternatives characteristics in their choice, this simulation was built around two major ideas—the arrangement of the scenarios and the realism of the adaptations. The aim of the arrangement of the scenarios is to introduce the final car-travel regulation by pricing scenarios. Thus, the first scenario tested calls on growing congestion which increases the travel time of the respondent; the second scenario shows a ban on car-use for a period of several days because of a pollution danger. A new public transport supply for the whole conurbation is then introduced and the following two scenarios are pricing regulation of car travel. In the first, pay parking is generalised throughout the centre of the conurbation, and in the second, a toll is levied on all vehicles travelling in the centre. The role of the first two scenarios (congestion and ban), is to dramatise the situation so that pay parking or a toll have to be used, whereas, the new public transport supply makes the latter two scenarios palatable. The realism of the simulation is based on its application to a day's activities and travel as carried out by the respondent (weekday). In each scenario, the stated adaptations of the person surveyed are checked, especially with reference to their constraints. This is true, not only for the space and time constraints within the person's specific activity pattern, but also with reference to his or her interpersonal constraints (driving others about, for example). Furthermore, the scenarios are precisely designed to measure the importance of the various travel choice characteristics (price, time, etc.), and the values at which changes in the organisation of travel and activities occur. This design of the scenarios and their measurement objectives are synthesised in Table 1. The data for a previous recent day was collected by phone in order to prepare the simulation in advance. The simulation usually took place in the person's home, sometimes at his or her office, during an interview which lasted between 1.2-2 hr. It used a schematic representation of the day (time diagram), conurbation maps and summaries of the various scenarios on cardboard coloured cards. This simulation was carried out on 16 people from December 1993 through February 1994, i.e. approximately 30 hr of survey. The respondents all had a professional activity and used their cars daily to get around Lyon and Villeurbanne. These people were all volunteers and came from as widely varied horizons and life-cycle positions as possible. There were

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Stages

Measurement Aims

Check of the day carried out

Identify the constraints on travel, and how much the person knows about the public transport alternatives

Growth of congestion

Acceptable level of congestion, not requiring any major behaviour change Comparison of the effects of duration and of random occurrences

Ban on traffic resulting from a danger of pollution

What resources other than the car does the respondent have available?

Introduction of a new public transport supply Generalised pay parking Measure the reactions to the price Pricing the use of roads in LyonVilleurbanne

Relationships between price and time in the reorganisation of activities

ten men and six women, aged 25-60 years. Half live in Lyon or Villeurbanne, three in inner suburbia and the other five in outer suburbia or outside it. Only six said they had any traffic problems, and these were only occasional. Most of them had no parking problems, five had to use pay parking fees on the day they were surveyed, of whom three were able to claim payment on their expense accounts. Of course, no mention was made of items such as "road pricing" or "congestion" until the actual running of scenarios. The selection of only professional people can be seen as limiting. This option was guided, in fact, by the need to obtain a set of activity patterns on which constraints could easily be applied. As we already know, gamingsimulation techniques are more efficient when applied in a context of constraints strengthening, rather than opportunities widening (Jones et

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al., 1983), in their ability to induce stated adaptations. Other constrained activity patterns involving car use also exist, such as nonworking mothers accompanying children to school. These kind of respondents are more difficult to find but would also need specific investigations. As the main purpose of this chapter is to test the ability of this method to simulate realistic adaptations to nonexperienced situation, such as urban roadpricing, we focus the discussion on the comparison between responses to congestion scenarios and responses to road pricing scenarios.

Attitudes and Reactions to Congestion Knowing the activities actually carried out by the respondent, we designed three scenarios about congestion. Each of them leads to an increase in journey time (+50, +100 and finally +200 percent), each increase with higher and higher repeat frequencies (every fortnight, every week and, finally, every other day), as shown in Table 2. Of course, respondents were presented with distortions to their diary not in percentage but with actual travel duration. Since travel time is relatively short within the Lyon region (mean commuting time is between 20 and 30min), it was necessary to imagine such increases in travel time—we wanted to oblige respondents to react to allday-long congestion right across the city. In these scenarios, public transport is taken as operating with the same journey times as at the present moment, and measures are taken to maintain their commercial speed.

Table 2 Exploration order for congestion scenarios Journey time increase (%)

Once a fortnight

Once a week

Every other day

+50 + 100 +200

1 4 7

2 5 8

3 6 9

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Diverse adaptations . . . All the respondents adapted their travel behaviour as congestion got worse and worse. For each of them, it is possible to classify these adaptations in the order in which they appeared. For instance, "first-level adaptations" are the set of first stated reactions when the respondents began to modify their behaviour. Among the first-level adaptations to appear was a "modification of departure time" (seven respondents out of 16), they would leave home earlier to be on time, and leave work later to compensate for the time lost because of the travel duration. Among second-level adaptations (7/16), was the "cancellation" (when possible) of certain trips: business dealt with by phone, put off to a later date, drop-offs cancelled when the passenger could find another solution. Finally, the "change to public transport" (in its existing state) appears only twice as a second-level choice, and is essentially a third-level one. Seven of the eight respondents, who still had to find a replacement solution when congestion got even worse, agreed to switch to public transport. This change over to public transport would appear to be a last-resort solution. One other marginal solution quoted was to "find work elsewhere", or to "move house".

. . . But a certain resistance to change Certain adaptations in reaction to congestion scenarios can be considered as being part of an individual's "behavioural response choice set". According to the individual, this set is made up of activity timetable changes, route changes, cancellations or postponements of certain trips, and the greater use of public transport for those who already use it to a certain extent. Outside this set, we find adaptations such as the switch to public transportation (for those who never use it), a change of job or home location and reorganisations of work over a period of a year (teachers, for example). These solutions fall outside the domain of what has been experienced, outside immediately conceivable and acceptable changes, and we will refer these solutions to as "extraordinary" adaptations. The journey time virtually has to be multiplied by two, every other day, for the first "extraordinary" adaptations to start to appear. It is only if this journey time is multiplied by three, once a week, that more than half of those surveyed (11/16) admit that they are really being inconvenienced

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and are prepared to start thinking of "extraordinary" solutions. These results show that: • as far as the development of congestion is concerned, we are far from saturation point at which there is a real impact on the total number of car journeys (more than simple time changes, or route modifications); • the scenario where journey time is multiplied by three is useful in that it causes the respondent to look for adaptation solutions other than routine ones.

A nonexperienced situation . . . Is it possible to link the reactions of the respondent to previous personal experiences? For most of them, (11/16), such levels of congestion have never been encountered (not a frequent multiplication by two, or sometimes by three, of their usual journey time in any case). Such congestion is unthinkable! The main reference they have, and which enables them to "play the game" by imagining such a disruption of their commuting, is to imagine a random occurrence (accident, road works, bad weather, etc.). For the other respondents (5/16), these scenarios are easily transposable to what they have already lived through, viz. commuting conditions in the Parisian region.

. . . Considered as improbable . . . Whether, or not, the referents used are random events due to external causes, or an endemic situation such as in Paris, such high levels of congestion are by no means perfectly credible for an inhabitant of Lyon. Two categories of reaction, of equal size, showed up in the attitudes of those surveyed. The first is among those who believe that such levels of congestion could be reached in Lyon, even if they have some reservations about it (5/16). The second is among those who simply do not believe that congestion could ever get as bad in Lyon (7/16). It is to be noted that all the people who use Paris as a reference are found in this category. This refusal to transpose the Parisian situation to Lyon is perhaps one way of warding off such a catastrophe, since travel conditions in the Parisian region are seen in a very negative manner. As far as the other respondents

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are concerned, it is somewhat difficult to see whether, or not, they really believe in the possibility of such levels of congestion.

. . . But taken as a realistic game We must now ask ourselves whether the respondents have "played the game", or not. Have they tried to find realistic solutions for these constraints, or not? It would appear that most of these respondents really did implicate themselves in the simulation—their real interest appeared when they were trying to find solutions adapted to their activity pattern for the day surveyed. For example, one respondent, who cannot benefit from any flexibility of his work schedules, tries to use his bike in order to weave his way through the traffic; but the growing pressure along congestion scenarios make this solution insufficient, and the respondent discards a drop-off of a child in the evening, which will be performed by the spouse, in order to stay later at work; with the growing pressure he then starts earlier in the morning; at the end the pressure is too high and the respondent starts the search for a new job location, which ends this part of the simulation. The pertinence of the declarations, without making too hasty a judgement about the carrying out of the stated adaptations, reinforces the idea that the respondents can play the game and are actually doing so. We must note, however, that two respondents, with timetables which varied enormously from one day to the next, found it difficult to imagine the adaptations they could envisage for that particular day under experiment. To sum up, it is the fact that the constraint was translated into additional minutes on their trips which leads the respondents to become aware of this constraint, to assimilate it concretely and to adapt themselves. Finally, it does not matter, the origin of this constraint, which it is, or is not, about a situation which could arrive one day. In the same way, the translation of the pricing constraint into a cost attached to each trip carried out by the respondents by car, like that made for the pricing scenarios, will lead the respondents to indeed take part in the play. We can consider, therefore, that the application of this method to pricing scenarios will produce relevant information about the adaptation of behaviour.

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Attitudes and Reactions to the Road Pricing Scenarios The toll which we propose to the respondents is a duration based toll for driving in the whole city centre (Lyon and Villeurbanne). There are two new aspects: • the use of roads, previously toll-free now have to be paid for; • the basis for payment is duration and not distance, contrary to what happens on French interurban motorways. As our task here is to measure the combination of price and time in the reorganisation of activities, we have worked out a series of scenarios that combine periods of operation and pricing levels (Table 3). This is why the operating hours for the toll scenarios have been designed to alternatively cover the morning rush hour, the morning and evening rush hours, or day traffic as a whole. It was possible to modify these schedules marginally, so that some trips of the respondent could be included in the simulation. In the presentation of the scenarios, the method of payment is by an electronic toll system designed to enable drivers not to have to stop at toll gates, and to see to it that they remain anonymous. A video system is assumed to be installed to detect vehicles entering without paying. Parking conditions are as at present. The specificity of these pricing scenarios, compared with congestion scenarios, is that there is another change in travel conditions. We show the respondent a new supply in public transport which supposedly existed when the toll was introduced. There are 17 new lines of trolley buses

Table 3 Exploration order for road pricing scenarios Operating time

0600-0930 0600-0930 1600-1900 0600-1900

Toll fee 5 fr/hr*

10 fr/hr*

15 fr/hr*

20 fr/hr*

not tested 4

1 5

2 6

3 7

8

9

10

not tested

* 1 US$ = approximately 6 French francs in July, 1997.

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using fully protected bus lanes for an aggregate length of 120km. The service frequency is high, with a bus every three minutes during tolloperation time. The fare is the same as at the survey time, i.e. 5.50fr for a single ticket valid for one hour, or 250 fr for a monthly buspass. With the introduction of a new public transport supply, the attitude of respondents was largely positive. There is, however, a nuance between discourse and practice. Spontaneously a few of them transfer to public transport, and those who express this spontaneous transfer in the discourse initially try to maintain the use of the car at the first stages of the pricing scenarios. However the main objective of the introduction of this new supply was not to test its own effect, but to offer a potential way out in the framework of constraints strengthening. For each type of toll (morning, morning and evening, all day), and for each price level, we presented the respondent with the extra travel cost per day, including tolls and possible pay-parking.

A game accepted These scenarios were tested on 15 respondents; the sixteenth went through a modified simulation combining road pricing and congestion. Despite our fears, almost all of the respondents agreed, in appearance at least, to play the game as far as the toll was concerned, since out of the 15 respondents, only one categorically refused the very idea of a toll. The lady was a trader very active in a local retail traders organisation and was very severely critical of City Hall financial management.

Diversified adaptations before a partial switch to public transport is considered Out of the 14 respondents who played the road pricing scenarios, 12 have the same final type of adaptation—a modal transfer of the commuter from the private car to public transport. Only two respondents stand out from this behaviour: one, who lives 35 km outside Lyon, finally considered moving home or job location; the other has a very flexible timetable and does everything possible to avoid both the toll and public transport. This final transfer to public transport is the result of a process which can be more or less long as the scenarios unfold. Four of the 12 respondents will immediately try the new public transport supply, i.e. as soon as

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the first scenario of a morning toll with an extra car-cost of 10 fr/day is presented to them. A fifth person will agree to paying more until the extra cost comes to 20 fr, when he will suddenly switch to public transportation. The remaining seven will first try to keep using their cars. In order to do so, they will either try to change their timetables to avoid the toll, or try to reduce the cost by cancelling certain activities, or by grouping them, or again by car-pooling. However, whether they try public transportation straight away, or try to keep using their own cars, many of them prudently say that they will try public transport, they will also try the toll and see if, in fact, driving is not much easier. Overall, this explains why the final transfer to public transportation is only a partial one. In seven out of 12 cases, the use of the car is maintained in conjunction with public transport, with a combination of different modalities: • the person agrees to pay the toll for certain types of activity: shopping, leisure activities and visits, or even for commuting on certain occasions, although which specific occasions are not specified; this latter attitude is the most frequent; • the car is still used for professional travel and the extra cost goes on to a professional expenses account; • the person tries to keep on using the car, but also tries to pay less, either by modifying his timetable, or by sharing cars with friends or neighbours. Do the various toll-operating periods have an influence on the reaction types of each of the 14 respondents? For three of them, the very existence of a morning toll is enough for a categorical switch, and in this case, it is unnecessary to continue. The two or three different operating periods were, therefore, tried out on the remaining 11 respondents, in accordance with their activity patterns. Only four of the 11 respondents clearly appeared to behave differently according to the toll-operating period. For two, the toll has to operate continuously—there is, therefore, no way out for them to transfer to public transport (completely for one, partially for the other). The third person, who finally switches to public transport when he has to pay 30 fr toll per day, still tries to save money when the toll is in operation morning and evening only by leaving work later in the evening. The fourth is the

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person who never envisages public transport, and each time the toll scenario becomes more constraining, will add in a further modification of his activity pattern. The seven other respondents maintain the same adaptation schema, whatever the period of toll operation may be. It would appear that they have fixed a daily, or monthly toll-cost limit, and when that limit is reached they will adapt, whatever the toll-operation period may be.

A certain resistance to pricing . . . Independent of the types of toll, the first changes which the 14 respondents make in the organisation of their working day appear quite quickly. Some react as soon as there is an additional cost of 5 fr and, from 20 fr up, all of them without exception carried out a first adaptation—the mean is situated just a little above 10 fr/day. However, if we consider the "extraordinary" adaptations, such as modal transfer or a change in activity location, a high resistance to the price pressure appears. If these "extraordinary" changes come about for some respondents as soon as there is an additional cost of 10 fr/day, the threshold level for most respondents is 20 fr or more. The extreme case is 50 fr for a shopping activity in the city centre, which one person maintained by car. The mean threshold switch level is slightly under 20 fr/day.

. . . But not a great deal of calculating This price resistance can be explained by the cost calculations made by the respondents during the simulation: • half the respondents react to toll scenarios without doing any calculations other than those made available in the simulations (total daily toll cost for that specific day for each scenario). For them, the toll is either a penalty which they try to get out of, or an extra cost to be added to petrol and pay-parking. They do not try to calculate a more global cost than that of the toll, nor do they try to compare it with another possible means of travel; • the other half make calculations which are different according to the approach chosen. The first group is very much in a minority and sees

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urban road pricing as questioning the continued use of the car; their calculations take into account the cost of the toll, time and petrol saved, or indeed the mileage depreciation on the car. The second group will start considering public transportation as soon as road pricing is introduced. They will compare public transport prices with toll prices, journey time by each mode, or they may even calculate a cost which combines car and public transport. Is it possible to attribute this virtual absence of the car-use costs calculation to the way the survey was carried out? In the survey, the respondents had difficulty in making a snap decision without seeing how things go over a period of months. We would be tempted, however, to believe that this lack of calculation also comes from an implicit refusal to do so. This refusal could be put down to their relatively negative attitude to public transport and their positive attitude to the car. These attitudes would seem to be linked to their having certain drawbacks in relation to public transport services in their area, and to the respective representations of the modes which the respondents perceive. Since the respondents have such a positive image of the car, their choices are essentially made with reference to the advantages of using a car. The advantages weigh much too positively for the respondents to be able to compare car-costs to those of public transportation.

An ambiguous credibility for the road pricing scheme . . . The attitudes about the credibility of the occurrence of road pricing schemes are somewhat ambiguous. More than half the respondents see it as realistic, but for different reasons: it may be something which is possible, or unavoidable, given the present extension of market economy to the public sector. It is "the war effort" to quote one respondent. But the introduction of urban road pricing may also be seen as a purely arbitrary decision, since its justification and rationality are unclear, in which case it is seen as a threat. The other half of the respondents is divided into those who do not take a position, and the complete sceptics.

. . . But an active implication in the game Virtually all of the respondents agreed "to play the game" actively. There are several indications of the quality of their participation. A few of them

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asked subsidiary questions about the time-operation of the toll, the control system and the operating days; others spontaneously applied the scenario to their working day without the interviewers having to ask them to do so. They made a large number of comments on the effects of the road pricing scenarios on their lifestyle, which were not pursued, or again, asked technical questions about the operating of the toll system. Only two respondents remained relatively passive and did not try to base their replies on the simulations offered—they had to be stimulated before reacting. It is worth noting that the participation in the game appears to be relatively independent of the credibility which is accorded to the policy tested. The sceptics, such as those who do not express an opinion, were very active in gaming. Conversely, among the respondents who consider the road pricing scenarios as a future possibility, there were the two respondents who did not really play the game, along with the one woman who refused to play.

The Potentialities and Limits of this Method In conclusion, we must underline the richness of information obtained through this simulation. Contrary to our initial fears, the road pricing scenarios are accepted for play in the simulation, despite the scepticism about their occurrence. Furthermore, it seems that the respondents took a realistic and active part in the simulation, whether it be for congestion, or the road pricing scenarios, even if both had never been experienced and are considered unlikely. This reinforces our positive judgement on the viability of this technique. During the simulation, the respondents react to, and argue against, road pricing in the same way as in the preliminary open interviews. But there is a considerable gap between the discourse on the foreseeable reactions of others and one's own stated behavioural reactions. Faced with a constraint, the person adapts and enters the constraint into his or her field of analysis in order to minimise the consequences through his or her behaviour. This indicates that this simulation method can produce valid information on the range of foreseeable reactions, even in a very unfavourable context, and with the reserve that there must be a setting which makes the urban road pricing scenario acceptable. This also means that the problem of scenario design for an urban road pricing scheme which is acceptable from the political point of view, and

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the problem of measuring behavioural reactions, can, and probably must, be separated. The first can be dealt with by open-interview surveys, as referred to in the second section, whereas, the second concerns the type of simulation described here, leading to a stated preferences survey on a larger sample. Empirical results concerning the adaptation strategies, although limited by the sample size, suggest particular behavioural adaptation processes which need further validation. They are: • the search for very diverse solutions for space and time modifications which enable the car to continue being used; • a relatively strong resistance to congestion, in the specific local framework of the study, since we have to attain the level of a multiplication by two, or even three, of journey time before "extraordinary" changes occur; • in the same way, the resistance to price, in the case of the road pricing scenario, reflects a virtual absence of calculation of car-use costs; the values observed can be considered as thresholds which can be used for the construction of the various options to be used in a stated preferences questionnaire; however, the different strategies of comparison between modes which respondents undertake, as identified in the road pricing scenarios, show that the roles of cost and time characteristics vary as the constraint becomes heavier; • the fact that modal transfer to public transport is only the last resort, and is often solely partial. This transfer to new public transportation in the case of the road pricing is tried out first and foremost. This prudence is symptomatic of a certain suspicion about the considerable changes proposed. This carefulness can also indicate the respondents' desire to stand back from the problem to examine it at leisure, and to show that their behaviour will only become stable after a certain trial period. Here, we touch on an issue shared by stated response methods, i.e. the control of the learning process. During the game, the succession of scenarios gradually improves respondents' understanding of the way each scenario affects them in practical terms. Repeating the exercise of reorganising trips under congestion, for instance, leads respondents to improve the

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way they control the parameters which conditions their choices. Moreover, the four categories of scenarios have a cumulative effect on behavioural adaptations. This experimental learning process could be seen as an artefact. We think, however, that the history that results from the setting up of scenarios reflects, in an accelerated manner, the learning by the individuals of the reality in which such a transport policy could be implemented. The other point, linked to this issue of learning process, is the introduction of the new transport supply in conjunction with the pricing scenarios. It could be argued that this prevents us from analysing the impact of pricing on its own, apart from public transport and that this introduces bias. As has already been said, the introduction of a new public transport supply is a kind of pretext to make more acceptable the introduction of pricing scenarios. To sum up, the history that we designed provides a learning bias: this is the price to pay to avoid trauma in the reactions of respondents and make them take part in the simulation. However, this history is a plausible one that could actually occur and this makes the stated adaptations not completely artificial. Another issue that must be stressed is the extent to which stated behavioural responses will turn into actual behaviour. The prudence expressed by the respondents about the use of public transport, for instance, and the fact that respondents mainly state that they will continue to use the car alternatively with public transport on a day-to-day basis, all show that the passage to actual behaviour is not so straightforward. Garling et al. (1997) showed that successful prediction of travel behaviour should rely on a distinction between planned, habitual and impulsive travel. Moreover, the fact already quoted, that gaming-simulation techniques are more efficient when applied in a context of constraints strengthening rather than opportunities widening, shows that this method is probably less efficient in predicting behaviour concerning occasional or impulsive travel. This simulation approach was originally designed to establish the range of possible reactions before the design and use of a conventional stated preference questionnaire on a larger sample. However, we found that the change introduced by a road pricing policy was so important in our car drivers daily life that what is learned from this gaming-simulation is the decision processes implemented by the respondents rather than the actual future adaptations themselves. Perhaps these are the main advantages of this kind of method when applied to disruption of travel routines and not only to marginal change: the exploration of choice processes and the working out of behavioural hypotheses.

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Acknowledgements We would like to thank Bruno Faivre D'arcier (INRETS) who has greatly participated in this research, also Martin Lee-Gosselin (Universite Laval) and Peter Jones (University of Westminster) for their very useful comments. This project has been financed, in part, by the French Ministry of Transport (PREDIT, No. 92.0013).

References Ampt, E.S. and Jones, P.M. (1992) Attitudes and responses to traffic congestion and possible future counter-measures. An exploratory study of household travel in Bristol. Transport Studies Unit, University of Oxford. Garling T., Gillholm, R. and Garling, A. (1997) Reintroducing attitude theory in travel behaviour research: the validity of an interactive interview procedure to predict car use. Transportation (in press). Goodwin, P.B. (1989) The rule of three: a possible solution to the political problem of competing objectives for road pricing. Transport Studies Unit, University of Oxford. Jones P.M., Dix, M.C., Clarke M.I. and Reggie I.G. (1983) Understanding Travel Behaviour. Gower, Aldershot. Jones, P. and Harvey, S. (1992) Urban road pricing: dealing with the issue of public acceptability—a UK perspective. In C. Raux and M. Lee-Gosselin (eds.), La Mobilite Urbaine: De la Paralysie au Peage? Editions du Programme Rhone-Alpes de Recherches en Sciences Humaines, Lyon. Jones, P.M. (1979) "HATS": a technique for investigating household decisions. Environment and Planning 11A, 59-70. Kroes, E.P. and Sheldon, J. (1988) Stated preference methods. An introduction. Journal of Transport Economics and Policy XXII, 11-25. Kurani, K., Turrentine, T. and Sperling, D. (1994) Demand for electric vehicles in hybrid households: an exploratory analysis. Transport Policy 1, 244-256 Leblanc, F. (1992) Elements methodologiques sur les methodes d'analyse

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des comportements face au peage. In C. Raux and M.E. Lee-Gosselin (eds.), La Mobilite Urbaine: De la Paralysie au Peage? Editions du Programme Rhone-Alpes de Recherches en Sciences Humaines, Lyon. Lee-Gosselin, M.E. (1990) The dynamics of car use patterns under different scenarios: a gaming approach. In P. Jones (ed.), Developments in Dynamic and Activity-Based Approaches to Travel Analysis. Gower, Aldershot. Lee-Gosselin, M.E. (1997) Portee et potentiel des methodes de collecte de donnees de type reponses declarees interactives. In P. Bonnel, R. Chapleau, M.E. Lee-Gosselin and C. Raux (eds.), Les Enquetes de Deplacements Urbains: Mesereur le Present, Simuler le Futur. Editions du Programme Rhone-Alpes de Recherches en Sciences Humaines, Lyon. Polak, J. and Jones, P. (1997) Using stated-preference methods to examine traveller preferences and responses. In P. Stopher and M. LeeGosselin (eds.), Understanding Travel Behaviour in an Era of Change, Pergamon Press, New York. Polak, J., Jones, P., Vythoulkas, P., Meland, S. and Tretvik, T. (1991) The Trondheim toll ring: results of a stated preference study of travellers' responses. Report to the European Commission DRIVE Programme, Transport Studies Unit, University of Oxford. Small, K.A. (1992) Using the revenues from congestion pricing. Transportation 19, 359-381.

Part II Stated Preference

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6

Reflections on Stated Preference; Theory and Practice John Bates

Abstract Stated Preference (SP) techniques are now generally established as one of the tools of demand analysis. They have been applied in hundreds of studies all over the world. Theoretical underpinnings have been provided from general utility theory and Discrete Choice Analysis in particular. Recent developments have led to a much greater understanding of the process of design, which are filtering through to generally improved practice. And yet there is still a sense that all is not quite well. Part of this is attributable to a group of confirmed sceptics who remain unconvinced that the technique is fundamentally sound. But perhaps a more important part lies in the unease among leading practitioners that the technique tends to underperform. For all the apparent wealth of information collected, at the end of most studies relatively little can be said. In addition, in the area where SP might be considered to have the most to offer—that relating to so-called "soft" variables like comfort, cleanliness etc.—the direct valuations provided are often unconvincing. This has led to various scalings being applied (to take account of "packaging", for instance) which are difficult to justify theoretically. Because of commercial pressures, many of the modifications that are implemented to "make sense" of the results tend not to be openly discussed— awareness of the problems comes about more by osmosis, as consultants are called in to review other consultants' work, or as individuals migrate between consultancies. In the author's view, it is high time for a more open debate about the less obvious shortcomings of SP. Therefore, this chapter will provide a short assessment of current practice, and then illustrate a number of problem areas which the author has encountered in the course of his work.

Introduction The aim of this chapter is to initiate some open discussion among practitioners of Stated Preference (SP). It is hoped that improvements can

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thereby be made to current practice, and a clearer understanding of the strengths and weaknesses of the technique established. Over a period of about 15 years, SP has developed into an extremely popular technique for providing data on attribute valuations and assisting with demand modelling. Hundreds of studies have been carried out in the UK alone, predominantly for public transport organisations. It seems fair to say that, at the outset, little was understood of the relative advantages of different types of design, or of the possible effects of different methods of presentation. Good practice tended to follow the general recommendations of Green and Srinivasan (1978), while individual practitioners learned by experience. The earliest applications made use of fixed experimental designs, usually uncorrelated fractional factorials, with most attributes at only two levels. An essential difference between experimental design as used in, say, biology and as used in SP relates to the nature of the observed response variable. The SP response relates to preference and is, strictly speaking, an ordinal rather than cardinal variable. This means that in SP the comparison of two alternatives where one "dominates" the other (i.e. is more favourable in respect of every component), is generally uninformative. This is not the case in more general scientific experimental work. Recognition of this has led to a considerably more careful and thorough approach to SP design, moving away from standard textbook examples. An example of good current practice is given in the third section of this chapter. A further major advance has been brought about by the advent of portable computers. This led to important improvements in the reliability of data collected, first by "customising" the problem to the respondent's current circumstances, thereby, ensuring greater relevance and realism and second, by using logical checks within the interview and largely eliminating coding errors. In addition, it has permitted adaptive designs where the options offered can be modified as a result of the responses to previous comparisons. Some aspects of such designs will be discussed in the fourth section. Another important development is that of estimation methods using data from different sources with potentially different error structures. Though this remains an area of some technical difficulty, theoretical methods have been developed to allow simultaneous estimation of revealed and stated preference data. SP techniques are now regularly requested by clients, including the UK Department of Transport. Training courses in the methodology are

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available, and an increasing number of consultancies and University research groups have developed the competency to carry out SP studies. In short, SP has come of age.

Some Problems Low expectations Although, as noted above, clients regularly request or expect SP techniques to be used, the level of experience on the client side (with some notable exceptions) is often low, and it is by no means clear that valuefor-money is always obtained. The author has seen many SP studies where it is reported in the analysis that "the coefficients on all variables are significant and of the right sign". While failure to achieve this could certainly be taken as evidence of a failed SP experiment, no perceptive client would commission a study in order to conclude that people really did prefer shorter journeys or lower fares! It is the relative magnitudes of the coefficients which is the key output and require such relative magnitudes to be both credible and accurately estimated. There are some fundamental questions to be asked prior to undertaking an SP study. For example, many studies carried out for local transport undertakings do little more than provide values of in-vehicle and waiting time. If average values were all that were required, could not recommended national values have been used (adjusted, perhaps, for local income differentials)? Or, was the aim to obtain a more detailed market segmentation. If so, was this achieved, and again, if so, what are the practical implications for marketing? If the final results are very different from national values, will they be believed? In the author's experience, market segmentation has seldom led to significant differences in valuations. When fine distinctions are made, for example, along the income scale, inconsistencies normally appear which result in a coarsening of the scale until an acceptable pattern is found. The process whereby this is achieved is not usually reported to the client! Segmentation by other obvious variables, such as age and sex, rarely produces significant results. On the other hand, insofar as significant differences are obtained, they are usually in line with general expectations (e.g. higher values of time for higher income travellers). A possible explanation, which needs to be systematically investigated, is that there may be significant variation in ability and inclination to

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respond to the SP tasks among the population. Most SP analysts include tests by which the most obvious "non-cooperators" can be weeded out, but there may be a significant number of respondents who, for one reason or another, are able to do sufficient to produce generally logical responses without attending to the fineness of comparison on which a successful SP experiment ultimately depends. If this is the case, then the presence of these "marginal cooperators" would tend to dilute the responses of those who take the tasks seriously and evince quite fine distinctions in their preferences.

Respondent's strategy The dangers of presenting respondents with tasks which are too complicated are well known to practitioners. This awareness has generally ensured that the tasks are not too long, and do not include too many variables. There has also been concern among some practitioners that "ranking" tasks, as opposed to "rating" and "choice" tasks, are too onerous. What is much less clear, however, is where the boundaries lie, and, in particular, how they might vary between respondents of different intellectual ability. The chief danger here is that respondents may choose "paths" through the task which do not correspond with the decision rules used by the analyst. A particular example is the case of lexicographic choice, according to which two options are evaluated only on the basis of the "most important" attribute. Only if this attribute has the same value for both options will the second most important attribute be examined, etc. This is not, in itself, an illegitimate response—it may correspond with how an individual would actually go about making a choice. However, if the resulting data is analysed, as if it had been obtained by reference to a compensatory utility function, erroneous conclusions can be drawn. In general, there is a need for much more research into how respondents actually carry out the tasks, using debriefing techniques and alternative decision rules. As a minimum, the data should be checked for possible lexicographic effects. In the author's experience, only a small number of practitioners do this as a matter of routine.

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Hard and soft variables By "soft" variables we mean those attributes that are likely to affect travel behaviour, but are inherently difficult to quantify: they relate to comfort, convenience, security etc. A related distinction is that between "primary" and "secondary" variables, where primary variables refer to well-established and significant attributes of a journey (e.g. total travel time), whereas, secondary variables are more incidental (for example, the clarity of announcements, the presence of escalators versus fixed staircases etc.). It was an early hope of practitioners that SP would prove particularly powerful in the general investigation of the value placed on soft and secondary variables. Many experiments have been done, particularly within public transport, to obtain appropriate valuations, which have typically been quoted as a percentage of the fare paid. In most cases, only a limited number of such attributes have been examined, and clients have been willing to believe the results. Problems have emerged when the values have been added over a significant number of such attributes. For example, one SP experiment may imply that passengers would be prepared to have their fare increased by 18 percent if a fixed staircase is replaced by an escalator, while another may indicate that an improved public address system is worth an 8 percent increase in fare. By the time, say ten, of these relatively minor aspects are included, it may appear that passengers are prepared for the fare to more than double. Such conclusions do not generally appear plausible. In the fifth section, there is a further discussion of this issue, which casts quite serious doubt on the validity of SP in certain circumstances.

An Example of a Problem Design The following example has been encountered by the author, although he was not involved in the work. In order to keep the work anonymous, we will pretend that it relates to the use of the RER rail to Charles de Gaulle airport in Paris. This is not the real subject of the study, however, and not all the details should be taken as reliable. The investigation was confined to business travellers from the centre of Paris, who may find the train a convenient and reliable way of getting to the airport. The object was to find their valuation of in-vehicle and waiting times. The normal journey takes about SOmin and costs FF35, and the average waiting time is 5 min.

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The SP experiment was designed as a series of within-mode pairwise comparisons of options against the existing journey. Thus, the design could be based on the differences between the three variables, fare, travel time and waiting time. Ten options were used, as set out in Table 1. Table 1 Illustrative experimental design Option

Cost difference (FF)

Time difference (min)

Wait difference (min)

1 2 3 4 5 6 7 8 9 10

-20 -5 +8 -10 + 12 -9 -15 -20 -17.50 +20

-30 +5 -19 +5 -8 +3 -5 -30 +6 -20

+5* + 21/2|

+3*

+11/2 -1

+4

+2 1/2 +91/2 +1 +4 1/2

The differences were defined such that they would be added to the existing values. Thus, option 5 would compare the base (fare FF 35, time 50 min, waiting 5 min), with an option having the fare at FF 47, travel time 42 min and waiting time 4 min. A three-attribute design can be conveniently summarised by the "ray diagram" which is now generally used by most leading SP practitioners (see, for example, Fowkes, 1991). If we choose fare as the "numeraire", then we can draw the diagram in the two dimensions of value of travel and waiting times. Each of the 10 options generates a "ray" within the diagram, effectively cutting the parameter space into two parts, as shown in Fig. 1. The option associated with each ray is noted in Fig. 1. Although it may well be possible to improve the design, it would seem, at face value, to permit reasonable coverage of the likely range of values. Prior expectations would suggest a value of waiting time about double that of in-vehicle time, and this is indicated by the shaded line starting at the origin. Since these are business travellers, we could expect values in excess of

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FF 2/min, and the design is somewhat sparse in this area. Nonetheless, it should be capable of returning such values. In the actual study on which this example is based, the value of invehicle time came out extremely low, and the value of waiting time was high relative to the in-vehicle value. The estimated combination is indicated in Fig. 1. All the coefficients were significant, in terms of the assessment criteria normally used in such studies. A possible reason for the outcome can be argued as follows. The respondent is invited to compare each option with his current journey. If he opts for his current journey, it is reasonably straightforward to calculate which side of any ray a respondent will be deemed to have chosen. This has been indicated by arrows in Fig. 1. For example, given option 5, if the respondent chooses his current journey this implies that his values of time and waiting are to the left of the associated ray. From this, we can begin to see what might happen if respondents tended to carry out the task using strategies which were incompatible with the standard analysis which assumes compensatory linear utility functions. For example, what would happen if respondents had a tendency to stay with their current option (this might be an easy response if they were not really prepared to put any effort into their responses or, perhaps, if they did not believe the options presented could be achieved)? A concern would arise if the space implied by such a reaction was considerably more restricted than the full space shown in Fig. 1. Looking at the direction of the arrows there is, in fact, no reason to believe that this is so. For example, choosing the current journey for options 1 and 7 would confine the valuations to the top lefthand corner, but for option 9 the valuations would be confined to the top righthand corner. Nonetheless, some problems do appear, which stem from the following. Looking at the 10 options set out in Table 1, we notice that in only three cases is the cost actually increased (options 3, 5 and 10). Moreover, even the smallest increase (option 3-FF 8) involves a 23 percent rise in fare, while the largest increase (option 10) involves a 57 percent increase. Suppose that, without assessing the possible gains in travel time etc., respondents tended automatically to reject fares increases. The rays for the relevant options have been drawn with a darker shading in Fig. 1. The figure shows that rejecting the high-cost options, in favour of the current journey, will tend to push the valuations into the area bounded to the right by the rays for options 3 and 5 (option 10 is, in this sense, "dominated" by option 3). Moreover, of the remaining seven options, only one (option 9) has any

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power to counteract this effect. Unfortunately, option 9 generally requires very high valuations on both variables (above and to the right of its ray), if it is to influence the values away from the bounded area. This analysis suggests that if there is a significant tendency among respondents to vote against fare increases, even if the remaining options are treated "sensibly", the final valuations could be heavily constrained to the lefthand side of Fig. 1. Without a careful examination of the data, we cannot be sure that this was the reason for the values obtained, but it is at least suggestive. The point of the illustration is to show that an apparently well-constructed design could be subverted by a small number of responses, which, for whatever reason, are not based on the assumed compensatory preferences. In this case, the problem may have been exacerbated by presenting all options relative to the current position. Indeed, based on wider experience, the author would counsel caution against such forms of presentation. What is clear is that more information is required on response strategies, plus appropriate tests at the analysis stage to see whether, or not, certain kinds of nonconforming strategies have, in fact, been followed. This experience will then sensitise SP designers to the possible pitfalls inherent even in designs which appear well constructed. The argument applies, a fortiori, to cases where the design process is carried out with less attention.

Adaptive Design While the earlier SP experiments were usually based on fixed designs, there has been a growing tendency, not only to ensure that the values used are appropriate to the respondent's current experience ("customisation"), but also to allow the design itself to vary according to the responses given up to that point. In principle, this should allow more accurate parameter estimations by narrowing down the range within which tradeoffs are offered. A recent paper by Bradley and Daly (1993) produced disturbing evidence that some forms of adaptive design may well lead to serious bias in valuations. At the same time, their work suggests that adaptive design may introduce correlation between SP attributes leading to loss of accuracy in valuation, although this is an odd conclusion given that a paper by Fowkes et al. (1993) demonstrates that negative correlation, as found by Bradley and Daly (1993), should improve the estimation of the ratio of coefficients. In order to discuss this, we will make further use of the example given

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in the previous section. Suppose that the existing journey was rejected for option 2, while for option 4, it was preferred. Interpreting the result literally with reference to Fig. 1, this means that the point corresponding to the valuation of in-vehicle and waiting times lies both below and to the left of ray 2 and above and to the right of ray 4. Within the reasonable constraint of positive valuations, there is no feasible point satisfying this requirement. What should we deduce from this? At least from the point of view of the linear compensatory model, one or both of these responses must be incorrect. In principle, it is possible to set up tests to identify respondents involving such cases. Having identified them, should they be dropped? The danger of doing so is that we may be imposing too strong a condition on the responses, given that the linear compensatory model is, at best, only an approximation to people's preference behaviour. This suggests that we require a certain amount of tolerance in the performance of the SP task, a tolerance which will allow both for minor errors in the respondent's judgement and shortcomings of the model specification. The choice of this tolerance level is crucial, since it must not be so wide that it permits wholly inappropriate and inattentive responses to go unchecked. The significance of this discussion for adaptive methods is that most of the adaptive methods that have been developed (including, it would appear, that tested by Bradley and Daly, 1993), effectively make use of zero tolerance, more or less by ensuring that contradictions of the type illustrated cannot occur, because the relevant choices are simply not presented. Thus, in terms of the example presented, if for option 2, the existing journey was preferred, option 4 would not be presented, at least in its current form. The potential contradiction would not be detected, because as a result of the response to option 2, all further options would be restricted to the area below, and to the left, of ray 2. Yet if option 4 had been presented first, very different results might have been obtained. An alternative adaptive approach, which specifically attempts to avoid "boxing in" respondents as a result of their responses to date, is described in Bates and Terzis (1992). The adaptive mechanism is only invoked after a set of prespecified options have been presented, sufficient to allow preliminary coefficient values to be estimated: thereafter choices are offered corresponding to points that are located an arbitrary distance on either side of the current estimate of the "iso-utility plane". This estimate is regularly updated. Nonetheless, this approach still does not address the basic question of what level of "tolerance" is desirable. It seems that the resolution of this

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problem lies in the same field as that of the preceding section, namely a greater understanding of the strategies used by respondents to carry out SP tasks. In the meantime, it would be prudent to avoid any adaptive approach based on an assumption that each response can be treated as 100 percent correct, in terms of its implications as to which side of the "ray" the parameter combinations lie in.

Soft Variables, etc. Reviews of past research have shown that the monetary values for time, frequency and other "hard" variables derived with SP methods have been acceptably consistent between studies. However, the valuations of soft variables, such as comfort and cleanliness, have been rather less convincing, particularly when viewed as components of an improvement package. There has been a general view amongst practitioners that the individual valuations derived from SP involving only a few "soft" attributes may be overestimated. As a result, it may be inappropriate to simply estimate the value of an overall package by the addition of individual attribute valuations obtained from independent SP exercises. The existence of such a problem has been demonstrated, first, in the unreasonable valuations which are implied for "packages" of improvements and, second, in the direct valuations obtained from hierarchically structured SP tasks. For example, separate SP experiments may be designed and distributed over the sample to obtain monetary valuations of improvements to soft variables A, B and C. In addition, a higher-level task is given to all respondents in which they have to trade-off a package of improvements involving all three soft variables against other primary variables. The results (see, for example, Kroes and Sheldon, 1988), have invariably been that the valuations attributable to the individual soft variables, when presented as part of a package, are much lower than those obtained from the independent SP experiments. Some practitioners have concluded that "they need to be divided by three!" In past research, it has been argued that the overestimation can be attributed to methods of presentation. In particular, it has been argued that "between-mode" choice exercises are more realistic than "withinmode" choice exercises and scaling has been applied to reconcile the approaches. However, whether, or not, the valuations are sensitive to methods of presentation (see, in this respect, Widlert, 1998), a systematic discrepancy of this nature raises serious questions. It is unacceptable to

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propose broad rules of thumb that purport to "correct for the package effect". Rather, it is essential to understand the source of the problem, whereby, the valuation of individual attributes is apparently seriously context-dependent. A number of other potential reasons for the discrepancy have been put forward in the past: • Nonlinearities of valuations within an attribute. This might relate, in particular, to the cost variable, whereby successive increases in cost produced more than proportionate disutility, leading to lower valuations at higher cost. • Interactions between attributes. The package effect could be attributed to negative interactions between soft variables, whereby the utility of improvements in both A and B were less than the sum of the individually assessed utilities. • The effects of the method of presentation of the SP exercise. Here there is not only the possibility of differences between mode versus within mode as mentioned, but also ranking versus pairwise. • The presence (or absence) of more than one primary ('hard') variable in the exercise. Such an effect would seem to relate primarily to individuals' ability to perform the SP tasks, in that their valuations of soft variables would appear to be "distracted" by the number of hard variables included. • The background context of the particular trade-off. A particular concern is that the level of description for individual soft variables may vary according to how many are included, so that experiments with single soft variables may make them seem in some sense "special". • The general effect that 'packaging' might have on the valuation, wherein, overall budget may constrain valuations. This relates back to issues of interactions and the context. A recent study carried out for London Underground (see Copley et al., 1993), set out to address these issues by testing a number of hypotheses in pilot studies. The conclusions from these pilot studies (which included a total of over 340 interviews) were:

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• Although in some cases there was a tendency for the disutility/cost slope to steepen at higher cost levels, no general conclusions about nonlinearity could be drawn—certainly not of the order required to explain the package effect. • Interactions between aspects of the journey can be significant and this must be considered in designing SP experiments—however, they are certainly not uniformly negative and cannot account for the scale of the "package effect". • No significant differences were found between the results of a withinmode and a between-mode experiment when based on the same variables and underlying design. • The relative valuations of a set of quality attributes are unaffected by the presence, or absence, of fare in the SP experiment. • Despite considerable endeavour to allow other influences to reduce the packaging effect, of which the most successful appeared to be an explicit and consistent definition of the soft variables throughout experiments, there remained a significant residual effect (though it was less than the factor of three suggested earlier). It is important to note that it did not appear to have any impact on the relative valuations of the soft attributes. The conclusion drawn from the study was that while the relative valuations of the soft variables as derived from SP was generally secure, it appears that any consideration of absolute values must be tempered by the general implication that travellers are unwilling to countenance major increases in fares to pay for improvements in comfort etc. In the study referred to, this was dealt with by endeavouring to determine a value for the 'perfect' journey by Underground. The concept of a perfect journey was deemed to be the situation when all aspects of the underground journey were improved to their best possible state and to be representative of the maximum value that could be attached to a package of improvements. For further details, the reader is referred to Copley et al. (1993). While this may be a practical way forward, the theoretical problem for SP remains that the direct valuations between changes in money cost and improvement in soft variables appear to vary according to the number of soft variables included in the experiment(s). Without a convincing

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explanation, this must seriously undermine the confidence we can have in such valuations.

Conclusions Although Stated Preference has become an accepted tool of the trade, there remain a number of doubts about its performance. In particular, more work is required to research how people actually carry out the task and how they are affected by presentational methods (the companion chapter by Widlert, 1998 suggests major variation in results according to presentation). Since this chapter was presented, there have been technical advances in estimation, addressing the often-cited "repeated measurements" problem. Cirillo et al. (1996) proposed a jackknifing approach to the estimate of the true standard errors in SP analysis, while Ouwersloot and Rietveld (1996) suggested estimation methods based on panel data analysis to develop an appropriate error structure. Recent work by Ortuzar et al. (1997) cast some doubt on these approaches, and Bates and Terzis (1997) show that under certain circumstances, failure to allow for an appropriate error structure may produce seriously biased coefficients, so that there may be more at stake than the question of over-optimistic standard errors. These developments suggest that we are reaching a stage where the technical aspects of design and analysis of SP data have achieved a high standard, even if this remains "state of the art" rather than "state of the practice"! It is therefore vital that these achievements should not be undermined by conceptual errors resulting from a failure to understand the respondent's approach to the SP task. For this reason, the concerns expressed in this chapter and that of Widlert (1998) deserve to be taken seriously.

References Bates, J.J. and Terzis, G. (1992) Surveys involving adaptive stated preference techniques. In A. Westlake et al. (eds.), Survey and Statistical Computing, Elsevier Science, Oxford. Bates, J.J. and Terzis, G. (1997) Stated preference and the "ecological

Reflections on Stated Preference fallacy". Proceedings 25th European University, September 1997, UK.

Transport

Forum,

103 Brunei

Bradley, M.A. and Daly, A.J. (1993) New analysis issues in stated preference research. Proceedings 21st PTRC Summer Annual Meeting, University of Manchester Institute of Science and Technology, September 1993, UK. Cirillo, C., Daly, A.J. and Lindveld, K. (1996) Eliminating bias due to the repeated measurements problems in SP data. Proceedings 24th European Transport Forum, Brunei University, September 1996, UK. Copley, G., Terzis, G., Bates, J.J., Heywood, C., Sheldon, R., Goulcher, A. and Weston, G. (1993) Use of stated preference methods to determine London underground passenger priorities. Proceedings 21st PTRC Summer Annual Meeting, University of Manchester Institute of Science and Technology, September 1993, UK. Fowkes, A.S. (1991) Recent developments in stated preference techniques in transport research. Proceedings 19th PTRC Summer Annual Meeting, University of Sussex, September 1991, UK. Fowkes, A.S., Wardman, M. and Holden, D. (1993) Non-orthogonal stated preference design. Proceedings 21st PTRC Summer Annual Meeting, University of Manchester Institute of Science and Technology, September 1993, UK. Green, P. and Srinivasan, V. (1978) Conjoint analysis in consumer research: issues and outlook. Journal of Consumer Research 5, 103-123. Kroes, E. and Sheldon, R. (1988) Are there any limits to the amount consumers are prepared to pay for product improvements? Proceedings 16th PTRC Summer Annual Meeting, University of Bath, September 1988, UK. Ortuzar, J. de D., Roncagliolo, D.A. and Velarde, U.C. (1997) Interactions and independence in stated preference modelling. Proceedings 25th European Transport Forum, Brunei University, September 1997, UK. Ouwersloot, H. and Rietveld, P. (1996) Stated choice experiments with repeated observations. Journal of Transport Economics and Policy XXX, 203-212 Widlert, S. (1998) Stated preference studies: the design affects the results. In J. de D. Ortuzar, D.A. Hensher and S.R. Jara-Diaz (eds.), Travel Behaviour Research: Updating the State of Play, Pergamon Press, Oxford.

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Stated Preference Studies: The Design Affects the Results Staff an Widlert

Abstract A large number of Stated Preference studies have been carried out during the last years. It is possible to make such studies in different ways and relatively little is known about how the general design of the study affects the results. The purpose of this chapter is to examine how different aspects of the design influence the results. The main aspects that we looked at were differences between rating, ranking and pairwise choices, the importance of customising the levels of the factors to the interviewees own experiences, the effects of different number of alternatives, the effects of different price levels, a comparison between absolute and relative factor levels and the importance of interviewer effects. For the project we designed 25 different types of interviews that were carried out during the same time period of the year on long distance trains in Sweden. The overall result is that there are great differences between the interview types—the largest and the smallest value-of-time differ by a factor of four. This big divergence occurs despite the fact that the questions are identical and that the samples are very similar. It is not possible to conclude which results, if any, are the correct ones from the goodness-of-fit measures, or from the levels of significance. Instead, we have to look into how the respondents reacted to the different designs to understand why the results differ so much. The conclusion is that the differences are mainly caused by two problems. The first is that people tend to simplify the task whenever possible. This led to varying proportions of so-called lexicographic answers, where the interviewee sorted the alternatives according to one or two factors. This tendency was strongest when the respondent was asked to rank cards, and much less frequent, rate the alternatives, or make pairwise choices. The second most important factor that caused the differences was whether the interviews were customised to the respondents own situation, or not.

Background and Purpose A large number of Stated Preference (SP) studies have been conducted during recent years. Few of them have tried to study how the general

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design of the studies affects the results. Our own interest in the area began when we tried to explain differences between results from two studies that had been carried out at the Technical University of Stockholm. In the first project, which was carried out during 1989, the valuations of people travelling by train between Stockholm and Gothenburg was studied with computerised interviews onboard the trains (Lindh and Widlert, 1989). Two years later the study was repeated (Lindh, 1992), but this time both computerised interviews, and manual interviews where the interviewees had to rank a set of cards, were undertaken. The results from the two studies showed that the values from the computerised interviews agreed fairly well between the years, but the values from the card games were substantially lower (only about one-third of the values from the computer games). Since the experimental design was not identical and there were some minor differences in the variables in the games, it was difficult to make firm statements about the cause of the differences. Still, the results left us with a sense of uneasiness. The purpose of this project was to study how different aspects of the design of a Stated Preference study influence the results. Some of those were: • comparison between pairwise choices on computers and ranking of cards; • comparison between ranking of cards and rating of alternatives; • importance of customising the levels of the factors to the interviewees own experiences; • effects of different number of alternatives; • effects of different price levels; • comparison between absolute and relative factor levels; • importance of interviewer effects. In order to do that we designed 25 different types of interviews.

Design of the Study The study was carried out on the long distance trains between Stockholm and Gothenburg, the two largest cities in Sweden, and on the trains between Stockholm and Sundsvall. The distance between Stockholm and Gothenburg is approximately 500 km and the distance between Stockholm and Sundsvall is 400 km. Only passengers in second class were interviewed.

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People who travelled the whole distance, and people who only travelled part of the distance, were interviewed. People with free tickets, with Inter-rail tickets and with some other types of special tickets, were not interviewed. Business trips were also excluded from the analysis, since the share of business trips varied somewhat between the interviews and business travellers also have rather different valuations than private travellers. The selected train lines were chosen because we had conducted interviews on one of them before (so we had previous results to compare with), and also because the travel time is long enough to give time for several interviews, and short enough to make it possible to make a return trip the same day. In all the interviews, train passengers were asked to evaluate different train alternatives. The alternatives included four factors, each with three or four levels. The "base design" used had the following levels for the factors: Price: Travel time: Frequency: Carriage:

—5, +5, +10 percent (compared to present price) ±0, -10, —25 percent (compared to present travel time) two trains per hour, one train per hour, one train every second hour renovated old carriages, today's Inter-City carriage, highspeed train carriage

Price, travel time and frequency were described in words to the interviewee, the type of railway carriage was illustrated with colour pictures. The different types of carriages shown were today's Inter-City carriages, renovated older carriages and fast-train carriages with more modern design and better comfort. The three types of carriages were also described in words. The travel time differences agrees with the possible travel time reductions with the present Swedish high-speed trains. The different levels are all plausible to the travellers. The frequency is approximately one train per hour per day. The same experimental design was used for both the computerised and manual games. The computerised interviews were done with the MINT program from the Hague Consulting Group. We used the possibility to randomly allocate variable levels to design levels, so in that sense the design was not completely identical. The program also tests for dominant choices (pairs where one alternative is better, or worse, for all factors than the other). Such pairs were not presented to the interviewees (and also excluded in the analysis). In the computer games,

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the respondents made pairwise comparisons between alternatives. Each respondent had to react to a maximum of 12 pair of alternatives. All interviews took place during June 1992 and June 1993. The interviews were spread over all days of the week and over different departures. Much care was taken to ensure that all types of interviews were randomly distributed over the departures and over the carriages in the trains. Part of the computerised interviews were done on ordinary sized laptop computers with back-lit screens. In this case, the interviewer sat beside the interviewee and helped him with the task—typically the interviewer typed in the answer on the computer, but the interviewee could do it himself if he wanted to. Another part of the computerised interviews were done on very small computers, the size of a video cassette (Poquetcomputers). These small computers did not have a back-lit screen and were handled solely by the interviewee. The interviewer distributed 4-5 such small computers at the time and then only supervised the work and answered questions. In this way 4-5 times as many interviews were collected per time unit. The "manual" games were self-completed. The interviewee received the form, the illustration material, plastic pockets to help sort the cards and a pencil. He then completed the form by himself. Both the manual and computerised interviews contained exactly the same questions until the SP game was completed. In the manual interviews there were also a limited number of follow-up questions that were not included in the computerised interview, but those questions were asked after the game was played. In general, the interview situation on the Inter-City trains is quite favourable. The travellers normally have plenty of time available and often regard the interview as a welcome interruption. Therefore, relatively few passengers refuse to participate. Some passengers were asleep (and were not awakened). Passengers with small children are sometimes impossible to interview. Since the task is somewhat demanding, other persons refuse when they see the form. Some interviews are also impossible since the traveller is near his destination. In total 5700 interviews were carried out with an average response rate of 71 percent.

A Summary of Estimation Results The data collected has been analysed with logit analysis. Logit analysis is fairly straightforward for the computer games, where the interviewees choose between pairs of alternatives. The choice is made on a scale where

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the alternatives are chosen "definitely" or "probably". When a set of cards is ranked, that ranking was transformed into discrete choices for the logit analysis. Here we concentrate on the results for price and travel time since they are most significant and stable. As discussed above, normally the time and cost variables are defined as percentage changes of the time and cost for the trip actually undertaken. We normally present the value of the different factors as the parameter for that factor divided by the cost parameter. This gives a value of time expressed as the percentage change of the price that has the same value as the value of a one-percent change of the travel time. To give a first impression of the magnitude of the differences between the designs, Fig. 1 shows the value of time. As can be seen, the differences between the designs are very large—there is a factor of four between the largest and the smallest value-of-time.

comp. cust. 1 computer 2 rank 9 cards 3 rank 9 no ex 4 rank (5 of 16) 5 rank (9 of 16) 6 rank (16 of 16) 7 rating 8 rank absolute 9 rank large diff 10

Y///////////A

rank negative 11 rank positive 12 computer large 13 comp. interviewer 14 comp. no interv. 15

0.2

0.4 0.6

0.8

Figure 1 Value of time, percent price/percent time

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This big divergence occurs despite the fact that the questions are more, or less, identical and the samples very similar. It is important to stress that all the time and cost parameters used in the calculation of the values are highly significant. It is not possible to conclude which results, if any, are correct from the goodness-of-fit measures, or from the levels of significance. Instead, we have to look into how the respondents reacted to the different games and why the results differ so much.

Lexicographic Answers Lexicographic answers occur when the interviewee sorts the alternatives according to the values of one of the variables. A perfect lexicographic sorting of the alternatives after two factors requires a very systematic behaviour from the interviewee. In this chapter, we only discuss lexicographic answers according to one factor. Lexicographic answers can have different causes. If the interviewee finds the task too difficult, or tiresome, he might sort lexicographically to simplify it. In this case, the rank-order does not really represent the true valuations of the respondent. Lexicographic answers can also occur if the design is such that one factor actually is more important to the respondent than the others. In this case, the rank-order is correct—but it is unsuitable to pick up the respondents valuations. In both cases, lexicographic answers cause problems, but problems of different kinds. If the interviewee sorts lexicographically to simplify the task, the effect is that the importance of the factors used for the lexicographic sorting are increased in the results from the analysis, and the importance of the other factors are decreased—all compared to the "true" values. This is quite obvious since the lexicographic sorting in this case means that the interviewee gives unrealistically high weight to the factors according to which he sorts. If we have a game with factors for time, price and comfort, and most interviewees sort lexicographically according to price to simplify the task, we get a higher valuation for the price factor and a lower relative valuations for the other factors. If we calculate values-of-time from the results, they will be too low, since the price parameter will be to high and the value of time is calculated as the ratio between the time and cost parameters. If, on the other hand, the respondents primarily sort according to travel time, then the value-of-time will be overestimated. This also

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leads to the observation that the effect of the lexicographic answers can cancel out if different people sort after different factors. If the respondent sorts lexicographically, because one factor really is that important, we have a different effect. Imagine a situation where one factor is exactly important enough to cause a lexicographic sorting after that factor. If we then increase the importance of that factor, by widening the range between the levels, we will get exactly the same ranking of the alternatives—there is no possibility for the interviewee to show that the factor is now even more important. There is also no possibility for the analysis to pick up the true importance of the factor. The result is that the importance of the factor is underestimated in the analysis. We can conclude that the effects in the two cases have different directions and that they may balance each other, but we will see in the following sections that this is not at all true in most cases. We also note that the fewer alternatives the interviewee chooses among, the greater the chance that the choices appear to be lexicographic for purely random reasons. This is illustrated in Fig. 2, where the results of interview type 1 (computerised interviews with customisation) are shown. When all 12 pairwise choices are included, we find that 22 percent of the interviewees

o/ /o

10 4

6 8 10 12 number of pairwise choices

Figure 2 Share of lexicographic choices with different mumber of pair-wise choices

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seem to choose lexicographically for one of the four factors in the game. We then randomly exclude one, or more, of the pairwise choices and test for lexicography among the remaining choices (this is the same as if we had presented a smaller number of alternatives during the interview). We can see from Fig. 2 that if we keep only six pairwise choices, almost 80 percent of the interviews seem to be lexicographic, compared to 22 percent with 12 pairwise choices. It is important to stress that this difference is not at all behavioural—the interviews are the same in both cases, except with different number of pairwise choices excluded afterwards. With fewer pairwise choices, more interviews seem to be lexicographic. Obviously, the share of lexicographic answers in different games can only be directly compared if the number of options is the same.

Results Computerised interviews with or without customisation The first two interview types compared are: type 1, where the interviewees were presented with alternatives where both the percentage change and the absolute value of both travel time and price were presented; and type 2, where only the percentage changes are presented on the screen. The computer makes it very easy to calculate the absolute values after questions about present values have been asked. This possibility of customisation to the actual trip is a major advantage of using the computer. The price parameters in the two models are not significantly different, but the time parameters are. The price parameter is lower in the customised model and the time parameter is higher. The value of time is calculated as the percentage change in the fare that is of equal value to a one percent change in travel time. The value is equal to the time parameter divided by the price parameter. The value of time is 60 percent higher in the game where the absolute time and cost values are shown to the respondent (0.78 and 0.40, respectively). Table 1 shows the share of lexicographic answers in the two models (in percent), broken down by factor (frequency and type of carriage are reported together). We report all observations that have made their choices lexicographically after at least one factor. Very few respondents choose lexicographically after two or more factors in the computer games. The total share of lexicographic answers is the same in models 1 and 2, but the lexicographic answers are much more unevenly distributed over

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Table 1 Computerised interviews with and without customisation 1. Computer, customised (%)

2. Computer, not customised (%)

Price Time Other

7 10 5

15 6 1

Total

22

22

the factors in model 1. As previously discussed, it is much less of a problem if the lexicographic answers are distributed over many factors. It seems as if the interviewees tend to give more priority to the price when they get less information about the levels of the factors. This is obvious in both the share of lexicographic answers and in the values of the estimated parameters.

Computerised interviews or ranking of cards One of the main purposes of the study was to compare computerised interviews with manual interviews, where the interviewees were asked to rank cards. As mentioned before, we had previously interviewed respondents using both methods on the same trains with quite different results. In a first step, the computerised interview of type 1 (the "base" interview) is compared to an interview where nine cards are ranked by the interviewee. The same design and levels are used in both cases. The time value is less than half in the game where cards were ranked —0.78 and 0.32, respectively. This agrees well with our previous experience that lower monetary values were obtained for all factors in games where cards were ranked. The cost parameter is almost twice as high in model 3 as in model 1. The difference in the time parameter is not as large. Table 2 gives an indication as to why this result is obtained. The share of lexicographic answers is almost twice as high in game 3 as in game 1. The "true" share of lexicographic answers in game 1 is, as discussed above, even lower than Table 2 shows, since only 12 of the possible 36 pairwise choices have actually been made. In game 3, one-

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Travel Behaviour Research: Updating the State of Play Table 2 Base model compared to model with ranking of nine cards 1. Base model (%)

3. Ranking 9 cards (%)

Price Time Other

7 10 5

35 4 0

Total

22

39

third of all respondents have ranked the cards according to the price of the trip. Few ranked the cards according to the time or other factors in the game. In game 1, the lexicographic answers are more evenly distributed over the factors. This is the case even though the factors and levels are identical in both games. If the lexicographic sorting in game 3 is caused by a wish to simplify the task, the result is an overestimation of the cost parameter, and a corresponding underestimation of the monetary values for the other factors. From these results, it seems obvious that the interviewees in this case try to simplify the task when they are asked to rank cards. Most of them sorted the cards according to the price—a factor that is both important and was presented at the top of the cards.

Ranking of cards with or without examples In the computerised interviews, it is very easy to customise the options to the actual conditions of the trip that the traveller is making when contacted by the interviewer. This is much more difficult in the manual interviews, where the alternatives are described on printed cards. It is possible, and often done, to let the interviewer calculate the values during the interview and fill them in on the cards. This procedure is both time-consuming and laborious. Errors are also likely to occur. We decided not to customise the cards, but to present only the relative changes on the cards. Instead, we chose to vary the amount of information given on the cards. In model 3 we gave the relative time and price changes, plus information on the resulting fare for a second-class ticket and the resulting travel time between Stockholm and Gothenburg. This information is sufficient for half the sample travelling the full distance, but it is obviously only of

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limited value for the other half. In model 4, we only gave information about the relative changes of the price and the travel time (see Table 3). The examples given only marginally affect the share of lexicographic answers. As expected, some more people simplify the task and sort systematically when less is said about the trip. The slight difference in the share of lexicographic answers reflects a corresponding small difference in the estimated models. The time value is slightly lower in the model where no examples are given (0.32 and 0.30, respectively). Table 3 Ranking of cards with or without examples 1. Computer

3. With example

4. Without example

Price Time Other

7 10 5

35 4 0

38 4 0

Total

22

39

42

Ranking of cards and computerised interviews with different numbers of alternatives In Table 4, we illustrate the effect of ranking different numbers of cards randomly selected from a design with 16 options. We can see that the time value decreases when more cards are ranked. If we look once again

Table 4 Ranking of different numbers of cards Game

Number of cards

Time value

5 6 7

5 9 16

0.36 0.27 0.25

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at lexicographic answers as a possible explanation, we find that the share decreases with the number of alternatives that have been ranked. With less alternatives there is a greater chance that the rank-order will look lexicographic, even if the respondent did not sort according to any factor. In Fig. 3, the line shows what happens if different numbers of cards are randomly excluded from the rank-orders that were produced in game 7, where in reality, 16 cards were ranked. Ten different random selections were made for each number of exclusions. The share of lexicographic answers is then calculated for each reduced rank-order. The difference, as shown by the line in Fig. 3, is solely caused by the fact that it is more likely that the rank-order will seem to be lexicographic when less alternatives are ranked. All cases along the plotted line in Fig. 3, are caused by the same ranking of the cards in game 7.

% 100

8

9

10 11 12 13 14 15 16 number of cards

Figure 3 Lexicographic answers with different numbers of ranked cards The results from games 5 and 6 are given in Fig. 3 as grey dots. We can see that when we take the different number of cards into account, the share of lexicographic answers is actually somewhat lower in games 5 and 6, compared to game 7. The difference is not very large. The reason for this might be that the interviewees in game 7 were asked first to sort the cards in four groups—ranging from "very good" to "very bad" —and then

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to rank the cards within each group. The probability of producing a perfectly consistent lexicographic sorting obviously decreases with this approach. We can also note that a larger proportion of the lexicographic answers are made according to the price factor when more alternatives are ranked. According to price in game 5, 74 percent of the lexicographic choices compared to 89 percent in game 6, and 90 percent in game 7. In the computerised interviews in game 1, only 32 percent of the lexicographic answers are according to price. This is probably the major reason for the difference in time values in the different games. Another method of analysing what happens when the interviewee has to rank a large number of cards is to estimate the difference in random error in the choices. If the respondents find the ranking exercise tiresome, it is possible that they will become less and less careful towards the end of the exercise. It is also possible that they first pick out the best and worst cards and that the quality is lowest in the middle. The rank-order is "exploded" to a number of discrete choices where the first is the choice of the highest-ranked card over all the others in the rank-order, the next is the choice of the second card in the rank-order over all cards with a lower rank, etc. In the logit model, the scale of the parameters is inversely proportional to the amount of "noise" in the data (Ben Akiva and Lerman, 1985). One can estimate separate models for the different choices and compare the scale. With a procedure given by Bradley and Daly (1992), it is also possible to directly estimate a scale factor that measures the difference in random error in the different choice situations. In the most complicated case, that is the game where 16 alternatives have been ranked, we place choices 1 and 2 in the first part of the tree, choices 3 and 4 in the second, etc. For the games with 5 and 9 cards separate scale factors were estimated for each choice situation. Figure 4 shows the scale factors from the games with ranking of cards. In the case with 16 cards, each scale factor applies to two choice situations. We can see that the scale factor decreases strongly between the first choices. This may indicate that the interviewee takes extra care when selecting the best alternative. The scale factors decreases more slowly in the game with 16 alternatives, possibly because we asked them first to sort the alternatives in four groups (this was only done in this game). The scale factor is quite low in the last choice situations for the game with 16 alternatives. Even though the scale factors are very low in the game with 16 alternatives, the results in terms of monetary values, are only marginally

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scale factor

0 2

3

4

5

6

7

8

9 10 11 12 13 14 15

choice number Figure 4 Scale factors in games with ranking of cards

affected when the scale factors are introduced into the analysis. The time value changes from 0.25 to 0.24 and the changes for the other factors are equally low. For the pairwise choices in the computerised games the procedure is simpler (Fig. 5). All of the pairwise choices are given separate scale factors (the scale is implicitly assumed to be one for the first choice). In the computer game with pairwise choices, it is hard to find any strong tendency in the scale factors. None of them are significantly different from one. Somewhat speculatively, one might see a tendency of learning in the first choices, resulting in an increasing scale factor, and a tendency of fatigue in the later choices. The time value only changes from 0.78 to 0.77 when the scale factors are applied. Even in cases where there is a tendency of fatigue in the computer games, the bias caused by this is less than in the ranking games. This is because the order of the pairwise choices in the computer games can be randomised so that different pairs are affected for different interviewees. In the ranking games, it is typically the least attractive alternatives that are affected by the fatigue which gives a much more systematic bias.

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scale factor 1

0 0.0 9

10 11 12 choice number

Figure 5 Scale factors in computerised game with pair-wise choices

Ranking or rating In one of the games, the interviewee was asked to rate each of the nine alternatives on a scale from 0-100, where 0 was "very bad", and 100 "very good". Exactly the same design with the same factors and levels was used as before. All interviewees got the same form, no randomisation was made. The alternatives were given in order of decreasing price, something that could have caused lexicographic answers. This did not turn out to be the case as can be seen from Table 5. In the rating game, only seven percent of the interviewees rated the alternatives lexicographically after one factor. Compared to the computer game, the rate of lexicographic answers is similar for the price factor. In the computer game, the lexicographic answers after price are "balanced" by lexicographic answers after time and other factors. Obviously, the rating task does not invite simplified answers in the same way as the ranking task. The result from the rating task is more similar to the computer game.

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Travel Behaviour Research: Updating the State of Play Table 5 Ranking compared to rating 1. Computer (%)

3. Ranking (%)

8. Rating (%)

Price Time Other

7 10 5

35 4 0

6 1 0

Total

22

39

7

This is not only true for the time factor, but also for the other factors. The major difference in the models is the size of the cost parameter. The size of the cost parameter in the ranking exercise is probably caused by the large number of people who have sorted the cards according to the price factor.

Presence of interviewer The small Poquet-computers used for most of the computerised interviews made it possible to carry out the interviews without the presence of any interviewer. The small computers also have quite small screens that are not back-lit, which sometimes makes it a bit difficult to read the text on the screen. To test if the presence of the interviewer and the quality of the screen affects the results, we carried out one interview with ordinary laptop computers (with a back-lit screen of high quality) and an identical one with the small computer (models 14 and 15 in Fig. 1). The difference between the models is small. None of the parameters in the two models are significantly different from each other and the time values are also similar (0.91 and 0.85). The conclusion from this test is that it is obviously possible to let the interviewees carry out the task themselves, with only minimum instructions. It is also obvious that the quality of the screen is not critically important.

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Conclusions The conclusion from the work is that results from SP studies are greatly affected by the way the task is carried out. The most important bias is caused by simplifications that the interviewees make when they carry out the SP games. The second most important bias arise when the games are not customised to the actual trip that the interviewee makes. A major conclusion is that the computerised games seemed to work much better than the manual ones—there were less problems with simplified answers and more stability when extreme variable ranges were introduced.

References Ben Akiva, M. and Lerman, S. (1985) Discrete Choice Analysis—Theory and Application to Travel Demand, The MIT Press, Cambridge, Mass. Bradley, M. and Daly, A. (1992) Uses of logit scaling approach in stated preference analysis. Sixth World Conference on Transport Research, Lyon, July 1992, France. Lindh, C. (1992) Train-travellers willingness to pay for improvements of punctuality, travel time and frequency (in Swedish). Traffic Planning Institute, Technical University of Stockholm. Lindh, C. and Widlert, S. (1989) Valuation of quality on Swedish rail (in Swedish). Traffic Planning Institute, Technical University of Stockholm. Widlert, S. (1991) Method and reliability. Appendix to C. Lindh, Customers Demand upon Regional Trains (in Swedish). Traffic Planning Institute, Technical University of Stockholm.

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8

Own Account or Hire Freight: A Stated Preference Analysis Lasse Fridstr0m and Anne Mads lien

Abstract The choice between own account and hire commodity transportation in the Norwegian wholesale trade industry is studied by means of conjoint analysis. To ensure generality, an attempt was made to draw companies and shipments as probability samples. During a computerised and customised Stated Preference (SP) interview, company officials were asked to consider alternative ways to dispatch a given shipment, picked at random from a collection of recent, outbound real consignments from the company. The following quality factors, in addition to cost, are included in the analysis: time, punctuality and damage security. The Box-Cox logit modelling approach, allowing for estimably nonlinear relationships, is used for the analysis. Marginal rates of substitution, such as the value of time, are derived and found, on account of the nonlinear model structure, to differ considerably between the shipments contained in the sample. In general, implicit values of time exceed the rate of interest by a two- or three-digit factor. Thus, the cost of capital appears to play only a rather secondary role when companies choose between slower and faster freight modes. There is considerable inertia in freight mode choice decisions, in the sense that companies tend to hang on to the kind of transportation actually chosen, be it a hire or an own account mode of transportation.

Issues and Problems in the Analysis of Freight Demand Over the last couple of decades, enormous progress has been made in the field of (passenger) travel demand modelling, partly in the form of increasingly sophisticated statistical techniques for disaggregate discrete choice analysis, and partly through the development of advanced, flexible and user-friendly computer software for the simulation of traffic flows

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within a network. Compared to the passenger transportation field, the state-of-the-art in the area of freight transportation modelling lags conspicuously far behind. Even simple, representative measures of nationwide market response, such as mode-specific, direct or cross-demand price elasticities, seem hard to come by or derive. The reasons for the relative backwardness of freight market modelling are manifold. Compared to travelling, the freight market is compellingly heterogeneous. Freight shipments differ greatly in terms of size and commodity type. Commodities differ with respect to value, weight, volume, perishability, robustness, etc. In a freight transportation chain, there are a multitude of potentially active decision-makers: the shipper, the freight forwarding agent, the carrier(s) and the receiver. In a broader perspective, even the manufacturer and consumer are making important decisions bearing on freight transportation demand. Only the transported item itself—the commodity—does not get a say. This apparently trivial fact is a prime distinguishing feature of freight transportation compared to the travel market. Traveller interviews are the main source of information for travel demand modelling. But commodities cannot be interviewed, and it is not straightforward to decide which person to interview "on behalf of" the commodity. In general, no personal respondent would, as in the case of travelling, possess all relevant information on the transportation chain. While travellers are usually faced with a single price, or, in the case of fare discount schemes, with a set of objective and uniformly applicable rules, freight users are not necessarily price takers. Larger clients may negotiate long- or short-term agreements directly with certain carriers. Thus, freight rates and the tariffs on which they rest vary greatly, and are not, in general, publicly available information. Own account freight transportation, for which price information is not only unavailable, but nonexistent, is common. A number of companies choose to carry out all, or part, of the transportation services demanded by means of their own personnel, vehicles or vessels. In Norway, own account freight transportation represents more than 20 percent of the tonkilometres dispatched by road, and close to 60 percent of the freight vehicle kilometres. It is poorly understood why so many companies choose to own and operate their own vehicles, rather than purchase the necessary freight services in the market, which in the typical case would appear more economical. Owing to the generally low rate of utilisation of company-owned vehicles, this mode of transport is also "unnecessarily" hard on the environment and road capacity, as seen in relation to the volume of ton-kilometres transported.

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The freight rate is only one of a number of factors which, in an adequate structural analysis of the freight market, would need to be treated as endogenous. The same applies to factors such as shipment size or the location of suppliers and customers. Freight transportation is basically a production input factor, of which the companies may demand more or less depending on the production technology, prices of other inputs, and the companies' degree of competitiveness on a national or international scale. The overall demand for freight transportation and, in particular, the matrices of zone-to-zone commodity flows, will be sensitive to all of these influences, and probably much less stable than in the corresponding travel demand case. In the passenger transportation case, it is a comparatively straightforward matter to draw probability samples representative of the relevant population under study. For this reason, disaggregate discrete choice analysis has become the dominant approach to travel demand research. Aggregate market response measures can be derived from the disaggregate models estimated by means of sample enumeration techniques (Ben-Akiva and Lerman, 1985). In the commodity transportation case, this approach is not nearly as easily applicable. Representative sampling is difficult, since sampling frames are hard to come by and, more fundamentally, because it is not even clear from which population the analyst should be sampling. Does a well-defined "population of freight" exist? If so, what kind of elementary units does this population consist of: shipments, orders, tons, cubic feet, ton miles, vehicles, vehicle miles, trips and shipper, receiver or carrier companies? In summary, complete and relevant revealed preference datasets on disaggregate freight market choices are practically nonexistent, and very hard to collect. Therefore, in an attempt to come to terms with the factors underlying freight user choices, in particular regarding the choice between own account and hire freight, a Stated Preference (SP) survey among Norwegian freight users was designed.

A Stated Preference Survey of Wholesalers' Freight Choice The wholesale industry was selected as our target group, in order to ensure (i) a certain degree of homogeneity with respect to the companies' type of production, and at the same time (ii) a fairly large and representative variety in terms of commodity types. The wholesale industry represents

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some 25-30 percent of the road freight transportation services carried out in Norway, when (the estimated value of) own account freight is included. A stratified random sample of wholesale firms was drawn from the Register of Establishments of the Central Bureau of Statistics. The country's municipalities were divided into two strata. From the first stratum, consisting of six major urban areas, a sample of 1000 wholesale firms was drawn, each firm being drawn with a probability proportional to the number of employees. From the second stratum, consisting of all the remaining municipalities, the drawing was done in two stages. In the first stage, five municipalities were drawn (from a total of more than 400), each with a probability proportional to the size of the municipality's wholesale industry, as measured by employment. In the second stage, 200 companies were drawn from within the five municipalities, each with probability proportional to the company's share of municipal wholesale employment.3 Thus, a total of 1200 companies were approached for interviewing. Some 300 companies were finally recruited to the study. Nonresponse occurred for a variety of reasons other than refusal to participate, such as no use of freight transportation, no answer on the phone, impossibility of obtaining the company's phone number, or unable to make contact with the person(s) responsible for freight decisions. A binary logit analysis of response versus nonresponse was carried out, using the data available in the sampling file, i.e. industry branch, sales volume, employment and geographic location. No strong partial correlation was revealed between these variables and the nonresponse rate. Since the choice between own account and hire freight is only open to companies possessing their own means of transportation, interviews were conducted corresponding to two separate levels of decision. At the strategic (upper) level, companies were asked to consider the purchase, or renewal of own vehicles versus a long-term agreement with a carrier firm. At the operational (lower) level, companies were asked to consider alternative ways to dispatch a given shipment, picked at random from a collection of recent, outbound real consignments from the company. In most cases, two different persons were interviewed, corresponding to the respective levels of decision considered. The company was asked to let a

The first stratum gathers somewhere in excess of 60 percent of the country's wholesale industry in terms of employment. For economic reasons, a somewhat higher sampling probability was used in the major cities than in the smaller towns and sparsely populated municipalities.

Own Account or Hire Freight

127

itself be represented by the very person(s) who would be making these decisions in a practical situation. Space does not allow us to go into the strategy interviews. Hence, in this chapter only the shipment level SP exercise will be dealt with. Prior to the interview, the participating companies had been asked to bring out a set of waybills or other shipment documents, preferably in such a way as to cover all outgoing shipments over a certain period (day, week or other). In some cases a computer file of shipments would be used instead of paper documents. From this set of shipments, one was drawn at random and used as a basis for the interview. A certain amount of background information was then elicited concerning this particular shipment, including its size, value, destination, commodity type, perishability, freight rate, transportation time, mode, required time of delivery, as well as an assessment of the risk of late delivery or damage. In an attempt to mimic the situation where the company has to make a decision under uncertainty, e.g. not knowing the cost of a certain alternative, the cost variable was sometimes left blank. In such cases, the respondent was asked to provide an answer based on his general knowledge of the freight market, taking the perceived uncertainty into account. The MINT software of the Hague Consulting Group was used for the interviews, which were conducted by Norsk Gallup Institutt AS by means of laptop computers. Interviews took place during October-November 1992. Two SP games were played with each interviewee. In each SP game, the interviewee was asked nine times to choose between two freight options shown on either side of the screen. Each option was defined in terms of four factors: freight cost (Norwegian kroner (NOK), actual value ±10-30 percent), transportation time (actual time, ±25-50 percent), risk of late delivery (percent as assessed, ± up to 10 percentage points, depending on initial level) and risk of damage (percent as assessed, ± up to 15 percentage points, depending on initial level). Thus, each interview was "customised" to the shipment and company in the sense that the independent factors were made to vary around the very values recorded during the background session, so as to make the games realistic in view of the particular shipment drawn. Moreover, the MINT software is interactive in the sense of exploiting the transitivity assumption to "learn" from choices made previously during the game, so that during a chain of nine questions, the options presented to the interviewee would in a sense "narrow in" on the indifference surface. Thus, in some cases all the information available (given the survey's quasifixed design) about the respondent's preferences had been exhausted before

128

Travel Behaviour Research: Updating the State of Play

nine choices had been made, in which case the game would become less than nine choices long. On account of the pseudorandom sampling, the heterogeneity of shipments contained in our dataset is very pronounced. Freight costs vary from NOK 3-1.5 million, however, with the large majority of shipments clustered between NOK 30 and 1000.b The time variable has a median and most typical value of 24 hr, few shipments take more than six days, however, the maximum transportation time sampled is 33 days. The sales value of the commodities shipped varies from almost zero to NOK 2.6 million, however, with most cargo values clustered between NOK 1000 and 10,000. The ratio of freight cost to commodity value has a median of about three percent, most shipments being clustered between 0.1 and 30 percent. There are, however, 11 shipments in the sample for which the freight cost exceeds the commodity value. The late delivery risk assessment for the shipment sampled varies from zero to above 30 percent, however, with 70 percent of the sample clustered below one percent. The damage risk assessment varies between zero and 20 percent, being less than 0.5 percent in three out of four cases.

Modelling Results Several previous attempts at SP modelling of freight transport choices appear to have encountered certain common difficulties. Standard, linear logit choice models often seem to yield a nonsensical, or counterintuitive, sign and/or size for the cost term coefficient and, in many cases, for other coefficients as well. It appears necessary in many of these models to specify costs in terms of relative (percentage) changes with respect to a base level, rather than as an absolute cash value freight charge (de Jong and Gommers, 1992; Widlert, 1990). This specification, however, renders the calculation of implicit values of time, reliability, damage security or of other quality factors less appealing, as these measures would become dependant on the level of freight costs charged. They are no longer directly calculable from the "indirect utility" (or cost) function estimated in a logit model of freight mode choice. We suspect that this difficulty is related to the fact that consignments differ enormously in terms of size (weight, volume), commodity type and value, shipping distance and freight rate charged. In our sample, one must suspect that this problem is further As of 1992, one Norwegian krone (NOK) was worth approximately US$ 0.13.

Own Account or Hire Freight

129

enhanced by the fact that shipments have been drawn as a (pseudo-) probability sample, rather than as a set of consignments "typical" to the respondent company. To meet these difficulties we have: (i) experimented with different ways to enter the cost term into the model; and (ii) made use of a software that allows us to specify the independent variables as a set of multiple BoxCox transformations. This transformation, due to Box and Cox (1964) and first introduced into transportation demand analysis by Gaudry and Wills (1978), is given by

Being continuous and differentiable at A = 0, the Box-Cox function includes the cubic (A = 3), quadratic (A = 2), linear (A = 1), square root (A = 0.5), logarithmic (A = 0), and reciprocal (A = -1) functional forms as special cases. The TRIO computer software of Gaudry et al. (1993) allows the user to specify several independent variables as different BoxCox transformations, the A parameters of which are estimated simultaneously with the ordinary (/3) coefficients of the logit regression:

where V, denotes the "indirect utility" function associated with alternative /. As one lets the data determine the functional form, the possibility of, e.g., decreasing marginal (dis)utility of certain attributes, is allowed for. As for the cost variable, three different specifications were tried: (i) the absolute cash value freight charge (or estimated marginal cost, in the case of own vehicles); (ii) the relative freight rate, as compared to the actual rate pertaining to the shipment sampled; and (iii) the freight charge divided by the value of the commodity shipped. Model results are shown in Tables 1 and 2. Table 1 covers a set of introductory SP games, in which the respondents were asked to choose between two hire transport options, in case this was the mode used for the sampled shipment, or two own account alternatives, whenever this was the solution actually used. Table 2 is based on a dataset in which respondents were generally asked to choose between company-owned vehicles and a professional carrier. In addition to /3 and A parameter estimates, we report marginal rates of substitution (MRS) with respect to

Travel Behavio\

Table 1 Logit models of choice between two hire or two own account options COST TERM FORMULATION:

Absolute charge

Relative to base

s:

Per unit value

Al

A2

A3

A4

A5

A6

FREIGHT COST (NOK) coefficient MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) conditional t-statistic Box-Cox parameter (F = fixed)

-0.19E-03 0.10E + 01 0.10E + 01 (-3.05) 1(F)

-0.27E + 01 0.10E + 01 0.10E + 01 (-17.26) 0.005

-0.24E + 01 0.10E + 01 0.10E + 01 (-16.20) 1(F)

-0.29E + 01 0.10E + 01 0.10E + 01 (-17.43) 1.385

-0.36E + 01 0.10E + 01 0.10E + 01 (-4.38) 1(F)

-0.44E + 01 0.10E + 01 0.10E + 01 (-17.55) 0.133

TIME, GENERAL (minutes) coefficient MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) conditional t-statistic Box-Cox parameter (F = fixed)

-0.23E - 03 0.12E + 01 0.12E + 01 (-5.13) 1 (F)

-0.40E + 00 0.27E + 00 0.28E + 00 (-12.41) 0.198

-0.49E - 03 0.21E - 03 0.21E - 03 (-9.25) 1 (F)

-0.41E + 00 0.37E - 03 0.30E - 02 (-12.43) 0.196

-0.25E - 03 0.68E - 04 0.68E - 04 (-5.41) 1 (F)

-0.40E + 00 0.30E - 04 0.44E - 04 (-12.54) 0.201

TIME, INCREMENT FOR COMESTIBLES (minutes) 0.29E - 03 coefficient -0.15E + 01 MRS at mean (alt. 1) -0.15E + 01 weighted aggregate MRS (alt. 1) (5.07) conditional t-statistic 1 (F) Box-Cox parameter (F = fixed)

0.42E + 00 -0.17E + 01 -0.93E - 01 (9.78) 0.198

0.53E - 03 -0.22E - 03 -0.22E - 03 (8.55) 1 (F)

0.43E + 00 -0.24E - 02 -0.10E - 02 (9.82) 0.196

0.31E - 03 -0.84E - 04 -0.84E - 04 (5.36) 1 (F)

0.42E + 00 -0.19E-03 -0.14E-04 (9.95) 0.201

MODEL:

ia o

| ^

S'

s-

*?

$ oT '•Q ^ a*

LATE DELIVERY RISK, GENERAL (per thousand) 0.36E - 02 coefficient -0.19E + 02 MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) -0.19E + 02 (2.50) conditional t-statistic Box-Cox parameter (F = fixed) 1(F)

-0.43E - 01 0.23E + 01 0.56E + 00 (-4.24) 0.536

-0.42E - 01 0.26E - 03 0.86E - 04 (-4.29) 0.544

LATE DELIVERY RISK, INCREMENT FOR ON-THE-HOUR PUNCTUALITY REQUIREMENT (per thousand) -0.77E - 02 -0.76E - 01 -0.82E - 02 -0.73E - 01 -0.83E - 02 coefficient 0.33E - 02 0.93E + 01 0.23E - 02 0.13E-01 0.43E + 02 MRS at mean (alt. 1) 0.33E - 02 0.11E + 00 0.23E - 02 0.43E + 02 weighted aggregate MRS (alt. 1) 0.11E-02 (-3.10) (-2.40) (-3.01) (-2.83) (-2.79) conditional t-statistic 0.536 1(F) 1(F) Box-Cox parameter (F = fixed) 1(F) 0.538

-0.76E - 01 0.10E-02 0.17E-04 (-3.19) 0.544

DAMAGE RISK (per thousand) coefficient MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) conditional t-statistic Box-Cox parameter (F = fixed) CONSTANT (ALT. 1) coefficient conditional t-statistic LOG-LIKELIHOOD RHO-SOUARED NUMBER OF OBSERVATIONS NUMBER OF ESTIMATED PARAMETERS -BETAS. VARIABLES .CONSTANTS -BOX-COX TRANSFORMATIONS

-0.44E - 01 0.33E - 02 0.61E - 02 (-4.29) 0.538

-0.73E - 02 0.38E + 02 0.38E + 02 (-3.62) 1(F)

-0.26E - 01 0.65E + 01 0.87E + 00 (-9.82) 1(F)

-0.20E - 01 0.84E - 02 0.84E - 02 (-8.27) 1(F)

-0.26E - 01 0.91E - 02 0.93E - 02 (-9.81) 1(F)

-0.80E - 02 0.22E - 02 0.22E - 02 (-3.94) 1(F)

-0.27E - 01 0.72E - 03 0.14E-03 (-9.94) 1(F)

0.26E - 01 (0.65)

0.46E - 01 (1.09)

0.49E - 01 (1.17)

0.45E - 01 (1.06)

0.25E - 01 (0.49)

0.40E - 01 (0.94)

-1775.34 0.018 2609

-1595.36 0.118 2609

-1629.90 0.099 2609

-1591.13 0.120 2609

-1779.28 0.016 2609

-1585.79 0.123 2609

6 1 0

6 1 3

6 1 0

6 1 3

6 1 0

6 1 3

Own Accoum

0.33E - 02 -0.89E - 03 -0.89E - 03 (2.29) 1(F)

-0.26E - 02 0.11E-02 0.11E-02 (-1.73) 1(F)

o

s •V f^

s1 f t— k (jj

Table 2 Logit models of choice between hire and own account freight COST TERM FORMULATION:

Absolute charge

Relative to base

u> to Per unit value

|

Bl

B2

B3

B4

B5

B6

FREIGHT COST (NOK) coefficient MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) conditional t-statistic Box-Cox parameter (F = fixed)

-0.18E - 03 0.10E + 01 0.10E + 01 (-1.97) 1(F)

-0.28E + 01 0.10E + 01 0.10E + 01 (-5.76) -0.169

-0.39E + 01 0.10E + 01 0.10E + 01 (-8, ,59) 1 (F)

-0.20E + 01 0.10E + 01 0.10E + 01 (-8.70) 6.969

-0.85E + 00 0.10E + 01 0.10E + 01 (-1.09) 1(F)

-0.14E + 01 0.10E + 01 0.10E + 01 (-5.74) 0.078

TIME, GENERAL (minutes) coefficient MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) conditional t-statistic Box-Cox parameter (F = fixed)

-0.48E - 03 0.27E + 01 0.27E + 01 (-5.50) 1 (F)

-0.46E + 00 0.87E + 00 0.57E + 00 (-8.24) 0.189

-0.59E --03 0.15E--03 0.15E--03 (-6.47) 1 (F)

-0.44E + 00 0.40E - 03 0.21E - 02 (-8.15) 0.190

-0.48E - 03 0.56E - 03 0.56E - 03 (-5.43) 1 (F)

-0.45E + 00 0.83E - 04 0.95E - 04 (-8.24) 0.192

MODEL:

to 3" a o' ^ Hi

a §,

"a |

S'

Crq

S-

TIME, INCREMENT FOR COMESTIBLES (minutes) 0.47E - 03 coefficient MRS at mean (alt. 1) -0.27E + 01 weighted aggregate MRS (alt. 1) -0.27E + 01 (5.01) conditional t-statistic Box-Cox parameter (F = fixed) 1(F)

0.48E + 00 -0.38E + 01 -0.14E + 00 (6.14) 0.189

0.59E --03 -0.15E--03 -0.15E--03 (5..99) 1 (F)

0.45E + 00 -0.17E-02 -0.51E - 03 (5.72) 0.190

0.49E - 03 -0.58E - 03 -0.58E - 03 (5.15) 1(F)

0.46E + 00 -0.36E - 03 -0.22E - 04 (6.08) 0.192

LATE DELIVERY RISK, GENERAL (per thousand) -0.35E - 02 coefficient MRS at mean (alt. 1) 0.20E + 02 weighted aggregate MRS (alt. 1) 0.20E + 02 (-1.30) conditional t-statistic Box-Cox parameter (F = fixed) 1 (F)

-0.69E - 02 0.53E + 01 0.64E + 00 (-2.61) 1 (F)

-0.56E --02 0.14E--02 0.14E --02 (-2. ,08) 1 (F)

-0.62E - 02 0.23E - 02 0.22E - 02 (-2.32) 1 (F)

-0.31E -02 0.37E - 02 0.37E - 02 (-1.19) 1 (F)

-0.69E - 02 0.50E - 03 0.11E-03 (-2.61) 1 (F)

*?

8 r$ <S^

ir v

LATE DELIVERY RISK, INCREMENT FOR ON-THE-HOUR PUNCTUALITY REQUIREMENT (per thousand) -0.62E - 02 -0.59E - 02 -0.57E - 02 -0.63E - 02 -0.54E - 02 coefficient 0.45E + 01 MRS at mean (alt. 1) 0.67E - 02 0.23E - 02 0.16E-02 0.31E + 02 weighted aggregate MRS (alt. 1) 0.67E - 02 0.16E-02 0.55E + 00 0.31E + 02 0.23E - 02 (-0.82) (-0.77) (-0.86) conditional t-statistic (-0.81) (-0.86) 1(F) 1(F) 1(F) Box-Cox parameter (F = fixed) 1(F) 1(F)

-0.64E - 02 0.47E - 03 0.10E-03 (-0.89) 1(F)

DAMAGE RISK (per thousand) coefficient MRS at mean (alt. 1) weighted aggregate MRS (alt. 1) conditional t-statistic Box-Cox parameter (F = fixed)

-0.16E-01 0.93E + 02 0.93E + 02 (-4.17) 1(F)

-0.24E - 01 0.18E + 02 0.22E + 01 (-5.76) 1(F)

-0.21E-01 0.56E - 02 0.56E - 02 (-5.27) 1(F)

-0.22E - 01 0.82E - 02 0.81E - 02 (-5.43) 1(F)

-0.16E-01 0.19E-01 0.19E - 01 (-4.08) 1(F)

-0.24E - 01 0.18E-02 0.38E - 03 (-5.78) 1(F)

INERTIA DUMMY FOR HIRE TRANSPORT (ALT. 2) coefficient -0.24E + 01 conditional t-statistic (-11.28)

-0.23E + 01 (-10.45)

-0.26E + 01 (-11.87)

-0.22E + 01 (-10.03)

-0.24E + 01 (-11.29)

-0.22E + 01 (-10.35) 0

CONSTANT (ALT. 2, I.E. OWN ACCOUNT IF AVAILABLE) 0.87E + 00 coefficient 0.97E + 00 conditional t-statistic (5.74) (6.45) LOG-LIKELIHOOD RHO-SQUARED NUMBER OF OBSERVATIONS NUMBER OF ESTIMATED PARAMETERS -BETAS . VARI ABLES8 .CONSTANTS -BOX-COX TRANSFORMATIONS

3

-0.14E + 01 (-7.81)

-0.16E + 01 (-9.62)

-0.13E + 01 (-7.64)

Account

DUMMY FOR CHOICE BETWEEN TWO HIRE TRANSPORT ALTERNATIVES (ALT. 2) -0.13E + 01 -0.18E + 01 coefficient -0.16E + 01 conditional t-statistic (-7.81) (-10.26) (-9.58)

0.11E + 01 (6.78)

0.76E + 00 (4.89)

0.97E + 00 (6.48)

0.86E + 00 (5.67)

0

-1110.28 108 1923

-1085.80 0.128 1923

-1070.98 0.140 1923

-1055.55 0.152 1923

-1111.99 0.107 1923

-1085.93 0.128 1923

8 1 0

8 1 2

8 1 0

8 1 2

8 1 0

1 2

tt:

1 I u> OJ

134

Travel Behaviour Research: Updating the State of Play

the cost term, computed in two ways, and the conditional /-statistic.0 All of these statistics are automatically computed and output by the TRIO software. Depending on the formulation of the cost term, the MRS has an interpretation as the implicit value of the attribute in question, as calculated per shipment (models Al, A2, Bl, B2) or per unit commodity value shipped (models A5, A6, B5, B6). In models A3, A4, B3, and B4, an additive change in the attribute is balanced against a percentage change in cost. While this may seem as an intuitively and theoretically less appealing approach, it does sometimes provide a superior model fit. Note that in a Box-Cox model, MRS are generally not constant (Gaudry et al., 1989). This occurs only in the special (linear) case where both Box-Cox parameters involved happen to be one. In general, the marginal rate of substitution for an attribute (t, say) with respect to the cost term (c, say) is given by:

where subscripts 1 and 2 refer to the parameters of the c and t terms, respectively. Given that the MRS differ between observations, there are several ways to summarise the information contained in the sample. One is to evaluate the MRS at the sample means of c and t. Another is to compute the MRS at each sample point, and then sum through the sample using the predicted choice probabilities as weights of aggregation (so-called sample enumeration). For completeness, both are shown in the tables. Whenever the c or t variables have a heavily skewed sample distribution, the two methods are likely to yield quite different results. We tend to recommend the latter, which is less sensitive to outliers and less subject to errors of aggregation.d

c

That is, conditional on the Box-Cox parameter. The unconditional /-statistics are not scale invariant, and hence, of limited value. d Note that the MRS sample enumeration could be done for either, or both, alternatives, with not necessarily coinciding results. The figures shown in the tables pertain to alternative 1, i.e. the left-hand side option shown to the respondents, corresponding to hire transport in the games involving unequal modes.

Own Account or Hire Freight

135

Within-mode choices Now, consider model Al. This is a standard linear logit model, i.e. one in which all Box-Cox parameters have been fixed at unity. In this model, the implicit value of time (the MRS) comes out at NOK 1.2 per shipment per minute, identically for all shipments in the sample. As we relax the linearity assumption, introducing Box-Cox parameters for cost, time and risk of late delivery6 (model A2), the model fit improves dramatically, and the average per shipment value of time decreases to NOK 0.28/min, or approximately US$ 2.25/hr. These values of time apply to all kinds of cargo except foodstuffs. For these, the model implies a surprising zero value of time, the general time coefficient being more, or less, offset by the interaction term added in order to capture the assumed higher perishability of comestibles. Our hypothesis that these commodities might have a higher value of time was flatly rejected. The value of a reduced risk of late delivery (as referred to a not too rigorous punctuality requirement, be it a certain day, week or month) is estimated (by sample enumeration) at NOK 5.60 per percentage point risk, as reckoned per shipment. Note that in this case, the MRS as evaluated at the sample mean is four times higher. Also, note that in the linear (Al) model, the risk unit factor has the wrong sign. As is often the case in Box-Cox modelling, the sign is corrected as we move on to more flexible models. For shipments that need to arrive on the hour, or with even greater accuracy, the value of late delivery risk is noticeably higher. The value of damage risk is estimated (by sample enumeration) at NOK 8.70 per shipment and percentage point of risk. As evaluated at the sample mean, the value is 7.5 times higher. In models A5 and A6, the cost term has been defined as the freight rate divided by the value of the commodity shipped, i.e. as the share of transportation to the total purchase cost. Here, the MRS are interpretable as implicit level-of-service values per NOK commodity value shipped. As a minimum implicit value of time one should expect a figure comparable to the current rate of interest, which at the time of the survey was running at approximately 12 percent per annum, corresponding to 0.0023 (NOK) per (NOK and) 10,000 min. In comparison, our average value of time comes out at 0.43 per 10,000 min, corresponding to a monthly interest rate of some 185 percent. Apparently,

e

The fourth Box-Cox parameter, on damage risk, tested not significantly different from unity and was, henceforth, kept fixed.

136

Travel Behaviour Research: Updating the State of Play

freight users demand speedy transportation for a number of reasons other than the cost of capital. According to this model, the damage risk has a (sample enumeration) value of NOK 0.0013 per percentage risk and NOK commodity value shipped. In the case of a risk neutral freight user, and assuming that in the case of damage the entire cargo is lost, one would expect a higher figure, viz. 0.01 (i.e. one percent) per percentage risk. The low value obtained may be a reflection of the fact that most shipments are insured, or fully compensated by the carrier in the case of loss. The constant term is not significantly different from zero, as expected. There is no inherent difference between the alternatives, except that one is shown on the lefthand side of the screen, and the other on the right-hand side/

Between-mode choices The second set of shipment choice games performed were slightly more complicated: (i) in that the respondents were asked to choose between a hire and an own account alternative (except for companies without access to own vehicles, in which case two hire transport solutions were specified); and (ii) in that respondents were sometimes shown a blank cost factor for one of the alternatives, and instructed to make a choice under uncertainty based on their general knowledge of the freight market. This situation so infuriated certain respondents that they refused to continue the interview, and preliminary attempts to estimate the certainty equivalent of the missing cost terms have resulted in rather counterintuitive models. Thus, in the analysis presented here, we have made use only of those observations where neither option included a blank cost term. Results are summarised in Table 2. Coefficient estimates differ considerably from those reported in Table 1, although it is fair to say that they are of a comparable order of magnitude. Marginal rates of substitution generally come out higher in our second set of games, the values of time, e.g. being at least twice as high (compare models B2 and B6 to A2 and A6). The value of one percentage point damage risk comes out at 0.38 percent of the commodity value under sample enumeration, and at 1.8 percent as evaluated at the sample mean (model B6). In this case, the constant term has a substantive economic interpretaf

One might wish to drop the constant term in a case like this. However, the Box-Cox logit model needs a full set of alternative specific constants in order to be scale invariant.

Own Account or Hire Freight

137

tion. Being assigned to alternative 2, it measures the inherent attractiveness of own account transportation, or the tendency to hang on to it, whenever this option is available and was actually used for the shipment drawn. In the linear models the value of this inertia is calculable at NOK 5390 (=0.97/0.00018) per shipment (model Bl), or NOK 1.14 (=0.97/0.85) per NOK commodity value shipped (model B5). The tendency to hang on to hire transport, once this has been chosen, is even stronger, and valued at the unlikely sum of NOK 1.68 (=(2.40-0.97)70.85) per NOK commodity value shipped in the linear model B5. In the nonlinear models (B2 and B6), much more plausible values ensue. At the median value of the cost/value ratio (0.03), the trade-off between own account inertia and cost can be calculated at NOK 0.017 per NOK commodity value, meaning that the freight user will switch from the (chosen) own account option to the cheaper hire transport alternative only if the freight-cost-to-commodity-value ratio decreases from NOK 0.03 to 0.013, i.e. if it is more than halved. Since our nonlinear models turn out approximately logarithmic in terms of cost, the inertia terms translate into geometric (percentage) rather than additive trade-off effects. The dummy capturing respondents having faced a choice between two hire freight alternatives is seen to more than offset the constant term. The sum of these two terms is generally not significantly different from zero, suggesting, as expected, that when the two alternatives are not inherently different, the respondent has no particular preference for one or the other side of the screen. While the two sets of games played with our respondents are seen to yield somewhat varying coefficients and MRS, there seems to be a common pattern with regard to the nonlinearity structure emerging from the two analyses. In general, cost terms are seen to obey a close to logarithmic law (except when specified as measures relative to an initial base level). Time terms consistently come out with a Box-Cox parameter very close to 0.2, i.e. as a fifth root law. The risk of late delivery risk hovers between the square root law and linearity, while the damage risk has no significantly nonlinear effect in any model. In some cases, the models in which cost is expressed in terms of relative changes with respect to an initial freight rate seem superior as measured by the fit obtained in a standard linear model—indeed, the linear model B3 has a higher likelihood than even the most flexible Box-Cox-models B2 and B6. However, as we introduce Box-Cox transformations into model B3, the somewhat artificial nature of the relative change specification becomes visible, in that this variable must be raised almost to the

138

Travel Behaviour Research: Updating the State of Play

7th (!) power, in order to provide a maximum degree of explanation (model B4).g

Discussion The heterogeneity of the freight market represents a special challenge to modellers. This is particularly so if one is concerned with statistical representation. Rather than artificially constraining the sample to a set of "average" shipments, we have attempted to capture the variability actually present in the real freight market. Using estimably nonlinear modelling techniques, we have tried to account for the presumably decreasing scale effects in such a dataset, without losing sample representation or the common structure of freight user choices. Yet certain qualifications would be in order. The sample enumeration technique as applied to a shipment sample, while less crude than the method of evaluating all effects at the sample mean, may still appear misleading when the sample distribution is heavily skewed. For example, in model A2, we found an average value of time amounting to NOK 0.28 per shipment/min. As evaluated at the sample median, however, the time value in this same model can be calculated at only half this rate, or approximately NOK 0.14. Half the sample exhibit even smaller time values than this. Across the sample, estimated values of time per shipment vary greatly, ranging from less than NOK 0.01 to more than NOK 5 per shipment/min. The cost of using a more flexible and general model specification is, therefore, that the information contained in the analysis is not easily summarised in a few single measures. More fundamentally, there might be reason to think twice about the appropriateness of disaggregate modelling in the case of freight transportation. Even if one were able to draw a probability sample from the population of shipments, this population is not nearly as stable as the corresponding population of people used for travel demand forecasting. In fact, the individual shipment ceases to exist as soon as it has reached its final destination. Now, in general, there is a fair amount of temporal stability in the patterns of economic activity and, hence, in the derived demand for transportation, so that next year's g

Yet this Box-Cox parameter is not significantly different from one, and hardly even from zero, the ^-statistics for tests against 1 and 0 being 1.41 and 1.64, respectively (not shown in the table).

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139

shipment population is unlikely to differ greatly from that of this year, in terms of its aggregate characteristics. We are, however, dealing with two entirely distinct physical populations, meaning that the same microunits making up this year's population will not reappear next year. An important part of the mechanisms operating in the freight market will translate into more, fewer, bigger or smaller shipments taking place between given pairs of zones—in other words, into freight movements originating or disappearing. The shipment population itself is, in a sense, endogenous. Therefore, one cannot expect to capture, or predict, all the behavioural adjustment taking place in the freight market by implicitly assuming a given population of shipments. This applies to revealed as well as to SP analysis. In the SP case, one is faced with the additional problem that the attributes of the alternative(s) are not unknown, but artificially created. Therefore, one cannot know how far the freight user is from preferring another solution. For this reason, we have not ventured to calculate elasticity estimates based on the sample. Although technically calculable, these measures would hardly have a meaningful interpretation. We feel less uncomfortable about the MRS derived, although in light of the above qualifications, even these need to be interpreted with considerable caution.

Acknowledgements This research was made possible through the financial support of the Norwegian Ministry of Transport and Communications and the Research Council of Norway (NORAS department). Thanks are also due to Knut Sandberg Eriksen, Nina Fjelde, Janne Hagen, Bj0rn L0vlie, Bard Norheim, the Federation of Norwegian Transport Users (TF) and a group of industry representatives, for their help in designing and organising the survey. Last, but not least, the authors are indebted to Marc Gaudry and his TRIO team for their valuable software support, and to Staffan Widlert for reading this paper to the 7th International Conference on Travel Behaviour in Valle Nevado, Chile.

References Ben-Akiva, M. and Lerman, S. (1985) Discrete Choice Analysis: Theory and Application to Travel Demand. The MIT Press, Cambridge, Mass.

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Box, G.E.P. and Cox, D.R. (1964) An analysis of transformations. Journal of the Royal Statistical Society 26B, 211-243. De Jong, G. and Gommers, M. (1992) Value-of-time in freight transport in the Netherlands from stated preference analysis. 6th World Conference on Transport Research, Lyon, July 1992, France. Gaudry, M.J.I, and Wills, M.J. (1978) Estimating the functional form of travel demand models. Transportation Research 12, 257-289. Gaudry, M.J.I., Jara-Diaz, S.R. and Ortuzar, J. de D. (1989) Value of time sensitivity to model specification. Transportation Research 23, 151158. Gaudry, M.J.I., Duclos, L.-P., Dufort, F. and Liem, T. (1993) TRIO reference manual, version 1.0. Publication 903, Centre de Recherche sur les Transports, Universite de Montreal. Widlert, S. (1990) Godskunders Stockholm, Sweden.

varderingar.

Banverket/Transek,

9

Behavioural Models or Airport Choice and Air Route Choice Mark A. Bradley

Abstract An understanding of air passenger route choice is crucial for airport capacity planning. Development of main and regional airports, as well as changes in the road and rail transport system for airport access, will influence the relative demand for flights from competing airports. Changes in the frequency and price of flights from the various airports are also expected to result from deregulation, airline mergers and aircraft technology improvements. This chapter describes a study undertaken by Hague Consulting Group for The Netherlands Civil Aviation Authority. The purpose of the study was to collect and analyse market data to provide models of air traveller route choice. Using Stated Preference (SP) survey methods, models were created for the choice between competing departure airports and, when relevant, the choice between direct and transfer flights. These models will be used to analyse future demand for Amsterdam Schiphol airport and for regional airports in the Netherlands. The chapter contains a discussion of the issues involved in the analysis of air traveller's route choice, summarises the design and execution of a SP experiment among passengers at Amsterdam, Eindhoven and Brussels airports, describes analyses done on the survey data, including the segmentation of the passenger market based on journey purpose and destination, presents choice models estimated using the SP data and provides a discussion of the results and their usefulness in planning.

Introduction An understanding of air passenger route choice is crucial for airport capacity planning. Development of main and regional airports, as well as changes in the road and rail transport system for airport access, will influence the relative demand for flights from competing airports. Changes

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in the frequency and price of flights from the various airports are also expected to result from deregulation, airline mergers and aircraft technology improvements. Existing models of the relative influence of these changes on air traveller's choices are generally based on aggregate data from past years and, thus, do not reflect the range of choice situations that are expected to exist in the future. The research described here was designed to derive more relevant and comprehensive models using data from individual travellers facing hypothetical future choice situations. This chapter describes a study undertaken by Hague Consulting Group for Rijksluchtvaartdienst (The Netherlands Civil Aviation Authority). The purpose of the study was to collect and analyse market data to provide models of air traveller route choice. Using Stated Preference (SP) survey methods, models were created for the choice between competing departure airports and, when relevant, the choice between direct and transfer flights. These models will be used to analyse future demand for Amsterdam Schiphol airport and for regional airports in the Netherlands. The second section of this chapter contains a brief discussion of the issues involved in the analysis of air traveller's route choice. The third section summarises the design and execution of a SP experiment among passengers at Amsterdam, Eindhoven and Brussels airports. The fourth section describes preliminary analyses done on the survey data, including the segmentation of the passenger market based on journey purpose and destination. The fifth section presents the results of segment-specific choice models estimated using the SP data. The sixth section provides a discussion of the results and their usefulness in planning.

Background A person travelling by air from fixed origin O to fixed destination D has a choice from among possible routes of type OXYZD, where, • X is the departure airport. • Y is the (possible) transfer airport. • Z is the arrival airport. For local airport capacity planning, the key choices are the choice of X for residents of the airport catchment area, and the choice of Z for nonresidents with destinations in the catchment area. The choice of flying on a direct route, or via transfer airport Y, can also be important. For

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143

Amsterdam airport, for example, it is important whether, or not, a passenger with a destination in the US makes an intermediate transfer at London, Brussels, Paris, Frankfurt or Copenhagen. It is even more important whether, or not, passengers departing from those airports make an intermediate transfer at Amsterdam (Y=Schiphol). "Mainport" competition for transfers of this type is expected to become more intense under future deregulation. Factors which may influence the choice of airports X, Y and Z are listed in Table 1. The choice between possible departure airports is often Table 1 Possible route choice decision factors Choice factor Air fare Modes available to/from the airport Travel time to/from the airport Frequency/timing of flights Congestion/punctuality of flights Extra journey time for transfer Airlines serving the route Parking facilities Check-in facilities Lounge/restaurant/shopping facilities Transfer facilities Baggage/customs/immigration facilities

Departure airport X

Transfer airport Y

Arrival airport Z

1 1 1 1 1

1

1 1 1 1 1

2 2 2 2

1 1 1 2

2

2 2 2

l = "primary" factors, 2="secondary" factors.

determined solely on the basis of travel time by road or public transport. Large differences in the "primary" air route level of service factors—the price and frequency of flights—may cause airports, other than the nearest one to enter the choice process. The "secondary" factors related to the quality of the airports and airlines are likely to influence route choice only in cases where the decision is already marginal. An example might be someone living between Rotterdam and Amsterdam choosing the smaller Rotterdam airport for a short flight to London because parking and checkin are less time-consuming there. Even when one is mainly interested in predicting choice of departure airport X, the entire journey must be taken into account, including the accessibility of X from the origin and the time, cost and convenience of flying from X to reach the destination over possible routes XYZ. This

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overall choice framework was used in designing the survey and analysis approach described in the remaining sections. Prior to the study, we reviewed previous research on airport choice and air route choice. N'doh and Caves (1990) estimated a model of route choice in the UK using Revealed Preference (RP) data. The main variables were access time, frequency, journey time, and seat availability. Airfare was not included. Hansen (1988) estimated a route choice model on aggregate RP data which included fare, frequency, journey time and a variable representing the extra utility of hub airports. The UK Civil Aviation Authority (CAA, 1990) also uses a model with fare, access time and frequency which is based on aggregate RP data. Gosling (1984) used RP data to estimate a model of airport access mode choice as a function of access time and cost. It was thought that SP methods could provide a more comprehensive and accurate judgement of the relative importance of these variables in air route choice.

The Stated Preference Survey The survey sample

Given that the primary focus of the study was the choice of Amsterdam Schiphol airport versus competing regional and main airports, one would ideally want to survey three types of air passengers: • Residents of the Netherlands, Belgium and bordering regions of Germany for whom Schiphol is the current or a potential departure airport (X). • Passengers with destinations in this same area but residing outside this area, for whom Schiphol is the current or a potential arrival airport (Z). • Passengers on long flights with both origins and destinations outside this area, but for whom Schiphol is the current or a potential transfer airport (Y). Of these three groups, the first is probably the most sensitive to local airport competition, particularly with respect to the development of the regional airports in Rotterdam, Eindhoven and Maastricht. Passengers in

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the first group are also the most homogeneous, given that they reside within a fairly small radius, and are the easiest to interview at the airport, given that they must wait before departure and they speak a manageable variety of languages. The decision was taken, therefore, to exclude any passengers not living in the Netherlands, Belgium or nearby provinces of Germany. Any passengers who were making very short flights within the study area were also excluded. Thus, all respondents were beginning their journey from home (or, in some cases, work). The issue remains as to whether the study results are also applicable to other passengers (potentially) arriving or transferring at Schiphol. This issue will be studied during further application of the results, and could possibly indicate a need to later survey the other passenger groups as well. Our initial plan was to interview passengers at three airports: Amsterdam, Eindhoven and Dusseldorf. Eindhoven is more centrally located in the study area than the other regional Dutch airports, Rotterdam and Maastricht. Dusseldorf and Brussels are the only major airports within the study area that compete with Amsterdam. When permission to interview passengers at Dusseldorf was refused, Brussels became the third survey site. For passengers currently choosing Brussels, Frankfurt and Paris may also be seen as reasonable alternatives, lying at a distance similar to that between Brussels and Amsterdam. Computer-assisted interviews were carried out at the three airports in the departure lounges and gates beyond passport control. The survey was programmed and administered using Hague Consulting Group's MINT software. The fieldwork at all airports was carried out by Mobiel Centre, a market research company based at Schiphol. Separate questionnaires were prepared in Dutch, French and English. The appropriate language for each respondent was selected from a menu to begin the interview. Each interview lasted about lOmin, on average. The contents of the interview are described in the next section. A target sample size was set at 800 respondents, segmented by purpose (business versus nonbusiness) and destination (Europe versus intercontinental (ICA)). Charter passengers were added as a small additional segment. Table 2 shows the original targets against the final number of interviews used in analysis. The total number of usable interviews is 985. The quotas were exceeded for all cells except nonbusiness trips at Eindhoven, which are relatively rare, and charter trips from all airports. The charter quotas were reduced after the pilot surveys when it became clear that the airport route choice context was less relevant for them than for line flight passengers.

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Travel Behaviour Research: Updating the State of Play Table 2 Achieved vs. (target) sample sizes

Segment/ Airport

Business Europe

Business Intercont.

Leisure Europe

Leisure Intercont.

Charter

Total

Amsterdam Eindhoven Brussels

228 (100) 85 (50) 92 (75)

58 (50) NA 31 (25)

124 (75) 37 (50) 54 (50)

90 (75) NA 55 (50)

49 (100) 19 (50) 35 (50)

577 (400) 141 (150) 267 (250)

Total

405 (225)

89 (75)

215 (175)

145 (125)

103 (200)

985 (800)

The survey design The interview consisted of seven parts: (1) (2) (3) (4)

General information about the type of trip and flight taken. Details of the flight(s) taken (airline, flight number, times, etc.). Information about the ticket price and method of booking. Details of the trip origin and the trip to the airport (mode, travel time, etc.). (5) Questions about the most likely alternative airport and travel to that airport. (6) The SP choice experiment, offering different routes at different prices. (7) Information about the respondent and his or her household.

In part (2), the flight number was entered from the respondent's ticket, and the computer searched a database to automatically fill in details about departure and arrival time, distance, etc. This database was compiled from up-to-date timetables. Up to two further connecting flights could be entered as well, using an additional database with possible transfer connections at all major airports in the world. This connecting flight information was extracted from the 1991 ABC database, and may have been out-of-date in some cases. In cases where the computer could not find the specified flight number in the database, the interviewer entered the additional details by hand. This manual procedure was used for all charter flights, which were not in the database. In part (3), the ticket fare class, flight distance, destination region and journey type (one-way or round-trip), were used to calculate a default fare level. This calculation was based on a regression analysis which explained fare as a function of distance, class and destination region. In

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most cases, this default fare level was overwritten with the actual fare level taken from the respondent's ticket. Because fare is a key variable in the SP experiment, however, it was important to have a realistic default level for cases where the actual fare was not available. Part (4) obtained data on the actual mode used and travel time to the actual departure airport. In part (5), the respondent indicated the most preferred alternative airport for their journey, assuming that flights to their destination were available from all airports, either directly or with a transfer. The respondent was then asked which mode of transport they would have used to get to the alternative airport, and approximately how long this would have taken. This information was later used in the SP choice experiment. The variables and levels used in the choice experiment (part 6) are summarised in Table 3. The departure airport was either the actual or the alternative airport stated by the respondent. The access mode and travel time in each case were based on data given by the respondent, and were not varied during the experiment. The most complex variable to include was the frequency/timing of flights. The available flights were presented to the respondent in a format similar to that used in airline

Table 3 Stated preference experiment levels Variables/ levels

Departure airport

Flight frequency/ timetable

Fare level

Level 1

Actual airport by actual mode, taking the actual travel time

Direct flight at high frequency per day or per week

Actual price for actual fare class

Level 2

Alternative airport by stated mode, taking the stated travel time

Direct flight at lower frequency per day or per week

Price reduced by 5-15% for actual fare class

Level 3

Change flights with short transfer time, lower frequency per day or per week

Price reduced by 10-30% for actual fare class

Level 4

Change flights with longer transfer time, lower frequency per day or per week

Price reduced by 15^5% for actual fare class

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timetable brochures. The levels for this variable had to be customised to be realistic for any destination. This was done using a database of current service levels for over 1000 destinations. The database was extracted from the 1991 ABC database, using the best connections from Amsterdam, Brussels or Dusseldorf. The computer accessed this data during the interview to create the appropriate SP levels. The first two levels both describe direct flights to the destination, but with different frequencies. For destinations with high frequencies, the flights were presented on a daily basis, showing up to three departure and arrival times during the relevant period of the day. For destinations where such high frequencies are not realistic, the frequency was varied as the number of days per week with flights, showing specific days on the screen. Some random variation was also introduced into the frequency levels and the specific times of day and days of week to provide more efficient data for model estimation. To ensure realism, no direct flights were offered to minor destinations in distant countries. The other two levels describe transfer flights via a specific transfer airport, selected in each case to be realistic for the respondent's destination. London Heathrow, Paris, Frankfurt and New York JFK were four of the most common transfer airports used. The frequency of transfer flights, described in the same way as for direct flights, was the same for both levels. The levels differed in the amount of time between connecting flights. The transfer times used were in the range of 45 min to 2 hr for European destinations, and 1-3 hr for 1C A flights. No transfer flights were offered to larger airports in nearby countries, such as London, Paris, Hamburg, Frankfurt and Copenhagen. The final choice variable was the ticket price, always presented for the fare class actually used by the respondent. Three levels of reduction were used with respect to the actual fare paid, each one randomly selected as 5, 10 or 15% less than the preceding level, for a total reduction of up to 45%. Thus, the SP experiment contains all of the "primary" factors in Table 1, with the exception of the punctuality of flights. It was assumed that this factor and the "secondary" factors in Table 1 related to airport, and airline facilities would be reflected by airport-specific constants in the modelling stage. During the choice experiment, respondents were instructed to imagine that all airports retain the current level of facilities, and that the airlines serving all hypothetical routes are of the same quality as the airline they actually used for their journey. For each respondent, the interview software created a unique orthogonal fractional factorial experimental design with 16 alternatives (only eight alternatives for those

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149

cases where either only direct or transfer flights were offered). Each respondent was asked to look at up to 11 different pairs of these alternatives and specify their preferred route from each one. An example choice screen is shown in Fig. 1. This respondent had actually travelled by bus to Amsterdam to catch a flight to Los Angeles, but would have a shorter trip, and could get a lift by car to Antwerp airport, if flights were available. In the hypothetical future situation, flights are available from Antwerp and are less expensive, but are much less frequent and require an intermediate stop. As one can imagine, trying to make such choice situations realistic and interesting for every type of passenger was a very challenging survey design task.

Description of the Sample A variety of analyses were done on the survey data prior to model estimation. The first task involved carefully checking the flights and destinations in the sample to reject any destinations within the study area and any cases where respondents were presented with obviously unrealistic choice alternatives. About 25 cases were rejected on this basis. Next, a descriptive analysis was done to contrast different market segments. The original segmentation based on journey purpose and destination was maintained, but the European flights were further broken down into "short" and "other Europe" segments. The "short" segments include direct flights to approximately 20 airports in England, France, Germany and Denmark. This segmentation was made because no transfer flights were offered to any of these airports and, thus, variables relating to transfers could not be included in the models for the "short" segments. These "short" destinations are also those served by direct flights from regional airports at present, so one would expect different types of route alternatives to be relevant for this segment. The characteristics of the seven segments are summarised in Table 4, which shows the percentages of those segments falling within various trip- and person-type categories.

Route characteristics For business trips, the European segments are larger than the ICA segments, while the opposite is true for the nonbusiness trips. The relative percentages of respondents from Amsterdam and Brussels are similar

Figure 1 An example of SP choice screen

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151

Table 4 Descriptive summary of the market segments Leisure Leisure Europe Intercon.

Charter

Segments

Business Short

Business Europe

Business Intercon.

Leisure Short

Sample size

182

223

89

85

130

173

103

Route characteristics (%) Left from Amsterdam Left from Brussels Left from Eindhoven Used KLM or Sabena Transferred en-route Went to UK or Ireland Went to South Europe Went to North America

48 17 35 68 0 43 0 0

63 28 9 48 25 18 34 0

65 35 0 48 47 0 0 44

40 21 39 63 0 62 0 0

69 28 3 48 11 14 55 0

68 32 0 41 36 0 0 50

48 34 18 0 0 0 84 4

Trip characteristics (%) Paid Ist/Business class Holiday trip Booked as package Booked flight self Day trip Away 6+ nights Travelling alone Parked car at airport Dropped off at airport Took train to airport

51 0 7 16 23 4 76 53 18 16

52 0 8 20 9 13 75 48 23 16

47 0 3 28 0 73 70 18 51 17

6 61 33 77 5 27 29 32 31 26

6 69 28 65 0 58 38 17 39 30

8 76 38 72 0 95 33 12 51 25

0 90 81 79 2 93 17 16 58 13

Person characteristics (%) Age less than 30 Age 60 or older Male Employed full time Household size 3+ 2+ cars in household No flights in last year 25+ flights last year

16 3 93 98 55 53 4 22

20 3 90 98 48 53 5 21

21 1 87 97 60 62 3 17

34 11 46 60 30 31 42 6

29 16 55 53 27 32 31 2

46 10 58 64 30 33 42 1

28 9 52 62 34 40 47 2

across the segments. The main difference is for the Eindhoven sample, who fall almost exclusively in the Short segments. This reflects the type of flights currently available from Eindhoven. The fraction of the sample using the major "home carriers", KLM and Sabena, is about two thirds to the Short destinations, and almost half in the other noncharter segments. The percentage of respondents who transferred at intermediate airports increases with distance and is higher for business than for nonbusiness trips. Almost half of the intercontinental business trips involved a transfer. The nonbusiness destinations tended to be more concentrated: over half of the Short, Europe and 1C A trips are to the UK/Ireland,

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Southern Europe or North America, respectively. The corresponding fractions are less than 50% for business trips.

Trip characteristics Roughly half of the passengers in all of the business segments travelled in Business Class. In terms of journey purpose, 60 to 75% of the trips in the nonbusiness segments were for holidays, increasing with distance. One third of nonbusiness flights were booked as part of a package including accommodation. Charter flights were nearly all holiday package trips. Roughly, three-fourths of nonbusiness and charter trips, but only about one fourth of business trips, were booked by the respondent. Day trips by air were only common in the business short segment (23%). Stays of one week or more were most common for ICA trips, and for the nonbusiness and charter segments. Business passengers were more likely to travel alone, more likely to park at the airport, and less likely to travel by train than passengers in the other segments. For the intercontinental trips, however, the mode choice of business and nonbusiness travellers was very similar. The attractiveness of parking at the airport appears to be strongly related to the length of stay away from home. The final section of Table 4 contains the household and person characteristics. Business travellers tend to be between the ages of 30 and 60, and are almost all males working full-time. The age, sex and employment status of the other segments are much more representative of the general population, with the possible exception of intercontinental travellers who tend to be aged under 30. Business travellers tend to come from larger households with higher car ownership than travellers in the other segments. Even more striking is the difference in number of flights made in the last year. About 20% of business travellers are very frequent fliers with 25 or more flights, and another 20% are in the range 13-24 flights per year. Charter passengers are the least frequent fliers, with nearly half not making any flights in the preceding year. Further results of interest, not shown in Table 4, are, • 10 to 15% of respondents in each segment had actually considered using an airport other than the one at which they were interviewed. • Rotterdam was selected as the alternative airport by about 50% of Amsterdam respondents, while Antwerp was selected by about 50%

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153

of Brussels respondents. Of the Eindhoven respondents, about 40% indicated Amsterdam and about 25% indicated Maastricht. • About 60% of Eindhoven respondents parked at the airport, but only about 30% for Amsterdam and Brussels. The fraction who travelled by train is 30% for Amsterdam, 10% for Brussels and 1% for Eindhoven. • The average travel time to the airport was shortest by car passenger and taxi and longest by train, and was shorter for all modes for Eindhoven respondents than for Amsterdam or Brussels respondents. • About 85% of those actually parking at the airport would also park at the alternative airport. The fraction of "nonswitching" for the other modes is 70% for car passenger, 60% for train, 35% for taxi and 30% for bus. A key result from the SP experiment is whether, or not, the hypothetical improvements in frequency and fares were sufficient to cause respondents to switch to the alternative airports. Prior to model estimation, simple indicative tabulations were done of the fraction of SP choices for which the alternative airport was chosen over the actual one. The percentages are shown in Tables 5 and 6 by segment and actual airport, along with the number of respondents in each cell (each of these respondent made multiple SP choices). Table 5 Switch to alternative airport by actual airport and segment Segments

Business Short

Business Europe

Business Intercon.

Leisure Short

Leisure Europe

Leisure Intercon.

Charter

Amsterdam switch (No. of respondents)

39% (88)

43% (140)

42% (58)

31% (34)

48% (90)

48% (118)

40% (49)

Brussels switch (No. of respondents)

16% (30)

29% (62)

33% (31)

29% (18)

46% (36)

47% (55)

42% (35)

Eindhoven switch (No. of respondents)

14% (64)

25% (21)

(0)

24% (33)

24% (4)

(0)

47% (19)

For the business segments, Amsterdam respondents switched about 40% of the time, but Brussels and Eindhoven respondents switched only 15-30% of the time. For the other segments, the percentages are similar across airports in the range 30-50%. In all cases, those making "short" journeys were less likely to switch than those in the Europe and ICA segments. The shorter the flight, the more important airport access time becomes relative to the rest of the journey time.

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Travel Behaviour Research: Updating the State of Play Table 6 Switch to alternative airport by actual/alternative airport

Alternative airports

Rotter- Amster- Einddam hoven dam

Maastricht

Antwerp Brussels Dussel- Frank- Paris dorf furt

44% Amsterdam switch (No. of respond- (303) ents)

NA

51% (86)

53% (22)

43% (27)

33% (76)

37% (42)

34% ((13)

— (0)

Brussels switch (No. of respondents)

— (0)

37% (75)

39% (4)

34% (9)

39% (137)

NA

47% (9)

15% (10)

23% (21)

Eindhoven switch (No. of respondents)

35% (8)

21% (58)

NA

32% (32)

21% (7)

17% (17)

23% (19)

_ (0)

_ (0)

Table 6 contains a similar breakdown by actual and alternative airport. Schiphol respondents are most likely to switch to regional airports in the Netherlands. In general, the lowest propensity to switch is for those stating a(nother) major airport such as Amsterdam, Brussels, Frankfurt or Paris as the best alternative. The models described in the following section provide some insight into the reasons for these trends.

Models of Air Route Choice Disaggregate binary logit choice models were estimated for each of the seven market segments described in the fourth section. Logit estimation (Ben-Akiva and Lerman, 1985), finds parameter estimates which maximise the likelihood of the observed choices, assuming an approximately normal error distribution. The variables included in the main models were, • • • • • • • • •

the logarithm of the one-way airfare (in guilders); the logarithm of the frequency (in flights per week); the access travel time to the departure airport (in hours); the stopover time at the transfer airport, if relevant (in hours); constants for each departure airport, relative to Amsterdam; constants for each access mode, relative to car parked; a constant for a transfer route, relative to a direct flight; constants for certain transfer airports, relative to the rest; constants for the respondent's actual airport, mode and flight type.

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155

Key model results for the seven market segments are shown in Tables 7 and 8. The models were based on 1000-2800 choice observations per segment. The overall fit of each model is given by p2; the fraction of total likelihood accounted for. The achieved fits of 0.3-0.5 are quite good for binary SP data. The number of significant parameters, in terms of estimates with f-statistics of two or more, is also satisfactory. The most significant variable in the models was the ticket price. Tests

Table 7 Main route choice models by segment Business Short

Business Europe

Business Intercon.

Leisure Short

Leisure Europe

Leisure Intercon.

Charter

Observations P2(0) Main variables:

1999 0.42 Coef. (r-stat)

2810 0.33 Coef. (r-stat)

1100 0.28 Coef. (r-stat)

965 0.51 Coef. (r-stat)

1729 0.33 Coef. (r-stat)

2189 0.39 Coef. (r-stat)

1259 0.42 Coef. (r-stat)

Log of fare ( /log fl) Log of frequency (% fare/100%) Access time (% fare/hr) Transfer time (% fare/hr) Transfer constant (% fare)

-7.73 (-19.3) + 17.5% (9.0) -38.9% (-14.3)

-3.52 (-13.6) + 15.3% (6.0) -44.6% (-16.4) -28.1% (-8.3) -36.7% (-7.3)

-5.14 (-11.9) +4.3% (2.3) -20.2% (-7.4) -9.7% (-5.4) -15.2% (-2.4)

-13.1 (-15.2) +4.6% (2.7) -20.4% (-7.7)

-6.98 (-17.3) +3.0% (1.9) -16.2% (-11.1) -11.9% (-5.4) -19.3% (-5.6)

-10.3 (-22.1) + 1.8% (3.0) -10.1% (-12.6) -4.9% (-6.6) -7.4% (-3.2)

-12.0 (-18.0) +4.8% (3.3) -12.8% (-10.0)

Segments

Table 8 Valuations inferred from the route choice models Segments Average one-way fare(fl) Average access time (min) Value of access time (% fare/hr) Value of access time at ave. fare (fl/hr) Average frequency (flights/week) Value of frequency (% fare/% freq.) Value of frequency at ave. (fl/flight/wk)

Business Short

Business Europe

Business Intercon.

Leisure Short

Leisure Europe

Leisure Intercon.

Charter

334

354

539

1480

213

321

735

41

47

54

43

57

64

46

39

45

20

20

16

10

13

138

240

300

43

52

74

42

45.25

15.93

8.15

58.49

15.15

4.67

1.40

0.17

0.15

0.04

0.05

0.03

0.02

0.05

1.37

5.19

7.78

0.17

0.64

2.91

11.28

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were done including the fare variable as the absolute fare level, the logarithm of the fare level and the percentage fare level relative to the fare actually paid by the respondent. The logarithmic and percentage variables gave similar results. Both were superior to using the absolute fare, even though fare was presented as an absolute value during the experiment (see Fig. 1). The logarithmic form was used for the models presented here. This form implies that people are less sensitive to a one guilder change in fare at high fare levels than at low fare levels. This trend can also be seen to some extent across the segments: the fare coefficient for the "short" segments is higher than for the other segments. The ICA segments, on the other hand, show higher fare sensitivity than the Europe segments. This result may reflect the higher intensity of price competition outside of Europe, as well as the different type of travellers making the longer ICA journeys. The greatest contrast is by journey purpose, with the nonbusiness segments roughly twice as price-sensitive as the business segments. Although one might expect even less fare sensitivity for business travellers, the fact that only half of them travelled Business Class indicates that there was at least some price consciousness reflected in the actual ticket choices. The charter segment is the most price-sensitive, as one would expect. To facilitate the interpretation of the remaining variables, the coefficients have been divided by the log fare coefficient to derive estimates in terms of equivalent percentage change in fare. A 100% improvement in frequency, for example, is worth about 15% of fare for business travellers within Europe, but only about 2-5% of fare for the other segments. Both logarithmic and linear variables were tested for frequency, as were separate variables for flights per day and days per week with flights. The single logarithmic variable was statistically superior, and also agrees best with existing models where frequency of flights is often used as a logarithmic airport "attraction variable". Access time to the airport is the second strongest variable in all models, nearly as significant as the fare variable. A one hour difference in travel time is worth 20-40% of fare for the business segments and 10-20% for the other segments, with the highest values for the shorter trip segments. In Table 8, this percentage value is translated into a more "traditional" value of time in guilders per hour by multiplying by the average one-way fare within each segment. The resulting values increase with distance, from 140-300 fl/hr for business and 40-75 fl/hr for other segments. Even though access time is relatively more important for shorter trips, the monetary valuation is higher for longer trips because of the higher fare

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levels involved. A similar trend is seen in Table 8 for the monetary evaluation of frequency: an extra flight per week is worth more on the longer routes which currently have high fares and low frequencies. The final group of variables is for the four segments with possible transfer destinations. First is the stopover time at the transfer airport, which is in addition to the constant for the transfer itself. The disutility of transfer time is about two-thirds as high as the disutility of access time for the Europe segments, and about one-half as high as access time for the 1C A segments. Note that transfer time is the only variable which represents journey time by air. For time in the aircraft, there is generally not enough difference in flying time between competing routes to measure the effect, either in reality or in the SP experiment. Relative to fare, the need to transfer (independent of transfer time) is viewed more negatively by business travellers than by nonbusiness travellers, and more negatively by European travellers than by 1C A travellers. The models in Table 7 were estimated without person- and trip-specific variables such as age, duration of stay, group size, etc. Such variables would require market data with similar detail for the eventual application of the models, so it is preferable to omit them unless they are highly significant. The likely influence of adding such additional variables was tested using "validation tables" which compare the model predictions to observed choices for specific subsamples of respondents. The most likely additional variables indicated by these tables were tested by adding them to the models and reestimating, but none of them was highly significant across the segments. Three interesting effects which were marginally significant were: • The resistance to switching to an alternative airport increased with the number of flights made by the respondent in the previous year. This result suggests some amount of airport "loyalty", but it could also be loyalty to specific airlines associated with specific airports. • Students, pensioners and part-time workers were somewhat more price-sensitive than other respondents, who were mostly full-time workers. • Passengers who travelled in Tourist Class were more price-sensitive than those travelling in First or Business Class. These effects, however, were not very large and are already captured for the most part through market segmentation by purpose and destination.

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Discussion of Results The model results described in the previous section contain significant estimates for all key variables, and the trends across the market segments seem reasonable. Segmentation by both trip purpose and distance class are important in distinguishing differing relative importance of the choice variables. Particularly those travellers in the longer distance nonbusiness segments appear to be prepared to travel further and perhaps use a less convenient flight in order to save on price. Business travellers are also somewhat price-sensitive, but would be more strongly attracted by improvements in travel times and frequencies, particularly for flights within Europe from the regional airports. While SP research can sometimes overstate travellers' willingness to change their behaviour, the level of realism and detail used in this choice experiment should prevent respondents from giving unrealistic answers. For most respondents, travel by air is fairly infrequent, and this should prevent them from making choices or responses purely out of habit. These reasons, along with respondents' generally positive reaction to the SP survey, give us confidence in the validity of the research results. Because the hypothetical alternatives used during the choice experiment often offered flights which do not exist today, the survey sample cannot be used directly for forecasting. Ideally, the airport-specific constants should be re-calibrated to reflect current airport choices under the current access times and supply of flights before the models are used in prediction for future scenarios. Prediction also requires application of the models to data which accurately represents, • the number of passengers living in each study area zone going to each destination; • the travel time from each zone to each departure airport by each access mode; • the frequency and price of flights from each departure airport to each destination. The air passenger route choice models are appropriate for inclusion in the RLD Integrated Model System (IMS) as described in Veldhuis et al. (1996). The market segmentation used here is compatible with that used in market growth models which have already been implemented in the system. In combination with an existing supply model of aircraft type and frequency, the route choice models can be applied in a dynamic simulation

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system: demand at each airport is predicted as a function of available flights (among other things), and the supply of flights is then adjusted as a function of the predicted demand. A dynamic simulation system of this type is used for airport capacity planning in the UK (CAA, 1990). The demand function in that system is essentially the same as that developed here: a logit probability function based on frequency, access time, air fare and airport-specific constants. Several parameters in the UK model had to be preset at assumed values, however, due to lack of appropriate data for full estimation. The models developed in this study can provide a more complete empirical basis for simulating airport capacity policies.

References Ben-Akiva, M. and Lerman, S. (1985) Discrete Choice Analysis: Theory and Application to Travel Demand, MIT Press, Cambridge, Mass. CAA (1990) Traffic distribution policy and airport and airspace capacity: the next 15 years. Report No. CAP 570, Civil Aviation Authority, London. Gosling, G.D. (1984) An airport ground access mode choice model. Report UCB-ITS-TD-84-6. Institute of Transportation Studies. University of California at Berkeley. Hansen, M.M. (1988) A Model of Airline Hub Competition, PhD Thesis, Institute of Transportation Studies, University of California at Berkeley. N'doh, N.N. and Caves, R.E. (1990) Air transportation passenger route choice: a nested multinomial logit analysis. In M.M. Fisher, P. Nijkamp and Y.Y. Papageorgiou (eds.), Spatial Choices and Processes. North Holland, Amsterdam. Veldhuis, J, Bradley, M., Brouwer, M. and Kroes, E. (1996) The integrated airport competition model: a model system for international long distance passenger transport. Tijdschrift Vervoerwetenschap 4, Samson HD Tjeenk Willink bv, Alphen a/d Rijn.

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10

A Model of Employee Participation in Telecommuting Programs Based on Stated Preference Data Jin-Ru Yen, Hani S. Mahmassani and Robert Herman

Abstract Telecommuting in its various forms has been advocated as a travel demand management strategy, with potential to reduce congestion, energy consumption and air pollution. It also affords certain segments of society the opportunity to participate in the work force, improving their quality of life and offering employers an expanded pool of qualified workers. Several other productivity and employee-morale benefits have also been attributed to telecommuting. A key factor in the effectiveness of telecommuting is the extent to which it is adopted by employers and employees alike. Recognising that two principal actors are involved in telecommuting adoption, this chapter is intended to formulate the employee adoption process, assuming such programs are provided by the employer in the organisation. On the basis of stated preference data obtained from a survey in three Texas cities in the USA, an employee telecommuting choice model is developed. The model is formulated and estimated under the framework of the dynamic generalised ordinal probit model developed by the authors, which is based on the ordered-response theory but advances existing ordinal probit models by allowing the specification of stochastic utility thresholds and autocorrelation among observations. Estimation results confirm that the employee adoption process is affected by his/her attitudes toward telecommuting and the program design, defined on the basis of who assumes additional telecommuting costs, and the corresponding salary changes for the telecommuter. The employee's choice of telecommuting is also influenced by his/her personal, household and job characteristics as well as commuting attributes. Another important feature that emerges from the estimation results is that the dynamic structure of the generalised ordinal probit model successfully captures the autocorrelation among responses from the same employee, which ultimately improves the precision of the parameter estimates.

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Introduction The possible substitution of transportation by telecommunications has been advocated as an approach that might alleviate demand in travel and congestion on transportation facilities and, hence, reduce energy consumption and air pollution. The basic idea is to substitute the movement of people and goods on transportation networks with information flows on telecommunications networks. With increasing rate of development, diffusion and acceptance of telecommunications technology, approaches such as telecommuting, teleshopping, teleconferencing, telebanking and teleeducation are generating considerable interest. Among these, telecommuting is considered one of the most promising substitutes of work trips, which are the major determinants of traffic congestion and air pollution during peak hours. It is also suggested that telecommuting could increase social welfare by providing job opportunities to workers with disabilities who may be unable to work otherwise. Telecommuting also induces advantages and disadvantages for both employees and employers who provide such a program in the organisation (DeSanctis, 1984; Salomon and Salomon, 1984; Katz, 1987). While the observational basis to conclusively establish the net impacts of telecommuting remains unavailable to date, replacement of travel has been documented in several pilot projects (Kitamura et al., 1990; Pendyala et al., 1991; Nilles, 1991). Although the concept of "electronic home worker" was first proposed in 1957 (Jones, 1957-1958), and the idea of telecommuting received public attention in the 1970s, motivated primarily by the so-called energy crisis (Huws, 1991), and in the 1980s, due to increasing concern over traffic congestion and air quality, systematic investigation of telecommuting adoption was limited. The prediction of how much telecommuting may be adopted is a key factor underlying the extent to which the potential impacts of telecommuting on transportation systems and business can be realised. The purpose of this study is to address the apparent dearth of research in this area by mathematically formulating the telecommuting adoption process. First, the dynamic generalised ordinal probit model used in this study is described in the following section. After discussing the survey data, the employee telecommuting adoption model is specified and estimated. Estimation results are then interpreted from the behavioural and policy viewpoints.

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The Dynamic Generalized Ordinal Probit Model In this study, telecommuting adoption is formulated as the outcome of a discrete choice process. Most of the proposed discrete choice models are grounded in (random) utility maximisation, which assumes that the decision-maker facing a finite set of discrete choices will choose the alternative from which s/he derives the greatest perceived utility. Depending on the assumed error structure, two model forms are widely known in the literature: the multinomial logit (MNL) model with independently and identically Gumbel distributed disturbances, and the multinomial probit (MNP) model with a general multivariate normally distributed error structure. Though MNL and MNP models have been successfully applied to various studies in transportation, they may not be suitable for decision problems with ordered alternatives where utility maximisation may not be applicable. For example, a customer's response to a five-score measurement of attitudes toward the quality of import cars (say very bad, bad, fair, good and very good) cannot be formulated by either the MNL or MNP model. An alternative approach is necessary to model choice problems with ordered responses. The telecommuting adoption model specified in this study is developed on the basis of the ordered-response theory, which maps the range of a continuous latent variable onto a set of discrete outcomes. For instance, for a given decision situation, a latent variable represents the decisionmaker's perceived utility or attractiveness toward the decision object of interest. A set of ordered thresholds for the latent variable associated with each decision-maker defines ranges corresponding to each discrete decision outcome. The decision-maker's choice then depends on the corresponding interval within which the latent variable lies. Specifically, this study employs the dynamic generalised ordinal probit (DGOP) model developed by Yen et al. (1994) to formulate the employee telecommuting adoption process. The DGOP model is the most general form of the wellknown ordinal probit model, which is based on ordered-response theory and the normality assumption of latent variable disturbances. The first ordinal probit model with multiple-alternatives was proposed by McKelvey and Zavoina (M-Z) (1975), which assumes that for a particular decision situation, the decision-maker's utility thresholds are constant and identical across the population, and disturbances of the latent variable are independently and identically distributed (IID). Although these two strong assumptions lead to a closed mathematical form for the choice probability and, thus, a straightforward estimation procedure, they are

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believed to be unrealistic in general because different decision-makers may have different utility thresholds, and the latent variable may not be independent of utility thresholds. An extension of the M-Z model was proposed by Terza (1985) to address the variation of utility thresholds among the population, though still under the assumptions of deterministic utility thresholds and IID latent variable disturbances. The DGOP model used in this study is capable of capturing the possible stochastic properties of the utility thresholds and allow a more flexible specification of the latent variable. First, utility thresholds can be specified as functions of the attributes of the decision object or decision-maker and, thus, are no longer constant. Second, thresholds are modelled as random variables, with possible correlation among thresholds and between the latent variable and thresholds. Finally, the model can be used to analyse observations with serial correlation or autocorrelation, such as panel data or Stated Preferences (SP) elicited from the same individual. Mathematically, in a study with more than one observation from the same respondent, assume that each individual is asked to provide responses to T-decision scenarios and that /-ordered alternatives (response categories) are included in each scenario question. For individual n, there are T-latent variables (Y*, . . . , Yj), 77-observable discrete variables (Zi w , . . . , Z'Jn) and T sets of thresholds (/io n , iL\n, • • • , /"•/«)• Z'ln = 1, if and only if, /4-i,w < Y'n < jjL\n\ Z\n = 0, otherwise. Therefore, the latent variables and utility thresholds of the DGOP model can be listed as follows:

In equations (1) and (2), V'n and uln represent the systematic and random components of the latent variable associated with individual n under see-

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nario t. Similarly, Slin and ej« are the corresponding observable and unobservable components of utility threshold i for individual n and scenario t. The DGOP model assumes that uln and €•„ (/ = 0,1, . . . , / and t = 1, 2, . . . , T) are multivariate normally distributed. The derivation of the DGOP model and the estimation procedure which includes a Monte Carlo simulation approach to evaluate choice probabilities are given elsewhere by Yen et al. (1994). The following sections present the empirical estimation of the employee telecommuting adoption model.

Survey Data Data used in this study are from a survey of employees in selected organisations in three cities (Austin, Houston and Dallas) in Texas, USA. The questionnaire is comprised of four sections. The first section is intended to capture the respondent's commuting trip information and job characteristics, including travel distance, travel time, job title, amount of time the respondent spends in communication with customers, supervisor(s), subordinate(s), or coworkers and the form of communication. The second section addresses the respondent's attitudes to telecommuting, measured by Likert's five-score, bipolar scales (Fishbein and Ajzen, 1975). The third section seeks the respondent's SP for alternative telecommuting scenarios (Table 1), defined in terms of different combinations of out-of-pocket costs assumed by the employee to work from home (ranging from no cost to adding a new telephone line or buying a personal computer at home), and corresponding salary changes to the employee (from a five percent

Table 1 Seven telecommuting program scenarios

1 2 3 4 5 6 7

Employee salary

Employee incurred costs

the same the same the same +5% +5% -5% -10%

no costs a new phone line a personal computer no costs some costs no costs no costs

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increase to a 10 percent decrease). The last section addresses the respondent's socioeconomic characteristics and computer proficiency level. Questionnaires were sent to selected organisations and distributed to their employees through personnel officers. Seventy-two organisations were selected on the basis of three criteria: (1) firm size, measured by number of employees or total billings; (2) geographical location (CBD versus suburb); and (3) business activity (e.g. computer software, engineering consultancy and accounting). Among them, 3814 questionnaires were sent for distribution to employees, of which 694 usable questionnaires were received. Descriptive statistics and exploratory analyses of survey data were reported elsewhere by Mahmassani et al. (1993).

Model Specification As mentioned above, employees were asked in the third section of the questionnaire to indicate their willingness to telecommute under each of the seven telecommuting program scenarios from one of the following four alternatives: (1) not work from home; (2) possibly working from home; (3) working from home several days per week; and (4) working from home every day. It is assumed that these four possible responses reflect the employee's preference for telecommuting, with "working from home every day" representing the highest preference and "not work from home" the lowest. It is also assumed that there is one latent variable and five utility thresholds (labelled from 0 to 4), associated with each employee in each program scenario. The latent variable is a measure of the employee's perceived utility of a given telecommuting program scenario, and the utility thresholds are in a monotonically increasing order such that the employee chooses option i if and only if the perceived utility is located in the interval between utility thresholds / - 1 and i, where / = 1, 2, 3 or 4. Recognising that responses were elicited for seven program scenarios from each employee and therefore autocorrelation may exist among observations, the DGOP model is used to estimate the employee telecommuting choice model under the normality assumption of the disturbances of latent variables and thresholds. Empirically, three major components need to be specified in the DGOP framework: the systematic components of the latent variable and utility thresholds, as well as the variance-covariance structure of the disturbances.

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Specification of the latent variable The systematic component of the latent variable is assumed to be a linear function of some known attributes, though the DGOP model does not preclude the analyst from specifying a non linear function. Thus, the latent variable in (1) can be specified as follows:

where Yln, V'n and u'n represent the latent variable, and its systematic and random components associated with individual n under scenario t; X'n is a vector of measured attributes known to the analyst, and /3 is the parameter vector to be estimated. Attributes that are expected to affect employee telecommuting adoption include: (1) commuting trip attributes experienced by the employee; (2) employee characteristics and activity patterns; (3) household characteristics, situational constraints and residential location; (4) employee job characteristics; (5) possible economic implications from telecommuting; and (6) employee attitudes toward telecommuting. These are discussed in turn hereafter. Commuting attributes experienced by the employee, such as travel time, average speed and delay, reflect influence of the transportation system performance on telecommuting adoption. It is reasonable to expect that people who incur worse-trip attributes to have greater motivation to telecommute. In an exploratory analysis of the survey data, travel time was found to significantly affect employees' likely adoption of telecommuting (Mahmassani et al., 1993). Employee personal characteristics, such as gender, age, marital status, educational achievement and computer proficiency level, are believed to also have a bearing on telecommuting adoption. Age and marital status serve as life-cycle indicators, and educational achievement is an index of lifestyle in the activity-based analysis literature (Bhat, 1991). It is hypothesised that both educational attainment and computer proficiency have positive effects on telecommuting adoption. Married employees have been reported to be more likely to favour telecommuting (Yap and Tng, 1990). Gender has also been identified as an important factor, with prevailing findings indicating that women tend to have a higher motivation to telecommute (DeSanctis, 1984; Mahmassani et al., 1993). The employee's

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activity patterns reflect his/her current household responsibility allocation, which influences his/her travel behaviour and eventual decision to telecommute. In activity-based analysis, trip chaining is a manifestation of the trip maker's activity pattern, and may be used to gain insight into this pattern. The frequency and duration of stops for different purposes on the way to work and on the way back home are two essential aspects of trip chaining. Since the idea of telecommuting is to substitute the activity (work) that induces commuting trips, the employee may find it more difficult to telecommute if work is only one of several activities associated with the commuting trip. Household characteristics that affect employee telecommuting adoption include life-cycle, lifestyle, car ownership and number of members with a driver's license. Both household life-cycle (e.g. number of adults or children, especially under 16, in the household) and lifestyle (e.g. household income and spouse's occupation) are primary determinants of household activity (Kitamura, 1988), and are expected to influence employee telecommuting adoption. Additionally, household car ownership and the number of household members with a driver's license affect the activity allocation among household members (Bhat, 1991). Household situational constraints include the number of different telephone lines, possession of fax equipment, subscription to electronic database services and the availability of personal computers. On the one hand, these factors reflect the availability of facilities at home to support or enable telecommuting. On the other hand, they reflect telecommunications adoption at the household level. It is expected that greater availability of telecommunications equipment at home increases the probability that the employee will adopt telecommuting. The trip distance from an employee's residence to the workplace can be used as a proxy of location patterns. Little is found in the literature as to how location patterns affect employee choices of telecommuting. The interaction between household location and telecommuting adoption may be twofold. On the one hand, people who live farther from work are more likely to telecommute because of greater travel cost savings than those who live closer. On the other hand, telecommuting availability has been suggested as a possible factor that encourages employees to live in suburbs and move farther away from their offices, therefore contributing to urban sprawl (Nilles, 1991). Employees' job characteristics affect their decision to telecommute through their own perceptions of, or speculation about, their supervisors' attitudes. An employee who needs to frequently communicate face-to-

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face with customers everyday may think that his/her job is unsuitable for telecommuting. In addition, this employee may feel that his/her supervisor is unlikely to allow him/her to telecommute. Clearly, changes in salary or job compensation resulting from telecommuting may also affect their preferences for telecommuting. The present study shows that most employees would be unlikely to trade-off salary for the opportunity to telecommute (Mahmassani et al., 1993). To implement the telecommuting adoption model, four groups of attributes are included in vector X'n, in equation (3). The first is comprised of the economic implications of the telecommuting program design (Table 1). The second consists of employee personal and household characteristics. The third includes employee job characteristics such as title, amount of time the employee spends in communication with other persons and in using a computer or typewriter on work everyday. Finally, employee commuting attributes, such as travel time and distance from home to the workplace, and number of stops on the way to work and back home are included in the fourth group. Descriptive summary statistics for specified attributes are referred to in Mahmassani et al. (1993). Variables in the first group are different across the seven telecommuting program scenarios for each employee. Other variables pertaining to the individual, such as household, commuting attributes and job characteristics, do not vary across the scenarios for a given employee, but do vary among employees. The combined specification of these four groups of variables allows the latent variable to vary among telecommuting scenarios and the population, and capture the effects of attributes of both the employee and the program design itself. The influence of employee attitudes toward telecommuting is captured in the utility thresholds, as discussed in the following section.

Specification of utility thresholds The linkage between a person's attitudes and behaviour has long been addressed in the psychology literature (Fishbein and Ajen, 1975). Therefore, employee attitudes toward telecommuting are believed to affect his/her preferences for participating in such a program. The influence of these attitudes is reflected in the utility thresholds in the telecommuting choice model. Similar to the specification of the latent variable, these thresholds, presented in equation (2), can be specified as linear functions of measured attitudes, recognizing that the DGOP model formulation

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does not exclude a non linear specification. The linear assumption leads to the following specification of the utility thresholds:

In equation (4), /*/„, S'in, and din respectively denote threshold /, its observable and unobservable components for individual n and scenario t. In addition, for utility threshold / in program scenario t, F\n is a vector of measured attitudes of the employee and a/, is the parameter vector to be estimated. Though the specification in equation (4) is theoretically sound, empirically the sample size may not be large enough to estimate each parameter in the vector a\, t — 1,2, ... ,7 and i = 0, 1, . . . , 4. Further assumptions are made in this study to simplify computation and improve the accuracy of estimates. First, since only relative magnitudes of the utility thresholds matter in ordered-response models, the lowest threshold (i = 0) is set at negative infinity while the highest one (i = 4) is taken as positive infinity. In addition, the mean value of the second threshold (i — 1) is set to zero (McKelvey and Zavoina, 1975). These assumptions lead to the specification of only two systematic components of the utility thresholds (/ = 2, 3) for each decision scenario in the model. Finally, since F\n represents the employee's attitudes toward telecommuting, it is reasonable to assume that F\n is the same across the seven decision scenarios for a given utility threshold. That is, F\n — Frin (t, T = 1,2, ... ,7 and / = 0, 1, ... ,4). These assumptions simplify the specification of the utility thresholds in equation (4) as follows:

The 18 attitudinal questions asked in the employee survey measure seven general employee attitudes (factors) toward telecommuting (Mahmassani et al., 1993). The regression weights of these seven general attitudes on the 18 directly measured attitudes for each employee are specified in the

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F vector in equation (5) to decrease the number of explanatory variables. This specification reduces the estimation effort, minimises possible multicollinearity among the specified variables, and ultimately improves the accuracy of the estimates.

Specification of the variance-covariance structure The simplifying assumptions made regarding the utility thresholds in the previous section lead to the specification of only two systematic components (F2n and F3n) and three disturbances (e1/z, e2n, and e3n) as per equation (5). In addition to the three utility threshold disturbances, there is a random component for the latent variable (u) in each scenario. Consequently, the general variance-covariance structure of the model disturbances is a 28 x 28 matrix, with four elements for each of the seven scenarios. This matrix consists of 16 sub-matrices, as shown in equation (6). For example, ?,uu represents the variances and covariances of the latent variable disturbances in seven scenarios, i.e. 2UM = E(uc, UT) (t l , 2 , . . . , 7 ; r = l , 2 , . . . , 7 ) . Similarly, Eue; includes the covariances of the latent variable and utility threshold /, i.e. 2we. = Cov(V, e[) (t = 1,2, ... ,7; T = 1,2, ... ,7) for i = 1, 2, 3. 2e.C;. corresponds to utility thresholds / and /; that is, Se,.e/ = E(eti, ej) (t = 1, 2, . . . , 7; r = 1, 2, . . . , 7) for / = 1, 2, 3 and / = 1, 2, 3. For simplicity, the individual index n is omitted in equation (6).

.

It is empirically impossible to estimate all parameters in the 28 x 28 matrix (Bunch, 1991). Therefore, some meaningful restrictions are imposed. First, it is assumed that the disturbance of the latent variable or a utility threshold in scenario t is correlated with only disturbances of the same random variable in the other scenarios. That is, both the covariances of

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(w f , ej, t + T) and (e-, ej, t + r and / =£_/) are assumed to be zero (i,j = 1,2,3). Therefore, all off-diagonal submatrices of 2 are diagonal. Second, the covariances of disturbances of two thresholds or the covariances of the disturbances of the latent variable and a threshold are assumed to be the same through the seven scenarios, i.e. Cov(z/, e-) = Cov(w T , ej"), and Cov(e;,ej) = Cov(e J T ,eJ) for i = l,2,3, 7 =1,2, 3, f = l , 2 , . . . , 7 , T = 1,2, . . . , 7 and /=£;'. Third, for diagonal submatrices, the respective variances of the disturbances of each utility threshold and of the latent variable are assumed to be equal for the seven scenarios, and the correlation coefficient between any two scenarios (for a given variable) is also the same. It follows that there are fourteen parameters to be estimated in the variance-covariance matrix, with two in each diagonal submatrix and one in each upper (or lower) triangle submatrix.

Estimation Results The employee survey data described in the third section were used to estimate the employee telecommuting choice model. A special-purpose estimation procedure of the DGOP model was developed and coded by the authors (Yen et al., 1994), along the lines of Lam and Mahmassani (1991) Monte Carlo maximum likelihood estimation procedure for MNP models. Table 2 lists the parameter estimates and their corresponding r-values for the employee choice model. Of the 694 questionnaires received from the employee survey, 545 were usable in model estimation. Estimation results in Table 2 show that the coefficients of all variables capturing the economic implications of the particular telecommuting program appear to be significantly different from zero. As expected, a five percent salary increase (SI5) has a positive influence on the employee's perceived utility or propensity for telecommuting (the latent variable in the model formulation). Therefore, a salary increase will increase the probability that the employee chooses a higher frequency of telecommuting, all else being equal. On the other hand, the effect of salary decrease (SD5 and SD10) is negative, implying that the employee is less likely to choose telecommuting if s/he has to sacrifice part of his/her salary. Similarly, responsibility for additional costs to work from home (ANL, BPC and PART) negatively affects employee preference, with all estimated coefficients being negative. The relative magnitudes of estimated coefficients reveal useful informa-

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Table 2 Estimation results of employee telecommuting choice model Variables Specified in the Latent Variable Constant Economic implications SI5: Change in telecommuter salary (1 if increase 5%; 0 otherwise) SD5: Change in telecommuter salary (1 if decrease 5%; 0 otherwise) SD10: Change in telecommuter salary (1 if decrease 10%; 0 otherwise) ANL: Additional phone costs assumed by employee (1 if need to add a new phone line at home; 0 otherwise) BPC: Additional computer costs assumed by employee (1 if need to buy a personal computer; 0 otherwise) PART: Additional partial costs assumed by employee (1 if need to pay part of the costs; 0 otherwise) Employee personal and household characteristics CHIL16: Number of children under 16 years at home HOMEPC: Number of personal computers at home SKILL: Index of computer proficiency (1 if at least one skill at medium or high level; 0 otherwise) Employee job characteristics HRFACE: Number of hours communicating with coworkers face-to-face per day HRCOMP: Number of hours using a computer on work per day Employee commuting attributes DSTRIP: Distances from home to the workplace, miles STOPS: Average number of stops on the way to work and back home per week Specified in Utility Thresholds Utility threshold 2 Constant FJOBSU: Regression score of employee attitudes on job suitability for telecommuting FFAMIL: Regression score of employee attitudes on telecommuting effect on family FSOCIO: Regression score of employee attitudes toward the importance of social interactions with coworkers

Parameter estimates* -0.190 0.293

(30.0)

—1.311 (-4.9) -1.909 (-9.8) —0.643 (—31.0)

-0.901 (-7.3)

-0.807 (-8.9)

0.142 (3.2) 0.202 (9.6) 0.272 (16.0)

-0.344 (-18.0) 0.175 (17.0)

0.028 (15.0) -0.124 (-14.0)

2.270 -0.436 (-33.0) —0.577 (—31.0) 0.568

(14.0)

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Travel Behaviour Research: Updating the State of Play Table 2 (Continued) Parameter estimates*

Variables Utility threshold 3 Constant FJOBSU: FFAMIL: FSOCIO: Specified in the Variance-Covariance Matrix cru Standard deviation of the disturbance of latent variable yu Correlation coefficient of latent variable disturbance under different scenarios a\ Standard deviation of the disturbance of threshold 1 71 Correlation coefficient of threshold 1 disturbance under different scenarios a2 Standard deviation of the disturbance of threshold 2 72 Correlation coefficient of threshold 2 disturbance under different scenarios 0-3 Standard deviation of the disturbance of threshold 3 y3 Correlation coefficient of threshold 3 disturbance under different scenarios Cov(u, 1) Covariance of disturbances of the latent variable and threshold 1 Cov(u, 2) Covariance of disturbances of the latent variable and threshold 2 Cov(u, 3) Covariance of disturbances of the latent variable and threshold 3 Cov(l, 2) Covariance of disturbances of thresholds and 2 Cov(l, 3) Covariance of disturbances of thresholds and 3 Cov(2, 3) Covariance of disturbances of thresholds and 3 Overall Statistics Number of observations Log likelihood value at zero Log likelihood value at convergence

2.864 -0.318 (-3.4) -0.126 (-2.0) (8.4) 0.820 0.734

(48.0)

0.138

(7.9)

0.982

(49.0)

0.573

(89.0)

0.986

(34.0)

0.096

(17.0)

0.914

(13.0)

0.615

(7.1)

0.206

(27.0)

0.033

(12.0)

0.134

(19.0)

1

0.450

(80.0)

1

0.174

(13.0)

2

0.426

(27.0)

the

545 -5228.7 -3909.0

* Numbers in parentheses are f-values.

tion on employee preference from the standpoint of program design and public policy. For instance, estimated coefficients of SD5 (—1.311) and 815 (0.293) indicate that a salary decrease exerts a stronger effect on employee preference than a comparable increase. Additionally, the

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175

coefficients of both indicator (dummy) variables for 10 percent salary decrease (-1.909) and five percent decrease (—1.311) confirm that the former has a stronger effect. However, the relative coefficient values suggest a nonproportional relationship between the amount of salary decrease and its influence on the latent variable, with a decreasing marginal effect of further salary decrease. Similarly, the significant differences among the coefficients of dummy variables ANL (—0.643), BPC (—0.901), and PART (-0.807) indicate that requiring the telecommuter to buy a personal computer (BPC) is a stronger deterrent to telecommuting than other additional cost items. The coefficients of SD5 and SDIO are statistically less than those of ANL, BPC, and PART, indicating salary sacrifice has a stronger negative effect than having to acquire a new telephone line or a personal computer. This finding has important implications on telecommuting program design for organisations willing to provide such work arrangement. Employee personal and household characteristics significantly affect the choice of telecommuting programs, evidenced by the estimated coefficients of number of children under 16 years (CHIL16), number of personal computers at home (HOMEPC), and computer proficiency level (SKILL). The estimated coefficients of CHIL16 (0.142) and HOMEPC (0.202) indicate that employees with more children under 16 years, or personal computers at home are more likely to adopt telecommuting, all else being equal. Similarly, employees with better computer proficiency exhibit stronger preferences for working from home, confirming the speculation in the literature that computer-related workers are a promising target group for telecommuting. As indicated in the fourth subsection, the number of children under 16 years variable (CHIL16) serves as a proxy of the employee household lifecycle, and HOMEPC is an index of the penetration of telecommunications and information technology at the household level. While computer proficiency is an employee characteristic, it is also an index of the prevailing technology at the individual level. Wider spread of telecommunications and information technology has a positive influence on employee telecommuting adoption. Among employee job characteristics, the longer the employee needs to communicate face-to-face with coworkers (HRFACE, —0.344), the lower the probability s/he will choose a high frequency of telecommuting. On the other hand, the number of hours in which the employee uses a computer on work each day (HRCOMP, 0.175) has a positive effect on the perceived attractiveness of telecommuting. These findings are consistent with widely accepted thinking in the literature that information-related

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jobs are more telecommutable than others, while jobs that require frequent face-to-face communication with other workers are less telecommutable. As pointed out above, the distance from home to the work place and daily commuting time represent proxies for the land use pattern and the transportation system performance that are believed to affect employee telecommuting adoption. Results in Table 2 indicate that only the coefficient of distance (DSTRIP, 0.028) is statistically significant, partly due to correlation between these two attributes. The results, however, confirm findings from other studies that employees who live farther from work are more likely to prefer telecommuting, other things being equal in that they can achieve greater savings from working at home than closer workers. The average number of stops (STOPS) associated with commuting trips is used as a proxy of the employee's activity pattern and his/her share of household duties. The empirical result, with —0.124 as the estimated coefficient of the STOPS variable, is consistent with the a priori speculation presented above that if work is not the only purpose of the commuting trip, the employee is more reluctant to replace the trip by working from home. With respect to the influence on utility thresholds, three employee general attitudes toward working from home are found to be significant: job suitability for telecommuting (FJOBSU), effect of telecommuting on family (FFAMIL), and importance of social interactions with coworkers (FSOCIO). The negative coefficient estimates of FJOBSU (-0.436 and -0.318 for thresholds 2 and 3), and FFAMIL (-0.577 and -0.126), suggest that high scores on those two attitudes will reduce thresholds underlying the telecommuting decision mechanism. The ordered-response model implies that for a fixed latent variable a decrease in thresholds increases the probability that the employee will choose an alternative with higher attractiveness. In other words, all else being equal, employees who feel that their jobs are suitable for telecommuting and that working from home will beneficially affect their relationship with other household members would be more likely to telecommute. In contrast to the first two general attitudes, the effect of the third one (FSOCIO, 0.568 and 0.820) on thresholds is positive, indicating that employees who find social interactions with coworkers important are less likely to adopt a high frequency of working from home. The results in Table 2 also indicate that all estimates of specified standard deviations, correlation coefficients and covariances are statistically significant. In addition, estimated correlation coefficients show that for

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the latent variable or a specific utility threshold i (i = 1, 2, 3) the disturbances in different decision scenarios are positively correlated. While all t values listed in Table 2 are computed to test the null hypothesis that the true parameter of the corresponding variable is zero, all estimates of the correlation coefficients (yu, 71, y2 and y3) are also tested against the hypothesis that the true parameter is equal to one. The results indicate that all four parameters are significantly different from one. The results imply that all correlation coefficients are greater than zero but less than one. Estimation results also show that all covariances between the latent variable and each utility threshold and between any two thresholds are positive, with the latter variable being greater than the former.

Summary and Conclusion The adoption of telecommuting by employees is essential in the potential effectiveness of telecommuting as a travel demand management strategy capable of reducing air pollution and fuel consumption in metropolitan areas. The employee telecommuting adoption process is formulated within the framework of the DGOP model that allows specification of nonconstant thresholds with random elements and a general covariance structure. The substantive aspect of the model specification reflects an activitybased approach to travel behaviour analysis. Attributes that influence the employee's personal and household activity patterns are expected to affect his/her telecommuting adoption and are captured in the model specification as well as tested using the empirical estimation results. Estimation results reveal that employee participation in telecommuting is primarily influenced by five groups of attributes: economic implications of program design, personal and household characteristics, job characteristics, commuting attributes, and attitudes toward telecommuting. Estimated coefficients of program attributes also reveal important information. First, both changes in employee salary and the costs incurred by telecommuters significantly influence employee telecommuting adoption, with the former having a stronger effect. Secondly, the relative coefficient values indicate that the effect of salary decrease is stronger than salary increase, and the marginal effect of salary decrease is decreasing. To the extent that the final adoption of telecommuting depends on the joint decision of employees and employers, a choice model for the latter is necessary to ultimately predict how much telecommuting may be

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adopted. The DGOP model also provides a useful framework for the investigation of employer adoption.

References Bhat, C.R. (1991) Toward a Model of Activity Program Generation. PhD Thesis, Department of Civil Engineering, Northwestern University. Bunch, D.S. (1991) Estimability in the multinomial probit model. Transportation Research 255, 1-12. DeSanctis, G. (1984) Attitudes towards telecommuting: implications for work-at-home programs. Information & Management 7, 133-139. Fishbein, M. and Ajzen, I. (1975) Belief, Attitude, Intention and Behaviour: An Introduction to Theory and Research. Addison-Wesley, New York. Huws, U. (1991) Telework: projections. Futures 23, 19-31. Jones, J.C. (1957-1958) Automation and design (1-5). Design 103, 104, 106, 108, 110. Katz, A.I. (1987) The management, control, and evaluation of a telecommuting project: a case study. Information & Management 13, 179-190. Kitamura, R. (1988) An evaluation of activity-based travel analysis. Transportation 15, 9-34. Kitamura, R., Goulias, K. and Pendyala, R.M. (1990) Telecommuting and travel demand: an impact assessment for state of California telecommute pilot project participants. Research Report UCD-TRG-RR-90-8, Transport Research Group, University of California at Davis. Lam, S.-H. and Mahmassani, H.S. (1991) Multinomial probit model estimation: computational procedures and applications. Preprints Sixth International Conference on Travel Behaviour, Quebec, May 1991, Canada. Mahmassani, H.S., Yen, J.-R., Herman, R. and Sullivan M.A. (1993) Employee attitudes and stated preferences towards telecommuting: an exploratory analysis. Transportation Research Record 1413, 31-41. McKelvey, R.D. and Zavoina, W. (1975) A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology 4, 103-120.

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Nilles, J.M. (1991) Telecommuting and urban sprawl: mitigator or inciter. Transportation 18, 411-432. Pendyala, R.M., Goulias, K.G. and Kitamura, R. (1991) Impact of telecommuting on spatial and temporal patterns of household travel. Transportation 18, 383-409. Salomon, I. and Salomon, M. (1984) Telecommuting: the employees' perspective. Technological Forecasting and Social Change 25, 15-28. Terza, J.V. (1985) Ordinal probit: a generalisation. Communications in Statistics-Theory and Method 14, 1-11. Yap, C.S. and Tng, H. (1990) Factors associated with attitudes towards telecommuting. Information & Management 9, 227-235. Yen, J.-R., Mahmassani, H.S. and Herman, R. (1994) A generalised ordinal probit model of employee participation in telecommuting programs. Working Paper, Center for Transportation Studies, The University of Texas at Austin, USA.

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11 Discrete Logit Modelling Based on Stated Preference Data of the Analytic Hierarchy Process for Parking Choice Shoji Matsumoto and Luperfina E. Rojas

Abstract The analytic hierarchy process (AHP) is a powerful and qualitative method, that can be considered a means of collecting stated preference (SP) data. But, when it comes to its application to a discrete analysis of travel behaviour or attitudes, the AHP has some methodological limitations. This chapter proposes a modelling framework to develop discrete choice models for a group by using SP data of the AHP. The model is applied to parking choice preferences in the central area of Nagaoka in Japan. We find that absolute measurement is a consistent and flexible method to apply the AHP to the analysis of travel behaviour and preferences, and nonlinear relationships can be specified between the grades of AHP and physical attributes. To estimate the discrete logit model with better statistical indicators, we recommend employing the alternatives ranking process, where the choice set of alternatives includes a few alternatives of higher rank. The estimated discrete logit model for parking consists of two parts with good statistical reliability: the capacity of parking places by using revealed preference (RP) data, and other factors such as convenience, facility and economy by using SP data of the AHP. In comparison with the discrete choice model using RP data only, the model using the AHP and RP data can include plural and intangible factors.

Introduction The modelling of travel behaviour has been dominated by discrete choice models based on the random utility theory, and a wide variety of advances has been achieved. Estimation of discrete choice models has relied on revealed preference (RP) data, but there is an increasing interest in the

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use of stated preference (SP) data. The SP data are usually collected by experiments whereby respondents are asked to rank or compare pairwise alternatives (Ortuzar and Willumsen, 1994). On the other hand, the analytic hierarchy process (AHP) is a powerful and qualitative method that allows us to achieve outcomes in a decision problem by reducing judgements to a sequence of paired comparisons throughout a hierarchy (Saaty, 1980, 1990). The AHP is based on the principles of hierarchic structure, where the models are constructed in several different levels of increasing priority, until a top level or objective is reached. Vargas (1990) notes that a useful feature of the AHP is its applicability to the measurement of intangible criteria together with tangible ones through ratio scales. In addition, by breaking a problem down into its constituent parts and sorting them in a logical fashion from the largest, descending in gradual steps, to the smallest, one is able to connect through simple paired comparison judgements from the smallest to the largest. The numerous applications of the AHP which have appeared in recent years corroborate its flexibility for forecasting, planning and multicriteria problem solving (Vargas, 1990). Kinoshita (1986) made a pioneering application of the AHP to discrete travel choice problems, which evaluated the preferences of route choice by using a hierarchy of three levels. Another application to discrete travel choice was made by Banai-Kashani (1989) who reported that both complemented each other well. Although the AHP can be considered a means of collecting SP data, no positive methods of applying them to discrete choice models have been reported. But, when it comes to its application to a discrete analysis of travel behaviour or attitude, the AHP has some methodological limitations. First, the AHP suggests the use of arithmetic or geometric averages to get the utility function of a group. But, the average method neglects the distribution of errors among a group. Second, paired comparisons are performed throughout the hierarchy including the alternatives in the lowest levels, and so the conventional AHP has some inconsistency and inflexibility when introducing and evaluating a newly introduced alternative. The objectives of this chapter are to develop an approach to estimating discrete choice models for a group, by using SP data of the AHP to expand its applicability and flexibility. The model is applied to parking choice preferences in a central area of a local city, Nagaoka in Japan. The study reveals that the estimated discrete logit model consists of two parts with good statistical reliability: the capacity of parking places by using RP data;

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183

and other factors such as convenience, facility and economy by using SP data of the AHP. The chapter is organised as follows: first, we present a combined procedure of the AHP and the discrete logit model. Second, we briefly outline the AHP procedure applied to evaluating parking preferences. Third, disaggregate logit models are estimated and the choice probability of parking is evaluated.

Parking Choice Model We assume that the utility function for choice of parking consists of two parts: the capacity of parking places and other components such as distance, types of parking, parking times and costs. The choice probability of parking can be defined as follows:

where P(J-15) is the probability of choosing parking / given that destination (shopping place) is in zone s; Vj\s is a linear function of utility of parking / where destination is in zone s and C, is the capacity of parking /. Figure 1 shows the modelling framework used to estimate discrete logit models from the AHP and RP data. The first part is the application of the AHP to each individual of a group. The AHP applications are carried out in two phases: hierarchic design and evaluation. For the evaluation phase, paired comparisons are performed to derive priorities for criteria with respect to the goal. Here, Saaty (1990) proposed two types of measurement, relative and absolute. In conventional relative measurement, paired comparisons are performed throughout the hierarchy including the alternatives in the lowest level of the hierarchy. In absolute measurement, paired comparisons are also performed throughout the hierarchy with the exceptions of the alternatives themselves. The level just above the alternatives consists of intensities, or grades, that are refinements of the subcriteria governing the alternatives. One obtains the grades of a subcriterion by comparing pairwise attributes under each subcriterion. After obtaining the weights of criteria and subcriteria, and the grades of the lowest subcriteria, a weighting and summing process yields the overall ranks of alternatives.

184

Travel Behaviour Research: Updating the State of Play I Hierarchy of Structure *

Choice Alternatives

Figure 1 Modelling framework

We adopt this type of absolute measurement since it is useful to estimate a consistent rank for a new alternative in terms of grades of the criteria. In addition, we introduce a grade function to estimate the individual grades of a new alternative. The second part is the estimation of parameters for the discrete logit model. Since the overall ranks of alternatives are evaluated for each individual of a group as a result of the AHP analysis, we can estimate disaggregate logit models and the choice probability of alternatives. To estimate the logit model, we employ alternatives ranking method and decide how to use pooled data. Then, we estimate the parameter a of equation (1) by using additional RP data. The utility function V}- can be estimated by using SP data of the AHP, and the parameters of capacity by using RP data.

Discrete Logic Modelling Based on Stated Preferences Data

185

Data The feasibility of our approach had been demonstrated in the CBD of Nagaoka, which is a local core city with a population of 190,000 in the Niigata prefecture. Figure 2 shows 20 parking places and 11 shopping centres located in the study area. We choose eight parking places in the CBD, which have a variety of differences in attributes and capacity as choice alternatives for the logit model estimation. Table 1 shows the capacity, type and price of the eight parking places chosen. A questionnaire survey for parking preference was conducted in the central area of Nagaoka on a Sunday in December 1991. The questionnaire was structured so that an individual could evaluate quantitatively his/her preference by paired comparisons on a scale of nine distinctions (the values 4 , 3 , 2 , 1,0, 1,2,3,4). We gave the questionnaire to shopping customers at several parking places and asked them to answer and mail it back to us. One thousand questionnaires were distributed, of

Parking place Big store

Figure 2 Parking place and big stores in the CBD of Nagoaka

186

Travel Behaviour Research: Updating the State of Play Table 1 Parking alternatives for the logit model

No.

Parking name

Capacity (cars)

Type

Fare (yen/hr)

1 2 3 4 5 6 7 8

Nagaoka Jonai parking ticket Sakanoue parking Ekimae rittai parking Nagaoka ekimae Otegichi Iwafuchi rittai Hotel New Otani Ito-Yokado Marudai Nagaoka shie Oteguchi parking

14 22 31 56 62 85 418 431

B B A B C B A A

320 250 320 200 320 360 400 300

A: Multistory parking lots; B: Surface parking places; and C: Mechanical parking lots.

which 369 were answered effectively and are used in the analysis. Respondents accounted for 61.5 percent male and 38.5 percent female, with 87 percent between 20-40 years old.

Analysis by the AHP To evaluate alternatives by using the AHP, we first establish the hierarchy for analysis, which identifies the goal to evaluate parking preferences in the CBD zones of a local city, and then the factors or attributes to be included in the analysis. The three-level structure in Fig. 3 is adopted for parking preference analysis. The factors which constitute the first level of the hierarchy are identified as convenience, facility (easiness to park a car) and economy. The capacity of a parking place might be an important factor for parking choice, but equation (1) shows that the size variable of capacity is excluded from the AHP hierarchy. For the second level, distance from parking to destination and waiting time are identified as the subcriteria of convenience; parking types and signs are identified as the subcriteria for facility; and fare and discounts are identified as the subcriteria for economy. The third level consists of grades, or intensities, of attributes which are refinements of the subcriteria of the upper level. For the third level, paired comparisons are also performed, but grades are treated as absolute values. The lowest level of the hierarchy is defined as the choice alternatives

Parking preference

LEVEL I

LEVEL

LEVEL HI 400m

200m

100m

5 min

with

0 min

without

¥200

¥320

¥400

ALTERNATIVES Parking 2

Parking 3

Parking 4

Parking 5

Parking 6

Parking 7

Figure 3 Hierarchy for parking preference 00

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Travel Behaviour Research: Updating the State of Play

of parking places. The alternatives are not compared pairwise, but simply rated as to what attribute they fall under each subcriteria of the second level. The weights of the first and second level, and the grades of the third level, were obtained by computing the Eigen values of the pairwise comparison matrices for each case and individual. The sample average of weights and grades, shown in Table 2, were obtained by computing the geometric means of 369 samples. The relative composite weights for the second level can be obtained by multiplying the weights of the first and second levels. Table 2 Weights and grades of the AHP for parking Level Convenience

Facility

Economy

Weights 0.444

0.207

0.348

Weights

Level

Grades

Distance to destination

0.545

400m 200m 100m

0.060 0.246 0.694

Waiting time

0.455

Omin 5 min

0.794 0.206

Type

0.739

Signs

0.261

Multi-storey lots Surface places Mechanical lots With Without

0.591 0.244 0.165 0.761 0.239

Fare

0.424

Discount

0.576

400 Yen 320 Yen 200 Yen With Without

0.061 0.189 0.750 0.837 0.163

Level

We assume nonlinear relationships between the attributes (physical values) and grades of the third level to generalise absolute measurement of the AHP systems. For example, their aggregate relationships were assumed to have the form of equation (2). The coefficient of determination for equation (2) was estimated to range from 0.942-0.815. (2)

where Y are the grades of the third level, /30 and j8i are coefficients and X are the physical values of attributes.

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189

Estimation of Choice Probabilities

Estimation of discrete logit model using the AHP data The total scores for parking places for an individual were obtained by using the weighting and summing procedure of the AHP. Here we computed the total scores where Daiei shopping centre was the destination for shopping trips. Therefore, the distance to the destination was the distance from a parking place to the shopping centre. To estimate the disaggregate logit model, we employed an alternatives ranking process, which means that an individual chooses an alternative with the highest total score over all the other alternatives. Table 3 shows the estimation results of the ranking process models. Model M-l is where an individual chooses a parking place with a highest total score (alternative ranked first) over the seven alternative parking places. Model M-2 is a choice of a parking place (alternative ranked second) over six alternatives after the first ranked alternatives are removed. The alternative ranking processes are successively repeated up to

Table 3 Estimation results of ranking process models Variables

Distance Waiting time Type Signs Fare Discount

L(0) P2 % right Sample No. of cases

Models M-7

M-l

M-2

M-3

M-4

M-5

3.786 (11.19) 3.305 (5.549) 2.611 (8.535) 1.094 (2.367) 2.403 (2.897) 2.941 (10.90)

3.102 (10.16) 2.605 (4.869) 2.455 (8.571) 0.972 (2.533) 2.102 (3.823) 2.832 (9.592)

2.921 (8.185) 2.187 (5.089) 2.127 (9.714) 1.162 (2.186) 1.865 (3.211) 2.725 (10.89)

2.876 (9.376) 2.219 (4.042) 2.278 (4.491) 1.496 (2.052) 1.756 (2.454) 2.349 (9.274)

2.437 (7.952) 2.071 (3.830) 2.345 (6.193) 1.585 (2.339) 1.512 (4.358) 2.014 (10.84)

2.022 (8.633) 1.890 (3.433) 1.841 (7.605) 1.270 (2.648) 1.960 (3.734) 1.926 (9.703)

1.868 (6.092) 1.630 (3.360) 2.118 (4.331) 1.375 (3.192) 1.456 (4.213) 1.714 (9.920)

-459.7 0.4009 58.27 369 2952

-540.5 0.3673 58.96 369 2583

-391.7 0.4076 63.82 369 2214

-469.7 0.3090 58.06 369 1845

-405.0 0.3873 62.15 369 1476

-261.3 0.3479 72.76 369 1107

-174.2 0.3177 78.18 369 738

/-statistics in parentheses.

M-6

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Travel Behaviour Research: Updating the State of Play

the last model M-7, where a choice of parking is made among two alternative parking places. The goodness-of-fit measures, such as the log likelihood at convergence, the log likelihood ratios and the percentage of correctly predicted (percent right) gave acceptable values for all models. And, as for the f-statistics, the null hypothesis that each of the parameter estimates was equal to zero was rejected at the 90 percent level of confidence. Also, the parameter estimates had the expected signs. Figure 4 shows the successive changes of parameter estimates of the seven models. The variety of parameter estimates among six attributes decrease from M-l to M-7, and the estimates converge at a certain value. This means that model M-l represents preferences for parking most distinctively and model M-7 does the least. It is also observed that the three models, M-l, M-2 and M-3, present some similarities.

M-1

M-2

M-3

M-4

M-5

M-6

M-7

Models [

Distance

Waiting time

Type

Signs

Fare

Discount]

Figure 4 Parameter estimates of ranking process This fact led us to proceed to a second stage of model estimation using pooled data. Three models were estimated; the first used the pooled data of models M-l, M-2 and M-3 (Pool 1-3), which is equivalent to a model

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191

of choosing options ranked first, second and third. The second used the pooled data of models M-l to M-4 (Pool 1-4), and the third used the pooled data of models M-l to M-7 (Pool 1-7). The results are shown in Table 4. The goodness-of-fit measures of all models are good, and model Pool 1-3 is slightly better than the rest. Table 4 Estimation results of pooled data models Variables

Pool 1-3

Pool 1-4

Pool 1-7

Distance

3.733 (11.35) 2.893 (10.88) 2.434 (13.75) 1.107 (5.333) 2.194 (12.76) 2.367 (8.780)

3.236 (13.54) 2.113 (10.40) 2.633 (12.232) 1.304 (8.025) 2.116 (14.15) 2.385 (9.630)

2.986 (12.14) 2.464 (9.762) 2.233 (8.425) 1.210 (3.205) 1.846 (9.314) 2.341 (11.45)

-1401 0.3786 57.42 1107

-1891 0.3201 55.93 1476

-2785 0.3245 56.12 2583

Waiting time Type of parking Signs Fare Discount 7" / /)\ JL^t \s )

2

P % right Sample size

Test for equality of coefficients (versus model M-l) Degrees of freedom 12 18 Test statistics 58.80 18.80 28.90 21.03 X2 0.05

36 168.41 47.19

The test for equality of the coefficient vectors across two or more data sets can be achieved by comparing the likelihood values of the pooled model with that of the separate models (Ben-Akiva et al., 1989). For example, the likelihood ratio test statistics are computed by comparing the log-likelihood of model Pool 1-3 with that of model M-l. The likelihood ratio test for model Pool 1-3, shown in Table 4, does not reject the null hypothesis that the coefficients are equal between the two models,

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Travel Behaviour Research: Updating the State of Play

while the ratio tests for models Pool 1-4 and Pool 1-7 reject the null hypothesis. This means that the parameter estimates of Pool 1-3 are not significantly different from those of M-1, but are different from those of Pool 1-4 and Pool 1-7. The choice probabilities of parking obtained from the various data sets are shown in Fig. 5. The model for Pool 1-7 and the AHP method present similar patterns with little variety of probability among alternatives. It must be noted that the AHP method uses geometric average to get the utility function of a group. The models M-1 and Pool 1-3 do not present significant differences of probability among alternatives, and have quite different patterns from the other two models. This suggests that Fig. 5 supports the results of the above-mentioned test for equality of coefficients. We select the model Pool 1-3 as the best model that does not represent average preference for a group, but specific preference of high priority for a group.

OL

15 10

4 5 No.of parkings M1

Pooled 1-3

Pooled 1-7

Figure 5 Choice probabilities of parking places

AHP

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193

Estimation by using RP data Finally, we estimate the parameter a of equation (1) by using additional RP data and adopting model Pool 1-3 for the part of utility function V}. The RP data were the distribution matrix of destination zones (five zones) and parking places (11 places), which were obtained from the questionnaire survey carried out in 1989 for householders living in Nagaoka. The sample size was 426. By using the least-square method, the coefficient a of parking capacity resulted in 0.401 with a determination coefficient of 0.94. This is the final result of estimating the choice probability of equation (1). We developed the discrete logit model of parking choice by using RP data obtained only from a survey in 1989 (Rojas et al., 1993). Table 5 shows one of the best parking choice models we have estimated. This model can predict the distribution matrix of destination zones and parking places (5 x 11) with a determination coefficient equal to 0.97. The models from the AHP and RP data (AHP model), and from the RP data only (RP model), yield almost the same statistical results. It is more time and is more costly to estimate the AHP than the RP model. But, the AHP model can specify more intangible factors than the RP model, and introduce nonlinearity and flexibility into discrete choice models.

Table 5 Logit model using RP data Variables Distance from destination to parking Parking fare Parking location dummy (LOCDM) In (CAPAC) L(0) p2 % right Sample size

RP Model —0.0152 -0.0024 0.4643 0.6651

(—10.78) (-3.282) (3.384) (5.537)

-384.1 0.2981 56.30 426

^-statistics in parentheses; LOCDM = 1 on arterial roads; CAPAC: parking capacity.

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Conclusions We have proposed a modelling framework to estimate discrete choice models for a group by using SP data of the AHP. The approach was applied to parking preferences in a central area of a local city, and we developed a discrete logit model of parking places, which uses both types of SP and RP data. The main results of the chapter are as follows: • The AHP has two types of measurement, relative and absolute. We revealed that absolute measurement is a consistent and flexible method to apply the AHP to the analysis of travel behaviour and preferences, since it makes it possible to estimate a consistent total score for a newly introduced alternative. In addition, we could specify nonlinear relationships between the grades of AHP and the physical attributes. • We have proposed a useful and promising approach that combines the AHP and a discrete choice model. To estimate the discrete logit model with better statistical indicators by using the AHP data, we recommend employing the alternatives ranking process, where the choice set of alternatives includes a few alternatives of higher rank. It must be noted that the geometric averaging method of AHP tends to make vague the preference of a group. • We have estimated a discrete choice model for parking consisting of two parts: the capacity of parking places by using RP data; and other factors such as convenience, facility and economy by using SP data of the AHP. In comparison with the discrete choice model only using RP data, the model using the AHP and RP data can include plural and intangible factors with almost the same statistical reliability.

References Banai-Kashani, R. (1989) Discrete mode-choice analysis of urban travel demand by the Analytic Hierarchy Process. Transportation 16, 81-96. Ben-Akiva, M., Morikawa, T. and Shiroishi, F. (1989) Analysis of the reliability of stated preference data in estimating mode choice models. In World Conference on Transport Research (eds.), Transport Policy,

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Management and Technology Towards 2001. Western Periodicals Co., Ventura, CA. Kinoshita, E. (1986) Analysis of travel route-choice based on the Analytic Hierarchy Process. Transport and Economy 46, 64-73 (in Japanese). Ortuzar, J. de D. and Willumsen, L.G. (1994) Modelling Transport. John Wiley & Sons, Chichester. Rojas, L., Matsumoto, S. and Yoshida, A. (1993) A hierarchical model for the full range choice of shopping travel behaviour. Journal of Infrastructure Planning and Management of JSCE 470/IV-20, 195-205. Saaty, T.L. (1980) The Analytic Hierarchy Process. McGraw Hill, New York. Saaty, T.L. (1990) How to make a decision: the Analytic Hierarchy Process. European Journal of Operations Research 48, 9-26. Vargas, L.G. (1990) An overview of the Analytic Hierarchy Process and its applications. European Journal of Operations Research 48, 2-8.

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Part III Travel Patterns

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12

Estimation of Origin-Destination Matrices Using Traffic Counts: An Application to Stockholm, Sweden Torgil Abrahamsson

Abstract The estimation or updating of trip matrices using traffic counts is an important problem that has received much attention during recent years. It has been argued that one major advantage of the descent-based approach is its computational tractability. Descent-based approaches solve a so-called bilevel formulation of the trip matrix-estimation problem. The upperlevel problem estimates the trip matrix while the lower-level problem is concerned with an assignment problem. In busy traffic regions, like Stockholm, it is realistic to take congestion into account. Route choices are assumed to follow Wardrop's (1952) user-equilibrium principle and, hence, methods based on equilibrium assignment of traffic are needed. In this chapter, we present applications of descent-based approaches to estimation problems of the Stockholm region using travel and network data from the year 1986. The Stockholm region is represented by a network consisting of 417 nodes and 964 road links with up to 2100 origin-destination pairs having a nonzero demand for traffic. The models are applied to the peak-hour period. The course of convergence is analysed and results compared. The results favour an approximate gradient approach, because of an effective and robust solution to the bilevel formulation provided. From the application of a method using second-order information, the uniqueness of the estimated trip matrix is not assured and, hence, possibly indicates multiple solutions.

Introduction The number of travellers that commute or the amount of freight shipped between different zones of a region, is contained in the Origin-Destination

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(OD) matrix. The current OD matrix can be "projected" by using recent traffic counts on links and an old OD matrix. Using this technique, the difficult and often costly process of direct measurements and interviews or surveys is avoided and a reasonable estimate obtained. In this study, we apply two approaches with four different solution methods to OD matrix-estimation problems in Stockholm and compare the results and computational demands. Different approaches to the OD matrixestimation problem were reviewed by Abrahamsson (1996). Investigating the relative performance of the four methods on a medium-sized congested network is the main purpose of this study. The collection of traffic count data on links is performed both routinely and accurately. These link volumes result from the assignment of the OD matrix to the network, implying that the demand for travel between zones (the OD matrix) is allocated to possible routes connecting the zones. Every route traverses a number of links and thus, the assignment of the OD matrix results in traffic volumes on each transportation link. The assignment procedure can be represented by an implicit assignment function relating the OD matrix and the traffic volumes. The OD matrixestimation problem is often referred to as the "inverse" assignment problem: determine an OD matrix that reproduces the observed traffic counts after assignment to the transportation network. Thus, the OD matrix-estimation problem seeks the relation between two sources of information about the transportation pattern, the OD matrix and data on traffic volumes of links. Normally there are many different OD matrices that reproduce a set of observed traffic counts. This is because the number of equations (links with traffic counts collected) is often much smaller than the number variables (OD pairs; elements in the OD matrix). Furthermore, the traffic counts are normally available only for a subset of all transportation links. The OD matrix-estimation problem thus needs additional assumptions, and/or information, to be well posed and possible to solve. One such source of information is the "target" OD matrix, normally available from an earlier period. We model the OD matrix-estimation problem with a network representation of the transport system. The transport system connects the different zones of the region where the traffic originates and terminates. In the congested network case, the OD matrix-estimation problem has a bilevel structure. The upper-level problem estimates the OD matrix taking the travel behaviour (traffic assignment) into account. At the lower level, the OD matrix is given and the problem is to determine the assignment pattern and link flows. The relation between the (estimated) link volumes and the

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(estimated) OD matrix appears in the lower-level problem of the bilevel formulation. In the congested case, this lower-level problem has the form of an equilibrium assignment problem. The route choices comply with equilibrium assignment when a traveller (user) cannot achieve a lower cost for travel by switching to another route. Following the survey by Abrahamsson (1996), we study three methods utilising "descent-based" solution techniques of the bilevel optimisation problem, and one method relying on a combined model for traffic planning. Gradient-based methods have been suggested by Spiess (1990) and Drissi-Kai'touni and Lundgren (1992). In applications, the upper-level problems minimise the sum of the squared-Euclidean distance between estimated and observed traffic volumes on links. The estimation results of the descent-based methods are contrasted with those from a combined trip distribution and route assignment model being an extension of a model by Fisk and Boyce (1983). The medium-size applications of this study investigate two OD matrixestimation problems from Stockholm. How should one compare and evaluate the results of the different methods? Are the calculations of a method accurate and efficient, and does the method solve the correct problem? Here, first, the distances between estimated and observed traffic counts and matrices are important. Second, the efficiency in terms of CPU-time, and memory space needed, are observed. It should be noted that the two approaches rely on different assumptions and, to some extent, solve different formulations of the problem of estimating an OD matrix using traffic counts. The descent-based methods consider the target OD matrix as an initial solution to the estimation problem and adjust this matrix iteratively to better reproduce the traffic counts. The combined model does not, on the other hand, reproduce the traffic counts but focuses on reproducing the observed travel cost. If the observed traffic pattern (traffic counts) is of the user-equilibrium type, Fisk (1989) showed an equivalence between the solutions to a combined model and to OD matrix-estimation problems with a bilevel structure. Following a more formal definition of the problem in the second section; a short description of the selected methods follows in the third section; and some application results are shown in the fourth section. For a comprehensive overview on approaches to estimating OD matrices, and related solution methods, we refer to the survey by Abrahamsson (1996).

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Problem Specification The geography of the region is modelled with a network representation. A transport system connects the zones (represented by centroids) where traffic originates and terminates. The directed transport links (A) of the network, each one connecting two modes, have traffic count data (v) available for a specific period (here the peak hour) and for a subset of the links (A}, traffic count data (v) available. From an earlier time a target (prior) OD matrix (g) is available. The estimation problem in focus in this study is equivalent to finding an OD matrix (g) that, when assigned to the transportation network, reproduces the observed traffic count data (v) taking prior information into account. In the first equilibrium problem studied below the observed traffic counts are internally consistent and reproduced by the solution of descent-based methods. The distorted problem is less well behaved and more demanding computationally but also interesting due to inconsistencies that may occur in reality for several reasons. The choice of assignment technique is a crucial part in the estimation of an OD matrix. The assignment procedure determines the use of possible route(s) for trips between zone pairs ij. The assignment matrix P contains the proportion of trips between zones i and j that uses link a, p"jE. [0, 1]. For a given link a, the sum of all interzonal flows traversing it is the link volume, va. The fundamental equations that relate the link volumes to the OD-flows may now be stated as

where R is the car occupancy factor and assumed to equal 1.25. The matrix P may depend on v and should then be correspondingly denoted P(v). There are basically two assumptions about route assignment depending on the role of congestion. The case of congestion corresponds to an endogenous determination of the /?* subject to v and equilibrium assignment of traffic while, in the case of no congestion, an exogenous computation of p^ is possible and the so-called proportional assignment valid. Various approaches to estimating the OD matrix using traffic counts result in different optimisation problems. A first category uses trafficmodelling concepts and a second category employs statistical-inference techniques. The former includes the "minimum-information" ("entropy

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maximising") model and the combined model for traffic planning. Snickars and Weibull (1977) contains a theoretical background of the minimuminformation model, and Fisk and Boyce (1983) proposes a combined model. A combined model for traffic planning integrates the trip distribution and route assignment subproblems, solving them simultaneously. Among statistical approaches, maximum likelihood (ML), generalised least-squares (GLS) or Bayesian inference, rely on the assumptions that the observed traffic counts and the observed (sample) OD matrix are generated by certain probability distributions. One obtains the estimated OD matrix from estimates of the parameters characterising the probability distributions. Methods that solve GLS problems have also been suggested that do not rely on any statistical assumptions (see e.g. Carey et al., 1981). The implementations of the descent-based methods (Spiess, 1990; DrissiKai'touni and Lundgren, 1992), both solve GLS problems. With observed link volumes v on a subset of the links A and an assignment matrix P(v), the OD matrix g that reproduces the observed traffic counts can be determined by solving the equation (1) system. Normally this equation system is highly under-specified: there are many more elements in the OD matrix g than links for which traffic counts are collected. Thus additional data (prior information) and/or assumptions about the travel behaviour are needed to find a unique OD matrix that solves the equation (1) system. Prior information on the OD matrix may be reflected in the target OD matrix. In the implementations of the descent-based solution techniques (see Spiess, 1990; Drissi-Kaitouni and Lundgren, 1992), an old OD matrix g is taken as an initial solution to the overall problem. As noted by Spiess (1990), the quality of the target OD matrix g is critical for the implementations of these descent-based solution techniques. The matrix g will be adjusted so that the observed traffic counts are better reproduced but the structure in g will persist. The matrix g is used in the combined model of this study as an a priori solution to the problem of finding an entropy maximising OD matrix. In both approaches, the problem of finding an OD matrix close to a target OD matrix can potentially be stated as minimising a function Fi(g,g). The estimated (projected) link volumes might not reproduce the observed link volumes exactly. One reason might be that the observed link volumes may not be in user-equilibrium, although equilibrium assignment is assumed in the estimation procedure. The question of whether, or not, the observed link volumes are consistent with a user-equilibrium flow pattern is not easy to answer and further complicates the estimation problem. Taking this into account, estimating an OD matrix that produces

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"small" differences between the estimated link flows v, and the observed link flows v, is often a realistic ambition. In the descent-based methods, this is also the explicit objective. For the combined model of this study, the relation between v and v appears as a constraint on the total growth of traffic and in a maximum-likelihood equation forces the estimated and observed total vehicle miles of travel to be equal. To sum up, we formulate the relation between the estimated and observed traffic volumes as a criterion F2(v, v) to be minimised subject to the assignment constraints. The two OD matrix-estimation approaches have different foundations but can both be, in general terms, formulated as optimisation problems:

Determine the demand for traffic between zones of the region, that is, the OD matrix g solving the program: subject to v = assign(g)

where g is the "target" OD matrix, and v the observed traffic counts with FI and F2 being some "distance" measures. The equilibrium-based assignment of g to the transportation network is denoted assign (g). The most common FI is of the "minimum-information" (entropy) type and F2 is usually a distance measure of the Euclidean type. In the applications of the descent-based methods of both Spiess (1990) and Drissi-Kai'touni and Lundgren (1992), only traffic counts are considered in the objective function of equation (2). This is also the case in the applications below using the descent-based methods. We interpret this as yi = 0. In the combined model, no explicit use of the relation between the individual traffic counts in v and v appears with the interpretation that 72 = 0. Here FI is of the minimum-information type.

The OD Matrix Estimation Problem: Two Approaches The two approaches are described very briefly below, and for a more complete description we refer to Abrahamsson (1996, chapter 4), or to the original papers.

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Descent-based solution techniques The procedures considered by both Spiess (1990) and Drissi-Kaitouni and Lundgren (1992), use descent-based solution techniques for solving the optimisation problem in equation (2). Here the bilevel structure of equation (2) with the estimation problem that determines g on the upperlevel, and the assignment problem concerned with link volumes v on the lower level, are exploited. The related solution algorithms have been applied to large city networks. All solution methods that aim at solving realistic sizes of the bilevel formulation are heuristic, because currently available exact methods for solving the general bilevel problem are only applicable to small problems. Many papers on bilevel formulations of the OD matrix-estimation problem only report tests on small-scale networks (see for example, LeBlanc and Farhangian, 1982, or Fisk, 1988). In the descent-based solution techniques considered here, the target OD matrix is taken as an initial solution to the OD matrix-estimation problem. The target OD matrix is "adjusted", or "changed", to reproduce the traffic counts by iteratively calculating directions based on the gradient of the objective function F. The link volumes v are implicit functions of the OD matrix g and obtained by the assignment procedure, v(g) = assign(g). In a theoretical part, the methods of Drissi-Kaitouni and Lundgren (1992) consider travel matrices in the objective function F. In applications all the descent-based methods only take the link volume part of the objective of equation (2) into account and the objective function is,

Except for the nonnegativity constraints on g this problem is unconstrained. Drissi-Kaitouni and Lundgren (1992) propose a general descent algorithm for solving equation (2). The search directions are projections of the gradient of the objective function on the nonnegative octant. The main difficulty with solving equation (2) with F, as in equation (3), is to compute the Jacobian J = {dva/dg,7}. Drissi-Kaitouni and Lundgren (1992) show how this matrix can be obtained by solving a set of quadratic problems. The gradient, VF(g), is then formed after some additional calculations. This results in the second method of the applications below. The first method is due to Spiess (1990) and here the Jacobian J is determined on the assumption that proportional assignment holds locally within any

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one iteration. In this case, the derivatives of the Jacobian are derived as sums over path probabilities, assumed to be locally constant. The search directions can be further improved by using second-order information. The gradients may be scaled by the inverse of the Hessian matrix of F, the matrix of second-order derivatives of F. Drissi-Kai'touni and Lundgren (1992) show how the diagonal elements of the Hessian can be calculated in a way similar to the procedure for calculating the gradient and, hence, be efficiently performed. Using this second-order information in the Hessian matrix of Fis equivalent to the third method in the applications below. As observed, the first method is obtained as one instance of the second method of Drissi-Kai'touni and Lundgren (1992). Thus, the "research" code developed for the computation of their methods can also be used as an implementation of the gradient method of Spiess (1990). The CPUtime required for the computations with the commercial code are substantially larger due to the reoptimisation capabilities of the research code. This difference holds even though the codes were run on different computer systems. In the research code, the assignment problems are solved using path-flow variables, making it possible to obtain the solution for any equilibrium problem (for each step length A in the line search) by reoptimisation of the previous solution. Together with a predetermined value used as the stopping criteria, an algorithm is formed. The stopping criteria should ideally also result in a convergence criterion fulfilled. In practice, it is not possible to give such a general guarantee. In our applications, the value is set by the modeller and based on experiences from solving the estimation problem. Below, a number of different values are studied resulting in various degrees of reproduction of the observed counts. The differences between the methods relate to how exact the gradient of F is determined, and how the linesearch step that improves consecutive solutions is executed. Spiess (1990) showed how the gradient-based method can be implemented using the standard version of the "commercial" EMME/2 (1990) transportation planning package. This method is also implemented as a macro DEMADJ in EMME/2.

Combined trip distribution and route assignment An alternative way of estimating the OD matrix is through the calibration of a combined distribution and assignment model. The model is extended to also consider the target OD matrix by using a "minimum-information"

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(entropy) term. To allow for a total growth in the demand for traffic, a corresponding growth factor (a) is derived from the relation between the sums of flows related to the observed traffic counts, and the traffic volumes obtained from an equilibrium assignment of the target matrix. The combined model is formulated to minimise the sum of integrals of cost of travel on links, and an "entropy" term concerned with OD flow variables. To see this model in the general form given above, we interpret the problem as a single-level reformulation of equation (2). The parameter y2 now equals zero. In the assignment problem of the constraints in equation (2), the sum of integrals of cost of travel on links, plays an important role in giving user-optimal link flows. The solution to the combined model can be obtained by forming the Lagrangian of the problem and by setting the first-order derivatives of the Lagrangian with respect to route and OD flow variables equal to zero. For this solution and a full description of the algorithmic steps, we refer to Abrahamsson and Lundqvist (1997). One of the first algorithms for combined trip distribution and assignment was proposed by Evans (1973). She employed a partial linearisation technique and analysed the convergence of the algorithm. We use the partial linearisation technique as implemented by Boyce et al. (1983).

Applications to Stockholm In the applications, Stockholm is represented by 46 zones connected by a road network with 964 road links and 417 nodes (including zone centroids). A target OD matrix is available for 1986. An equilibrium assignment of the target matrix for 1986 results in flow values on links. The descentbased methods take these values as the initial link flow estimates, and the combined model uses the values to estimate the growth in demand for traffic (a) and the total travel cost. The Office of Regional Planning and Urban Transportation at the Stockholm County Council provided the data for the applications. A future scenario has been defined in terms of a proposed regional structure in the year 2020 (road network and land use pattern), and a related OD matrix has been determined in which the total number of trips has increased by about 35 percent as compared to the base year with location of observed traffic counts. The OD matrix for this future scenario is very different from the target OD matrix for 1986. A "goal" OD matrix g (approximately representing the year 1990) is obtained by adding a

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fraction (0.1) of the change (growth) in travel demand between 1986 and 2020 to the OD matrix for 1986. In a first equilibrium problem, the observed traffic counts v, for a subset of links a e A, are defined as: va = va(g), with the link flows va(g) obtained from an equilibrium assignment of the goal OD matrix g. This means that the objective function of any descent-based method relying on equilibrium assignment should be zero at the exact optimum. In the computations, we used stopping criteria implying that the objective function should be less than 10, 5, 2 and 1 percent of the initial value of the objective function. In a second distorted problem, the observed traffic counts of the first problem are scaled with random factors in the interval (0.9, 1.1), and may not be consistent with any equilibrium assignment. Here the results focus on the 10, 5 and 2 percent criteria. The links for which counts are assumed to be observed are important road links of Stockholm, see Fig. 1. These 54 links make up about five percent of the total number of links. The three descent-based methods, the first by Spiess (1990) and the second and third by Drissi-Kai'touni and Lundgren (1992), are applied to these two OD matrix-estimation problems. Also, the results from the combined model are computed below. One important parameter in OD matrix estimation, the requirement for convergence in the traffic assignment sub-problems, is that the relative gap in the objective function of the traffic assignment problem should be less than 0.5 percent. The evaluation measures include the number of global iterations, the (minimum-information and the squared-Euclidean) distances between the estimated OD matrix and the target and goal OD matrices, the degree of reproduction of the observed link volumes and the CPU time required for the computations. Also, the elements with maximal deviation from the target and goal matrices are reported. For all figures describing these measures we refer to Abrahamsson (1996). A small distance to the target OD matrix implies that there exist solutions close to the target OD matrix, but also a reluctance of the method to allow for deviations from the target matrix. Thus, a minimal distance to the target matrix is not unquestionably preferable. A small distance to the goal OD matrix should be preferable (at least in the first equilibrium problem), since in our case this is the OD matrix that generated the observed counts.

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Figure 1 Road network for the Stockholm region with location of observed traffic counts

Applications of descent-based methods First equilibrium OD matrix-estimation problem The value of the objective function (sum of squares of link flow deviations), see equation (3), is plotted against the number of global iterations in Fig. 2. As expected, the observed traffic counts are reproduced if no

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I

Figure 2 Objective function (3) against the number of iterations for the first (series 1), second (series 2) and third (series 3) methods (first problem)

internal contradiction is present. Figure 2 shows that the estimated link volumes can be considered to reproduce the observed volumes after about 25 iterations for the first two methods, and after about 15 iterations for the third method. The links that have maximal difference between estimated and observed volumes are shown in Table 1. In the later parts of the iterative estimation procedure, the value of the objective function does not decrease monotonously. This may be interpreted as the presence of local optima encountered by the third method. Another explanation for

Table 1 Estimated and observed traffic volumes, link with maximal difference (estimated volume/observed volume (global iteration no., link number)) (first problem) Converge level (%) 10 5 2 1

First method 1059/1146 427/482 441/482 462/482

(13, (20, (27, (47,

Second method 182) 678) 678) 678)

1069/1146 418/482 443/482 454/482

(13, (17, (27, (34,

182) 678) 678) 678)

Third method 421/482 442/482 2210/2180 1583/1554

(6, 678) (7, 678) (17, 324) (95, 408)

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the non-monotonous behaviour of the objective function lies in the limited exactness in other steps of the algorithm. At convergence levels between 10 and 2 percent, the smallest maximal deviation between estimated and observed link volumes appears to be estimated by the third method (see Table 1). Here the results of the second method are similar to those of the first. Differences between these two methods appear after about 25 iterations, where the value of the objective function decreases more rapidly for the second method. The (minimum-information) distances between the estimated matrix, and the target and goal matrices, are shown for the various methods and convergence levels in Table 2. The differences between the third method, and the two other descent-based methods, are obvious already at the 10 percent convergence level, where the third method results in larger distance to the target matrix. This indicates a considerable difference in structure between the third solution and the solutions of the other two methods. Table 2 Minimum-information distance between the estimated and target OD matrices and the goal OD matrix (first problem) Convergence level (%)

10 5 2 1

First method 0.00030 0.00048 0.00063 0.00090

0.0013 0.0014 0.0015 0.0017

Second method

Third method

0.00032 0.00045 0.00065 0.00073

0.0025 0.0039 0.0061 0.0230

0.0013 0.0014 0.0015 0.0015

0.0035 0.0048 0.0070 0.0240

The third method performs extremely well during the first 8-10 iterations. In the later parts of the iterative estimation procedure, the objective function does not decrease monotonously, and the one percent convergence level requires 95 iterations for fulfilment. There are two parts in the solution procedure that may cause this failure to converge successfully. The first is the accuracy used in the traffic assignment (TA) subproblems. As an alternative to the base case accuracy of 0.5 percent, a relative gap of 0.25 percent has also been studied, see Abrahamsson (1996). Second, the line-search step involved has been subject to improvements. Even with higher accuracy in the TA subproblems, and with attempts to improve the line-search step, complete convergence was not obtained. This may

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be interpreted as local minima encountered by the third method not being at a low convergence level. If this interpretation is correct, the difficulties of the bilevel formulation are even more stressed. These problems show important practical difficulties in the application of the third method. The values of the minimum-information distances of the one percent solution of the third method should be observed. The corresponding OD matrix seems questionable because of the large differences to values estimated at other convergence levels. The minimum-information distances to the goal matrix in Table 2, also indicate somewhat higher values for the third method, especially at the one percent level. The squared-Euclidean distances of the estimated matrices show too that the values related to the third method are initially less than those of the other two methods. In the later part of the iterative procedure, the distance estimated by the third method increases considerably (see also, the above comment on minimum information distances). All distances estimated to the goal matrix are large and increase, especially in the case of the third method, with the number of global iterations. The problem structure with a goal matrix implying one unique set of traffic counts, but one set of traffic counts possibly corresponding to many OD matrices with different distances to the goal matrix, may explain this failure to approach the goal matrix. A general conclusion, from the various distance measures between the estimated matrix and target and goal matrices, is common for all descentbased methods. First, the OD matrices estimated at convergence levels ten and five percent (possibly two percent), seem preferable to the estimates at the one percent. It may be possible to find some early "good" points with both low values of the objective, and low distances to the target and goal matrices. Second, the goal matrix is not closely reproduced by any descentbased method, irrespective of convergence level. The estimated OD matrix of the third method has smaller maximal deviation of elements and the squared-Euclidean distance from the target matrix, and larger minimum-information distances than for the two other methods. This indicates that the differences between the OD matrix, estimated by the third method and the target matrix, are more evenly distributed over all elements of the matrix. The total differences between the matrices, estimated by the other two methods and the target matrix, is allocated to fewer elements. This conclusion holds only for the matrices estimated in the early part of the iterative OD matrix-estimation procedure. Table 3 shows that at comparable "good" early solutions, there are some reasons to prefer each of the methods. The only measure on the

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Table 3 Evaluation measures of descent-based methods at early "good" points of the iterative OD matrix-estimation procedure when the objective function attains low values (first problem)

No. of global iterations Objective function Link flows on maximal volume difference links Minimum-info, distance Squared-Euclidean distance Maximum deviation between matrix elements

First method

Second method

Third method

23 94.6' 433/482

18 6.8' 424/482

8 5.8' 621/659

0.00055 0.0014 614.3' 242' 50/707 -73/772

0.00048 0.0014 12.7' 239' 61/536 -73/772

0.0038 0.0047 3.6' 244' 32/38 -73/772

differences between the solutions of the methods is that the solution of the third method appears to have altered the target more evenly. The required CPU-times per iteration for the methods are very different. The CPU-times needed to attain a certain level of convergence are less different (for results see, Abrahamsson, 1996). For the third method, this is because substantially fewer global iterations are needed (see Table 1). For the third method, the CPU-time required to attain a certain level of convergence (except one percent) is larger but of a similar magnitude and the method should not be rejected only because of a higher demand for CPU-time in the early iterative scheme. In the tests of this study, the performance of the line search in the second and third methods of Drissi-Kaitouni and Lundgren (1992) has not been fully optimised. Thus, the results displayed may not do complete justice to these methods. The memory requirements can be noted as an additional advantage for the first method of Spiess (1990). Results indicate that the third method may benefit from a higher accuracy in the traffic assignment subproblems. Second distorted OD matrix-estimation problem In the OD matrix-estimation problem, the observed traffic counts of the first problem are scaled with random factors (0.9, 1.1). Hence, the observed traffic counts are inconsistent with equilibrium assignment of the goal matrix and may be incompatible with equilibrium assignment. For this problem, the number of iterations required to attain the different conver-

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gence levels are larger than was the case in the equilibrium problem. The number of global iterations required to attain the 10, 5 and 2 percent levels of convergence are shown in Table 4, together with maximal differences of link volumes. Table 4 Estimated and observed traffic volumes, link with maximal difference (estimated volume/observed volume (global iteration number and link numbers)) (second problem)

2851/2730 2810/2730 2778/2730

10 5 2

Third method

Second method

First method

Converge level (%)

2834/2730 2821/2730 2787/2730

(18, 348) (25, 348) (49, 348)

(15, 348) (31, 348) (47, 348)

2831/2730 2809/2730 2791/2730

(11, 348) (36, 348) (83, 348)

The value of the objective function is plotted against the number of global iterations in Fig. 3. The values for the first 50 iterations of the three methods are displayed. The good initial performance of the third method can again be seen. After the first phase, it can be observed that the third

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

48

50

Figure 3 Objective function (3) against number of iterations for the first (series 1), second (series 2) and third (series 3) method (second problem)

Estimation of Origin-Destination Matrices Using Traffic Counts

215

method produces a slower improvement of the objective function than the other two methods. For the third method, it was found that the objective function does increase in some iterations. The choice of line-search strategy in these cases was found to be critical in terms of computational burden, but also for ensuring the global convergence of the method. This problem has not been fully resolved. An important experience obtained in the usage of the third method is the high demand for memory storage. For the second problem, the memory requirements became too high after about 95 iterations leading to disruption of the computations. The differences between the third and the two other methods are also seen in this distorted problem. For this problem, the estimated values relating to the first two methods differ more than in the equilibrium problem, and the second solution comes out somewhat better. The squared-Euclidean distances to the target and goal OD matrices are smaller, but the maximal deviations of elements also show lower values than those estimated by the first method. The first method estimates link flows with maximal difference to observed values less than the values of the second method. The minimum-information distances estimated to the target and goal OD matrices are about equal (see Table 5). Also, in this case we compare the estimated results at early "good" points, where the objective functions have favourable values (see Table 6). The matrix estimated by the first method has the largest squaredEuclidean distances to the target and goal matrices. Again, the minimuminformation distances of the third method are largest. The nature of matrix differences (with large deviations allocated to fewer elements in the first two methods) is also recognised for this distorted problem. If small minimum-information distance, and low CPU-time together with low memory requirements, were important, a gradient method would be pre-

Table 5 Minimum-information distances of the estimated OD matrix to the target and goal OD matrices (second problem) Convergence level (%)

First method

Second method

Third method

10 5 2

0.00083 0.0018 0.0013 0.0021 0.0026 0.0033

0.00063 0.0016 0.0015 0.0023 0.0023 0.0030

0.0083 0.0091 0.0180 0.0190 0.0380 0.0380

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Table 6 Evaluation measures of descent-based methods when the objective function attains low values, early in the iterative OD matrix-estimation procedure (second problem) No. of global iterations Objective function Link flows on links with maximal volume difference Minimum-info, distance Squared-Euclidean distance Maximum deviation between matrix elements

First method

Second method

Third method

23 9.5' 2810/2730

18 11.3' 2821/2730

8 22.5' 2831/2730

0.0014 0.0022 69.8' 286' -151/1034 -151/1839

0.0010 0.0019 41.1' 263' 127/1816 128/1816

0.0083 0.0091 10.2' 248' 40/46 -73/772

ferred. The conclusion that the first method provides a reliable and "safe" solver to the OD matrix-estimation problem is also supported in this second problem.

Combined method applied to OD matrix-estimation problems In the estimation of the combined model, the technique suggested in Abrahamsson and Lundqvist (1990), with iterations between the network equilibrium and maximum likelihood problems, is used. Iteratively, the travel pattern (with given parameter values) and parameter values (given values on travel costs) are determined. From the quotient of the sums of observed link counts, and also counts corresponding to an equilibrium assignment of the target OD matrix the growth factor of the travel demand, a is calculated as 1.035. For the first equilibrium problem, the estimated parameter value is /JL = 0.00398. For the second distorted problem the parameter estimate is ^t = 0.00327. The growth factor a is now calculated as 1.0374. For this solution, the value of the sum of the squared-Euclidean distances between estimated and observed link flows, i.e. the objective function (3), has, however, increased eight times relative to the initial value displayed in Fig. 2. The maximal difference in link volume of any link compared to the observed flow is 876 on a link with 1535 vehicles estimated. Thus, it is clear that the combined model does not reproduce the observed traffic counts. For the distorted problem, the value of the sum of squared-Euclidean distances between estimated and observed link

Estimation of Origin-Destination Matrices Using Traffic Counts

217

flows, equation (3) has increased 12.6 times compared with the initial value depicted in Fig. 3. The link having maximal difference in traffic volume has 1702 vehicles, that is, 1144 more than the corresponding observed value. For the equilibrium problem, the minimum-information distance to the target matrix of the combined model estimate has a value between the values of the descent-based methods, while the squared-Euclidean distance and the maximal deviation of elements of matrices are larger. For distances to the goal matrix, the same conclusions hold (see Table 7). In the distorted problem, both distances to the goal matrix have estimated values favourable to those estimated by any descent-based method. The maximal deviation to the goal matrix (by element) is of the same magnitude, but the maximal estimated deviation to the target matrix is considerably larger. Table 7 Distances to the target and goal matrices (combined model) Equilibrium problem

Minimum-information distance Squared-Euclidean distance Maximal element deviation

Distorted problem

Target

Goal

Target

Goal

0.0019 771' 512/6632

0.0021 327' 391/5455

0.0011 594' 459/6579

0.0016 231' -104/2476

Thus, using the same arguments as the ones for comparing descentbased methods, one may conclude that the combined model allocates the deviations from the target matrix to fewer elements than the descentbased methods. More experiments are needed, however, to support this hypothesis. The CPU-time required for the computations of the combined model outperforms any descent-based method (the CPU-time requirement is about 10 times less). The combined model does not, as expected, estimate an OD matrix reproducing the observed counts. Although the OD matrix estimated may be termed "reasonable".

Conclusions and Further Research An OD matrix that reproduces the observed traffic counts is estimated by the descent-based methods of Spiess (1990) and Drissi-Kaitouni and

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Lundgren (1992). In the results, it is also seen that the OD matrices estimated by the different methods are "close to" the target OD matrix. From the results of the Stockholm applications, it was observed that good solutions were already obtained in early stages of the iterative process. Here, at the early stages, the third method appears to estimate an OD matrix different from that estimated by the two gradient-based methods. The changes of the target matrix are more evenly distributed over all elements by the third method (the OD matrix-estimation problem cannot be guaranteed to have one unique solution). In the current implementation, the third method showed good performance only during early parts of the iterative estimation procedure. In terms of computational burden, the first method should be preferred. Both the second and third methods have higher demands for CPU-time and memory space. In the combined model, the target matrix is explicitly considered. Here, replication of traffic volumes do not appear in the problem formulation, and a reproduction of observed counts is not achieved. The distances estimated to the target matrix of the minimum-information type is similar, but the squared-Euclidean distance is worse than the values of the descentbased methods. From the distance measures on the estimated OD matrices, we term these matrices "reasonable". An OD matrix that reproduces the observed traffic counts is efficiently and robustly estimated by Spiess' descent-based method. The other two descent-based methods have not received the same degree of algorithmic fine-tuning, and our results may not do full justice to these methods. The OD matrices estimated by any descent-based method are close to the target OD matrix, but not to the goal OD matrix. If, on the other hand, closeness to the goal matrix is a high priority objective, the combined model produces high quality results with low computational requirements. Combining the two approaches by also considering travel matrices in the upper-level problems of a descent-based method should be possible and is to be tested in future research. Numerous suggestions on such models exist, but the reports of applications to estimation problems from larger regions are few. In Chen (1994), this extension is studied using a squared-Euclidean distance between the travel matrices in the upper-level problem. This formulation was also suggested by LeBlanc and Farhangian (1982) and there are earlier bilevel formulations (e.g. Jornsten and Nguyen, 1979), but only Chen (1994) has published experiences from applications to larger networks.

Estimation of Origin-Destination Matrices Using Traffic Counts

219

Acknowledgements This research was supported by the Swedish Transport and Communications Board (KFB). I thankfully acknowledge Professor Lars Lundqvist, KTH for valuable comments and suggestions throughout the work with this chapter. The careful reading of an earlier draft by Jan Lundgren, Linkoping is acknowledged. Jan Lundgren is also acknowledged for the generous provision of the research code he has developed together with Omar Drissi-Kaitouni. Staff an Algers, KTH has provided helpful guidance on the EMME/2-system. Anders Karlstrm, KTH and Lene S0rensen, Ris0, Denmark, are thanked for valuable comments on earlier drafts of this chapter.

References Abrahamsson, T. (1996) Network Equilibrium Approaches to Urban Transportation Markets—Combined Models and Efficient Matrix Estimation. PhD Thesis, Department of Regional Planning, The Royal Institute of Technology, Stockholm. Abrahamsson, T. and Lundqvist, L. (1990) A combined trip distribution, modal split and assignment model applied to Stockholm. 30th RSA European Congress. Istanbul, August 1990, Turkey. Abrahamsson, T. and Lundqvist, L. (1997) Implementation and application of nested combined models for trip distribution, modal split and route choice —a comparative study of models in the Stockholm region. Transportation Science (under review). Boyce, D.E., Chon, Y., Lee, Y. Lin, L.-T. and LeBlanc, L. (1983) Implementation and computational issues for combined models of location, destination, mode and route choice. Environment and Planning ISA, 1219-1230. Carey, M., Hendrickson, C. and Siddharthan, K. (1981) A method for direct estimation of origin/destination trip matrices. Transportation Science 15, 32-49. Chen, Y. (1994) Bilevel Programming Problems: Analysis, Algorithms and Applications. PhD Thesis, Centre de Recherche sur les Transports, Universite de Montreal. Drissi-Kaitouni, O. and Lundgren, J. (1992) Bilevel origin-destination

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matrix estimation using a descent approach. Technical Report LiTHMAT-R-92-49, Department of Mathematics, Linkoping Institute of Technology. Evans, S. (1973) Some Applications of Optimisation Theories in Transport Planning. PhD Thesis, University College London. Fisk, C. (1988) On combining maximum entropy trip matrix estimation with user optimal assignment. Transportation Research 22B, 69-73. Fisk, C. (1989) Trip matrix estimation from link traffic counts: the congested network case. Transportation Research 23B, 331-336. Fisk, C. and Boyce, D. (1983) A note on trip matrix estimation from link traffic count data. Transportation Research 17B, 245-250. Jornsten, K. and Nguyen, S. (1979) On the estimation of a trip matrix from network data. Publication No. 153, Centre de Recherche sur les Transports, Universite de Montreal. LeBlanc, L. and Farhangian, K. (1982) Selection of a trip table which reproduces observed link flows. Transportation Research 16B, 83-88. Snickars, F. and Weibull, J.W. (1977) A minimum information principle, theory and practice. Regional Science and Urban Economics 7, 137168. Spiess, H. (1990) A descent based approach for the OD matrix adjustment problem. Publication No. 693, Centre de Recherche sur les Transports, Universite de Montreal. Wardrop, J. (1952) Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers Part II1, 325-378.

13

Two New Methods for Estimating Trip Matrices from Traffic Counts Otto Anker Nielsen

Abstract This chapter describes different methods for estimating traffic models and trip matrices. Most conventional methods assume that either traffic counts are error-free, deterministic variables or they use a simplified traffic assignment model. Without these general assumptions, the methods often demand prohibitive calculation times. In order to overcome these problems in practice, two matrix-estimation methods are formulated and discussed in this chapter. Both methods are able to handle traffic counts with inconsistencies and uncertainties. The estimated trip patterns reflect the route choice patterns given by traffic assignment models following the Method of Successive Averages (MSA), including Stochastic UserEquilibrium (SUE). The first method, for Single Path Matrix Estimation (SPME), is easy to implement as it utilises existing implementations of traffic assignment models. SPME is, however, very heuristic in nature and utilises only the counts along the optimal path between each zone-pair. Therefore, a second method, Multiple Path Matrix Estimation (MPME) is also presented. MPME utilises all counts along paths according to MSA and, thus, reflects the route choice better than SPME. However, MPME is more difficult to implement. An examination of the methods was carried out on several full-scale cases, where both SPME and especially MPME gave very reasonable results. For practitioners, the methods are most promising in cases where an old trip matrix needs to be updated for use in sketch-plan models, or as a pivot matrix in larger traffic models. The final part of the chapter deals with the promising prospect for cost-efficient traffic modelling in practice, when using the methods presented in the study.

Introduction Traditionally, traffic models are estimated by using comprehensive traffic surveys based on interviews. However, in recent years, interest in alterna-

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tive estimation methods has increased. To reduce the cost of data acquisition, most of these methods are based on traffic counts supplemented by some assumptions on road users route choices. In this chapter, two methods for estimating trip matrices from traffic counts are presented. Both methods are practical, easy to implement, converge reasonably quickly, are able to handle inconsistencies and uncertainties in traffic counts and are based on advanced route choice models. The background for the development of the two methods was a number of Danish cases, where there were problems updating old trip-matrices of poor quality using different traffic modelling packages. Thus, the main focus has been the usefulness in practical applications, which leads to the methods' heuristic nature. The first method SPME (Single Path Matrix Estimation), was originally formulated by Nielsen (1994), who also suggested the second method MPME (Multiple Path Matrix Estimation). A solution algorithm for this was presented by Nielsen (1997a). While the main focus of SPME was that it should be easy to implement, MPME was developed to reflect the route choice pattern better. The second section of this chapter discusses, in general, methods for estimating trip matrices and traffic models, while the third section presents the SPME method and the fourth section the MPME method. Experiences with the methods on full-scale cases are described in the fifth section, while the sixth section discusses the use of matrix estimation methods in practice. Finally, prospects for the use of the methods are outlined in the seventh section.

The Traditional Basis for Traffic Modelling When choosing a traffic model, one of the main considerations is to match the model, the estimation method and standard of data. The source of data has traditionally been traffic surveys, but the use of traffic counts has increased due to the development of the structured, unstructured and data fusion methods (see Fig. 1). In traffic surveys, road users, transit passengers or simply a sample of the population, are asked questions about their travel behaviour. Techniques such as Revealed Preference (RP), or Stated Preference (SP), can be used to estimate a traffic model directly from traffic surveys. Although interviews are often essential for estimating traffic models, there are also disadvantages of using traffic models estimated only by traffic surveys because: • the cost is high, as many interviews are needed to describe the trip

Two New Methods for Estimating Trip Matrices

223

Figure 1 Classification of traffic models after the estimation method

patterns between many zones. Usually, only a limited number of people can be interviewed due to budget constraints, which results in a rough estimate of the traffic flows; • fewer interviews make it difficult to describe special local characteristics by the models; • traffic models based on surveys often compare poorly with traffic counts on the individual stretches of road, because the traffic counts are not used for the model estimation, but only for controlling the final results; • often, a considerable source of knowledge is not used since existing trip matrices are not used for the estimation. The unstructured estimation methods (Tamin and Willumsen, 1989) use traffic counts for estimating trip matrices without using any general model expression (or structure) to describe the trip-making behaviour. Due to budget constraints, this often needs to be done using only link counts and knowledge about route choices. However, an old trip matrix is needed as

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supplementary information about the trip pattern, because the number of matrix elements usually far exceeds the number of counts. The estimated trip matrices may be subsequently used to estimate the traffic model itself, which is done in an indirect way, and may be used as pivot-matrices for a traffic model or may be used directly in a road scheme appraisal. Such methods will often make the models fit well to the counted traffic flows, but, nonetheless, the methods can cause problems. • It is not necessarily true that assigned traffic flows equal the actual flows, as the estimation problem is very indefinite. This is because the number of zone-pairs is much higher than the number of traffic counts. • Data from old traffic surveys are only indirectly used in the calibration process in the form of an original trip matrix. • The methods provide only an indirect, general explanation of traffic patterns. Thus, they are unsuitable for more strategic or long-term forecasts. Due to their cost-effectiveness in practice, matrix estimation methods have attracted considerable focus by researchers (see Yang et al., 1994; Sherali et al., 1994, for a review of existing methods). The structured methods (Ortuzar and Willumsen, 1990; Willumsen, 1981) estimate the traffic models directly from traffic counts. Thus, it is assumed that the tripmaking behaviour in the study area can be well represented by a certain general model form, the structure (Tamin and Willumsen, 1989). The methods share some of the disadvantages of the traditional traffic survey, because, • special local characteristics are not taken into consideration; • the methods do not make use of existing trip matrices. Another problem is that the whole traffic modelling complex has to be estimated in one step from the traffic counts. Usually, this is only possible for very simplified models. Even sketch-plan models often use nonproportional assignment models that are solved by an iterative algorithm, which makes the estimation problem difficult to formulate. Ben-Akiva and Morikawa (1989) define data fusion as "the process of combining two or more complementary sources into a single comprehensive database. The data fusion method can exploit the advantages of the data sources and compensate for their disadvantages by combining them into a single database". Ben-Akiva (1987) used as an example both traffic surveys and traffic

Two New Methods for Estimating Trip Matrices

225

counts for direct model estimation. The data-fusion methods proved advantageous for small-scale models when the all-or-nothing principle can be considered as a proper traffic assignment model. However, the estimation problem increases significantly when using larger multiple path traffic assignment models, or when one considers full-scale cases. In practice, it appears to be difficult to use both traffic counts and surveys for estimating traffic models simultaneously. However, instead of not using counts at all, they can be used to estimate trip matrices, and subsequently used alone, or together with surveys, to estimate the traffic model itself. In addition, the matrices can be used as pivot matrices or directly used as input to simplified models for road scheme appraisals. The two methods presented in the following sections should be seen in this light.

The SPME Method This section describes the new heuristic SPME method for estimating trip matrices from traffic counts. Among other reasons, the method was developed to update an old trip matrix for the Copenhagen Region, where there are many alternative routes on the road network with frequent delays and sometimes queues. In addition, the available traffic counts showed a considerable stochastic component—some counts were even clearly inconsistent. This could be due to the counting method, the route choice model, or the simplified network representation and zone-structure in the model. Most existing methods and software packages for matrix estimation cannot handle these circumstances.

The principle of SPME SPME estimates a new trip matrix to fit as well as possible with the traffic counts (see equation (1)). A consequence of this is that the original matrix is changed more than by many other matrix estimation methods. This approach is easily justified when updating an older matrix using newer, more accurate traffic counts. (1)

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where Ta is found by a traffic assignment model Ta = f2( r/7; ti}:) is the original trip matrix describing traffic from zone / to ;', 7^- is the new trip matrix, Va is the counted traffic on link a and Ta is the assigned traffic. /! estimates the new matrix, /2 is the traffic assignment model. The traffic assignment model, f2, can be any model type, and can be run on standard software. But the behaviour of SPME depends naturally on the reasonableness of the assignment model. The Matrix estimation model, /i, estimates each element (or zone-pair) in the new trip matrix, to minimise the average deviation between counted and assigned traffic along the optimal path between the zone-pair (thus, the name Single Path Matrix Estimation Method). The procedure is to calculate the expected traffic T^E)ija for each road segment where traffic has been counted:

• w h e r e T(E^ja i s t h traffic count on link a. ti} is an element in the original trip matrix, or in the matrix from the preceding iteration. VJTa defines the fraction by which Ta should be multiplied to replicate Va. The rationale is, that all matrix elements, with respect to this specific count, should be modified with the same ratio to replicate the count. Based on the least-square or maximum-likelihood method, the arithmetic mean can be used to estimate the Ti/s from the T^^'s (if the traffic counts can be considered as normal or poisson distributed):

where T^E)iia is the expected traffic between the zone pair i,j at link a. T is the set of links with counted traffic along the (optimal) route r. N is the number of counts along the path. Alternatively, the harmonic mean as an estimator minimises the square error between the counted and assigned traffic:

Two New Methods for Estimating Trip Matrices

227

If the assignment is traffic dependent, the new estimated matrix will lead to other flow patterns than those used for the estimation. Thus, the estimation must be solved by an iterative approach. If this converges (which, in practice, can be easily tested as shown below), then the matrix elements will fulfil equations (3) or (4). The simplest approach is to run the assignment and matrix estimation in a loop: 1. Initialisation: Set the iteration number, n = 1 and set the trip-matrix Tij(p) equal to the seed matrix. 2. Assign Tij(n-i) onto the traffic network. Save the flows Ta(n-i). 3. Estimate the matrix according to equations (3) or (4), the optimal paths must be found by Dijkstra's or another algorithm. 4. Stop criteria: Stop according to a set stop criteria, otherwise go to step 2. The algorithm is very efficient, as only one traffic assignment is needed for each main iteration. In addition, the memory needed for saving paths is no larger than that within the assignment model (typically / • / elements and not a - i • j elements as with some other methods, e.g. Yang et al., 1992; Ben-Akiva and Morikawa, 1989). Thus, for a big traffic model, such as the Copenhagen Model, the required memory for saving routes can be reduced considerably (in this case from about 800 to about 0.3 Mb).

Calculation examples using SPME Table 1 shows the use of SPME on the network in Fig. 2 (values have been rounded off from a spreadsheet). The seed matrix has two zonepairs, 7\5 = 300 and T25 = 360, but the solution is independent of the seed matrix in this overspecified estimation problem. The assignment model is fixed; T2s chooses routes 2-3-5 and 2-4-5 with the probabilities of 2/3 and 1/3, respectively. In each iteration, the expected traffic concerning each matrix element (e.g. T15) is calculated as the matrix element from the prior iteration (e.g. 300 from the first iteration), multiplied by the ratio between counted and assigned traffic (e.g. the expected traffic of 240/300 • 300 = 240 for link 1-3). Each matrix element is then estimated as the average of the expected traffic along the route. At the tenth iteration T15 and T2s only change at the first decimal place, and have values of 253.44 and 474.85.

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Travel Behaviour Research: Updating the State of Play Table 1 The SPME method used in the example given by Fig. 2

Outer loop

Routes

Assignment and expected traffic at links #1-3

#3-5

#2-3

Traffic counts, Va and seed matrix 7"/7-(o)

240

600

300

Assignment

300

300 240 -

240 -

540

240

ri_3_5 ^2-3-5 ^2-4-5 7"a(0)

Matrix estimation

Assignment

Matrix estimation

Matrix estimation

120

Ti5(n - i) T25(n - 1)

300

-

360

120

120

333.33

! (£)2-3-5

400

450

-

-

286.67 _

286.67 283.33 _

— 283.33 _

—

—

141.67

141.67

rfl(1)

286.67

570

283.33

141.67

141.67

T(E)i-3-5

240

301.75

-

-

-

270.88

T(E)2-3-5

-

447.37

450

-

-

-

448.68

299.12

149.56

149.56

285.13

-

-

-

262.57

-

472.3

450

-

-

-

461.15

570

307.43

153.72

153.72

ri_3_5 r2_3_5 /2-4-s

270.88

7"(£)1_3_5 240 ' (E)2-3-5

Assignment

120

#4-5

140

T(E)i-3-s 240

Assignment rfl(2) Matrix estimation

300

#2-4

120

Matrix estimation

Ta(3)

262.57

570

-

286.67 -

425

T^i-a-s 240

276.39

-

-

-

258.19

-

7(02-3-5

485.42

450

-

-

-

467.71

-

Figure 3 shows another example of a network with inconsistent counts. In this case, the seed-matrix has three zone-pairs r24, T23 and 7\3 (here, just set to 200 each). At the 30th iteration, the elements only changed at the second decimal place, and had values of 208.31, 272.49 and 769.20. For comparison, the analytic solution of minimising the weighted square

Two New Methods for Estimating Trip Matrices

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Estimated traffic:

Figure 2 Network with inconsistent traffic counts

between counted and assigned traffic gives values of 208.00, 272.00 and 767.00 (see below for a further discussion of this property). Figure 4 shows an example of a network with consistent counts, which by definition, are reproduced exactly by SPME. The seed matrix has three zone-pairs Tt2 = 200, T34 — 200 and T56 = 600. At the 10th iteration, the elements only changed at the second decimal place, and had values of 184.32, 115.69 and 815.66. For comparison, the analytic solution of minimising the weighted square between the seed matrix, and the estimated matrix, gives values of 185.71, 114.29 and 814.29, provided the counts are reproduced exactly.

Choice of assignment model within SPME Route choice and traffic assignment models have attracted considerable focus in the literature. The early logit-based stochastic models rest on the assumption that different routes are independent, e.g. Dial (1971). Thus,

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Travel Behaviour Research: Updating the State of Play

Figure 3 Network with inconsistent traffic counts

Counted tratiic:

Figure 4 Network with consistent traffic counts

they lead to problems in networks with overlapping routes (Sheffi, 1985), which is nearly always the case in real-size networks. Daganzo and Sheffi (1977) suggested the use of probit-based models to overcome this problem, and Sheffi and Powell (1981) presented an operational solution algorithm. A similar concept is used as a part of the Stochastic User Equilibrium (SUE) suggested by Daganzo and Sheffi (1977) and operationalised by

Two New Methods for Estimating Trip Matrices

231

Sheffi and Powell (1982), but here the travel times are also flow-dependent. Thus, the SUE-principle states that "an equilibrium should be reached where no travellers' perceived travel resistances can be reduced by unilaterally changing routes". It is often discussed as to when .to use probit-based assignment, UE or both (SUE). The probit-based assignment may be used in uncongested networks and UE may be a good approximation for the SUE solution in congested networks. The SUE approach should then be used at intermediate congestion levels (Sheffi, 1985). However, as all three circumstances occur in most cities, and many routes consider both uncongested, intermediate and full-congested links, it is recommended to always use the SUE approach (Nielsen, 1996). Compared with more heuristic methods, the models referred to above all follow the Method of Successive Averages (MSA), which can be shown to converge. Sheffi (1985), van Vuren (1994), Nielsen (1996) and Slavin (1996) among others, give literature reviews on traffic assignment models, and recommend the use of SUE. Nielsen (1996) developed SUE further to describe differences in road users' preferences, Nielsen (1997b) discusses the stochastic distributions within SUE, while Nielsen (1997c) recommend including delays in intersections in the assignment.

Discussion of SPME In SPME, only the traffic counts along the optimal path are used for the estimation. The rationale is that the relative deviations between counted and assigned traffic along this path give a fair estimate for the element. This simplification is made to lower the calculation complexity. The author's, as well as other users' experiences with the method shows that it usually converges relatively fast (it is implemented in TransCAD 3.0 by Caliper, 1996). This indicates that SPME is usable in practice. However, SPME does not completely represent the SUE flow-pattern, and it does not always converge smoothly. This is especially true in the case of networks with many routes with similar travel resistances between zone-pairs. Figure 5 shows, on a simplified road network, results from the well-known ME2-method (Maximum Entropy matrix estimation method, van Zuylen and Willumsen, 1980; Ortuzar and Willumsen, 1990), SPME, and the MPME method where all counts are used (see the following description of MPME). Figure 5 shows how many of the counts influence the final result (middle column) and for this the assigned traffic (the right column). T16 was assigned for SPME and MPME onto the road network using a

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Travel Behaviour Research: Updating the State of Play Counted traffic:

Information used in ME2:

Shortest path model, original matrix:

Information used in SPME

Assigned traffic, Mb2, New matrix

Assigned traffic, SPME, New matrix 185

Stochastic assignment model:

Information used in MPME

Assigned traffic, MPME, New matrix

r *i>¥

^

Figure 5

Comparison of ME2, SPME and MPME for traffic from nodes 1 to 6

stochastic assignment model with fixed route proportions. In ME2, the estimated traffic for the zone pair 1-6 is equal to the last count used in the algorithm, say the road segment from node 1-4. The estimate would then be 640 cars (refer to the references for a detailed description of the ME2-algorithm). In SPME, relative errors along the optimal path are (640-800)7800 = -20 percent and (840-800)7800 = 5 percent. Thus, the expected traffic would be 1,300 • 80% = 1,040 and 1,300 • 105% - 1,365, and the estimated traffic is (1,040 + 1,365)72 = 1,203. In MPME, the traffic is estimated to be 1,265, as shown in Table 2. It appears that the SPME and MPME methods give a far better result than ME2, while MPME only results in marginal improvement compared with SPME. On larger networks, MPME can be expected to give larger improvements, because there are many more alternative routes on such networks.

Two New Methods for Estimating Trip Matrices

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Table 2 The MPME method used on the example given in Fig. 5 Path

1-2-5-6

1-3-6

1-4-6

Expected traffic

Link 1-2: 220

Link 1-3: 240

Link 1-4: 640

Link 2-5: 190 Link 5-6: 220

Link 3-6: 390

Link 4-6: 840

210

315

740

Estimate

Sum

1265

The MPME Method As indicated above, the idea in MPME is for each path to use all counts along the path to estimate the corresponding matrix element. Inconsistencies in some counts along the path are thereby moderated by other counts. However, in opposition to SPME, where only the counts along the optimal path are used, this is done for all paths according to the probability of choosing each one. Thus, the traffic between each zone-pair should be the sum of the expected traffic along each route between the pair multiplied by the probability to choose that route (Equation (5a)). This assigns a high weight on the route choice, as each route is assigned the same weight (according to its probability), regardless of the number of counts along the route (to be discussed below). The expected traffic along each route can be assumed to be the average of the expected traffic as defined by each traffic count along the route (equation (5b)). The expected traffic according to each count (equation (5c)) equals equation (2) for SPME.

where

and

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where T^E)ija is the expected traffic between zones i and j at link a; r is the set of links with counted traffic; pijr is the probability that route r is used between zone / and /; n is the iteration number. In very simple cases (such as the example in the third section), this can be done in one step. However, usually pijr depends on the traffic on each link (nonproportional route choice), and Ta(n-i) depends on other matrixelements than Tiy(„_!). In this case, an approach could be to use equation (5) in an iterative loop (where n is the iteration number). If this converges (which can be tested easily in practice), the solution fulfils the assumptions leading to the equation.

Some calculation examples Table 3 shows the use of MPME on the same network as shown in Fig. 2 (values have been rounded off from a spreadsheet). The results are shown in Fig. 6. At the 10th iteration, 7\5 and T2s only change on the second decimal place, and have values of 261.82 and 438.18. For comparison, the exact solution of minimising the weighted square between counted and assigned traffic gives values of 260.28 and 434.04. As seen, MPME gave a better solution than SPME in this case, due to its ability to utilise the counts along all routes. Regarding the other examples with SPME (Figs. 3 and 4), there was only one route between each zone-pair, and SPME and MPME will give, therefore, the same results.

Some characteristics of MPME The main focus of MPME is the traffic counts. Thus, in networks with more counts than matrix elements (very rare), the solution will be independent of the seed matrix. If the counts are inconsistent, MPME will find a solution where the average expected traffic along each route (equation (5b)), and the sum of the expected traffic on the routes between the concerned zone-pair (equation (5a)), have converged. If the counts are consistent, equation (5) will continue to modify the matrix elements until a perfect fit has been obtained. Besides these characteristics, practical tests (including the ones in Figs. 3 and 6) have shown that the solution is quite close to a minimisation of the weighted square between counted and assigned traffic (although the assumption behind MPME does not equal this minimisation problem):

Two New Methods for Estimating Trip Matrices

235

Table 3 The MPME method used on the example given in Fig. 6 Outer loop

Results of inner loop

Assignment: traffic at links and expected at links

fl3_5

fl2-3

Traffic counts, Va and seed matrix Tij(Q)

240

600

Assignment ri_3.5

300 -

300 240 240 -

120 120

300

540

120

240

333.33

r2-3-5 ^2-4-5

Matrix estimation

T(E)i-3-s T(E)2-3-5 T(E)2-4-5

Assignment r^3_5 r2-3-s r

2-4-5

-

OD matrix estimation: expected traffic at routes and estimated matrix elements

300

240

120

-

140

300 360

-

120

-

266.67 300 -

-

286.67 286.67 120

283.33 140 130

-

413.33

286.67 286.67 275.56 275.56 137.78 137.78 286.67 562.22 275.56 137.78 137.78

Matrix estimation

T(En_3_5 T(E)2-3-5 T(E)2-4-5

240

305.93

-

272.96 272.96

-

294.07 -

300 120

297.04 140 130

Assignment Ta(2)

272.96 557.65 284.69 142.35 142.35

Matrix estimation

240

7\£)i-3-5 T(E)2-3-5 T(E)2-4-5

-

293.69

-

306.31 300 -

120

-

266.85 555.62 288.77 144.38 144.38

Matrix estimation

240 T(E)2-3-5 T(E)2-4-5

288.16

-

311.84 300

-

-

-

120

266.85 266.85

303.15 140 130

Assignment

-

-

-

264.08 264.08

-

305.92

140 130

-

427.04

433.15

435.92

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Travel Behaviour Research: Updating the State of Play Counted traffic:

Estimated traffic:

Figure 6 Network with inconsistent traffic counts

.

In cases with more matrix elements than counts, all elements concerning one count will be changed in the same direction. Naturally, this might be equalised due to other counts. The-modification of the matrix elements does fulfil the strong restriction that the route choice model must be followed and that equation (2) must converge. The solution is quite close to a minimisation of the weighted square between the seed and estimated matrices (although the assumptions behind MPME do not equal this minimisation problem):

Two New Methods for Estimating Trip Matrices

237

Solving the assignment model For large-scale studies, the main challenge in MPME is to handle the route choice, Pijar, in a computable manageable way. To do this, the properties of the SUE solution algorithm are utilised. In principle, the algorithm consists of an inner and an outer loop, but good results can be obtained with only one iteration in the inner loop (Sheffi, 1985). As SUE is a substantial part of MPME, this version is replicated here: 1. Initialisation: Set the iteration number n = 1 and set the traffic flows Ta(G) = 0 for all links, a. The (0) in ra(0) stands for iteration number zero (initialisation). 2. Update Travel Resistances, c(e)a: Calculate ca=f(c^)a, 7 fl(n _i))Vfl, where /(•) is the travel resistance function, and c(0)a is the travel resistance with no congestion. Then sample c(e)a G 3>(ca, err.ca)V«, using a Monte Carlo simulation. ) • Ta(n-iy + £(«) • Ta{tmp), Va. 6. Stop Criteria: Stop according to a set stop criteria, otherwise set n = n + 1 and go to step 2. The question is how the route choices given by the SUE can be modelled within MPME. One might think that the matrices in equation (5) would demand prohibitive computer memory. However, this can be avoided by the following approach presented in Nielsen (1997a): 1. Initialisation of outer loop: Set the iteration number n = 1 and the trip matrix Tij(Q) equal to the seed matrix. 2. Assignment: SUE-assign T^-i) onto the traffic network. Save the flows Ta(n _ 1}. 3. Matrix estimation (inner MPME-loop): A modified SUE is used: a

Refer to Sheffi (1985), van Vuren (1994), Tatineni et al. (1997) and Nielsen (1997b) for a discussion on the stochastic distribution. As the Normal distribution must be truncated (link-costs cannot be negative in Dijkstra's) one may consider using other distributions. Often, the rectangular distribution will give the best results (Nielsen, 1997b). In all cases, the best results will be obtained if the distribution is truncated symmetrically.

238

Travel Behaviour Research: Updating the State of Play 3.1. Initialisation: Set the inner-loop iteration number m = 1, and all 7^(0) and T-y(0) equal to 0. 3.2. Update Travel Resistances, c(e)a: Based on 7^(m_!) as in step 2 in SUE. 3.3. All-or-nothing assignment: T1,y(«-i) is assigned to the network with updated c(e)a's. Whereby T'a^tmp) is modelled for all links, a, and each element in the temporary matrix is calculated according to equation (8). 3.4. Step Length is set: £ (m) = 1/ra.

3.5. Update of link-flows: T'a(m)

=

(1 ~ £(m)) ' ^a(m-l) + £(m) ' ^a(fmp)? Vfl.

3.6. Update of trip matrix: T'ij(m) = (1 — £(m)) ' T'ij(m-i)

+ £( m ) ' Tij(tmp),

V/,/.

3.7. Stop Criteria, Inner loop: Stop according to a set stop criteria, otherwise set m = m + 1 and go to step 3.2. 4. Updating: Tij{n} = Tij(m} V/, /. 5. Stop Criteria, outer loop: Stop according to a set stop criteria, otherwise set n — n + 1 and go to step 2.

Regarding step 2, if this is excluded, the T^-i/s in step 3 will correspond to the T,;(AZ_2)'s (except for the first iteration), and the model will not converge. On the other hand, the assignment models in steps 2 and 3 must be 'equal'. This can be secured by using a sufficient number of iterations in the assignment model. Equation (8) calculates the expected traffic, if the whole trip matrix is assigned according to the all-or-nothing principle (one route between each zone-pair). This is equal to equations (5b) and (5c). However, this traffic is first adjusted by the £ (m) 's in step 3.5 for iteration m in the inner loop and, thereafter, by 1 — ^w in each of the following iterations (where x is the iteration number). The accumulated weight of the routes from iteration m is then,

Two New Methods for Estimating Trip Matrices

239

where m (max) is the maximal number of iterations. This weight is the proportion of road users, which follows the all-ornothing routes from iteration m, that is, Pijr—or in other words the product in equation (5a). Step 3.7 also summarises the contribution from all other iterations, which is the sum in equation (5a) for all routes. Thus, the algorithm will equal equation (5) for each inner loop (and the outer loop is simply the MPME iterations). If g(X) = l/x, all inner iterations have the same weights: pm = l/m(max). In terms of practical use, the MPME-algorithm has the following advantages: • There is no demand for saving a route choice matrix, p~, as in some methods. • The calculation complexity per iteration in the outer loop is not significantly larger than for SUE (slightly more than twice as large as it is used both in steps 2 and 3). However, the outer loop must be run a number of times. Practical tests have shown that MPME is feasible for full-scale models using standard PCs.

How to secure convergence at reasonable calculation time As MPME consists of two loops, it is tempting to reduce the number of iterations in both in order to speed up the calculation time. However, this might affect the convergence. Regarding the inner loop, the convergence of UE and SUE has often been discussed in the literature (e.g. Sheffi, 1985; Powell and Sheffi, 1982; van Vuren, 1994 and Nielsen, 1996). To use too few iterations in the inner loop can strongly be dissuaded as this will lead to different flow-patterns between each iteration in the outer loop, and thus seriously affect the convergence of MPME. About 100200 iterations in the inner loop were sufficient in the test-studies above. It is much easier to determine the required number of iterations in the outer loop, as this can be found by different measures of convergence. It converged within 50 iterations in the case studies—but 100 were used to be sure. Nielsen (1997a) discusses methods to speed up convergence of

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MPME in more detail, and Nielsen (1996) discusses methods to speed up SUE.

Practical Experience Both MPME and SPME have been used on several real-size Danish cases. SPME was implemented much earlier than MPME.b They could therefore not be compared on calculation time, but could be compared regarding all other questions as they have been used on the same data.

Case studies and data used for the examinations Four traffic models were used for the evaluation: 1. The smallest model described the traffic to and from the International Airport of Copenhagen. The model had only 25 zones and 121 road segments in the area of analysis but was based on a comprehensive traffic survey. The results could therefore be compared with a detailed knowledge of actual route choices. This was used to evaluate the Copenhagen model (see point 4). 2. The medium size model covers the provincial town Naestved. The model has been implemented in two versions; a smaller one with 134 links and 33 zones, and a larger with 314 links and 106 zones, and with a much better coherence between zone- and net-structure. The area of analysis covers 120,000 inhabitants. The seed-matrices have a fair quality. 3. The large-scale model covers the City of Bandung, Indonesia with about 5.0 million inhabitants. This model has 180 zones and 980 links and the seed-matrix is quite poor. 4. The largest model covers the Copenhagen Region with 1.7 million inhabitants. This model was also implemented in two versions; a b

SPME was implemented in 1992 as a C-application connected to the GIS TransCAD 2.0. It could use existing assignment models within TransCAD and new models. SPME has later been implemented directly in TransCAD 3.0. MPME was implemented in 1996 as a Cprogramme connected to the GIS ARC/INFO. Regarding MPME, great concern has been made to optimise the code (especially Dijkstra's). As Caliper (1996) changed some of the formats in TransCAD, the implementation of SPME has not been updated since 1992 and is thus very slow.

Two New Methods for Estimating Trip Matrices

241

smaller version with 97 zones and 2.422 links and a larger version with 269 zones and 2.765 links (the latter in order to cope with a poor coherence between zone- and net-structure in the smaller version). The seed-matrix was good in the small version and fair in the large one.

Methods applied for evaluations and quality control Several methods were used for evaluation and quality control. Average deviations between assigned and counted traffic were calculated and road segments with especially large deviations were displayed on thematic maps. To evaluate the assignment models, the paths between different zones were displayed, and the models were used for forecasting. Using the methods within a GIS extensively facilitated the evaluations. Without these facilities the work could not have been carried out within the time schedule, and the quality control would have been very difficult to perform. Besides comparing at link level, the matrices have been compared with different surveys that covered parts of the areas of analyses. In addition, some of the matrices were compared with 'synthetic' matrices from traffic models that have been estimated by disaggregated data (RPand SP-interviews). Although, the space in this paper does not allow presentation of these comparisons it can be noted that the matrices were found to give a reasonable description of the trip pattern.

Evaluation of SPME SPME was tested on the traffic models for Naestved and for the Copenhagen Region. Figure 7 shows the average relative deviations between counted and assigned traffic as a function of the number of iterations (iteration number 0 is the result when assigning the original trip matrix onto the road network). The original matrices in the two old models were originally obtained by using ME2. As the figure shows, SPME improves the results considerably. It can also be seen that the method converges relatively fast (due to the old software SPME was only run with few iterations). To supplement the aggregated measures of convergence, the methods mentioned above were used for the evaluation, the main conclusions of which were:

242

Travel Behaviour Research: Updating the State of Play Start value from ME2 D

Old Naestved, All-or-Nothing New Nasstved, stochastic capacity dependent Old Copenhagen, stochastic capacity queue dependent New Copenhagen, stochastic capacity queue dependent

Figure 7 Average relative deviations between counted and assigned traffic as a function of iterations in SPME on four cases

SPME improved the overall results under Danish conditions. Problematic zone pairs in the matrix were estimated with less deviations because it was possible to use advanced traffic assignment models within SPME. The effect of inconsistent traffic counts was reduced, which improved the results on critical road stretches, typically near the boundaries between the districts of different road authorities. The traffic on competitive routes was modelled better. The traffic pattern in areas and on stretches with capacity problems was modelled better.

Evaluation of MPME MPME was tested on the same cases as SPME, as well as on the Bandung model. In all comparable cases, MPME resulted in lower deviations from traffic counts, while at the same time representing the SUE-flow pattern.

Two New Methods for Estimating Trip Matrices

243

The deviation curve converged smoothly in all cases. Space does not allow presentation of all the tests in detail, but Fig. 8 shows the estimation record. Notice, that the seed matrices in the different cases were of very varying quality (it was especially poor in the Bandung Case). The larger deviations in the old Nasstved and old Copenhagen models compared with the new, were due to a too simplified zone-structure in the old models.

Figure 8 Deviations between counted and assigned traffic as a function of iterations in the outer loop in MPME on five cases

Practical Considerations In the following some practical considerations and pitfalls when using the methods in practice are discussed. The solutions presented are quite practical, but are nevertheless much better than just ignoring the problems.

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Travel Behaviour Research: Updating the State of Play

Modification to handle zone-internal traffic The zone-internal traffic is problematic when estimating OD-matrices from traffic counts because it is never assigned onto the network and therefore is not included in the estimation process. However, it is often relevant to estimate the zone-internal traffic, as it contributes to the total travel costs, the trip length distribution, etc. The relative changes between O's and D's in the seed-matrix 7\,(0) versus the estimated matrix Ttj may be assumed proportional to the needed relative adjustments of the zoneinternal traffic. A corrected matrix (index cor} can then be estimated by equation (10):

This equation does not have general validity, as it assumes no changes in trip length distribution and the urban structure in general, but it can be useful if there are too few resources to follow better approaches for estimating the zone-internal traffic.

Modification of the method to handle routes without counts Another problem is if there is no traffic counts along some of the paths between some of the zone-pairs, as the matrix elements in question will not be updated. In MPME this should be considered for each iteration in the inner-loop, as the routes are different from iteration to iteration (in SPME only for the one optimal path). A heuristic approach could be formulated somewhat parallel to equation (10): Zone-pairs with no counts are adjusted proportionally with corrected O's and D's for the two zones. To do this, step 3.3 in MPME has to be adjusted to: When doing the allor-nothing assignment, ^7(m) is set to 1 if there is at least one count along the route from i to /, otherwise it is set to zero. Hereafter, the matrixelements with no counts are adjusted according to:

Two New Methods for Estimating Trip Matrices

245

where T^n-i) — Sy-(5/y-(fmp) • T^y^-i)), T y -( n _i) — 2,- (o,7(,mp)) • j^-(n-i))' 7\ = 2y (8ij(tmp)' Tij(tmp)) and Ty = 2,- (S//(fmp) • Tij^mp)). For each iteration one might update <5/;(m) = (l-£ (w) ) • 5,7(m_i) + £ ( m > ' f>ij(tmP), which then can be used as a measure of how well a zonepair is described by traffic counts. 5y(m) -^0 is poor and 5,y(m) —> 1, may be good (there may only be one count along each route even if ?>ij(m) = !)•

The problem with missing counts was especially relevant in the Bandung case, where the use of equation (11) led to a drastic improvement of the results. However, the procedure only alleviates problems caused by insufficient data. Thus, it is strongly recommended instead to use enough traffic counts well distributed in the area of analysis. The use of 5,/s indicates whether this is the case.

Routes with one or few counts A third problem with matrix estimation methods which mainly focus on counts and route choices (and partly other methods as well) is if a zonepair is estimated from only one or few traffic counts. This can be due to short routes, inefficient distribution of counts in the network or problems with the zone- and network structure. In this case, the algorithm can adjust this zone-pair to make a perfect fit to the few counts, which in fact might be inconsistent with other counts. If the matrix is used as a pivotmatrix, for sketch-level models or for road-scheme appraisals this simply removes (or hides) problems with the models data foundation. However, if the matrix is used to estimate a traffic model (e.g. a trip length distribution) this might be problematic. A practical approach to test for weak matrix-elements is to count the number of traffic counts along each path per iteration, riij(tmP), and then update it as j]ij(m} = (1 - £ (m) ) • ifo^-i) + £ (m) • rjij(tmp}. Thereafter, matrix-elements with large differences from the seed-matrix and with small i7r/s can be found. It can be debated whether each route should be weighted equally regard-

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Travel Behaviour Research: Updating the State of Play

less of the number of counts along the route (all else being equal). Instead, each count may be weighted equally. This may reduce the average deviations between counted and assigned traffic, but it may also result in a less accurate distribution on routes and in more changes of the matrix.

Quality of the counts When using the expected traffic as in (5), each count along a route is weighted equal. However, the formula may be adjusted route-wise in order to weight the counts along each route according to link-length or quality of counts (when, how and period length for the counts). Such weights have not been tested in MPME, but they gave good results when using SPME. In addition, one might want to weight matrix elements adjusted according to equation (11) (no corresponding counts) lower than by equation (5) (at least one corresponding count).

Validity of the result Many different trip matrices can often approximate the same traffic counts. Any matrix estimation method may therefore estimate a trip matrix with low deviations between counted and assigned traffic, which nevertheless does not represent the actual travel behaviour. The main reasons for such a misrepresentation are usually: 1. 2. 3. 4.

The trip pattern in the seed-matrix has in reality changed too much. The trip length distribution is faulty. The assignment model is inefficient. There are problems with the network and zone representation in the model.

In the first case, the matrix estimation method cannot stand alone, but should be supplemented or replaced by traffic surveys, e.g. RP- or SPanalyses. In the second case, this may happen if the seed-matrix has been created 'synthetically', e.g. by a gravity model estimated on weak data material. In the third case, even though the seed-matrix describes the trip pattern fairly, the estimated matrix will correspond to the assignment model within the matrix estimation method. Thus, besides comparing

Two New Methods for Estimating Trip Matrices

247

with traffic counts, additional knowledge about route choice behaviour is needed in order to formulate and estimate the assignment model. Finally, the problems in case 4 might be reduced by the following good practice guidelines: • Check that the net and zone structure are appropriate, and that the traffic counts are reasonably distributed within the area of analysis. Use the 5,/s and ify's as an indication of problems. Check that counts do not carry a lot of zone-internal trips (the counts are best placed at zone-borders). • Examine the cells in the matrix for large absolute or relative deviations to the seed matrix. If such occur, use local knowledge to check whether this is reasonable. • Check the trip production rates in the individual zones and compare these with surveys or modelled rates. • Compare assigned and counted traffic at the link level. Evaluate the traffic assignment model by displaying paths between different zones.

Conclusion and Perspective By using matrix estimation methods, traffic models can often be estimated more cheaply and more easily than by comprehensive and costly traffic surveys. In this paper two new methods for estimating trip matrices from traffic counts have been presented. Both methods can handle inconsistent and uncertain counts, and can be based on any assignment model that follows the MSA, including SUE. If inconsistent counts occur, this will not affect the results as seriously as in many other matrix estimation methods. The first method, SPME, is the easiest to implement but has a more heuristic nature than the second method, MPME. MPME uses all counts along all routes between each zone-pair for the estimation, while SPME only uses the counts along the optimal path. In the case studies, this meant that MPME converged more smoothly than SPME and that the solutions gave better fits to traffic counts and more reasonable estimates of the matrix. However, both methods gave significant improvements compared with the seed-matrices. This is especially the case in networks where multiple route choices often occur such as in most urban areas. The main aspect for practitioners is that both methods are quite easy to implement and converge within reasonable calculation times. This has

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Travel Behaviour Research: Updating the State of Play

been achieved by building the methods on rather simple assumptions, instead of formulating them as mathematical programmes—which from a theoretical point of view would be preferable. SPME is simplest to implement, as it can utilise existing implementation of assignment models. Both SPME and MPME are dependent on the pattern of the seedmatrix (if there are less counts than matrix-elements, which is usually the case), but they may alter this pattern significantly in order to fit the counts. This is an advantage in low-budget analyses, where an existing (often old) matrix needs to be updated to be the basis for estimating a new traffic model, to be used as a pivot-matrix in the model or to be directly used in a road scheme appraisal. However, because the methods are dependent on the information in an original trip matrix, they have to be supplemented by traditional traffic surveys from time to time. For more ambitious traffic models, matrix estimation methods should be replaced or at least supplemented by new traffic surveys.

References Ben-Akiva, M. (1987) Methods to combine different data sources and estimate origin destination matrices. In N.H. Gartner and N.H.M. Wilson (eds.), Transportation and Traffic Theory, Elsevier Science, London. Ben-Akiva, M. and Morikawa, T. (1989) Data fusion methods and their applications to origin-destination trip tables. In World Conference on Transport Research (eds.), Transport Policy, Management and Technology Towards 2001, Western Periodicals Co., Ventura, CA. Caliper (1996) Travel Demand Modelling with TransCAD 3.0. Caliper Corporation, Newton. Daganzo, C.F. and Sheffi, Y. (1977) On stochastic models of traffic assignment. Transportation Science 11, 253-274. Dial, R.B. (1971) A probabilistic multipath traffic assignment algorithm which obviates path enumeration. Transportation Research 5, 81-111. Nielsen, O.A. (1994) A new method for estimating trip matrices from traffic counts. Preprints Seventh International Conference on Travel Behaviour, Valle Nevado, June 1994, Chile. Nielsen, O.A. (1996) Do stochastic traffic assignment models consider

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differences in road users' utility functions? Proceedings 24th European Transport Forum, Brunei University, September 1996, UK. Nielsen, O.A. (1997a) Multi-path OD-matrix estimation (MPME) based on stochastic user equilibrium traffic assignment. 1997 TRB Annual Meeting, Washington, D.C., January 1997, USA. Nielsen, O.A. (1997b) On the distribution of the stochastic component in SUE traffic assignment models, Proceedings 25th European Transport Forum, Brunei University, September 1997, UK. Nielsen, O.A. (1997c) Stochastic user equilibrium traffic assignment with turn delays in intersections, Seventh International Conference on Information Systems in Logistic and Transport, Gothenburg, June 1997, Sweden. Ortuzar, J. de D. and Willumsen, L.G. (1990) Modelling Transport. John Wiley & Sons, Chichester. Powell, W.B. and Sheffi, Y. (1982) The convergence of equilibrium algorithms with predetermined step sizes. Transportation Science 16, 45-55. Sheffi, Y. (1985) Urban Transportation Networks. Prentice Hall, Englewood Cliffs, NJ. Sheffi, Y. and Powell, W.B (1981) A comparison of stochastic and deterministic traffic assignment over congested networks. Transportation Research 15B, 53-64. Sheffi, Y. and Powell, W.B (1982) An algorithm, for the equilibrium assignment problem with random link times. Networks 12, 191-207. Sherali, H.D., Sivanandan, R. and Hobeika, A.G. (1994) A linear programming approach for synthesising origin-destination trip tables from link traffic counts. Transportation Research 28B, 213-233. Slavin, H. (1996) An integrated, dynamic approach to travel demand forecasting. Transportation 23, 313-350. Tamin, O.Z. and Willumsen, L.G. (1989) Transport demand model estimation from traffic counts. Transportation 16, 3-26. van Vuren, T. (1994) The trouble with SUE stochastic assignment options in practice. Proceedings 22nd European Transport Forum, University of Warwick, September 1994, UK. van Zuylen, H.J. and Willumsen, L.G. (1980) The most likely trip matrix estimated from traffic counts. Transportation Research 14B, 281-293. Willumsen, L.G. (1981) Simplified transport models based on traffic counts. Transportation 10, 257-278.

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Yang, H., Sasaki, T., lida, Y. and Asakura, Y. (1992) Estimation of origin-destination matrices from traffic counts on congested networks. Transportation Research 26B, 417-434. Yang, H., lida, Y. and Sasaki, T. (1994) The equilibrium-based origindestination matrix estimation problem. Transportation Research 28B, 23-33.

14

Simple Models of Highway Reliability: Supply Effects Luis G. Willumsen and Nick B. Hounsell

Abstract It is accepted that one of the most significant problems generated by congestion is not only the increase in travel time itself, but also a deterioration of its reliability. Drivers often complain that it is the unpredictability of travel time that they dislike most of a journey in a congested city or area. From the point of view of demand, surveys can be undertaken to ascribe values to changes in the reliability of travel time, probably using Stated Preference, or related techniques. This can contribute to the development of richer and better utility functions for use in aggregate or disaggregate choice modelling. However, in their application, these models will require predictions of how the reliability of travel time will change when conditions in the network change: these are the supply effects. One would expect reliability to depend on similar factors to those affecting congestion: capacity, travel time and flows. However, there may be also some new factors like the number of junctions encountered in a route, their type and so on. This chapter reports on a exploratory research project aiming at developing simple and manageable models of these supply effects. The models were developed using a combination of simulation and survey work, one complementing the other. The resulting models seem to explain a good deal of the variability of travel time encountered in the study area. Nevertheless, further work is needed in other areas and with other functional forms to develop more transferable and robust models.

Introduction Congestion increases travel time but it is also likely to affect its reliability and, with it, our ability to estimate how long a journey would take before we embark on it. Greater uncertainty in these estimates would make us take preventive action, perhaps departing many minutes earlier than

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strictly necessary as we do not want to pay the penalty of a late arrival at our destination. The UK Department of Transport has funded a substantial research programme into urban congestion and the possible role of road pricing. A key element of this research was the development of a strategic road pricing model (APRIL) to enable the impact of alternative road pricing proposals to be evaluated. To enable travellers" responses to road pricing to be assessed (e.g. change of mode, time of travel, route, destination etc.) APRIL has been specified to be sensitive to a number of attributes of travellers and of the "supply system"—in particular, the highway network model. One factor which is perceived to influence demand is travel time reliability. APRIL'S formulation, based on generalised cost concepts, was therefore extended to incorporate a reliability indicator, the precise nature of which was to be derived through empirical research. The Department of Transport commissioned Steer Davies Gleave, with the Transportation Research Group at the University of Southampton, to undertake a three-month research project into highway travel time reliability and its supply effects. This chapter describes our findings and conclusions. The methodology adopted covers the following stages: (a) A general review of research on travel time reliability and its relationship with supply and demand; this is summarised in the second section of this chapter. (b) The development of a suitable simulation model to explore the effects of congestion and changes in supply characteristics of travel time variability; this is described in the third section. (c) The design and implementation of a limited survey in London to calibrate the model form selected in (b); this survey and the resulting calibration and validation of the model are reported in the fourth section. (d) To draw conclusions from the research, as reported in the fifth section.

Review The first phase of the study involved a detailed literature review to identify previous studies concerned with journey time variability and its prediction. In particular, the review was aimed at identifying:

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253

(a) Possible traffic and network indicators for inclusion in the models; and (b) Typical levels of journey time variability for comparison with the results predicted from the subsequent modelling work.

Sources of travel time variability There could be many reasons for variability in travel time; one of them is, of course, "inter-vehicle" variability in travel time can still occur due to differences in driver styles and vehicle type. Other causes of such variability can be related to junction operations such as the arrival time at signals relative to the signal aspect and to characteristics of the road, e.g. loading/unloading or lorries, parking and pedestrian movements. However, a key factor affecting travel times and their variability is the level of congestion, which itself depends on the relationship between demand and supply. Factors which influence demand include time of day (travel to and from work), day of the week (working days, Fridays) and time of year (influenced by holidays, school terms etc.). Factors which influence supply including weather conditions (e.g. rain and fog), lighting conditions and incidents such as accidents, breakdowns, signal failures and road works.

Previous studies A number of surveys have been undertaken in London to measure travel times and associated variability on selected routes. All studies reflect between-day variability, and most reflect inter-vehicle and within-day variability to some extent. Key findings are: (i) The coefficient of variation (CoV) of travel time, i.e. the ratio of standard deviation to the mean, increases with reducing average speed. Thus, variability increases with increasing congestion. For example, early work by Smeed (1968) indicated CoV values of 0.33, 0.70 and 2.30 at speeds of 20, 10 and 5 mph, respectively. In later work (Smeed and Jeffcoate, 1971), CoV values ranging from 0.11 to 0.15 for mean journey times of between 62 and 79min, corresponding to different starting times in a peak period, were recorded. (ii) For current average speeds in central London of 10-12 mph, the

254

Travel Behaviour Research: Updating the State of Play typical CoV found on one route was 0.15-0.20 for journeys on repeated days with the same start time (excluding journeys affected by incidents).

Surveys have also been carried out in Leeds (Montgomery and May, 1987) and also in a few other cities; in general, little research has been carried out on these supply effects: how to explain travel time variability as a function of easily obtainable network and flow data.

Modelling Simulation models The second phase of the study involved the use of network modelling to generate a database of typical journey time variability for origin-destination (OD) movements from which generalised predictive models for journey time variability would be produced. The key requirements for the model were that it should adequately reflect time-varying demand, queuing and congestion, and provide journey time predictions for individual OD pairs so that both within- and between-day variability could be monitored. The model had also to be well-established, with proven capabilities for dynamic assignment and junction/link modelling on a network of sufficient size for the study. These requirements led to the selection of CONTRAM (Leonard et al., 1989), and its incident-derivative, CONTRAMI (University of Southampton, 1992), for use in the study. CONTRAMI loads routes from the normal case and these remain fixed when modelling an incident, except that "regular" drivers can divert at any junction if they encounter an unexpected queue ahead and if a reasonable alternative route exists.

The network The network used in this study was a CONTRAM model of an area in inner London (north). The network area is defined by the River Thames to the south, the A102(M) to the east, the North Circular to the north and Huston Station to the west. This represents an area of around 100 km2, with trip lengths of up to 15 km. Network congestion is high in this part of London. The average network speed in the time periods modelled was

Simple Models of Highway Reliability: Supply Effects

255

14km/h. The network consists of over 1,600 links (of which over 50 percent are signal controlled), 560 junctions and 195 ODs.

Methodology The key requirements of the modelling were that is should be possible to represent the main causes of between-day journey time variability and that, by suitably combining runs of different scenarios, a reasonable representation of journey time variability could be obtained for a large variety of OD movements in the network. The modelling was aimed at generating indicators of the main factors affecting journey time variability, and typical trends, with calibration being subsequently achieved from surveys. Three main causes of journey time variability were identified for representation in the modelling: (i) day-to-day fluctuations in demand; (ii) environmental effects on capacity; (iii) traffic incidents. Random between-day variability in demand was generated following a procedure adopted by the MVA Consultancy (1989) in an earlier study. This involved attributing a normal distribution to each OD demand level, in which the variance was set equal to the mean, and randomly sampling from this distribution to produce a "new" OD demand. This produced a mean and variance of the percentage change in demand of 0 and 18 percent, respectively, when averaged across all OD pairs. This procedure was repeated several times, using different random numbers, to produce a set of randomly differing OD demand files. Systematic between-day variability in demand was introduced by applying a multiplying factor to all OD demand levels (i.e. factors of 0.94, 0.97, 1.03 and 1.06). Environmental effects on capacity were introduced by reducing junction saturation flows by six percent to account for the effects of wet weather, as reported by Kimber et al. (1986) for traffic signals. Aside from the availability of CONTRAMI, a further enhancement was made to CONTRAM to allow between-day variability in minor incidents to be reflected. Although empirical evidence is scarce, experience suggests that repeated minor incidents—illegal parking, short breakdowns and so forth—are an important contributory cause of between-day travel time variability. This enhancement consisted of introducing random (but con-

256

Travel Behaviour Research: Updating the State of Play

strained) saturation flow reductions on around 50 percent of links, which gave an average decrease in capacity (for those links affected) of around five percent (with a range of between 1 and 20 percent).

Analysis From our review of the literature we chose the standard deviation of the travel time (s) as the main indicator of travel time variability; this is our dependent variable. The average route journey time for 2,000 selected OD pairs for one time period was recorded for each of the CONTRAM runs indicated above. The standard deviation of the route journey time was calculated for each OD pair from this dataset. The selection of 2,000 OD pairs gave rise to a large database, incorporating a variety of trip attributes: (i) (ii) (iii) (iv)

different levels of congestion; a mixture of trip lengths; trips in "inner/outer" London; radial/orbital routes.

The independent variables considered were largely constrained by the need for compatibility with APRIL—for this reason variables, such as lagged flows, which were suggested from the literature review, could not readily be used here. For example, we suspected that the "total number of traffic signals" in a route would also contribute to travel time variability. However, this is a difficult choice as we would have to develop also a route choice model incorporating this element. Moreover, APRIL considers only a very simplified network with no network data distinguishing signal controlled junctions. Therefore, the variables chosen were free flow travel time (FFTT), delay (JT-FFTT) and a congestion index (CI = JT/FFTT), where JT is journey time. Many trips incorporated a mixture of inner/outer and radial/orbital links, and it proved impractical to attempt to separate these with the network available. "Atypical" trips with a journey time of less than two minutes, or a congestion index of more than five minutes, were discarded from the database.

Simple Models of Highway Reliability: Supply Effects

257

Results We looked at the correlation between travel time variability and the proposed explanatory variables. We found considerable scatter in the data indicating that no one variable by itself is able to explain most of the travel time variability. Conceptually, it may be expected that the standard deviation of travel time (a) should increase with increasing CI. This is consistent with the results of Smeed (1968), who reported increasing coefficient of variability with reducing speed. It could be that, at high values of CI, increased congestion does not cause increased travel time variability perhaps because traffic has entered a "forced flow" state. We expected that travel time variability cr would increase with distance or its proxy FFTT. However, FFTT was found to explain only some seven percent of travel time variability in the dataset. On the other hand, we found a stronger correlation between a and delay (JT-FFTT). Also, there is evidence to suggest that the rate of increase of cr reduces as the level of delay increases. It must be noted that it is desirable to segment models by trip length or for the resulting models to incorporate trip length (or a suitable proxy) as an independent variable. Otherwise, the model may be valid only if the trip length distribution of the area where it is applied is similar to that of the original database used to calibrate it. Various linear and nonlinear regression relationships were investigated. The following four model formulations gave the best results:

The values of the best fit coefficients are given in Table 1. In this table the coefficient of determination (R2) is defined as: R2 - 1 - (RSS/TSS), where RSS is the residual sum of squares, and TSS is the total sum of squares. It is useful to consign the data ranges for the simulation runs. These runs considered Congestion Indices in the range: 1 < CI < 3, Journey Times in the range 140 < JT < 4,200 seconds and Free Flow Travel Times in the range 120 < FFTT < 2,000 seconds.

258

Travel Behaviour Research: Updating the State of Play Table 1 Regression relationships Model

Model No.

1 2 3 4 3 4

Simulation a = 131 (CI - 1) a = 98 CI + 0.07FFTT - 97 a = 37FFTT0 2 (CI - 1)

R2 (%)

cr = 13 (JT-FFTT)0 4

35 42 39 40

Survey a = 0.9FFTT0'87 (CI - 1) a- = 2 (JT-FFTT)0 75

88 94

The above models explained between 35 and 42 percent of the travel time variability found from the simulation runs. The simulation runs proved to be very helpful in understanding the issues and exploring alternative model forms; they also assisted in the design of the subsequent surveys used to provide a final calibration for these models.

Data Collection

Survey programme The final phase of the study required calibration of the "preferred" model (resulting from the CONTRAM runs) and subsequent validation of this model. To enable this, a programme of journey time surveys was undertaken by driving along a sample of those links represented in the network and noting the link travel times. In total, 40 weekday AM peak survey runs were conducted. To ensure consistency, the surveys commenced at the same time each morning and covered the same route. Considerable care was taken to ensure that the selected route was representative of the wider network. It was recognised that it was almost impossible to have a network that would fully represent all possible journeys in the strategic model APRIL. Moreover, our survey measures link (and not journey) travel times and their variability; because of their nature it is not possible to associate APRIL links directly to either

Simple Models of Highway Reliability: Supply Effects

259

CONTRAM or real (surveyed) links. Therefore, the survey was designed so that trips of different length could be identified and modelled. The journey times relating to five of the 40 links were "held back" to permit model validation at a later stage.

Results In order to study the relationship between trip length and travel time variability we grouped our observations into chains or 1, 3, 5 and 10 links. Regression relationships were obtained for each chain length for each of the four model formulations (l)-(4) which were proposed from the CONTRAM modelling. The two linear models, (1) and (2), demonstrated coefficient values which increased as the number of links in the chain increased. This result was not unexpected. In urban areas, the majority of the delay takes place at junctions and therefore the number of them are encountered in a route is likely to affect travel time variability. As such, models (1) and (2) were discontinued. Earlier regressions using the model form a = aFFTT (CI - 1) revealed a values that decreased as the chain length increased. In order to stabilise the a values, FFTT was raised to a power j8 < 1. After exploration using a range of values the power of 0.87 was found to give the most consistent a values (Table 1; model (3)). This result suggests that trip length, as a proxy for number of junctions in a route, has a multiplicative effect on travel time variability through the congestion index. Model (4) (Table 1) was also found to meet the criteria of good fit (high R2) and parameter stability. Both models, (3) and (4), were strong candidates at this stage having the following attributes: (i) Relatively simple model forms, being based on parameters available in APRIL. (ii) The models are logical in that a is zero when congestion (JT/FFTT) or delay (JT-FFTT) is zero and in that
260

Travel Behaviour Research: Updating the State of Play

CoV outside of the data ranges which were used to calibrate them. To this end, survey data was used and the models required to predict CoV and a for observed JT and FFTTs. Part of these results are shown in Table 2 for model (4); here the results of the model calibrated from simulation runs and from survey data are shown. As can be seen, the model calibrated on survey data is more consistent than that based on simulation runs. The predictions given by model (3) were found to be similar to those found in practice (Smeed, 1968) whereas model (4) underpredicted CoV at high values of FFTT and CI. Table 2 Predictions of journey time variability JT

(s) 450 600 900 900 1200 1500 1350 1800 2700

FFTT (s)

CI

300 300 300 600 600 600 900 900 900

1.5 2 3 1.5 2 3 1.5 2 3

Predicted a (CoV)

JT-FFTT (s)

Surveya

Simulation13

150 300 600 300 600 1200 450 900 1800

86 (0.19) 144 (0.24) 242 (0.27) 144 (0.16) 242 (0.20) 408 (0.22) 195 (0.14) 328 (0.18) 553 (0.20)

96 (0.21) 127 (0.21) 168 (0.19) 127 (0.14) 168 (0.14) 222 (0.15) 150 (0.11) 198 (0.11) 261 (0.10)

a

L Model (4) based on floating car data: a = 2(JT-FFTT)\0.75 Equivalent model based on simulation data: a = 13 (JT-FFTT)0 4. Figures in brackets are coefficients of variation (oYJT).

Conclusions Research has been undertaken to identify simple models to incorporate travel time variability into fairly conventional transport models. The strategic model for road pricing, APRIL, uses an extended generalised cost formulation where travel time variability is an additional cost element; this treatment is supported by research into the behavioural responses to travel time variability.

Simple Models of Highway Reliability: Supply Effects

261

Alternative functional forms for modelling the supply side of this formulation were explored using a combination of simulation work and detailed surveys in London. This work resulted in the development and calibration of the model: a = 0.9FFTT0 87 (CI - 1) This model offers a simple form for relating the standard deviation of travel time to network conditions and is relatively insensitive to trip length, therefore offering promise or adaptation to environments different from London. One advantage of this treatment is that journey time variability can be estimated after assignment and then incorporated into other choice models (time of day, mode, destination choice). Complex interactions between congestion, travel time variability and route choice are then avoided.

Acknowledgements The authors would like to acknowledge the assistance and dedication of F. McLeod of Southampton University and R. Bain from Steer Davies Gleave, in undertaking this research as well as the advice and ideas provided by John Bates during the project.

References Kimber, R.M., McDonald, M. and Hounsell, N.B. (1986) The prediction of saturation flows for road junctions controlled by signals. TRL Research Report RR67, Transport Research Laboratory, Crowthorne. Leonard, D.R., Gower, P. and Taylor, N.B. (1989) CONTRAM: structure of the model. TRL Research Report RR178, Transport Research Laboratory, Crowthorne. Montgomery, P.O. and May, A.D. (1987) Factors affecting travel times on urban radial routes. Traffic Engineering and Control 28, 452-458. The MVA Consultancy (1989) Estimates of autoguide traffic effects in London. TRRL Contractor Report CR129, Transport and Road Research Laboratory, Crowthorne. Smeed, R.J. (1968) Traffic studies and urban congestion. Journal of Transport Economics and Policy II, 2-38.

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Smeed, RJ. and Jeffcoate, G.O. (1971) The variability of car journey times on a particular route. Traffic Engineering and Control 13, 238243. Steer Davies Gleave (1993) Highway Reliability: Supply Effects. Final Report to the Department of Transport, Steer Davies Gleave and Transportation Research Group, University of Southampton, London. University of Southampton (1992) CONTRAMI: modelling the effects of incidents in urban networks. Report to the Transport Research Laboratory, Transportation Research Group, University of Southampton.

15

Detecting Long-Term Trends in Travel Behaviour: Problems associated with Repeated National Personal Travel Surveys Uwe Kunert

Abstract In Germany as in some other countries, household travel surveys have been repeatedly conducted on a national scale. The German KONTIV surveys of 1976, 1982 and 1989 are samples of some 35,000 to 40,000 people, reporting their travel for one day. The results of the two earlier surveys have been used for numerous analyses and are also the basis for travel demand forecasts and thus policy formulation. This chapter will first address the design features of the surveys and the effects of changes in the design of response quality. It will be argued, that even minor changes in survey design and handling may have effects on the measured responses. Furthermore, these effects can hardly be separated from real behavioural change as the true values of both effects remain unknown, and because of the long time intervals between surveys. Some indications for improvements of survey design will be given. A modelling approach identifies the main determinants of individual travel demand separately for different days of the week and different characteristics of demand (whether mobile at all, trip generation by purpose, by mode, by length) with logit and ANOVA techniques. The effects estimated by those models for the various years will be compared and interpreted with respect to behavioural patterns, changes and methodological influences.

Introduction Large-scale household travel surveys have been frequently used at the urban, regional and national level to collect information on the demo-

264

Travel Behaviour Research: Updating the State of Play

graphic characteristics and the travel behaviour of the population. For all three levels, significant sample sizes were collected to either represent regional variations on a national scale (e.g. 22,000 household in the 1990 US NPTS, Hu and Young, 1992), or to be able to estimate OriginDestination (OD) matrices for a specific geographical area. Generally, differences in survey design exist between both successive surveys for the same area and surveys for different territories or nations. The areas in which the differences occur are the sampling strategies, the instrument design (questionnaire) and the retrieval method. The sampling procedure may be based on household or people address registers, random route contact to households by an interviewer, or random digit dialling of telephone numbers. Some form of stratification of the sample may be employed. If the household is contacted by mail or interviewer, .some form of diary is used to ask each individual to record all trips for a selected day or days. Instead of a self administered questionnaire (SAQ), a home interviewer, or a telephone interview, may collect the household and travel information. Finally the retrieval of the completed questionnaire may be by mail, an interviewer or the information in the questionnaire may be retrieved by telephone using the CATI technique. There are many other variations possible within those dimensions of survey design, however, there is some preference for the one-day diary format (Brog et al., 1985a; Stopher, 1985). Associated with all kinds of travel surveys are problems of nonresponse of parts of the sample (response rates range from 20-70 percent), item nonresponse and under-reporting of trips (Brog et al., 1982; Barnard, 1985; Wermuth, 1985; Golob and Meurs, 1986). Particularly short, nonhome-based trips appear to be under-reported. It is also documented in the literature that different survey designs yield different return rates and nonresponse effects (Kersten and Moning, 1985; Sammer and Fallast, 1985; Barnard, 1986; Stopher, 1992). Although there seems to be a certain consistency in the structure of the nonresponse effects, their magnitude is unique to each survey depending on the survey design and the actual empirical setting. This is why comparisons between survey results and the inference of travel trends from repeated cross-sectional surveys are difficult. This chapter will address this problem for the German KONTIV surveys and will propose research strategies to handle appropriately some of the effects of nonresponse.

Detecting Long-Term Trends in Travel Behaviour

265

Design Features of the Kontiv Surveys The German KONTIV surveys (the Continuous Travel Survey of the Ministry of Transport) conducted in 1976, 1982 and 1989 are general purpose census-type surveys. The samples comprise some 35,000-40,000 people reporting their sociodemographic characteristics and travel. The results of the two earlier surveys have been used for numerous analyses and are also the basis for travel demand forecast and, thus, policy formulation. The main elements of the KONTIV design have been developed in the seventies and early eighties and are well documented (Brog et al., 1985a, b). This design is now the common source of many other surveys. While there are some differences in the sampling strategies, the wording and layout of the questionnaires remain essentially the same for all three surveys (Table 1). The main distinction is that the two earlier surveys use a mailout, SAQ, mailback method, whereas, the 1989 survey is interviewer assisted at the delivery and/or retrieval of the questionnaire. There is no indication in the dataset as to whether help and if so what kind of help was given to the respondents, if it was a recall of yesterdays trips at the time of retrieval, or if the respondent gave information on the mobility of other household members, etc. This change in method is due to a change in the institute commissioned with the survey. Thus, the field work for the 1989 KONTIV survey was inserted with other surveys on the routes of the interviewers. In a comparative analysis of the methodology and results of different surveys, one can only incorporate information given in the dataset, or the accompanying documentation. One possibility is to control the completeness of the sociodemographic variables. For the three KONTIV surveys, the proportion of people with valid information for seven basic variables clearly declines (1976: 98 percent, 1982: 90 percent, 1989: 86 percent). Much of the information given cannot be controlled for its validity, e.g. the household size given in the questionnaire may be aligned with the number of household members willing to respond to the survey. We can check, however, the number of people with information about their mobility against the reported size of the respective household. This indicates a slight decline in the proportion of missing-person information for the three surveys (1976: 4.8 percent, 1982: 4.3 percent, 1989: 4.0 percent). However, for missing-person diaries, the field work institutes have imputed, to some extent, the person data to make up for the reported household size. This is partially reflected in the variable "reason for not being mobile" (Table 2). In the 1976 and 1982 surveys, the respondents

ON ON

ba

Table 1 Comparison of the KONTIV-surveys 1976 Sampling concept 1. stage unit procedure 2. stage unit procedure 3. stage unit procedure Diary day per person Distribution over week Sample size (households) gross sample non-genuine nonresponse cleaned-up gross sample net sample household response rate Field period Integrated additional non-response survey

Stratified random

TO

1982 Stratified random

1989 Stratified random

a S" § TO3 TO

Planning regions Stratified random

Communities Unproportional stratified random

Electoral districts Stratified random

Communities Stratified random

Households 34% address records 66% random route

Households Random route

•>s

s-

"

"a &. ». <£)

Households 100% address records 2 or 3 consecutive days Mon-Sun each 1/7 of sample

32,351 4,656 27,695 19,906 72% 1 Jan. 1976 to 31 Dec. 1976 no

S1 Mon-Fri 4/7 of sample Sat, Sun 3/7 of sample

1 Mon, Fri, Sat, Sun each 1/5 of sample Tues-Thurs 1/5 of sample

Cn ST

27,560 3,859 23,701 15,582 66% 1 Feb. 1982 to 30 Jan. 1983 no

38,811* — 38,811* 24,849* 64% 5 Feb. 1989 to 31 Jan. 1990 Telephone survey of households, which refused to answer main survey or could not be reached.

^ "a

TO

» ^

Gross-sample 4794 households Net-sample 2024 households Response rate 42% Survey method distribution of questionnaire completion of questionnaires retrieval of questionnaires Send out material notification of forthcoming survey data privacy information household questionnaire age at which persons become eligible person questionnaire stamped return envelope possibly reminder and second mailing of questionnaire Number of eases for net sample** communities households persons trips persons 10 years and older trips of persons 10 years and older cases in dataset

By interviewer Self-administered, interviewer may help and check for completeness By interviewer

mail Self-administered by respondent mail yes -

yes

yes yes questions about household and personal characteristics 10 years

up to 7 trips per person yes

_ yes

6 years

—

yes

yes

-

262 15,601 41,297 113,240 41,241 113,131 122,044

263 15,685 39,239 107,403 38,411 105,740 116,737

904 20,644 42,283 110,434 40,181 105,951 118,008

* Includes sample additions in Northrhine-Westfalia Emnid-Institute could not calculate response rates separately for the parts of the sample. ** Cases of data set used by DIW, i.e. only the first diary day for 1976.

b

TO TO

S'

OQ

O 3 i TO^ § ^ 3 §•

s' ^ 1 TO3

a 5' s ON

268

Travel Behaviour Research: Updating the State of Play

were asked to state the reason for not being mobile in an open question, whereas, this was asked by the interviewer in the 1989 survey at the time of retrieving the questionnaires. A review of Table 2 shows that this yields the lowest share of missing or nonusable person diaries in 1989: 82 percent of the respondents report mobility, 14 percent state reasons for not being mobile and the information is missing for two percent. For the earlier surveys, the share of respondents reporting mobility is lower and the proportion of missing diaries is higher, especially for 1976.

Table 2 Respondents reason for not being mobile given in the KONTIV surveys KONTIV 76 People (%) No reason, i.e. trips reported Age Illness Weather Homework No out-of-home activity Other reasons Not at place of residence No person diary returned Nonusable person diary Not mobile, no stated reason

32,471 1,186

78.7 2.9

200 187 1,629 CN 772 CE 934 3,866

0.5 0.5 3.9 — 1.9 — 2.3 9.4

KONTIV 82 (%) People

KONTIV 89 People (%)

29,430 209 1,562 572 1,146 1,908 702 1,194 1,688 CN —

33,366 98 1.508 325 1,005 2,111 669 796 613 CN 42

76.6 0.5 4.1 1.5 3.0 5.0 1.8 3.1 4.4 — —

82.3 0.2 3.7 0.8 2.5 5.2 1.7 2.0 1.5 — 0.1

CN: Code nonexistent. CE: Code existent, but unused.

Comparing Results: Trends or Design Effects? Table 3 summarises some of the main results of the three KONTIV surveys. The volume and structure of the estimated total travel demand are determined by the proportion of people reporting mobility and tripmaking patterns (modes, trip-chains, duration, length). Since the proportion of people with valid3 responses and, of those, the proportion of mobile people differs so greatly, the design effects will obviously dominate the results. While the daily number of trips (of distance and duration) increased for 1976-1982, they sharply dropped in 1989. This development is not supported by any background variables and it can also be observed in Valid does not mean correct in the sense of "true values" but simply means usable diaries.

Detecting Long-Term Trends in Travel Behaviour

269

Table 3 Results of KONTIV-surveys* Proportion of persons with valid responses

%

86.0

91.8

96.5

Proportion of mobile persons among persons with valid responses

%

90.0

82.2

85.0

Proportion of mobile persons among all persons

%

77.8

75.6

81.1

Trips per mobile person and day Km per mobile person and day Hours per mobile person and day

km h

3.43 29.9 1.27

3.70 37.1 1.45

3.24 31.6 1.21

Trips per person and day Km per person and day Hours per person and day

km h

3.09 26.9 1.14

3.04 30.5 1.19

2.75 26.9 1.02

Average trip length Average trip duration

km min

8.7 22.2

10.0 23.6

9.8 22.2

33.9 9.0 34.1 11.0 12.0

27.5 11.2 37.9 10.3 12.3

28.2 12.0 37.8 12.1 9.7

4.4 2.6 50.3 21.9 20.9

3.3 2.9 50.4 18.4 24.4

4.2 3.6 53.8 20.7 17.3

21.9 7.8 4.7 2.3 30.5 32.7

21.2 8.2 5.6 2.6 28.8 33.4

23.0 6.9 4.2 1.9 27.7 35.7

24.0 6.2 10.8 1.5 12.6 44.9

21.9 7.5 12.8 1.9 12.9 42.7

26.8 5.8 9.8 1.0 13.4 42.6

Modal shares of trips walk bicycle car driver car passenger public transit of kilometres walk bicycle car driver car passenger public transit Purpose share of trips work-commute school work related service shopping recreation of kilometres work-commute school work related service shopping recreation * Persons 10 years and older, weighted. Sources: KONTIV 76, 82, 89; DIW.

%

270

Travel Behaviour Research: Updating the State of Play

the most unlikely segments in a disaggregate analysis by sociodemographic groups. Therefore, it is reasonable to conclude that the control of the diaries by the interviewer at the time of retrieval yielded an increase of mobile people with lower number of trips. When reporting at the door about one's own mobility, and especially about that of other household members, respondents may have made even more simplifications than when completing the diary by themselves. This is supported by an analysis of trip-chaining in the three surveys: the proportion of simple trip-chains is considerably higher in the 1989 survey. However, for some segments of the population, the higher proportion of mobile people and lower average trip numbers of the 1989 survey, may better reflect the true values than the earlier surveys: Housewives and retired people may have been persuaded after prompting by the interviewer to report their relatively few trips which they might not have done in a postal survey. For a regional travel demand survey, it is possible to obtain traffic flows from the network assignment of the weighted and expanded OD matrix and to balance those with traffic counts and public transit on board counts (Barnard, 1985; Wigan, 1985). The accuracy of this check is limited due to methodical problems and differences in the relevant trips. However, for nationwide travel surveys the feasibility of comparisons with external data sources are even more coarse. For Germany, comparisons are possible with the public transit and railway ridership reported in the annual national reports and with the estimates of the total mileage of cars based on fuel consumption models. For example, total mileage of the weighted and expanded survey results is 97 percent for 1976; 95 percent for 1982, and 69 percent for 1989 of the respective consumption model estimates and other possible comparisons are in line with this result. Thus, we conclude that the estimates for totals of the two earlier surveys are critically high, whereas, the 1989 survey yields mobility indicators and totals which are too low. In the results of the three surveys structural changes in the population, behavioural changes of the individuals and effects of different survey design are inseparably confounded.

A Modelling Approach to Identify Individual Determinants of Mobility and Trends in Their Effects The basic concept of this approach is for each survey to develop crosssectional separate disaggregate models for different dimensions or aspects

Detecting Long-Term Trends in Travel Behaviour

271

of mobility. The different dimensions of travel demand analysed by the stepwise modelling are: • • • • • •

Any out-of-home-activity reported (yes/no). Number of trips per mobile person. Number of trips per mobile person by six trip purpose categories. Number of trips per mobile person by four modes. Trip length by four trip purpose categories. Trip length by four modes.

Here, the first step—a logit analysis—is indicated because the differences in survey methodology, and in the treatment of the returned questionnaires, produce incomparable proportions of out-of-home-activity participation. Consequently, the following model steps are conditional on the first and represent mobile people only. It is then supposed that the more detailed the aspect of mobility is, the smaller the nonresponse and design effects will be in a comparative analysis. Thus, even though the reported trip length may be biased upwards due to under-reporting of short trips, the effects will be similar for the given trips in the three surveys. For each model step, first the significant contribution of each variable for explaining this aspect of mobility was tested separately for the three datasets, and the observed patterns of which and how the variables contribute were compared. Since these patterns show some conformity, models with the same structure were estimated for all three datasets in order to subsequently compare single effects, which may then be interpreted with a temporal dimension. With the stepwise procedure, both behavioural assumptions and suspected design effects should be represented. The models identify the main determinants of individual travel demand as possible with the accompanying demographic variables separately for different days of the week. For illustrative purposes, the results for weekday trip generation of mobile people are presented here. These are ANOVA models where the effects for significant variables are estimated by least-squares using SAS. The linear and additive effects are given in Table 4. To calculate fitted values for a given combination of characteristics, one creates the linear combination of all variables, with their marginal effects being evaluated at their respective means. Judging by the size of the estimated effects, the variables job position, age, occupation, car availability and education appear to be important in explaining weekday trip-making of individuals. The number of trips made

272

Travel Behaviour Research: Updating the State of Play

Table 4 Weekday trip generation of mobile people—variables and estimated effects (estimated with one way ANOVA) 1982

1976

Variables Intercept Age 10 to <18 18 to <25 25 to <65 65 to <75 75 + years Education elementary school, no exam. elementary school with exam. medium level exam. university entry level no answer/not applicable Occupation housewife no prof, education housewife prof, education retired in vocational training in school/college jobless part-time working full-time working Car availability own car and license car in household own license car in household no license no car no license Household size 1 person 2-4 people 5 people 6 + people Housing type rented room rented apartment rented house condominium farm own house Job position blue-collar worker white-collar worker public official farmer self-employed helping household member no answer/not applicable Community type big cities towns with central function towns rural Mean of dependent variable: trips per mobile person

1989

2.50

(0.19)

2.35

(0.19)

2.52

(0.15)

0.19 0.39 0.35 0.13 0.00

(0.12) (0.11) (0.10) (0.10) (-)

0.50 0.66 0.55 0.29 0.00

(0.14) (0.11) (0.10) (0.09) (-)

0.54 0.44 0.39 0.35 0.00

(0.10) (0.08) (0.07) (0.07) (-)

0.13 0.22 0.46 0.59 0.00

(0.10) (0.09) (0.10) (0.10) (-)

-0.16 -0.11 0.06 0.19 0.00

(0.09) (0.09) (0.09) (0.09) (-)

-0.11 -0.04 0.08 0.19 0.00

(0.05) (0.05) (0.05) (0.05) (-)

-0.04 0.10 -0.05 0.25 0.59 0.15 0.22 0.00

(0.14) (0.14) (0.15) (0.15) (0.17) (0.11) (0.05) (-)

0.18 0.35 0.27 0.22 0.56 0.16 0.38 0.00

(0.12) (0.11) (0.13) (0.14) (0.13) (0.16) (0.06) (-)

0.09 0.35 0.17 0.22 0.24 0.46 0.44 0.00

(0.07) (0.07) (0.07) (0.08) (0.07) (0.09) (0.04) (-)

0.71 0.39 0.07 0.00

(0.04) (0.04) (0.04) (-)

0.64 0.40 0.03 0.00

(0.06) (0.06) (0.06) (-)

0.38 0.30 0.09 0.00

(0.04) (0.04) (0.05) (-)

0.04 -0.02 -0.06 0.00

(0.08) (0.04) (0.05) (-)

0.32 0.11 0.13 0.00

(0.11) (0.09) (0.10) (-)

0.01 -0.25 -0.19 0.00

(0.11) (0.10) (0.11)

-0.01 0.07 0,05 -0.12 -0.22 0.00

(0.09) (0.03) (0.05) (0.06) (0.06) (-)

0.04 0.15 0.15 -0.01 -0.29 0.00

(0.13) (0.03) (0.08) (0.07) (0.10) (-)

0.14 0.09 0.03 0.26 -0.02 0.00

(0.07) (0.03) (0.05) (0.05) (0.11) (-)

-0.20 0.01 0.28 0.04 0.61 0.03 0.00

(0.13) (0.13) (0.14) (0.20) (0.15) (0.17) (-)

-0.07 0.21 0.51 0.48 0.85 0.08 0.00

(0.11) (0.11) (0.13) (0.26) (0.13) (0.16) (-)

-0.01 0.07 0.27 0.63 0.52 0.19 0.00

(0.06) (0.06) (0.07) (0.24) (0.08) (0.19) (-)

0.03 0.15 0.13 0.01

(0.04) (0.03) (0.03) (-)

-0.07 0.13 0.19 0.00

(0.05) (0.04) (0.04) (-)

-0.07 0.09 0.12 0.00

(0.03) (0.03) (0.03) (-)

3.57

Standard error of estimate in parenthesis. Sources: KONTIV 76, 82, 89; DIW.

3.74

3.31

(-)

Detecting Long-Term Trends in Travel Behaviour

273

on a weekday decreases with age, but increases with the educational level and car availability. The variable "occupation" shows lower trip-making for full-time employed, retired people and housewives without professional education. For the variable job position, small effects are given for workers, employees and household members helping self-employed people. High effects are associated with officials and self-employed people. At all times, people living alone, and residents of towns,5 exhibit higher trip rates than the rest of the population. Thus, quite similar patterns for explaining weekday mobility have been found with the three surveys. This is also valid for weekend mobility. On weekdays, the variables associated with compulsory activities like occupation and job status are important, whereas, on the weekend car availability, marital status and other variables indicating lifestyle and affluence are of higher importance (see Kloas and Kunert, 1993). Looking at changes over time,0 the estimated effects for education and gender (significant for the weekends) exhibit diminishing differences, i.e. the extent of higher trip-making for people with better education, and for men when compared to women, is reduced over time. Similarly differences between the categories of car availability and of job positiond diminish. On the other hand, for the categories housewife, jobless and part-time employed of the variable occupation, trip-making increases while it decreases for people currently in education. The evidence shown is valid when the estimated effects are corrected for the differently sized means of the three surveys, which are suspected to result, at least partially, from the methodological differences. Also, effects in the other models show some plausible trends, e.g. household size influences the number of service trips for other household members increasingly positively; people living alone have increasingly more leisure trips; the higher propensity of men compared to women to use the bicycle decreases; differences between blue- and white-collar workers and public officials in the frequency of using the car and transit nearly disappear, and the greater length of trips to shopping and educational activities in sparsely settled areas becomes more pronounced. Thus, different trends can be observed for the relation between the b

The variance explained by the models for overall trip generation is low (<10 percent) and for models of trip generation by purposes and modes, it varies between 3-55 percent. c Very few of the estimated effects are significantly different. d For job position, the categories farmer and helping household member have small numbers of cases and should be interpreted with care.

274

Travel Behaviour Research: Updating the State of Play

analysed dimensions of travel demand and the individual characteristics. For trip generation by purposes or modes, the variance between segments of the population is decreasing. This seems largely to be the result of the diffusion of car ownership, but can also be observed for purely sociodemographic criteria (men/women, more/less educated, worker/employee). On the contrary, for trip length, a clearer differentiation appears over time, especially related to the settlement structure in which the mobility takes place.

Conclusions This study has outlined the main features and results of the three German KONTIV surveys of 1976, 1982 and 1989. It has been shown that changes in the survey design which have been considered as minor at the outset (mail-out/mail-back SAQ versus SAQ with interviewer) and the handling and coding of the returned questionnaires, have drastic effects on the measured responses. Hence, the latest survey yields higher shares of mobile people and lower average number of trips per mobile and per person. As the differences in the results of the surveys are confounded, the effects of structural changes of the population, of real behavioural changes, the survey design and at least the true values of the two latter effects remain unknown, the relative contributions of these sources and population estimates of travel indicators cannot be reliably calculated. The presented approach to analyse the individual determinants of several aspects of mobility is sensitive to the hypothesised behavioural changes, and to the response quality which is heterogeneous over time and across the aspects of mobility. Therefore, out-of-home-activity participation (mobile yes/no), trip generation per mobile person, etc., are modelled separately. For each model stage, either unbiased values of the dependent variable are expected, or some good guess about the direction and the size of the bias can be accounted for. For example, trips per person would be severely biased, whereas, the two stages proportions of mobile people and trips per mobile person reflect the nonresponse process and yield consistent model structures for the three surveys and, thus, interpretable results. Here, the estimated effects for weekday trip generation are presented and some unbiased temporal trends can be derived. "Garbage-in, garbage-out" also applies, to some extent, to the use of data in transportation modelling and policy formulation. The end-user of data collected with travel surveys has only very limited opportunities to

Detecting Long-Term Trends in Travel Behaviour

275

correct for errors and uncertainties prevailing in the phases of the planning and field work of surveys. Thus, repeated cross-sectional surveys should be planned carefully, incorporating past experience and new methodology, and should be guided by the experiences of experts of fieldwork and data analysis (see Taylor et al., 1992). Changes in the survey methodology should be gradual. For each survey, a tailored analysis of the nonresponse of households, people and trip underreporting is essential, and should include a nonresponse evaluation with respect to methodological changes from earlier surveys. The individual person and household data should be supplemented with information about the data-collection process (interviewer number, number of contact trials, questionnaire completion by whom—with help of interviewer, etc.). Only then it is possible to analyse the sources and effects of changes in the survey method in more depth. If the motive for collecting data is to analyse travel trends, behavioural changes and causal relationships, a panel design instead of repeated cross-sectional surveys should be employed (Hensher, 1985).

Acknowledgements This chapter is based on research work funded by the German Department of Transportation. The views expressed are solely those of the author. The author wishes to thank Jutta Kloas' contribution to this research.

References Barnard, P.O. (1985) Evidence of trip under-reporting in Australian transportation study home interview surveys and its implications for data utilisation. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Barnard, P.O. (1986) Use of an activity diary survey to examine travel and activity reporting in a home interview survey: an example using data from Adelaide, Transportation 13, 329-357. Brog, W., Erl, E. and Meyburg, A.H. (1982) Problems of non-reported trips in surveys of non-home activity patterns. 61st Annual Meeting of the Transportation Research Board, Washington, D.C., January 1982, USA.

276

Travel Behaviour Research: Updating the State of Play

Brog, W., Meyburg, A.H., Stopher, P.R. and Wermuth, M. (1985a) Collection of household travel and activity data: development of a survey instrument. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Brog, W., Fallast, K., Katteler, H., Sammer, G. and Schwertner, B. (1985b) Selected results of a standardised survey instrument for largescale travel surveys in several European countries. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Golob, T.F. and Meurs, H. (1986) Biases in response over time in a seven-day travel diary. Transportation 13, 163-181. Hensher, D.A. (1985) Longitudinal surveys in transport: an assessment. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Hu, P.S. and Young, J. (1992) Summary of travel trends, 1990 nationwide personal transportation survey. Report No. FHWA-PL-92-027, US Department of Transportation, Washington, D.C. Kersten, H.M.P. and Moning, HJ. (1985) Differences in estimates due to changes in methods of data collection. Netherlands Central Bureau of Statistics, Voorburg. Kloas, J. and Kunert, U. (1993) Vergleichende auswertungen von haushaltsbefragungen zum personennahverkehr (KONTIV 1976, 1982, 1989). Report to the Federal Department of Transportation, Berlin. Sammer, G. and Fallast, K. (1985) Effects of various population groups and of distribution and return methods on the return of questionnaires and the quality of answers in large-scale travel surveys. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Stopher, P.R. (1985) The state of the art in cross-sectional surveys in transportation. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Stopher, P.R. (1992) Use of an activity-based diary to collect household travel data. Transportation 19, 159-176. Taylor, M.A.P., Young, W., Wigan, M.R. and Ogden, K.W. (1992) Designing a large scale travel demand survey: new challenges and new opportunities. Transportation Research 26A, 247-261. Wermuth, M. (1985) Errors arising from incorrect and incomplete infor-

Detecting Long-Term Trends in Travel Behaviour

277

mation in surveys of non-home activity patterns. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht. Wigan, M. (1985) The secondary use of transport survey data. In E.S. Ampt, A.J. Richardson and W. Brog (eds.), New Survey Methods in Transport, VNU Science Press, Utrecht.

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16

Mobility Surveys in Lisbon and Porto; A Comparative Analysis of Results Jose Manuel Viegas and Faustina Guedes Gomes

Abstract Large-scale mobility surveys in Portugal were conducted for the first time in Porto in 1992 and in Lisbon in 1993. In both cases, it was felt that the information thus collected was indispensable to support decision processes about transport networks and policies. Since the two studies have been made using essentially the same methodology, results are easily comparable and provide a deeper understanding of the reasons behind the statistics in each case. This chapter reviews some of the main indicators, presented in parallel for the central city and the suburban municipalities of both areas, and develops some comments about the possible explanations for the differences.

Introduction Objectives of these mobility surveys A Mobility Survey is much more expensive to undertake than a traditional Origin-Destination (OD) survey, since it must collect and process information about household composition and professional status, as well as information about their own means of mobility and all the trips made in a day by one or several of the household members. The main reason why the extra cost is considered worthwhile is that a much better understanding of mobility decisions can be obtained (Taylor et al., 1992), from which (hopefully) a more direct interpretation can be made of what elements or attributes the transportation system is lacking. Additionally, better

280

Travel Behaviour Research: Updating the State of Play

predictions can be made about how people will react when confronted with new transportation conditions, be it in the modes available, the frequencies and itineraries of those modes or even in the prices. No Mobility Survey was undertaken in Portugal until the beginning of the nineties. The last OD surveys were conducted in the early seventies in Lisbon and Porto, after which a widespread process of suburbanisation occurred in these two cities, accompanied by a large increase in car ownership. In Porto in 1992 and Lisbon in 1993, similar Mobility surveys were launched, from which substantial gains in the understanding of the mobility conditions can be achieved. In the case of Porto, the client was (STCP) the public transport company serving the city itself as a monopoly, but with a relatively extended network into the suburbs, serving parts of five additional municipalities. The surveyed area was defined by the 49 boroughs (freguesias) served by the company, and the fieldwork undertaken between February and May 1992. In Lisbon, the client was Metropolitano de Lisboa, a company operating the underground transit system. Although this system only serves part of the city itself, the fact that many commuters from suburban areas regularly use the Metro daily led to the decision that the whole Metropolitan Area should be surveyed. This is a much wider area, and necessitated the organisation of the survey into two phases, as reported later. The fieldwork for the first phase took place between March and June 1993, and the second phase started in March 1994. These two surveys were conducted using the same technical direction and very similar methodologies, so that comparisons between the two cities could be made, in the hope that this would also help explain the values obtained in each of them. This chapter presents some of the results, and develops some interpretations for the similarities and differences.

Brief characterisation of the Lisbon and Porto metropolitan areas Lisbon and Porto are the centres of the two largest conurbations in Portugal. Both are coastal cities, located adjacent to large rivers, the Tejo and Douro, respectively. Table 1 presents some indicators about the areas surveyed. As mentioned above, the area surveyed in the Porto region is only a part of the Metropolitan area (which is formed by nine municipalities). Still, some conclusions can be taken from the data in Table 1:

Mobility Surveys in Lisbon and Porto

281

Table 1 Main dimensions of surveyed areas in Lisbon and Porto Surveyed area

No. of municipalities

Area (km2)

Resident Population (1991 census)

Porto (central city) Suburban municipalities

1 5

42 517

302,535 710,849

Total (Porto)

6

559

1,013,384

Lisbon (central city) Suburban municipalities (1st Phase)

1 6

84 901

663,404 785,564

Total (Lisbon 1st Phase) Suburban municipalities (2nd Phase)

7 11

985 1852

1,448,968 1,042,980

Total Lisbon

18

2837

2,491,948

• The area and population surveyed in Lisbon is much larger than in Porto, even if we consider only the first phase (40 percent more population, 75 percent more area). If we include both phases of the Lisbon survey, the area is five times larger, and the population is 2.5 times larger. This has been an important factor (but not the only one) in the order of realisation of these surveys. • The percentage of the population in the central municipality, in relation to the whole surveyed area, is similar in the two cases if we consider the global programme for Lisbon: 30 percent for Porto and 27 percent for Lisbon.

Methodology

Survey form The survey instrument used in both surveys was identical, with only changes in detail. This form was developed, and tested, so that the terms used were intelligible by less literate people, and most answers were given through multiple choice. The survey instrument was divided into three main blocks: Family identification, with postal address, town and administrative

282

Travel Behaviour Research: Updating the State of Play

unit (county or borough) of residence, number of people living in the house, number of cars and motorcycles in the household. • Characterisation of all persons in the family through the following variables: year of birth, sex, main professional activity, working hours, public transport title (type of ticket) normally used. • Description of all trips made by one of the members of the family in the day before questioning, with a detailed description of every trip, including place of origin and destination, time of start and duration, trip motive, number and location of transfers made in that trip, transport mode used on arrival at destination (and in every trip-leg, if there were transfers), whether the trip was made alone or in company (in the latter case, whether, or not, any of the accompanying persons was of reduced mobility), and the main reason for choosing that mode or combination of modes. An activity recall approach was used for keeping the interviewee's memory in line with his travel of the previous day (Axhausen and Garling, 1992).

Contact and survey procedures Before the general Mobility Survey was conducted in Porto, a previous pilot survey had been made there by the same team in 1991, in order to test procedures and estimate productivities (Groves, 1989). In that pilot case, most surveys were conducted by the interviewer at the homes of the interviewees, and others by telephone (Brog and Meyburg, 1983). Probably because there is still an emerging market for telemarketing procedures in Portugal, the percentage of people not wishing to answer the survey by phone was smaller than with the live interviewer (in both cases a letter signed by the Chairman of the transport company promoting the survey was sent to all interviewees). Moreover, the average number of trips reported was very similar in the sets of interviewees by both types of contact, so it was decided to adopt the phone as the main type of contact, given its advantages of cost and speed. In both Porto and Lisbon, most areas have over 80 percent of houses equipped with telephones. Thus, only areas of much lower coverage by phones were surveyed by the physical presence of interviewers. In the case of Porto, it was decided that the survey would cover two different segments of users of the transport system—residents and visitors. Residents were contacted and interviewed by phone or inhouse, and visitors were contacted (but not interviewed) as they crossed or exited a cordon around the study area, and declared

Mobility Surveys in Lisbon and Porto

283

not to live there. They were then given an envelope with the questionnaire and all explanations, and could answer by prepaid mail or by token freephone, with an interviewer to conduct the survey. Most visitors preferred to reply by phone. In Lisbon, given the much larger dimension of the region, it was decided to exclude visitors (the relative weight of this segment diminishes as we enlarge the study area and most suburban citizens are classified as residents), and also to conduct all first-phase surveys by phone. The secondphase survey also used phones as the primary form of contact for the areas not yet covered, and the house visits for secondary contact where the number of possible phone surveys was unsatisfactory, or a lower percentage of houses equipped with phone would imply a significant risk of sampling bias.

Site dictionary In developing the survey for transport companies, it was obvious from the start that zoning would be a problem, since statistical robustness of the estimates produced would require relatively few and large zones, but practical considerations of bus-stop and underground access locations would create a permanent pressure for many smaller zones. In the case of Porto, the main justification for the completion of the Mobility Survey was the need for this information in order to develop a much needed restructuring of the bus network, for which relatively detailed locations are required, in relation to transfers between lines. In both cases, tariff regimes were, still are, visibly in need of change, but for this the Government (both companies are nationalised) will inevitably require a comparison of before and after revenue estimates, for which the identification of boarding and alighting stations is needed. Thus, we understood that we needed not only a reasonable level of detail in the location of trip starts and ends, but also a variable zoning scheme, relative to the question being treated. So, it was decided to adopt a detailed coding of origin, destination and transfer points, for which the interviewee was asked about town, borough or county, street name and number or, in the absence of the latter, a landmark of common knowledge. This could be a shop, monument, cinema or an administrative unit, etc. In the background, a segment-based geographical information system was being devised, called the Site Dictionary. This was first used in the Porto survey and later also in Lisbon. The concept is very simple. Any

284

Travel Behaviour Research: Updating the State of Play

location within the study area reported with the information referred above must be translated into a (x,y) pair of coordinates. This spatial codification should be reasonably rigorous and it is believed that, for most cases, margins of error below 50m in the consolidated urban areas (and below 300m in lower density suburban areas) have been obtained. The developed dictionary is organised around a database with six different layers: counties, towns, streets, street network nodes, street network segments and landmarks. For the larger towns and streets, their nodes and segments are described, whereas, for the smaller towns, only the town itself is described. For each street segment, the attributes coded are the street to which it belongs, the node numbers that define the segment and the extreme door numbers (minimum and maximum, even and odd). In the presence of a certain door number of a street in a survey, the segment of that street is detected for which this number is located between the extremes of that parity, and the coordinates of that house are obtained by linear interpolation between these extremes (for which we know the door numbers and the coordinates). Another interesting feature is that this dictionary was devised with some tolerance for incorrect description of names at all levels (towns, streets, landmarks). Any such reference is decoupled in words, and each word is used as a search key. The sets so defined for each word are then intersected, and as long as at least one word has been spelled correctly, the correct register will be in the set. For any candidate register, the name it includes is then compared, wordby-word, with the name given in the survey. In this process, a fuzzy algorithm is used to determine intermediate levels of "likelihood" of the word being the same in both entries. In the end, the register with the highest mark is selected, as long as its global likelihood is above a certain threshold. When a site is referred to in a survey that cannot be attributed to any of the items in the database, it is impossible to load its coordinates directly in the survey file. The site must be loaded in the dictionary, and the allocation procedure run again, so that there is a permanent process of enrichment of the database. For each analysis that had to be conducted, the zoning schemes were redefined, sometimes wholly, sometimes only partially. In any case, a set of polygons totally covering the study area (and the "rest of the world", so that external points can also be coded) must be defined. Once those polygons are defined and the trip extreme points have their (x,y) coordinates, a simple point-in-polygon algorithm allows the reallocation of zones to all those points.

Mobility Surveys in Lisbon and Porto

285

Comparison of some Mobility Indicators

General indicators Table 2 shows some of the general mobility indicators obtained in these surveys. Here (and in the remaining tables of the chapter), it was decided to present the results separately for the two areas of Lisbon and Porto, but also distinguishing the central city from the suburban municipalities in both cases. This will possibly allow a clearer view of the main factors behind the different values obtained for any of the subpopulations. As Table 2 shows, the percentage of people not leaving home is similar between these two areas, although Lisbon has a higher value of almost 10 percent. As for the total trip time per day, Lisbon presents a higher value, which is certainly due to the larger size of the conurbation. Since the geographic coding procedure for Lisbon is not yet complete, it is impossible to corroborate this statement by values of total distance travelled. In both cases, total trip time is larger for the suburbs than for the central city, the difference for Lisbon being larger than for Porto. Lisbon also has more trips per day, but with average shorter times per trip. This may be due to the fact that in Lisbon there is an underground system that allows much better speeds than surface transport; contrary to Porto in which only these are operating. Here again, the central city has a more favourable situation (higher number of trips) than the suburbs, but the difference is larger in the case of Porto. An interesting situation can be detected when we analyse the number of noncompulsory trips (all except work or school related, returning home, or meals) per day in both areas. It would be expectable that Lisbon would present higher values in this respect, but, in fact, it is Porto that leads by a considerable margin. We find two possible explanations for this. First, in the Lisbon survey, there was an explicit trip motive identified as "returning home", whereas, in Porto this was not in the list of possible motives. Serious efforts have been made to make the two trip motive sets comparable, but there may be a margin of error that explains part of this difference. The second factor is that in the Lisbon area, a larger percentage of the feminine population is working at home, so they do fewer noncompulsory trips, while the women in Porto have a smaller total number of trips, but the majority of those would be classified as noncompulsory.

286 Travel Behaviour

Table 2 General mobility indicators

>3

General indicators

Non-mobile people (%) Average travel time per day (min) Average number of trips per day (per inhabitant) Average number of trips per day (persons with mobility) Average number of noncompulsory trips per day

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

§

§ ft"

14.6 75.5 2.30

18.4 79.5 1.99

17.1 78.1 2.10

20.5 83.4 2.23

22.4 95.4 2.11

21.5 90.0 2.17

2.69

2.44

2.53

2.80

2.72

2.76

1.06

0.96

1.00

0.79

0.62

0.70

•**

5' °^

TO 00 5? TO*

^

Mobility Surveys in Lisbon and Porto

287

Car ownership Table 3 shows the values relative to some car ownership indicators, not only for the number of cars per thousand inhabitants, but also about the distribution of families according to their level of motorisation. It is interesting to note that in both areas, families in the central city are less motorised than those living in the suburbs, the difference being much more visible in the case of Lisbon. A normal explanation for this would be that the public transport networks are much denser in the centre, so that people have less need of a car. But, we believe the main reason is different. The population of these central cities has a considerably larger stratum of old people than is the case for the suburbs. In the case of Porto, the percentage of population over 65 years-of-age is 14.8 percent for the central city and 9.0 percent for the suburbs. In Lisbon the difference is even larger, 18.4 percent in the central city versus 9.4 percent in the suburbs. In a global comparison, this part of the Lisbon area has a slightly higher car ownership level than Porto (about 4 percent difference).

Modal split Table 4 presents modal split figures for both cities. In Porto central, shortrange public transport is the market leader, being used for over 50 percent of the trips made. The global value for the Porto area is slightly smaller, but nonetheless clearly ahead of the other modes. In the suburbs, the lost share is captured by walking, bicycle and by the private car. Long-distance public transport has a very low share in all of this area. In Lisbon, although short-range public transport is still the market leader, its difference to the others is considerably smaller, the corresponding share going to private cars and longer-range public transport (subregional transport in most cases). It is also worth noting the comparatively high value of 'Park & Ride' for the suburban municipalities of Lisbon. This is clearly due to the existence of the Metro, but also probably due to the suburban railways, which play a much stronger role in this region than in Porto.

288 Travel Behaviour Rese

Table 3 Household car ownership indicators Families with

No car (%) One car (%) Two or more cars (%) Cars per 1000 inhabitants

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

40.5 40.8 18.7 257

33,.8 44,,7 21..5 238

36.2 43.3 20.5 243

38,.7 45,.6 15,.7 242

25,,8 54,,8 19,.4 254

31.8 50.5 17.7 249

^ & S' Crq ^

ST

Table 4 Distribution of transport modes per trip Modal split

On foot/bicycle (%) Private car/motor bike (%) Short range transit (%)* Medium + long range transit (%) Taxi (%) Transit + private car (%)

Porto (central)

24.7 22.4 51.6 0.3 0.5 0.5

Suburban municipalities

28.2 29.1 40.9 0.8 0.5 0.5

* Short range transit denned as having a trip duration under one hour.

Total Porto

26.9 26.6 44.9 0.6 0.5 0.5

Lisbon (central)

22.1 29.0 42.0 4.4 1.4 1.1

Suburban municipalities

22.6 32.6 32.0 7.8 0.2 4.8

Total Lisbon (1st phase)

22.4 30.8 36.8 6.2 0.8 3.0

^ 2"
^ On

a' S3O

a a o. o o N> 00 VO

290

Travel Behaviour Research: Updating the State of Play

Reasons for choice of transport mode Table 5 shows information concerning the reasons declared for the choice of mode in every trip. Two main differences are evident in Table 5. In Lisbon, people are more inclined to declare that their travel time is an important factor, whereas, in Porto, more people feel that they had no alternative. Even if these two factors are the most important in all subgroups, the lack of alternatives is perceived as the most important one in the suburbs of Porto. It is also interesting to note that, although public transport prices of nationalised companies are very similar in the two cities, the "price" reason is substantially stronger in Porto than in Lisbon. This may be due to the fact that, in the suburbs around Porto, there are a number of private operators in direct competition with the nationalised company, charging a higher price than the latter. The higher significance of the "quickness" reason in Lisbon may be explained by the presence of the Metro in the transport habits of its citizens, since it lowers the tolerance for waiting times in other transport modes.

Trip motives Table 6 shows the distribution of trip purposes in these populations. As noted above, there was one difference in the set of motives allowed for in these two surveys, since in Lisbon, the motive "Return Home" was added, after the experience of Porto showed that the final leg of a multipurpose trip-chain was difficult to classify in its absence. In spite of this difference, it is still clear that the Home-Work (or school) relationship is still the most important one. In the case of Lisbon, if we deduct the percentage of trips returning home, there are some 60 percent of the trips left, and half of these are from home to work (or school). The remaining 30 percent include all other home-based and nonhome-based trips. Shopping/Leisure is also an important motive in both cases, but with a greater weight in the case of Porto. It is interesting to note that this is the first set of indicators in which the distributions of central city and suburbs are practically equal, and this happens in both areas.

Table 5 Reasons declared for choice of transport mode Main reason (%)

Quickness (journey time) Price No alternative Difficult parking Conditioned by previous trip No car available Arranged with other people Other reasons

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

43.2 8.2 31.0 2.4 1.6 1.5 4.5 7.6

34.2 9.4 37.6 1.1 1.1 0.9 3.9 11.8

37.6 9.0 35.1 1.6 1.3 1.1 4.1 10.2

63.6 1.1 21.1 0.4 0.3 0.4 0.9 12.2

51.5 1.8 28.1 0.2 0.2 0.7 1.3 16.2

57.4 1.5 24.7 0.3 0.2 0.5 1.1 14.3

o

to

5s

Table 6 Distribution of trip purposes Trip purposes (%)

Home-work (or school) Return home Work-work On duty Shopping/leisure Picking up family member Personal matters Meals Others

a

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

c

51.4 — 2.8 5.7 13.2 3.1 13.6 6.5 3.7

53.9 — 2.5 2.6 16.0 2.8 14.0 4.2 4.0

53.0 — 2.6 3.8 15.0 2.9 13.8 5.0 3.9

29.5 39.5 — 2.6 10.7 2.0 8.6 4.3 2.8

32.9 41.4 — 2.9 8.2 2.1 6.7 3.8 2.0

31.3 40.5 — 2.8 9.4 2.1 7.6 4.0 2.3

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Mobility Surveys in Lisbon and Porto

293

Trips per day Table 7 shows the distribution of the number of trips made per person and per day. In both areas the largest set is that of people making two trips per day, although this set is a little higher in the case of Porto. As expected, the percentage of people doing more than two trips a day is higher in the central city than in the suburbs. In this respect also, Lisbon globally is a more mobile area than Porto, with approximately 34 percent versus only 26 percent of the people making more than two trips a day. One consequence of this fact, although not reported in this chapter, is that the hourly distribution of trips in Lisbon is less peaked than in Porto. It should also be noted that the fall in the average number of trips per day between the city and the suburbs is very small in the Lisbon, in contrast to the Porto areas.

Transfers Table 8 shows the results concerning transfers made within trips. Transfers were counted only when a change of vehicle was included in motorised modes, but not when a trip had a first leg made on foot, and then another leg made by public transport. The percentage of trips (all modes) made with transfers is identical in both areas—around 16 percent. Naturally, this value is higher for the inhabitants of suburban municipalities. When we consider only the universe of trips made on transit, these percentages take much higher values, 32.0 and 35.6 percent for Porto and Lisbon, respectively. In Lisbon, and counting only the suburbs, almost 45 percent of the trips involve the need for at least one transfer, and more than half of these have two or more transfers. This is partly explained by the presence of the Metro, whose much greater speed reduces time even if the person has to make an additional transfer.

Loyalty to Modal Choice Table 9 presents the results relative to the loyalty of modal choice during the day. This may be due to the actual degrees of freedom lost for the modal choice of the trips started away from the base, but also due to the

to

Is to

Table 7 Distribution of the number of trips per person and per day Families with

1 2 3 4 5 6 7+ Average trips per day

1 o'

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

6.2 61.9 6.4 15.8 2.9 4.2 2.6 2.72

4.1 72.8 5.5 13.0 1.8 1.5 1.3 2.46

4.8 69.0 5.8 14.0 2.2 2.4 1.8 2.55

0.9 62.5 9.6 19.3 3.0 2.9 1.8 2.78

0.8 67.1 5.9 18.8 3.3 2.5 1.6 2.72

0.9 64.8 7.6 19.0 3.2 2.7 1.8 2.76

s: i a a-

§ | a' Qrq ffc

On

j| 0 S

Table 8 Incidence of transfers Transfers (%)

Total trips with transfers Trips with transfers (PT) By PT, with 1 Transfer By PT, with 2 Transfers By PT, with 3 Transfers By PT, with 4+ Transfers

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

14.1 25.6 20.7 4.4 0.4 0.1

16.3 36.8 25.6 9.4 1.5 0.3

15.5 32.0 23.5 7.3 1.0 0.2

14.5 29.4 23.3 5.3 0.8 0.0

18.6 44.7 21.0 16.2 7.0 0.5

16.6 35.6 22.4 9.7 3.3 0.2

o 2"

^!

^

S' £?' o 3

K> ^O

o\

. Table 9 Loyalty to modal choice

:

Loyalty level (%)

Porto (central)

Suburban municipalities

Total Porto

Lisbon (central)

Suburban municipalities

Total Lisbon (1st phase)

Same mode all day Always on foot/bicycle Always private car Always public transport Always private car + public transport Variable modal choice

80.6 19.3 19.4 41.5

82.2 21.6 24.2 36.1

81.6 20.7 22.6 38.0

91.1 17.0 26.4 46.9

91.4 17.7 40.0 29.5

91.3 17.4 33.4 37.9

0.4 19.4

0.3 17.8

0.3 18.4

0.8 8.9

4.2 8.6

2.6 8.7

a i

Mobility Surveys in Lisbon and Porto

297

mental attitude of planning at one time for both the outbound and for the return trip. This loyalty has very high values in both areas, although in Porto the percentage of people using different modal solutions during the day is about double that of Lisbon. In the case of Porto, both central city and suburbs show a maximum loyalty for public transport. In the case of Lisbon, there is a substantial difference of behaviour between the central city and the suburbs, whereas, the central city is mostly faithful to public transport, but in the case of suburbs, this preference is for the private car.

Conclusions In retrospect, having conducted the two first Mobility Surveys in our country, it is with satisfaction that it can be reported that the overall results are of the order of magnitude expected from other experiences, given the level of development of Portugal. The consistency of the methodologies used in the two largest urban areas allows for a comparison between the values obtained in either case, and the differences in those values could be explained primarily by the visible differences in the geographic and demographic level, and by the supply of transport systems, particularly the Lisbon Metro. The results obtained are presently being subjected to modelling efforts, to try to interpret the differences in smaller geographic units within each of the areas, so that a better understanding of the determinants of mobility and modal choice can be achieved.

References Axhausen, K.W. and Garling, T. (1992) Activity based approaches to travel analysis: conceptual frameworks, models and research problems. Transport Reviews 12, 323-341. Brog, W. and Meyburg, A.H. (1983) Influence of survey methods on the results of representative travel surveys. Transportation Research 17A, 149-156.

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Travel Behaviour Research: Updating the State of Play

Groves, R.M. (1989) Surveys Errors and Survey Costs. John Wiley & Sons, New York. Taylor, M.A.P., Young, W. and Wigan, M.R. (1992) Designing a largescale travel demand survey: new challenges and new opportunities. Transportation Research 26A, 247-261.

17

Changes in Urban Travel Behaviour of Elderly People Pascal Pocket

Abstract For a number of years now, France has been undergoing an ageing of its population. This ageing, which will become greater and continue over the coming decades is accompanied by profound modifications in the lifestyles of retired people. They are more and more motorised in the cities and less and less prisoners of the necessity to walk or use public transport. In this chapter, we will try to study the changes in the mobility of the elderly using diachronic data obtained from household surveys carried out in the seventies and eighties in the Grenoble conurbation. At an analytical level, the factors explaining these changes can be linked to the renewal of the generations and the modification of the socioeconomic environment which counter the ageing effects. We first situate the travel pattern and modal use evolution of elderly people within the context of the population as a whole. We then deal with the central question of the evolution of modal distribution, i.e. the individual's access to the private car and its daily use. The longitudinal study of the successive cohorts enables us to visualise the differences in behaviour between men and women on the one hand, and the determining character of the development of car ownership for successive generations on the other hand. Using a breakdown of car driving into three effects (demographic, ownership and actual use of cars), we show that it is the increase in car ownership, much more than the other two effects, which leads to an increase in car driving after the age of sixty. The same type of analysis applied to people who are presently in the 40-60-age group shows that women, who drive relatively little for the moment, are rapidly going to catch up in the future.

Introduction Traditionally, elderly people cannot get about easily and no longer travel for professional reasons. Over the last few years, however, their numbers,

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Travel Behaviour Research: Updating the State of Play

lifestyle, and their access to individual modes of transport have changed very considerably. These evolutions raise a certain number of questions which urban transport systems will be confronted with in the years to come such as, • In a country with a high car-ownership level, will the ageing of the population, increased motorisation, and modifications in the behaviour of elderly people, lead to an increase, or decrease, in the importance of the automobile for daily travel in the cities? • What can the consequences of these changes be on the future of urban public transport, the problems of traffic in cities and the satisfying of the travel needs of the elderly who cannot use this travel pattern? In this chapter, we will try to study the changes in travel behaviour of the elderly using diachronic data obtained from household surveys. These changes can be explained by effects linked to the renewal of the generations, and to the modification of the socioeconomic environment which conflict with the effects which are due to ageing. We will first place the evolutions which concern elderly people in a wider context and then deal with the central question in the evolution of modal distribution, i.e. the access to, and the use of, the private car. To study changes in behaviour, the more appropriate data are the panel surveys, but, as far as we know, they do not exist in the field of urban mobility in France. So we use household travel surveys carried out in the Grenoble conurbation in 1978, 1985 and 1992. A longitudinal analysis of the different cohorts, and a modelling of the growth of car driving using three parameters (demography, motorisation and actual driving) allow us to show that the growth of motorisation, rather than the other two parameters, leads to growth in driving. Using the same surveys carried out among people who are presently in the 40-60 age group, we will show that women, who drive little for the moment, are more than likely to catch up over the next 1020 years, as a result of increased motorisation and car-use.

General Context In France, as in many industrialised countries, elderly people's place in society is undergoing very considerable change as the result of multiple factors, whether they are demographic, sociological or economic. To begin with, from the demographic point of view, the considerable lengthening

Changes in Urban Travel Behaviour of Elderly People

301

of life expectation and decrease in birthrates have come together to increase the percentage of elderly people in the population. Thus, the 1990 census shows that there were more than 11 million elderly people in France, i.e. almost one-fifth of the population. In the long term, if this evolution continues along the same lines, one out of every four people will fall into this category by 2010. But this demographic fact needs to be interpreted correctly: for the same chronological age, elderly people's living conditions have been completely transformed over the last 20 years—improvements in the state of health,3 a considerable increase in retirement revenues; so much so, in fact, that they are even higher than those of working people. However, despite these positive evolutions, the elderly population does not make up a homogeneous group. It is perhaps more a question of inequalities in cultural background, life expectation and state of health all brought together, which lead to such contrasting postretirement situations, rather than differences in revenue. What has an 80-year-old, living alone, with health problems and belonging to a generation which hardly knew the car, in common with a recently retired couple in full possession of their physical and intellectual faculties, and who are fully active even if they no longer have any professional activities, and have, moreover, a rich social-life and are car drivers? More generally, this longer period of retirement led gerontologists to consider two distinct periods in the life-cycle of the elderly: younger and older pensioners. Younger pension age is usually lived in good health, in the company of the pensioner's companion and can last, depending on the individuals, until the age of 75 or, indeed, 80. After that, older pensioners suffer from physical handicaps and a certain amount of social isolation, which severely limit travel patterns. Both these periods of retirement are subjected to socioeconomic change, to the renewal of the generations and to the effects of ageing, but in very different ways.

Framework for Analysis and Methodology Various authors have shown that it is possible to classify the different factors which act on lifestyle evolutions and mobility into three categories:

Expectation of life at birth is in constant progression and is presently near 82 years for women and 73 years for men. Furthermore, this progression is accompanied by a like lengthening of the period in which people are in good health. (Robine and Mormiche, 1993).

302

Travel Behaviour Research: Updating the State of Play

the effects of age, generation and period (Wachs, 1979; Kessler and Masson, 1985). The effects of age cover several factors. There is first a continuous but nonlinear process of individual ageing, be it physical or mental, along with the weight of experience acquired and habits inherited from the past. A certain amount of work of social orientation (Guillemard, 1972; Paillat, 1989), shows that daily activities at retirement age generally reproduce the activities which were already frequent in the past—new activities are rare. To this individual aspect of ageing we must add the discontinuities induced by the transitions in the life-cycle and their specific social constraints. Thus, for elderly people, the departure of children, retirement or the death of a spouse, can be events which determine their way of life and mobility. In particular, for active people, retirement creates a vacuum of occupations and professional relationships, leading to a brutal reorientation of their field of activities. How they face up to this depends on their cultural background, the social position acquired during their active period and on their ability to adapt. The notions of generation, or of cohort, enable us to consider the individual's date of birth just as important a variable as age for analysing social behaviour evolutions. Because of their past, and specific characteristics, the effects of generation, or cohort, are seen when one or more generations adopt behaviour which differs from that of preceding generations at the same age. These intergeneration changes can be explained by an evolution of the economic environment of each generation. The notion of period effects tries to integrate change which is linked to specific historic events, and to the particular economic and social context of each epoch. For example, the growth rate of revenues, improvement in the public transport system and change in the relative prices of the various modes of transportation, can all be classified as period effects. Therefore, for there to be a period effect, similar evolutions must concern a large number of age groups and generations during the period under study. From a prospective point of view, it is very interesting to try to distinguish the influence of the three effects—age, generation and period. Thus, the permanence of the effects of age enable us to highlight the invariable part of behaviour in time. Furthermore, generation changes, already seen among younger people, should enable us to anticipate future evolutions

Changes in Urban Travel Behaviour of Elderly People

303

for the elderly. What is much more difficult to forecast are the effects of period linked to future variations in the economic and social environment. From a practical point of view, however, these three effects are not independent. It is not always easy to see where effects of generation stop and effects of period begin. In particular, generations evolve under the influence of modifications in the sociocultural environment, and this leaves a different mark on every generation as a result of its position on the age scale—the least elderly considered as the most permeable to change. In the same way, the effects of age evolve under the influence of the renewal of generations and according to the period—on the contrary, generational differences can diminish with age. In order to carry out the study of past evolutions, diachronic data was necessary. We used a series of household surveys carried out in the Grenoble conurbation in 1978, 1985 and 1992 (for certain aggregate results we added in the results of a 1973 survey). Grenoble is one of the rare French cities subjected to so many household surveys.13 Furthermore, the regular seven-year interval between the last three surveys makes possible the longitudinal study of successive seven-year amplitude cohorts. Finally, the Grenoble conurbation with 400,000 inhabitants presents various transportation possibilities. There is an excellent urban transportation network of cycling tracks.0 And despite these factors, the car ownership rate is relatively high. In this context, the evolutions in travel behaviour of elderly people must first be replaced within the context of the overall evolutions to be seen in Grenoble, if we hope to obtain a clear picture. When we consider the population as a whole, the evolution over two decades shows an alignment of the travel models of men and women who have a high level of motorised mobility. The reasons for this evolution are now reasonably well known. An example is the development of twocar ownership, which is sustained by two tendencies which are highly characteristic of French society in the seventies and eighties: • the spectacular growth of the rate of feminine activity. France is the European country with the highest number of women in full-time employment;

b

For each survey, approximately 4,000 individuals were polled on their travel behaviour during the previous day—thus, between 400 and 700 over 60s were surveyed each time. c The Grenoble public transport network is old-people friendly (easy access to tramway, free travel outside peak hours).

304

Travel Behaviour Research: Updating the State of Play

• the extension of suburbs as a result of people's preferring individual dwellings, and a widening out of the locations of activities, employment and equipment. One of the major consequences of this suburbanisation is a mean increase in commuting distances.

Mobility and Use of Transportation Modes: The Particularities of Elderly People General evolutions in the use of modes Over the last two decades, it is more than clear that there has been a very considerable evolution as a result of the ever-increasing domination of the private car over other modes of transport, whether we consider women or men of whatever age group (cf. Fig. la, c). Urban public transport is on the increase because of a considerable improvement in choice and quality of service. This growth has not been to the detriment of the car, but rather to the proximity modes such as walking and cycling. As far as the evolution concerning walking is concerned, it may be partly due to a variation in the area of the poll. In the case of Grenoble, in particular, the people living in the suburbs were more numerous in the 1992 than in the 1985 poll. However, this does not put the reality of a decrease over these 15 years into question, since this fall has been noted in other French cities (Orfeuil, 1992), German cities (Brog, 1992) and Canadian cities (Chapleau and Cote, 1989; Bussiere, 1992). This decrease has generally benefitted the private car. In this context, the evolution of the behaviour of people aged 60 and over is logically a little behind. Here, the feminine travel model is very different from that of males (cf. Figs. Ib, d). For women, car-use is very marginal indeed, and only observed among a certain category who were in salaried employment before retirement and whose sociocultural level is high. On the other hand, retired men's level of car-use is close to that of working men. This mean behaviour must not be allowed to hide the very considerable differences which exists in the mode of transport used after the age of 60. These differences are not only due to sex, age and generation, but also to the action of other factors which may be linked to them, such as the place of residence, former socioprofessional category, level of education and matrimonial status.

sa

TO_

to

Figure 1 Comparative evolutions in the use of modes of transport for the population as a whole and for elderly people

306

Travel Behaviour Research: Updating the State of Play

A very different

use of modes of transport by elderly people

With active people, the main constraints are temporal, these disappear or weaken on retirement, and are replaced by space constraints. The activities undertaken outside the home are now limited by the range of places which can be reached, taking into account the level of car ownership, personal access to a car, public transport service available and the person's state of health. Of course, these differences affect elderly people's daily mobility. Thus, the very old (over 80 years), generally go out half as much as people in their 60s. This also explains why proximity trips remain important for downtown residents, where the density of habitation, shops and equipment of all sorts are high. Thus, in 1985, on-foot mobility for downtown dwellers over 60 years in Grenoble was 80 percent higher than in the suburbs. Conversely, at the same date, elderly people who can drive, use their cars twice as often when they live in the suburbs. The use of public transport becomes of paramount importance for nonmotorised people. In particular, nonmotorised women over 70 years living in the suburbs made a quarter of their trips using public transport in 1985, whereas, this proportion falls to less than five percent for motorised men in the first half of their sixties. The former profession, and in a closely correlated manner, the level of studies and income, play a double role in travel behaviour. As far as these generations of people are concerned, it was the "well-off" who benefited most from motorisation. The most mobile potential drivers here are ex-professional men or ex-executives. Finally, the importance of matrimonial status is not so visible. In actual fact, it has little effect on mobility, whatever mode of transport is considered. On the other hand, it has a certain influence on car driving for motorised women, as we shall see later. Since we have now set out the general framework, we come back to the all-important question for the future, namely, the evolution of elderly people's car driving in relation to the growth of car-ownership for successive generations of men and women.

The Elderly and the Car The elderly and motorisation The household surveys do not give us details about the real availability of a vehicle for the different members of the family polled. Therefore, we will refer to licence-holders whose household has at least one car, as

Changes in Urban Travel Behaviour of Elderly People

307

motorised persons, actual or potential drivers or "drivers" for the sake of simplicity. Using Fig. 2, we may look at the motorisation rates of the successive cohorts of men and women (Figs. 3a, b). We see clearly that the generalisation of car-use came about in cumulative fashion with the renewal, of the generations, and it affected women much later than men. As Gallez and Madre (1992) showed in French statistics series, the first wave of motorisation of households took place at the end of the fifties and through the sixties. This phase of massive introduction of the car can partly be assimilated to an effect of period, since it concerned a large number of generations, albeit to different degrees. Motorization was followed throughout the seventies and eighties by two-car ownership and the arrival of a considerable number of women on the employment and car-buying

A2

A3

A4

AS

A6

Y: Measure of travel behaviour A1...A6: Age groups C1...C4: Cohorts

Figure 2 Reading guide for Figs. 3 and 4. Each cohort is logged by an interval of birth (seven years) and represented by the mean date of birth. The segments of the curve (profiles per cohort) enable us to follow the effects of ageing for each cohort between 1978, 1985 and 1992. For a given age, the vertical deviations between the cohorts enable us to measure the deviations from one generation to the next

!

Percentage

Percentage

Changes in Urban Travel Behaviour of Elderly People

309

markets. Hence, this explains why the present generations of men from 60-80 years (i.e. born between approximately 1910 and 1930) contain 6080 percent of actual or potential drivers. Conversely, the rate of motorisation of women from the same generations is two or three times smaller! The use that the two sexes make of the car is also very different.

Car-use in different generations of drivers Figures 4a and b show, for each cohort, and by sex, the evolution of the number of daily trips made at the wheel of a car by the actual or potential drivers in the sample. The high rate of overlap in the segments of the curves, taken along with their fall after the age of 60, show that the effects of age play an all-important role, especially by the important threshold represented by retirement. The only clear behavioural difference for motorised people concerns the cohort of men who reached the age of 6066 years in 1992. The explanation for this surprising inflexion can be partially found in the residential location and the social make-up of this subgroup in the 1992 survey. In that year, 70 percent of the people polled in that age group lived outside Grenoble, as against 54 percent in 1985 and 30 percent of them were former middle- or upper-executives, as against 20 percent in 1985. As far as the evolution of feminine behaviour is concerned, women over 60 years are not yet concerned, but women-drivers who either have children of school-going age, or salary-earners, are concerned, especially those who concern us most, i.e. in the 45-60 age group. The other lesson which we can learn from these figures is the persistence of the differences between 60-year-old men and women, once we ignore the inequalities of car access. While actual or potential women drivers usually make one trip a day on average, men drivers are nearer to two trips a day, if not more. For the present generations of elderly people, the distribution of roles within the household appears to be relatively rigid, with the man as driver. Thus, elderly married women who are licence-holders are as often passengers as drivers in the family car(s).

Formalising the evolution in car driving In order to highlight the different effects in the evolution of car-driver mobility better, we divided the total volume of trips by age, according to

Number of trips/day

—

Number of trips/day

!

Changes in Urban Travel Behaviour of Elderly People

311

the weight of each age, to the number of motorised persons in each age group and to the mean number of daily trips made by "drivers" at the wheel for each age group (Greene, 1987). The evolution in the use of the car by a driver between dates 1 and 2 is, therefore, a ratio of the two sums of number of trips for all age groups i:

with Pil, Pi2 = number of people in age group i on dates 1 and 2; Cil, Ci2 = percentage of drivers in age group i (i.e. licence-holders whose household owns at least one car) in dates 1 and 2, and Mil, Mi2 = mean number of daily trips made by drivers at the wheel on dates 1 and 2. In order to measure precisely the influence of the demographic changes, the growth in motorisation and the evolution in the use of cars by drivers, the evolution of the mean number of car-driver trips, can be considered as the product of:

this is a "demographic" effect E(P) equal to the variation between dates 1 and 2 (where all the other variables have no incidence) of the number of people in each age group, depending on ageing or deaths resulting from the two world wars. In the same way, there is a "motorisation growth" effect E(C), and a driver behaviour change effect E(M), which are, respectively, equal to SjPi2CilMil Si PilCilMil

E(Q =

Sj PilCi2Mil Si PilCilMil

E(M) =

Si PilCilMi2 Si PilCilMil

which are the three interaction effects of these factors taken two by two. Thus, for example, E(P, C) represents the demography/motorisation interaction effect, and so on for E(P, M) and E(C, M) as follows:

312

Travel Behaviour Research: Updating the State of Play E(p c) =

=

(E i PilCilMil)(E i Pi2Ci2Mil) (Si Pi2CilMil)(Si PilCi2Mil) (SiPilCilMil)(SiPi2CilMi2) (Si Pi2CilMil)(Si PilCilMi2) (Si PilCi2Mil)(Si PilCilMi2)

Finally, the interaction of the three factors taken simultaneously is:

E(P, C, M) = (Sj Pi2Ci2Mi2)(2i Pi2CilMil) (St PilCi2Mil)(Sj PilCilMi2) (Si Pi2Ci2Mil)(2i Pi2CilMi2) (Si PilCi2Mi2)(Si PilCilMil) The interaction effects take into account the fact that the evolution in the number of trips is not only equal to the product of the pure factors, but the effects of variation of composition are taken into consideration as well. But the analysis shows that these interaction effects are quite unimportant, compared to the E(P), E(C) and E(M) effects. These calculations were carried out between the 1978 and 1985 surveys on the one hand, and the 1985 and 1992 surveys on the other hand— with the same division into age groups as those presented in the above figures. Furthermore, because of the considerable behavioural differences noted between men and women, these calculations have been carried out for both sexes. Finally, we studied separately, on the one hand the population of people of 60 years and over, and on the other hand people aged from 39-59 years, according to sex. The results indicating the importance of the principal effects in overall evolution are presented in Table 1 (for people between 60 and 66 years) and in Table 2 (for 39-59 years old) . The first result is the preponderance of the evolution of the motorisation and licence-holder rates in the overall evolution, compared with the demographic or behaviour change effect. The evolution in the use of the car by "licence-holders" is greater between 1985 and 1992 aged 60 and over, especially as far as women are concerned. Furthermore, the interaction effects are somewhat limited, and the product of the three simple effects is close to the overall evolution. The only exception is for women of 39-59 years old between 1985 and 1992, for whom the combined effects are also important: demography/ motorisation and demography/behaviour. No doubt, these combined ef-

Changes in Urban Travel Behaviour of Elderly People

313

Table 1 Breakdown of car-driving growth for men and women of 60 years and over Men

Overall growth Product of the 3 effects P, C, M Product of the 4 interaction effects Breakdown: "Demographic" effect P "Motorisation" effect C "Behaviour" effect M

Women

1985/78

1992/85

1985/78

1992/85

1.36 1.41 0.97

1.19 1.28 0.94

1.82 1.81 1.00

1.82 1.90 0.96

1.06 1.28 1.03

1.02 1.11 1.13

1.06 1.55 1.11

1.03 1.44 1.28

Table 2 Breakdown of car-driving growth for men and women of 39-59 years old Men

Overall growth Product of the 3 effects P, C, M Product of the 4 interaction effects Breakdown: "Demographic" effect P "Motorization" effect C "Behaviour" effect M

Women

1985/78

1992/85

1985/78

1992/85

0.93 0.93 1.01

1.03 1.03 1.00

1.38 1.35 1.02

1.56 1.31 1.00

0.98 1.05 0.90

1.01 1.03 0.98

0.93 1.34 1.09

1.06 1.24 1.19

fects come from the drop in the size of age groups during the second world war, for whom motorisation and use progress less than in the other age groups of 40-years-old. Last, but not least, these changes in the use of modes of transport are not only the reflection of increased motorisation, but even more so of the more fundamental changes in lifestyles. These complex ways of life cannot be fully understood as a result of the household surveys which we analysed. However, the activities which give rise to trips, and are listed in the various surveys, give us a certain number of indicators about the evolution of lifestyles over 60 years old. Commuting almost completely disappears for the new generations of 60-year-olds. This is not surprising, since it has been possible to retire at 60 rather than 65 years old since 1982, and because of the development of forms of preretirement. The second lesson concerns the evolution of leisure- and visit-linked trips as opposed to

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shopping trips. The new generations of elderly people are more and more inclined to group their purchases in hypermarkets rather than use nearby stores. This evolution is made easier by greater motorisation, which actually reinforces it.

Conclusion Therefore, what prospective lessons for the next 20 years is it possible to get from these modal evolutions in travel behaviour of the elderly? The relationships between the social and economic environment on the one hand, and transport demand on the other are multiple and complex, and it is wise to be very cautious. Moreover, the formalising of the different effects which we propose is simple and only concerns the use of the private car without going into its consequences on other transport modes. In order to be more explicative, it should notably take account of the behavioural differences of drivers according to the number of vehicles in the household, and distinguish between "young" and "old" retired people. Unfortunately, the size of the samples limits the degree of breakdown which we can hope to obtain. However, this analysis shows that among the effects of age, generation and period, the first two are more obvious in both the past and present evolutions in car driving. Among the present generations of elderly people, the major changes come from motorisation which increased with the renewal of the generations, especially as far as women are concerned. No doubt, this rise in the level of motorisation will continue with the arrival of new generations of women going into retirement—the present level of motorisation of women of 40-60 years old bears witness to this. On the other hand, the growth of car ownership as far as men are concerned, is not going to go on much longer. In licenceholder use of cars, the major changes over the next 20 years will come from women. This increased domination by the car is going to have an opposite effect on the other modes of transport, especially on walking and public transport. However, what remains to be evaluated is the size of the effects of ageing, which could affect the importance of demotorisation for the elderly. At the present moment, just like the results pointed out by Gallez and Madre (1992), the profiles per cohort show that no demotorisation is apparent for men before the age of 80 years. Women are less motorised already and the figures show that more of them abandon the use of the car. This evolution is only paradoxical in appearance, since this demotoris-

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ation can often be explained by the decease of the husband who was the sole driver. The results presented by Jansson (1989) show that in the same way, in Sweden, demotorisation is higher and starts earlier for women (from 70 years upwards) than for men who keep on driving until 75 years at least. In the years to come, more and more retired people are going to be two-car families. Are these couples going to give up one car? The reply to this question will enable us to have a better idea of the number of cars belonging to the elderly but also how easily elderly women are going to have access to a household car. Other demographic, economic and social factors, which are not easy to forecast, will influence car ownership and modal choice for elderly people and affect the present trends. From the demographic point of view, the future trends should logically show an ageing of the elderly population, and a correlative increase in "older" elderly people to the detriment of "younger" elderly people. The continuing improvement in the state-of-health of elderly people may well cancel out this ageing effect. From an economic point of view, the financing of pensions and superannuation schemes is becoming more and more uncertain. But here again, the consequences may be variable—a fall in income which could have a depressive effect on car ownership, the lengthening of active life which would encourage motorisation. As far as society is concerned, future evolution of lifestyles of elderly people would seem to be just as difficult to forecast. The best we can do is to imagine certain trends, using present indicators: less central places of residence, modification of the social composition and level of education of elderly people, more "active" retirement, and, for the first time, retirement for people who have only known the consumer and leisure society (Dim, 1991). The future is, therefore, wide open.

References Brog, W. (1992) Changements structurels de la population et impact sur la demande de transports de voyageurs. Table Ronde 88, 7-43. Bussiere, Y. (1992) Forecasting travel demand from age structure, urban sprawl and behaviour: the Montreal case, 1986-2011. 6th World Conference on Transport Research, Lyon, July 1992, France. Chapleau, R. and Cote, J. (1989) Evolution de la mobilite des personnes de 1'agglomeration urbaine de Quebec. 24th Annual Congress of the

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Association Quebecoise des Transports Routiers, Jonquiere, March 1989, Canada. Dirn, L. (1991) La Societe Franqaise en Tendances. PUF, Paris. Gallez, C. and Madre, J.L. (1992) Le pare automobile dans les annees 2000: methodes demographiques et projection a long terme. Selected Proceedings of the 6th World Conference on Transport Research, Lyon, July 1992, France. Greene, D.L. (1987) Long run vehicle travel prediction from demographic trends. Transportation Research Record 1135, 5-12. Guillemard, A.M. (1972) La Retraite, Une Mort Sociale. Sociologie des Conduites en Situation de Retraite. Mouton, Paris. Jansson, O.W. (1989) Car demand modelling and forecasting: a new approach. Journal of Transport Economics and Policy XXIII, 125-140. Kessler, D. and Masson, A. (1985) Cycle de Vie et Generation. Economica, Paris. Orfeuil, J.P. (1992) Changements structurels de la population et impact sur la demande de transports de voyageurs. Table Ronde 88, 45-106. Paillat, P. (ed.), (1989) Passages de la Vie Active a la Retraite. PUF, Paris. Pochet, P. (1995) Mobilite Quotidienne des Personnes Agees en Milieu Urbain: Evolutions Recentes et Perspectives. These de Doctorat en Sciences Economiques, Universite Lyon 2. Robine, J.M. and Mormiche, P. (1993) L'esperance de vie sans incapacite augmente. Insee Premiere 281, 1-4. Wachs, M. (1979) Transportation for the Elderly. Changing Lifestyles, Changing Needs. University of California Press, Berkeley.

18

Potential Estimate for the Acceptance of a New Motorised Bicycle in Urban Traffic: Methodic Aspects and Results Gerd Sammer, Kurt Fallast and Fritz Wernsperger

Abstract Present day and future traffic problems in cities and conurbations cannot be solved by the car. The question arises as to how far an as-yet nonexistent motorised bicycle developed for urban requirements can contribute to the solution of urban traffic problems. The plan and requirements profile of a "New Motorised Bicycle" (NMB) suitable for the city and daily use was developed in an expert workshop. Essential characteristics are: simple handling, high safety in traffic (without compulsory helmet), simple maintenance, low purchase price, low running costs, simple parking, low noise and exhaust emissions, passenger and luggage transport, protection against the elements, attractive appearance, low space requirement, etc. The traffic infrastructure and traffic organisation of cities should be so tailored to the NMB that its advantages compared to the car are fully realised. The likely acceptance and travel behaviour was examined with the aid of multistage scenario techniques with in-depth, interactive interviews (stated preference). In this study three scenarios were tested: Scenario A: special NMB-traffic infrastructure; Scenario B: special NMB-traffic infrastructure and paid parking in the inner city; Scenario C: special NMB-traffic infrastructure and driving ban in the inner city for vehicles with internal combustion engines.

Introduction Formulation of the problem European cities are not planned to be "auto-friendly". Should one attempt to replan them to be auto-friendly—and there are such attempts—they

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would no longer be what we in Europe understand as a "city", that is, a place where streets and squares are scaled to suit pedestrians. If one considers the future development of motorised private transport, one must also take into account the further development of urban traffic, especially in the developing industrial countries one must expect rampant growth in motorised traffic.

A possible solution Most of the plans for the creation of city-oriented transport are based on the promotion of existing environmentally benign modes of transport. Another possibility is the development of a completely new city-oriented motorised means of transport. This vehicle should combine the advantages of the conventional motorised bicycle (space saving, easily manoeuvrable) with those of the private car (comfortable, large transport capacity). The essential characteristics of this vehicle should be: • • • • • • •

low demands on space; low noise and exhaust emissions; high degree of safety for the driver and other "weaker" road users; simple in operation and maintenance; attractive appearance; weatherproof; high acceptance, above all by car drivers.

For the safety of other road users (pedestrians and cyclists), and the short distances covered by urban transport, a city-oriented maximum speed of the vehicle is desirable. At lower speeds active and passive safety precautions are easier to realise for the driver and passenger. A new kind of motorised bicycle, called the "New Motorised Bicycle" (NMB) could meet the above-mentioned requirements. For the NMB to make an effective contribution to the creation of a city-oriented traffic system it is necessary to provide an infrastructure suited to this vehicle, which gives the user certain privileges, for example, in parking. The idea of the NMB assumes that a new, city-oriented motorised vehicle with a suitable infrastructure will become available and the legal requirements will be created by the revision of road traffic regulations.

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Aim of the study The question arises as to whether, or not, an NMB could attract a sufficient number of users in the new conditions of a cycle-friendly city: • Can the idea of a cycle-friendly city traffic system obtain a reasonable share of the modal split and provide good traffic performance in order to contribute to an environmentally benign city traffic? • What effects (advantages and disadvantages) would the introduction of the NMB have?

The NMB-Vehicle Conception The state of development Today, there are already designs for vehicles whose characteristics approach those of an NMB. A typical example for a new kind of motorised bicycle is the BMW Cl design (Fig. 1). At present, this vehicle exists only in the form of a one-seat 1:1 model without a motor. The Honda Canopy is a three-wheeled vehicle in which the passenger cabin is articulated with the rear axle (Fig. 1). As a result, the vehicle handles on bends nearly the same as a conventional bicycle. To ensure stability, when stationary, the articulated joint can be fixed. The Honda Canopy is already in service in Japan.

The NMB-types as the basis for the study A central problem in determining the future user-potential of an NMB is informing potential users and making them aware of the characteristics of a vehicle that as yet does not exist. Therefore, the characteristics of an NMB were explained to potential users together with supporting visual material about the examples in the previous section to aid understanding. The technical data and characteristics of an NMB were defined as follows for this investigation: • two or three wheels; • internal combustion engine or electric motor; • performance approx. 5 HP; maximum speed 45 km/h;

Figure 1 Existing NMB-like vehicles

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emissions: quieter than private car, with electric motor no exhaust gas, otherwise a maximum of 50 percent of car exhaust; driving licence, from 16 years of age, no licence required; high degree of user friendliness, automatic gears, simple operation, comfortable; weather protection, the driver will not get wet, therefore protective clothing unnecessary; carrying capacity: maximum 2 people; seat belt possibility, no helmet needed.

The NMB Traffic Infrastructure So that the NMB makes an effective contribution to the creation of a city-oriented transport system, it is necessary to adapt the corresponding infrastructure to the NMB. An essential approach to an NMB-friendly city traffic system is an integrated, comprehensive transport plan which offers the user both the "software" (traffic organisation and public relations work), and the "hardware" (infrastructure) appropriate to the NMB.

The zonal concept The zonal plan serves as a basis for the infrastructure planning. Access for cars is reduced as one approaches the city centre, whereas, the NMB can travel freely within zones 1 and 2 (Table 1).

The NMB infrastructure exemplified by a model city In order to inform and raise awareness in potential users, the NMB infrastructure plan for the model city of Graz (240,000 inhabitants) was studied. In essence, a basic network for the NMB was provided within the major road network, supplemented by traffic abatement streets in the minor road network with a 30 km/h limit. The basic network consisted of NMB traffic lanes, NMB streets, bus lanes and traffic abatement streets open for use by the NMB. The results of this planning were depicted through plans of actual roads and streets.

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Travel Behaviour Research: Updating the State of Play Table 1 The zonal plan adapted to the NMB New motor cycle (NMB)

Pedestrians, cyclists, public and private transport

Zone 1 Inner city

Use of certain streets permitted Reserved parking

Pedestrian precinct Public transport and cycles allowed in certain streets Loading/unloading at limited times No parking

Zone 2 Outer city

Completely open to NMB (30 km/h limit) Parking allowed Reserved parking

Completely open to public transport and cycles Access for residents, commercial traffic, taxis, etc. Paid short-time parking for those with authorised access, residents parking

Zone 3 Compact built-up areas,

Completely open 30 km/h limit except for priority roads Network for NMB Reserved parking

Cycle path network Public transport with priority Private cars with 30 km/h limit except priority roads Paid short-time parking, residents right to parking

Zone 4 New building areas, suburban

Completely open Network for NMB Reserved parking

Cycle path network Public transport with priority Private cars with 50 km/h limit on priority roads

Stated Preference Analysis Methodical aspects on the potential estimate for the NMB The existing mode choice and, above all, the estimation of future behaviour when choosing a means of transport in the light of new modes of transport is undoubtedly not a simple, one-dimensionally explicable type of individual behaviour. It is rather a host of objective and subjective aspects that combine and create relatively complex, subjective situations of choice in each individual case (Brog, 1981). Such a task calls for a suitable research approach, thus a 'situational approach based on an interactive interview technique' was used. For example, this more sensitive approach to behavioural analysis is used in the field of public transport (Brog and Erl, 1981) and integrates socio-demographic, economic, supply-

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related and situational variables. It gives a considerably better insight into the aspects affecting travel behaviour than purely formal mathematical models. This is due, especially, to the fact that in this concept emphasis is placed on a consistent disaggregation in all phases of the analysis in order to take the individual case fully into account. The scope for action that actually exists is determined for each individual unit of decision (here: the individual trip), and against the background of this subjective choice situation the possible reactions (e.g. whether switching from the car to the NMB, or not) are estimated compared to alternative planning cases. This situational approach has been developed and tested in particular in the area of urban traffic. The situational approach proceeds on the assumption that the individuals are given certain scope for action ("objective" situations) by their environment. This scope for action is determined by: • the material offered regarding transport infrastructure (here, it is the vehicle NMB and the NMB infrastructure); • the constraints and freedom derived from social demography of the individual and the other members of his household; • the social values, norms and opinions with respect to the areas relevant to travel behaviour. Each individual experiences these "objective" situations in a specific way. Individually different "subjective" situations (consisting of variables from all three areas mentioned) are created. These "subjective" situations differ from the "objective" ones by incomplete, consciously or unconsciously distorted perceptions. The degree of deviation depends on the individual person and his/her specific experience. In these subjective situations, individual decisions are taken. In order to create a model of travel behaviour, it is necessary to reconstruct the chain of "objective situation - personal perception - subjective situation - individual choice - behaviour". If one wishes to influence travel behaviour, it is possible to intervene at any point in this chain to accomplish this. Consequently, such a model structure allows us to determine individually the probable reactions to measures with the help of the individual explanations of travel behaviour. Since measures, such as the provision of an NMB and the corresponding infrastructure, always have only an indirect influence on the situation and resulting behaviour, it is necessary to first determine which situations are changed by possible measures, and for which individuals. In the course of a second step it is possible to

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estimate the probable behaviour of the road-user involved in the changed situations with the help of the individual reaction probability. The choice of action towards alternative means of transport basically can be described with the aid of the following eight "dimensions": (1) Is there an objective possibility of choosing an alternative? (2) Are there any constraints ruling out the use of an alternative (e.g. carrying luggage)? (3) Does a lack of information play an important role for the individual decision regarding the means of transport to be used? (4) Is time of any importance for the individual decision regarding the means of transport to be used, and how does the alternative compare with the mode of transport actually used. (5) Do route-related aspects (gradients, travel safety etc.) play an important role for the individual decision regarding the means of transport to be used? (6) Are aspects of cost of any importance for the individual decision regarding the means of transport to be used, and how are the alternatives and means of transport actually used seen as aspects of cost? (7) Are aspects of convenience of any importance for the decision regarding the means of transport to be used, and how are the alternatives and means of transport actually used seen as aspects of convenience? (8) Does the specific individual take a basically positive standpoint towards the alternatives, so that their use can be taken into consideration? In the course of the situation analysis it is determined to what degree the various "dimensions" exist. By individually interconnecting the various dimensions, situation groups are created. The various decisions in favour of a certain means of transport can be explained with the help of the situation group structure. In each dimension, revisions are carried out to ensure it sufficiently explains the corresponding travel behaviour. This is the case if there is "a negative connotation". Then the corresponding trip is no longer taken into consideration, since there is an explanation concerning the means of transport used, or the alternative not taken advantage of (the information on the degree to which the other dimensions exist is not lost, however). In this way, we obtain a situation group which could also have used the corresponding alternative—the so-called "group

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of freedom of choice". This group of freedom of choice already represents a potential for a certain means of transport in the corresponding status quo. The aim of this research project is to identify the measures creating a freedom of choice of the road-users towards the NMB. A reaction is only possible in cases where the measure taken creates a state of freedom of choice. The probable reactions of the members of the group of freedom of choice to the NMB are determined, taking into consideration the established individual reaction probability under changed framework conditions (scenarios). Another difficulty of this research project for consideration in a methodical way, is the fact that road-users neither had any experiences with, nor have any ideas about, the as-yet nonexisting NMB as an alternative. Therefore, no behavioural parameters, can be derived from actual observed behaviour. The new, as-yet nonexisting NMB must be described with the help of characteristics known to all road-users through their use of other means of transport (stated preference method). Registration of these factors of influence on the individual situation of choice-making requires adequate empirical measuring procedures. It needs to be pointed out that the conventional questioning techniques and stimulation-reaction mechanisms certainly do not meet these requirements. It is clear that no interviewee is aware of his/her individual situation of decision-making and its changeability to such a degree that s/he can talk about it spontaneously. What is needed in this case are exploratory, so-called "interactive measuring procedures". They represent a special form of in-depth interview in the course of which the information required is gained by a common process between the interviewer and the household members questioned (Brog and Erl, 1981). Such an interview lasts between one and two hours per household.

Database and sample The results of a written traffic survey performed in 1991 (a random sample of 7,700 households with 18,700 people) formed the basis of a first survey level. In addition to the socio-demographic figures we also know the daily travel routine from this survey: the purpose of the trip, the time the trips last, type of means of transport, place of departure and destination, availability of means of transport, etc. Based on all these factors, an indepth survey was carried out on a second survey level with the help of an interactive measuring procedure. In the course of this process, a total of

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302 people in 117 households were interviewed, with each oral household interview lasting 90 min. A total of 1304 trips were examined during these interviews. With a specific sampling in mind, emphasis was placed on interviewing households with as many cars, motorbikes and moped trips as possible, since the assumption is that those using the aforementioned means of transport will account for the largest potential of NMB users. With the aid of the following weighting, the result was brought back to the average distribution of means of transport in Graz and was thus rendered statistically representative.

Projection of the sample of the stated preference survey The aggregation of individual behavioural results was achieved by means of a so-called classification procedure (Sammer, 1982). This means that the trips observed during the consolidation survey were divided into behavioural homogenous strata for possible reactions. For each stratum, the reaction probability is known as a mean value. These strata were then weighted and were formed in accordance with the stratification characteristics below.

• Trips of residents and nonresidents of Graz. • Internal and external trips. • Trips by mode, i.e. pedestrian, bicycle, public transport, car driver and passenger.

Because of the relatively small number of random samples (1,304 trips), a combination of the strata of the three stratification characteristic groups was not possible. A specially developed method was therefore applied ensuring that the distribution within the categories of each stratification characteristic group is identical to that of the parent population (Sammer and Fallast, 1990). The parent population of all trips for these behaviourally homogenous strata is known from a large sample survey. The reaction behaviour of the consolidation sample was aggregated and/or extrapolated to the parent population.

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The course of the interview In order to familiarise the interviewees with the subject and to "relax" them, we first determined the present means of transport at the disposal of the family as if playing a card game. The trips by members of the family, previously given in a written survey, were depicted clearly and memorised. All trips were analysed with respect to the motives for using a specific means of transport (Fig. 2). Here it was less a question of the conditions on one specific day than the generally valid reasons for choice of a means of transport by the person in question. The interviewees were finally asked to plan anew the daily schedule given in the written enquiry taking into account the conditions given by Scenarios A, B and C (reorganisation of the daily programme). Three different scenarios were presented. • Scenario A: special traffic infrastructure for NMB. • Scenario B: Infrastructure as in Scenario A, in addition to paid parking in the inner city (except for NMB). • Scenario C: Infrastructure as in Scenario A, in addition to a driving ban for vehicles with internal combustion engines within the inner city. In the scenarios, the trip time by the means of transport previously used was compared with the fictitious trip time by NMB, whereby, an average speed of 25 km/h by NMB was assumed. In addition, the conditions pertaining to the traffic organisation for the model zone must be observed, for example, limitations on parking for private cars. In the reorganisation of the daily programme care was taken to consider that, in certain circumstances, there could be changes in the availability of means of transport, and also the necessary activities the household members had to perform.

The Use of Means of Transport in the Scenarios

Shift of means of transport Investigation of shifts of means of transport in Scenario A gave the following results:

Figure 2 The course of the interview

• The seven percent shift in share of trips to NMB is so high that one can speak of a noticeable change in the choice of transport mode. • Half the potential NMB trips were originally made by car. Figure 3 reflects the complex reactions of switching means of transport. It shows that some of the car passengers switch to public transport. This

bicycle

Legend: 35,4%

percentage share of means of transport of trips by Graz inhabitants 1991

(->31,6%) percentage share of means of transport of trips by Graz inhabitants in szenario A

^o carpassenger moped motorbike

Figure 3 Shift in means of transport in scenario A (NMB-friendly infrastructure). Shifts affecting less than 0.2 percent of trips not shown

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is because some of those car passengers must (or wish to) use public transport because the car driver has switched to the NMB. If one compares the seven percent share with the previous moped and motorbike share of 1.6 percent, one can see that the NMB appeals to people who do not consider present-day mopeds and motorbikes as an alternative to the car. The NMB is also considered an attractive alternative by moped and motorbike riders, but related to all trips this share is only 0.6 percent. By using the NMB, changes in the choice of means of transport are necessary for some previous car passengers, thus, one percent of all trips by car passengers shift to public transport. A similar number shifts to the NMB from public transport (1.2 percent) and from the pedestrians (1.0 percent). In Scenario B, overall paid parking is assumed in the inner city. Thus, changes in some car trips will be necessary and are also expressed in this scenario as a considerable change in the choice of means of transport (Fig. 4). The paid parking effects a minor shift from private car to NMB, and to public and nonmotorised transport (pedestrians and cyclists). In Scenario B, there is a reduction in the share of car driver trips from 35.4 to 28.6 percent and an increase in the public transport share from 18.9 to 19.8 percent. The NMB share increases by 0.5 percent over the share in Scenario A to 7.5 percent. This shift can be attributed to the NMB acquired in Scenario A being used for other trips in this scenario. In the present conditions, additional NMB trips to those in Scenario A are chiefly made in the private car as a driver or passenger. Because of the restrictions, some of the private car trips shifted to environmentally friendly means of transport (pedestrians, cyclists and public transport). Its share increased from 54.4-55.6 percent. In the case of Scenario C, the results of a driving ban for vehicles with internal combustion engines within the inner city (CO2 zero scenario) are shown in Fig. 5. The share of trips by private car drivers decreases from 35.4 to 22.6 percent, whereby, the greater part (5.1 percent of all trips) shifts to the NMB. In this scenario, as in the others, some of the trips by public transport and on foot shift to the NMB. Together with the other effects, there results a share for the NMB of 8.9 percent of all trips. There were considerable shifts from the private car to public transport (car drivers 3.2 percent, car passengers 1.7 percent) and to the electric car (2.9 percent for all trips). The possibility of buying and using an electric car was a condition of this scenario. All the other shifts caused by this scenario affect less than one percent of trips in each case.

bicycle

Legend: 35,4%

percentage share of means of transport of trips by Graz inhabitants 1991

1 ->28,6%) percentage share of means of transport of trips by Graz inhabitants in szenario B

carpassenger

moped motorbike

Figure 4 Shifts in means of transport in scenario B (NMB-friendly infrastructure and paid parking). Shifts affecting less than 0.2 percent of trips not shown

ba

Legend: 35,4%

percentage share of means of transport of trips by Graz inhabitants 1991

(->22,6%) percentage share of means of transport of trips by Graz inhabitants in szenario C

Figure 5 Choice of means of transport in scenario C (driving ban for vehicles with internal combustion engine in the inner city). Shifts affecting less than 0.2 percent of trips not shown

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Modal split depending on sex and age The actual state of the modal split shows the familiar picture for European cities, men originate twice as many trips with a motorised vehicle than women. In the scenarios, this distribution is also valid for the NMB (Fig. 6). Thus, the NMB is chiefly regarded as a vehicle for men. In comparison to the present motorbike or moped, a share of four percent for women in Scenario A must be considered as high. In the case of the other means of transport, this difference in frequency between the sexes is also evident: women walk twice as frequently as men, ride a bicycle half as frequently and use public transport more than twice as often. In Scenario C, women would use an electric car three times as often as men. Consideration of the modal split according to age groups (Fig. 7) shows that younger people would use the NMB over all. How many young people would actually change over to the NMB depends greatly on the cost involved. In the survey, it was assumed that the most favourable NMB would be available from 4,500 German Marks.

Modal split depending on journey purpose If one considers the modal split depending on the purpose of the journey, one sees clear differences (Fig. 7). As the typical potential NMB user is relatively young, the largest NMB share will be achieved by educating commuter traffic. Depending on the scenario, it is between 13-15 percent. Working commuter traffic is dominated by private cars. Here the NMB share is above average—between 10 percent in Scenario A, and 11 percent in Scenarios B and C. In Scenario A, this value corresponds to the share of public transport. The following reasons for this high share may be given as: • A large part of the working commuter traffic goes into the inner city where the advantages of the NMB are pre-eminent. • In working commuter traffic occupancy is generally very low, i.e. no other person travels with the driver. Therefore, there are no problems of capacity regarding the transport of people. • In most cases no articles that need a large space are transported. In leisure traffic, the NMB share is between six and eight percent and, thus, corresponds roughly to the average NMB share of all purposes.

3r-<

Figure 6 Modal split depending on age and sex (scenario A)

Figure 7 Modal split depending on the purpose of the journey in scenario A

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In shopping traffic, compared with the other purposes, there is a considerably lower share switching to the NMB. The reason for this may be the higher number of women engaged in shopping traffic. In business traffic the lowest NMB share is reached—with three percent it lies just below the cycle share.

Trip-length distribution The trip-length profile for the NMB corresponds approximately to the private car, but the development in the 3-5 km category is somewhat greater than for the private car (Fig. 8). Comparison with the bicycle shows clearly that the NMB would be used, especially for distances where the bicycle would be of limited suitability. Altogether, about 75 percent of all NMB trips would be made at distances of 3-10 km. At these distances the desired maximum speed of 45 km/h can be considered sufficient.

Conclusion At the present stage of the investigation, the present results are to be considered as an interesting approach to overcoming future traffic problems in conurbations and should be pursued further. The following procedure is recommended: Development of a prototype of the New Motorised Bicycle in cooperation with vehicle manufacturers. Examination of the NMB's potential in other countries with other conditions.

Acknowledgements This study was carried out on behalf of the Industrieverband Motorrad, Essen, Germany in 1992-1994.

on foot bicycle moped/ motorbike NMB car passenger car driver

2-3

3-5

5-10

10-15

distances in kilometre categorys

I TO SX

Figure 8 Distribution of trip lengths in scenario A

ba

U)

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References Brog, W. (1981) Individuelles verhalten als basis verhaltensorientierter modelle. In Schriftenreihe der Deutschen Verkehrswissenschaftlichen Gesellschaft No. B57, Verkehrsnachfrage-Modelle, Koln. Brog, W. and Erl, E. (1981) Die anwendung eines individualverhaltensmodelles unter beriicksichtigung haushaltsbezogener aktivitatsmuster, Socialdata, Munich. Sammer, G. (1982) Untersuchung zur verkehrsmittelwahl im personenverkehr. Heft 179 der Schriftenreihe Strassenforschung, Kommissionsverlag Forschungsgesellschaft fur das Strassenwesen, Vienna. Sammer, G. and Fallast, K. (1990) A consistent simultaneous data weighting process for traffic behaviour. Proceedings of the 3rd International Conference on Survey Methods in Transportation, Washington DC, October 1990, USA.

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Configurational Modelling of Urban Movement Neworks Alan Penn, Bill Hillier, David Banister and Jianming Xu

Abstract Transportation research has usually seen road networks as inert systems to be navigated and eventually filled up by traffic. A new type of "configurational" road network modelling, coupled to detailed studies of vehicular and pedestrian flows, suggests that road networks have a much more constructive role. They strongly influence the pattern of flows through quantifiable properties of the network "configuration". Recent research results have found that rates of both vehicular and pedestrian movement in road segments are to a greater extent than previously realised the direct outcome of the location of those segments in the network configuration as a whole. This is the case even in the fine structure of urban back streets. Moreover, systematic differences in the ways which pedestrians and vehicles navigate the system, as shown in the different flow patterns for each, suggest that these effects of network configuration on movement arise at least in part from how the network is intelligible to those seeking to move through it on longer or shorter journeys. The results show that in addition to the configuration, each mode is affected by one other factor. Pedestrian movement is affected by densities of development measured by building height, while vehicular flows are affected by the effective capacity of the roadway. A supply/demand model is proposed for vehicular traffic in which the location of a particular street within the network defines the demand side, while effective capacity defines the supply side. These findings suggest the possibility of using urban design parameters such as the plan configuration of the street grid, height and width of streets, to arrive at a better controlled relationship between vehicles and pedestrians in urban areas.

Urban Network Configuration as a Factor Affecting Movement Behaviour Conventional traffic models use relatively simple representations of the road network coupled to quite complex cost functions which are calibrated

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using data on origins and destinations of trips and observed flows on the network. Traffic assignment models assume perfect knowledge of the system, and since "cost" is generally taken as travel time, knowledge of congestion of the route options ahead of the driver is assumed so that drivers make a "rational" choice of route. Since the drivers' choices create the patterns of congestion, their decisions feed back into the cost functions, and the models iterate until they settle to a solution. These modelling techniques are now well established and are proven in application, however there are a number of areas in which they appear to have limitations. The construction and calibration of traffic models is a costly procedure in which the cost is related to the resolution with which the Origin-Destination (OD) data are gathered and the size of the model measured in terms of the number of nodes and links represented in the network. Models are therefore seldom constructed to represent the finest scale structure of the street network, and their performance at this scale is not well understood. Models are generally developed based on the travel to work trip, for which the best OD information is available on other trip types and for other modes. In particular, OD information is lacking for the pedestrian mode (Pushkarov and Zupan, 1975), and this is where it seems likely that the fine scale network will be of most relevance. At the same time there is an emerging demand from the engineering community for the ability to give rapid, qualitatively correct appraisals of design proposals, and for the ability to address the more "human" aspects of urban traffic many of which involve both vehicular and pedestrian modes. Advice on traffic calming schemes which require predictions in the finest scale structure of the street grid for both vehicular and pedestrian modes provide a case in point. For these applications conventional modelling techniques have begun to show their limitations and engineers rely more often than not on intuition, experience and experiment. Methods for the analysis of spatial configuration developed by Bill Hillier and his colleagues at University College London are beginning to suggest the possibility of a new approach. These methods are based on the use of a detailed representation of the pattern of space through which pedestrians or cars move. By measuring the properties of these patterns considered, not merely as localised spatial elements—this street or that intersection—but as an entire configuration of elements each related to the others, it is possible to search for effects of the design of the street grid on the way that flows are distributed through the network, and the way that different modes are brought into contact with each other. Pre-

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vious research has shown that these models provide strong predictions of pedestrian movement patterns (Hillier et al., 1993). More recently the methods have been applied to studies of simultaneous vehicular and pedestrian movement patterns (Penn and Dalton, 1994). Now the methods are being tested under a far wider range of different urban conditions, and are beginning to shed light on the way that city structure and patterns of movement are related. This chapter reports on the research carried out during 1992-1994 in London.

Configurational Analysis Using "Space Syntax" Techniques Configurational analysis quantifies the pattern properties of the urban street network by first breaking up the pattern of continuous open space through which one moves (Fig. la) into the fewest and longest lines of sight and access that pass through all circulation routes (Fig. Ib). We call this simplified representation of the two-dimensional space pattern of an urban area its "axial" map. Next, each line in the map is represented as a node in a graph with each intersection between lines represented as a link in the graph. In this way, Configurational analysis reverses the conventional traffic model's description of the network in which road intersections are considered as the nodes and street segments links. This reversal has several effects. First, it eliminates metric distance from the representation since both short and long streets may be represented as single nodes. Second, "oneway" systems, turning restrictions, road capacity and traffic-light timings are not represented directly in the axial map, or the graph. Third,

Figure 1 Open space of an irregular street grid (a) and its axial representation (b)

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there is no explicit representation of factors such as land use and development density, or of major attractors and generators of movement, although, as we shall show, factors such as capacity or development density can be included as explanatory variables in regression analysis. Since configurational analysis effectively eliminates all the main cost and demand factors associated with conventional traffic modelling techniques, it is worth considering what the axial graph does represent. Since each node is a line of sight and access, and each link in the graph is an intersection between lines, a transition from one node to another corresponds to a change of direction in the street grid. The axial graph, therefore, represents the street grid as it might be experienced in terms of direction changes along a route. Once a graph has been constructed, measures can be devised of the properties of the graph, and then conventional statistical methods can be used to see whether, or not, there is any detectable correlation between the pattern properties of the street grid represented and quantified in this way and observed traffic behaviour. The essence of the method is, therefore, analytic, aiming to quantify certain morphological properties of the street grid, in order to allow an investigation of whether, or not, morphology alone can have detectable effects on aspects of behaviour, such as route choice and traffic flows. The models that follow from this are conventional regression models. One of the simplest measures of the graph is the "connectivity" (valency or degree) of the node, however this is a purely local measure of the pattern. As it turns out, more useful measures are more "global" in that they quantify aspects of the way a node figures in a larger scale pattern. One of the most useful of these is a measure of the mean depth (MD) of a node within the graph—taking every move along a link to add a step of depth. Since a transition along a link is a change in direction in the street grid, MD in the graph quantifies how simple or tortuous routes are on average from one line to all others (taking the simplest possible route in each case). By convention we normalise the MD measure twice. First, we calculate the "relative asymmetry" (RA) of a node according to how deep that node could possibly be in a graph with a given number (k) of nodes according to the following formula:

Next, we use an empirical normalisation which takes account of the way real cities overcome the effects of sheer size through the use of a longer

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and better connected primary line structure. To do this, we divide a node's RA value by the RA of the corner of a diamond shaped system with the same number of nodes (D&). This normalisation produces a measure we call Real Relative Asymmetry (RRA) where,

and the D-value (D^) is given by

Finally, by convention we call the reciprocal of RRA "global integration", since it measures the degree to which a node in the graph "integrates" all other nodes in a network. The full derivation of all these measures is given in Hillier and Hanson, (1984). Figure 2 shows the "global integration" map for London within the North and South Circular roads and west of the Lea Valley. The map represents all street segments open to vehicular traffic within the area using some 16,000 lines and 50,000 links, coloured up from black for the "shallowest" most integrated lines through the grey scale to light grey for the "deepest" or most "segregated" lines in the area. It is striking that the most integrated line in the whole of this area is Oxford Street (the horizontal line near the centre of the map), and that the remainder of what we would recognise as the primary route structure of the area, is picked out by a purely configurational analysis, without any reference to land uses, capacities or oneway systems. There is, however, a notable "edge effect" evident in Fig. 2. Certain lines near the edges of the mapped area are segregated purely as a result of our selection of the boundary for analysis. If we had selected a larger boundary they would have appeared to be more integrated. This is a natural result of any completely global depth measure which measures the "depth of this line with respect to this system of lines". One way of overcoming these edge effects involves calculating the MD of all nodes within some fixed radius (number of steps of depth) of each node in turn. This effectively creates a moving boundary around each line in turn, rather like a cookie cutter. The restricted radius measures of integration turn out to be important for urban movement patterns, and particularly for disentangling the relationship between different modes and different roles of routes in the road hierarchy. The most local of these measures is "radius 3 integration" (Fig. 3) which takes account of a line, its neighbours and

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Figure 2 The pattern of global integration for London within the north and south circular roads plotted from dark for the highest integration lines to light for the lowest integration

their neighbours, although we find that a range of other radii are of interest. Figure 3 shows the almost complete elimination of the "edge effect", and highlights the most locally integrated lines distributed throughout the London area, many of which turn out to be local shopping streets. It seems that these simple measures of the topology of the road network reveal a subtle range of properties of urban systems without the need to invoke the metric concepts of "distance" or "cost".

Spatial Configuration and Movement Several factors seem intuitively apparent. First, it is clear that there is some relationship between the importance of routes, their degree of inte-

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Figure 3 The pattern of local radius 3 integration for London within north and south circular roads plotted from dark for highest integration lines to light for lowest integration

gration, the densities and kinds of land uses they serve and the predominant scale of spaces, both in terms of length of lines and the width of the streets. Second, it seems clear that different spaces figure differently with regard to different radii of catchment. Some spaces are locally integrated but not globally so, others such as Oxford Street are both locally and globally integrated. Third, it seems clear that in global terms there is an integrated "core" of streets corresponding to the central commercial and retail areas of London, that this core clings to the main radial routes leading from edge to centre, and that the more suburban residential districts fall in between the radials. To this extent the configurational logic appears to mirror both the development density and land use characteristics of the city. Fourth, it seems fair to guess that there is a relationship

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between volumes of traffic and the degree of integration of streets within the different parts of the area. As far as pedestrian movement is concerned, we now have considerable evidence for the last of these. It is clear that the configuration of the street grid gives rise to a pattern of "natural movement" for the pedestrian population as a whole, and this is reflected in a correlation between spatial integration and pedestrian flow rates. The more integrated a street becomes, the greater the pedestrian flow rate. However, since it also seems that patterns of land use and development density are related to spatial configuration there is clearly a question of what causes what. We have argued elsewhere that the question of "which comes first, the people or the shops", is easily resolved by looking at mixed use areas including retail and monofunctional residential areas (Hillier et al., 1993). In the former, there is an exponential rise in pedestrian flows with increased integration and, in the latter the correlation is more or less linear. A possible explanation is that the pattern of the grid gives rise to a pattern of pedestrian movement, and this in turn attracts retail land uses to take advantage of the passing trade. In mixed areas, the shops site themselves in spaces that are used for through-movement, and then become the destinations for to-movement, acting as a multiplier on the original flows. The exponential relationship we observe between configurational measures and flows results from this "multiplier effect". The model has considerable appeal. It explains both the common experience that where there are shops there are people, and it allows an explanation of how the traditional city seems to have evolved to get the right land uses in the right numbers in the right locations without, more or less, tight master planning controls. It begins to explain why it is that, for pedestrians at least, trying to achieve high levels of space occupancy by locating shopping "attractors" in the middle of residential estates, is so often prone to failure. The key to retail success is not only the attractiveness of the shop, but the "passing trade" which, almost by definition, is on its way from, and to, other spaces and so is sensitive to the configuration of the street grid. Further weight has been given to these findings by a simultaneous study of vehicular and pedestrian movement reported by Penn and Dalton (1994). This study found that the degree to which vehicular traffic dominated pedestrian movement in the primary route structure of an urban area varied radically according to the dominant land use. On routes lined with residential land uses, vehicular traffic outnumber pedestrians at a rate of eight to one, but where the dominant land use is shopping the rate is

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nearer one to one. The key question in seeking to maintain a more viable ratio of vehicles to pedestrians is how to achieve a sufficient quantum of retail land uses on the primary route system. The data suggest that only under certain circumstances do shopping streets become viable: streets that secure high levels of retail need to be both well integrated into the global network, and well integrated into a local pedestrian catchment. A local catchment alone would attract small scale convenience shopping, but would not reach the threshold required to start the multiplier effect needed to create an urban shopping "centre". Global integration alone led to vehicular "rat runs" that failed to gain significant retail land uses, and also failed to reach the "multiplier" threshold. In order to begin to investigate these relationships in more detail, six study areas were chosen to reflect a range of different predominant land use types and mixes, densities of development and street grid morphologies. Within each study area nearly all street segments were observed for over 50 minutes (two sets of five-minute observations in each of five time periods throughout the working day). In one study area, the City of London, two sets of observations were made to observe the effects of changes to the effective street grid on patterns of movement, before and after, the introduction of a massive traffic management scheme as a part of the antiterrorist security zone following the 1992 bombing of the city. However, since the effects of the road closures and subsequent traffic management had a significant effect on the traffic behaviour in this area the data are omitted from the main analysis presented here and is only discussed briefly below. Simultaneous counts of both pedestrian and vehicular flows were made, and the study areas were surveyed to determine factors for each street segment such as the predominant land use, the mean and maximum building height (as a measure of development density) and the total and effective road-widths at the narrowest point on the segment. Taken together these data allow us to investigate whether, or not, the apparent relationships between spatial configuration and other factors are really present. In the North London residential area of Barnsbury, for example, both pedestrian (Fig. 4) and vehicular (Fig. 5) flow rates are very well predicted by measures of spatial integration. However, in this area land uses, density of development and street-width are all fairly homogeneous. When we look at the other areas which have much greater variation in their land use patterns and densities, it turns out that for pedestrian movement the density of development and the types of land use are also of importance. The data show that residential development does not produce pedestrian

348

Travel Behaviour Research: Updating the State of Play y = .811 x + 1.172, R-squared: .744

3

35

Figure 4 The correlation between local radius 3 integration and the logarithm of pedestrian flow rates in the Barnsbury study area (r = 0.862, p = 0.0001)

"S5

1.5

2.5 3 RA3(2v)

3.5

4.5

Figure 5 The correlation between local radius 3 integration and the logarithm of vehicular flow rates in the Barnsbury study area (r = 0.881, p < 0.0001)

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movement on the street in significant quantities, it takes commercial office and retail development to do that. They also confirm that pedestrian movement levels depend on the density of development (measured by building height), coupled to the more localised measures of the configuration of the street grid. Figure 6 shows the correlation between pedestrian flow rates and the measure of radius 5 integration for the whole sample of 466 London observation sites (excluding the City of London). However, the pedestrian movement patterns are relatively localised and sensitive to different radius measures, falling on different regression lines for each of the study areas. For example, pedestrian movement in Barnsbury is best predicted by radius 3 integration (Fig. 4), while that for the Calthorpe Street area is best predicted by radius 7 integration (Fig. 7). For vehicular flows, there appears to be far greater consistency from area to area. This is reflected both in a higher overall correlation (r = 0.82, p < 0.0001, n = 402), for all vehicular street segments (Fig. 8), and in the similarity between all the regression lines for each study area within that scatter (Fig. 9). The Brompton Road area has a somewhat lower slope than the remainder, but all lie within the 90 percent confidence interval for mean and slope. A multiple regression analysis for vehicular flows against a range of other variables, including building density, predominant land use, radius 3 integration and the effective capacity of the roadway, shows only the last two to be significant (Table 1). The multiple regression including only the two significant variables shows that both perform more or less equally in the regression (Table 2), however if we divide the sample into observations on primary routes and the remainder (Tables 3 and 4) then we find, as might be expected, that capacity is the main determinant for the primary route structure, but integration is the main determinant for the secondary and finer scale structure. By constructing a fitted variable on the basis of the regression in Table 2, we can explore the degree of agreement provided on the basis of these two variables alone. Figure 10 shows the correlation between vehicular flows and this fitted variable. It turns out that vehicular flows are best normalised by taking the 4th root and this is the normalisation used in Fig. 10.

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8

•S5

Figure 6 The correlation between the log of observed adult pedestrian flows and radius 5 integration (r = 0.726, p < 0.0001, n = 466)

Figure 7 The correlation between the log of observed adult pedestrian flows and radius 7 integration (r = 0.864, p < 0.0001, n = 62)

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Figure 8 The correlation between the logarithm of average vehicular flows per hour (excluding buses) with radius 3 integration (r = 0.82, p < 0.0001, n = 402)

Figure 9 Correlations for each study area showing the similarity between regression lines

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Table 1 Multiple regression of radius 3 integration, the logarithm of net roadwidth land use and maximum building height against the logarithm of vehicular flows DF

r

r2

adj r2

p

std. error

395

0.883

0 .779

0.777

0.0001

0.794

t

P

14.128 13.949 0.725 1.999

0.0001 0.0001 0.4691 0.0463

RA3vehLondon Log of net road-width Max. building height Land use

Table 2 Multiple regression of radius 3 integration and the logarithm of net road-width DF 395

r 0.881

r2 0 .777

adj r2 0.776

RA3vehLondon Log of net road-width

p 0.0001

std. error 0.796

t

P

14.524 14.276

0.0001 0.0001

Table 3 Multiple regression of radius 3 integration and the logarithm of net road-width for the primary route observations only DF 98

r 0.853

r2 0 .728

RA3vehLondon Log of net road-width

adj r2 0.723

p 0.0001

std. error 0.259

t

P

1.814 13.504

0.0728 0.0001

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Table 4 Multiple regression of radius 3 integration and the logarithm of net road-width for all observations except the primary routes DF 296

r 0.814

RA3vehLondon Log of net road-width

r2 0.663

adj r2 0.660

P 0.0001

std. error 0.844

t

P

13.593 10.418

0.0001 0.0001

Figure 10 Correlation between normalised vehicular flows and a fitted variable including radius 3 integration and net road-width (r = 0.91, p < 0.0001, n = 395)

A Supply and Demand Model for Urban Movement The strength of these findings, as well as their apparent robustness in the face of different land use characteristics, development densities and grid morphologies, holds great promise for the development of a predictive capability, based on the new simplified modelling techniques. One of the more surprising findings, however, is that taken at the level of individual street segments the best correlate of vehicular movement incorporates the

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most local radius 3 measure, rather than the global measure which might have been expected to perform best as a predictor of longer vehicular trips. This may be due to the predominance of relatively local streets in the observed sample of street segments. Certainly, when we look at the primary, secondary and local roads separately, we find that primary roads are better correlated with the more global larger radius measures (r = 0.784, p < 0.0001, with radius 7 integration), while secondary and local roads are better related to the smaller radius measures (r = 0.734, p < 0.0001, with radius 3 integration). This leads us to suggest that global integration contributes the demand side and capacity to the supply side of the equation for vehicular flows in the primary road structure. However integrated you make an area, average flows through it will never rise far above those at capacity. Equally, however wide you make a street segment, the flows through it depend on how it is embedded in the network and whether, or not, it is in demand as a through-movement space. In this way, global integration quantifies the potential for through-movement that the lines within an area hold when considered in terms of the whole network topology, and so effectively quantifies travel demand, not for specific origin-destination pairs, but for all origins and destinations in the network. We think that this clarification is a useful one in the light of current concerns over the effect of road construction on generated demand. Increased capacity on an existing link will have little effect on the distribution of integration in the network, and so models based on existing demand using current OD data, are likely to provide a reasonable guide. However, where new network links change the configuration of the network, such as with the construction of London's M25 orbital, patterns of integration will also change and new patterns of demand are likely to follow. We believe that one of the effects of this is the way that traffic management, and in particular the supply of effective road-width, evolves over time to fit the demand side of the equation. When we look at the effect of the road closures in the City of London immediately following the terrorist bomb in 1993, it is clear that the relationship between vehicular flows and capacity had begun to break down. Figure 11 shows that although the correlation is tight in the narrower, lower flow rate streets of the City, among the primary route structure there was a great divergence between road-width and flow. This is the immediate effect of the closure of two main through-routes as a result of the bomb. However, when those routes were reopened, a massive security cordon was established around the whole of the commercial heart of the city.

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3000

16

18

20

Figure 11 Correlation between vehicular flow rates and the effective road-width in the city of London after the Bomb Road closures (r = 0.883, p < 0.0001)

In effect, the cordon restricts entry to the security zone to a limited number of locations, and had a great effect on vehicular flow patterns across the whole area. The effect of this can be seen in the far greater degree of variance in the lower parts of the scattergram in Fig. 12. This suggests that in the evolution of the city, a mechanism is in operation which restricts capacity in those street segments that are not in demand for through-movement, for instance by allowing on-street parking. However, in the primary (globally integrated structure), where there is a demand for through-movement, parking will be restricted and capacity maximised through the normal process of traffic management to ease congestion. Following a local change to the network, such as that caused by the bomb, the effects are only seen on the routes directly affected by road closures. However, after a massive change in the network topology, such as that produced by the security cordon, it seems clear that although the flow patterns will shift overnight the pattern of effective capacity will take some time, possibly years, before it adapts to suit the new demand structure. The model this implies is a spatial market in which the demands imposed by the configuration of the grid are met by the supply of road capacity

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Figure 12 Correlation between vehicular flow rates and effective road-width in the city of London after implementation of the security zone (r = 0.829, p < 0.0001)

through the continual adaptation, and adjustment, of individual traffic management and parking provision schemes. The mechanism is self-regulating in much the same way as we propose for the allocation of retail land uses to urban sites through the multiplier effect. At the root is the configuration of the network which, it seems, may play a far more active role in determining the way the city evolves and behaves, than has been thought up to now.

Mean Movement Rates in London Areas We might expect that as a city evolves, feedback mechanisms of the sort we have described will lead to differentiation of one area from another, as well as the generation of characteristic relationships between patterns of movement, land use and development density. In common with many cities, London displays a marked local area structure with a series of "named" areas in close proximity, each with their own characteristics. Each area exhibits quite different morphological properties in terms of the pattern of the street grid, the height of buildings and densities and

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patterns of land use, as well as different characteristics in terms of the predominant modes and patterns of movement, and their changing profiles at different times of the day. The case studies in the present research selected a series of well-defined areas including the commercial City of London, the shopping area around the Brompton Road, the high-class residential and museum complex in South Kensington and the 19th century residential suburb of Barnsbury. Each whole area was described in terms of the main land use, movement and configurational variables, and a search was made for regular associations between these for all the areas. At the level of whole areas, two factors are correlated with average pedestrian flow rates, a measure of development density—the average of the maximum building heights for each street segment (Fig. 13)—and the measure of local radius 3 integration of the street grid (Fig. 14). Although there are other correlates of average pedestrian movement rates, notably measures of the predominant land use, these two outrank them by a clear margin. Mean vehicular flow rates are not particularly well related to these two measures, however, they are strongly related to the average effective roadwidth (total road-width less pedestrian pavements and car parking bays,

1100

Figure 13 Correlation between mean pedestrian movement rates and mean maximum building height across the London study areas (r = 0.919, p = 0.0034)

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Figure 14 Correlation between mean pedestrian movement rates and local radius 3 integration across the London study areas (r = 0.93, p = 0.0024)

see Fig. 15), and the average "global integration" of lines in the area (Fig. 16). The findings on an area-by-area basis, suggest that average pedestrian flow rates depend on both development density and the degree of local integration of the street grid morphology, while vehicular flow rates depend on a measure of the average capacity of the roads. Also, their global location in the city as a whole confirm existing thinking: development density and capacity are major factors dictating flows. But they move beyond this to suggest that the degree of locality or globality of the street grid configuration measures may indeed be able to quantify aspects of different distributions of trip lengths for different traffic modes, and through this suggest a far more active role for the network configuration than has usually been allowed. Importantly, multiple regression analysis suggests that global integration and capacity measured in terms of effective road-width account for nearly all the variance in mean vehicular flow rates for the study areas (r2 = 0.966, Table 5) with each contributing almost equally. This suggests that it is the location of an area in the whole city that determines its mean level of vehicular movement, with more centralised locations gaining higher average flows than more peripheral ones, but that the mean flow is almost equally constrained by

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Figure 15 The correlation between mean vehicular flows on all observed segments in an area and mean effective road width (r = 0.901, p = 0.0057)

.

Figure 16 The correlation between mean vehicular flows on all observed segments in an area and mean global integration (r = 0.904, p = 0.0052)

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Table 5 Multiple regression of mean global integration and mean net road-width against mean vehicular flows in the six study areas

r 0.983

DF 6

r2 0.966

adj r2 0.949

Global integration Net road-width

p 0.0011

std error 28.807

t

P

4.728 4.189

0.0129 0.0138

the capacity of the network. For pedestrians, it is the degree of local accessibility measured in terms of radius 3 integration coupled to the density of development and the land uses that have most effect, with global location being a less important factor.

Generalising the Methodology as a Design Tool These findings have important implications for the strategies we adopt to try and control, and humanise, the motor car. First, it is clear that there are four key tools at the disposal of the planner in trying to civilise urban traffic: (1) (2) (3) (4)

the the the the

configuration of the street grid; capacity of the street segment; distribution of land uses; distribution of development density.

In order to civilise the car, we would suggest that it is necessary to bring pedestrian movement onto more equal terms. As long as cars outnumber pedestrians in a street by eight to one, they will always appear to dominate urban space. The data show that it is only by attracting a sufficient density of retail and commercial land uses that pedestrian numbers can be significantly raised, and that the recipe for viable long-term retail centres depends on achieving sufficient levels of both local and global integration for the "multiplier effect" to take off. Second, it seems possible that by exploiting self-perpetuating and self-

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regulating mechanisms, such as the multiplier effect that stable long-term conditions can be achieved. Other strategies, which seek to work against the natural effects of spatial configuration, require continued effort and investment to sustain them. The shop placed in the centre of the housing estate in order to "liven it up" is a case in point. Experience shows that shops considered as "attractors" need subsidies or continued investment to survive. The more robust formula allows the pattern of through-movement generated by the grid configuration to do at least part of the work. Third, the requirement for both local and global integration for the shopping multiplier effect seems to be founded on the need for shops to both maximise the level of passing trade and to even it out through time. In more segregated residential areas, the difference in movement levels between the peaks and the low points is significantly higher (in percentage terms) than on primary routes (although it is clearly not so in numeric terms). This seems to give the logic for locating newsagents in local integrators—these shops do their business during the peak periods. However, more specialist types of shop need a greater size of catchment and a more globally strategic location in order to gain a greater passing trade. For the kind of mix of shopping types that characterise a "shopping centre", a full range of local and global catchments is needed. We believe that this last effect underpins one of the key features of urban space. If cities are, as Jane Jacobs suggested, "mechanisms for generating contact" one of their main tools lies in the way that they relate local and large-scale patterns of movement, and how both are brought into contact with land uses. In studying the character of urban subareas in large cities like London, we find a consistent pattern in which the measures of local and global integration for all the spaces within a named area regularly correlate strongly together. We believe that these local to global correlations between spatial properties are exactly what allows the parts of cities to come together to form a global whole, and more importantly, they make the urban network intelligible to us, whether we are pedestrians or drivers. Essentially, intelligible space allows individuals to behave in a rational way as they move around the city. At the same time, the consistent relations between local and global movement patterns are what allows us to behave rationally in our choice of location for land uses, whether these are where to work, sell or live. It is the effects of the configuration of urban space that allows individuals to behave rationally, which we believe is the precondition for the social function of the city and, hence, for the civilisation of new technological innovations, such as the motor car.

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References Hillier, B., Penn, A., Hanson, J., Grajewski, T. and Xu, J. (1993) Natural movement: or configuration and attraction in urban pedestrian movement. Environment and Planning 20B, 29-66. Hillier, B. and Hanson, J. (1984) The Social Logic of Space. Cambridge University Press, Cambridge. Penn, A. and Dalton, N. (1994) The architecture of society: stochastic simulations of urban pedestrian movement. In N. Gilbert and J. Doran (eds.), Simulating Societies, UCL Press, London. Pushkarev, B. and Zupan, J. (1975) Urban Space for Pedestrians. The MIT Press, Cambridge, Mass.

Part IV Dynamics of Route Choice

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Day-to-Day Dynamics of Urban Commuter Departure Time and Route Switching Decisions: Joint Model Estimation Rong-Chang Jou and Hani S. Mahmassani

Abstract This chapter focuses on the day-to-day dynamic decisions of departure time and route by actual commuters in the Dallas, Texas urban area. A model previously developed based on "laboratory like" experiments provides the framework for analysing this phenomenon. The underlying behavioural mechanism is a boundedly-rational search to achieve an acceptable commute. Joint Indifference Bands (IBs) for route and departure time acceptability decisions are formulated, and specifications are developed for both the systematic and random components. In particular, econometric issues associated with specifying the random error structure are addressed for parameter estimation purposes. Insights into the effects of attributes are obtained through the analysis of the model's performance and estimated parameter values. A general probit model form is used for the dynamic switching model, allowing the introduction of state dependence and serial correlation in the model specification. The Monte Carlo simulation approach is followed to obtain maximum likelihood parameter estimates of the multinomial probit choice probability function. The data used for estimation were obtained from a field survey in Dallas, Texas conducted over a period of 10 working days, yielding observations on consecutive day-to-day decisions of commuters.

Introduction Various transportation system management (TSM) strategies including peak period spreading, incentives for car-pools, and road pricing schemes

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have been proposed to improve the efficient use of existing transportation systems. Advanced technologies, such as intelligent transportation systems (ITS) and changeable-message signs, provide opportunities to improve highway productivity by offering real-time information to drivers who may switch routes and adjust the departure times of their trips. Since many of these solutions are aimed at the congested commuting periods of the day, their success requires a better understanding of commuter choice behaviour. Therefore, commuter behaviour must be treated as a central element in the development and implementation of demand side congestion relief strategies. Over the past decade, there has been extensive investigation of departure time and route choices in interactive laboratory-like experiments by Mahmassani and Chang (1986), Mahmassani and Tong (1988), Mahmassani and Stephan (1988), and Tong (1990). While these experiments provided valuable insights into complex trip-maker decision behaviour, the transferability of these insights to commuter behaviour in actual traffic networks could not be sufficiently established without actual field observations. This has motivated the field study approach followed by Mahmassani et al. (1993, 1997) and Jou and Mahmassani (1996), to observe actual commuters' daily travel decisions in real traffic networks. This novel survey diary approach, initially developed and tested in Austin, Texas, was subsequently adapted and used to observe actual commuter behaviour in Dallas, Texas. The surveys resulted in a unique set of observations to support the development of models of commuter behaviour dynamics. A detailed description of these can be found elsewhere (Caplice, 1990; Hatcher, 1991; Jou et al., 1992). The Dallas data form the basis of day-to-day departure time and route switching models presented in this chapter. These models are founded on the same behavioural framework developed in conjunction with the previous laboratory experiments. In particular, departure time and route switching behaviour is predicted on an indifference band of tolerable schedule delay, according to a satisficing mechanism that reflects boundedly-rational commuter behaviour, as described in the next section. In this chapter, an indifference band that captures behaviour of both early and late arrivals (at the workplace, relative to one's desired arrival time) is developed instead of separate early- and late-side indifference bands. A recent multinomial probit (MNP) estimation procedure developed by Lam and Mahmassani (1991) is applied to estimate these models. The next section provides a background review of the previous related work. The theoretical framework for the joint indifference band model is

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presented in the third section. The fourth section gives a brief discussion of the model specification. The estimation procedures and results are discussed in detail in the fifth section. The last section presents our conclusions.

Background Review Previous studies have confirmed that arrival time is a major concern to commuters, and presented strong evidence that the indifference band of tolerable "schedule delay" (defined as the difference between the actual arrival time and the preferred arrival time (PAT) for a given commuter) is the most important criterion governing the day-to-day responses of commuters to congestion. In their daily commutes, trip-makers are assumed to maintain the same choice as long as the outcome does not fall outside a tolerable range (i.e. deviation from PAT is smaller than the indifference band). Otherwise, if the previous outcome is considered unacceptable, commuters will adjust the previous decision through some mechanism. That is, let PAT, denote the preferred arrival time at the workplace of commuter z, / = ! , . . . , TV. This quantity reflects inherent preferences and risk attitudes of each commuter, as well as the characteristics of the workplace. Let ATit denote the arrival time of commuter i on day t. The boundedly rational character of the decision process uses Simon's satisficing rule, whereby, the commuter does not switch departure time and/or route so long as the corresponding schedule delay,

remains within the user's indifference band, as follows:

where ESD,r denotes the early-side schedule delay and LSD,, the late-side

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schedule delay; Sit and A,-, are the departure time and route switching decision indicator variables. Sit = 1 when user i switches departure time after the commute on day t (i.e. for the commute on day t + 1), with 8it equal to —1 otherwise; \it has a similar definition route switching. There are four possible combinations of departure time and route switching decisions, corresponding to the combinations of values for (8it, A,-,). For example, (-1, -1) denotes that both departure time and route will not be changed on the next day. EBDit and LBD;r are the respective departure time indifference bands of tolerable schedule delay corresponding to early and late arrivals (relative to PAT/) for day t. EBRit and LERit are the early- and late-side indifference bands for route switching. The indifference bands are latent terms, internal to each individual, and therefore can neither be observed nor measured directly. Instead, they can be inferred from actual observations of commuters' decisions to switch or not in response to experienced traffic conditions and to exogenous information. The specification and estimation of the indifference bands and their daily variation requires time series observations of switching decisions of individual commuters. Such data are available from the twoweek field survey of commuter behaviour conducted in Dallas. For estimation purposes, the indifference bands are treated as random variables, distributed over days and across commuters with systematically varying mean values as illustrated in Fig. 1 (Tong, 1990). Commuters are assumed to have separate components corresponding to early and late arrivals at the workplace and different indifference bands for departure time and route. These are estimated jointly for the first time in the present study.

Early-side indifference band The derivation of early-side (SDit - ESDit > 0) indifference bands is presented in this section:

The subscript 'e' represents early-side arrival relative to the PAT. The systematic components of departure time and route are /e(0 and he(-),

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Arrival Time

Late Band for Route (LBR)

Late Band for Departure Time (LBD) Early Band for Departure Time (EBD)

Preferred Arrival Time

Early Band for Route (EBR)

Days Evolution Period

Figure 1 Early- and late-side indifference bands for departure time and route

respectively. The vector of user characteristics Xt and the vector of performance characteristics Zit capture user /'s experience up to day t\ 6it is a vector or parameters to be estimated. The random terms e^e and rit^ i = 1, . . . T, are assumed to be jointly normally distributed, over days and across commuters, with zero means and general covariance matrix Se, where 2e is expressed as follows:

S€e and STe represent T x T matrices that capture the serial correlation due to the persistence of unobservable attributes across the sequence of departure time and route decisions made by the same individual. Cov represents the correlation that might exist between the departure time and route bands for a given user /, at time period t — 1, . . . , T. Also, state dependence is likely to be present and can be captured by the specification of/ e (-) and h&(-}. Although the exact specification of the structure of this matrix is ultimately an empirical issue, a structure of

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the variance-covariance matrix Se proposed by Mahmassani (1990) is as follows:

where the subscript 'D' represents the departure time components and 'R' represents the route components. Se can also be written as follows:

A summary of the error structure for departure time and route switching indifference bands is shown in Fig. 2 (Mahmassani, 1990). Given a specification for /e( •) or he( •), the available observations of the switching decisions made over T days by the N commuters in the sample provide a basis for the maximum likelihood estimation of parameters. A general framework to deal with the associated estimation issues of multivariate normal error terms has been presented by Daganzo and Sheffi (1982), who showed that the probability of a sequence of decisions is essentially equivalent to a multinomial probit MNP probability function. Detailed derivation of the likelihood expressions and variance-covariance structure for the equivalent MNP function is given in Mahmassani (1990)

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Figure 2 Summary of error structure for departure time and route indifference bands

for separate estimation of early- and late-side bands. In the third section, we present the derivation of the equivalent MNP function for the joint estimation of the early- and late-side components in a combined indifference band model.

Late-side indifference band Late-side (SD,r = LSD,, < 0) indifference bands are derived as follows:

where the subscript '/' represents late-side arrival and//(•), /*/(•)> and 0 have comparable definitions to early-side case. The random terms eitj and Tit,i, i = 1, . . . ,T, are also assumed to be multivariate normal with zero means and general covariance matrices and can be expressed as,

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Joint Indifference Band Model Framework The previous section reviewed the early- and late-side indifference band formulations. These can be combined in a joint indifference band framework as follows:

that is,

Iwhere Wit is a binary indicator variable, equal to 1 if SD^ = ESD/f > 0 (early-side), and equal to 0 if SDJf = LSD, t <0 (late-side); / e (-), //(•)> *it,e, £it,h and 0 were defined in the preceding section. The route indifference band can be derived in the same way. Now if and

the previous equations can be rewritten as:

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The expression of 2 (joint) is given by,

where

The probability of outcome (5 /f , A /f ) for individual /, after the commute on day t, is given by,

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The probability of a decision sequence ((8it, A,,), t = 1, . . . , T) for individual / is thus given by,

Following the approach of Daganzo and Sheffi (1982), and its application to the indifference band estimation problem given in Mahmassani (1990), the individual's 2T decisions over T days are viewed as a single MNP choice from 2T + 1 alternatives with respective "utilities": Auxiliary alternative Departure time, day 1

Departure time, day T

Route, day T The probability of a sequence of decisions over T days is given by,

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Equation (6) can be rewritten as:

where f ( X t , Z,-,, 6it) = Witfe(Xt, Zit, Oit) + (1 - W,,)/i(*,-, Z,-r, ftr), and £(*,, Zit, eit) = With&(Xt, Zit, Oit) + (1 - W,,)*^, Z,-, A). Therefore, equation (11) can be rewritten as,

Auxiliary alternative Departure time, day 1

Departure time, day T Route, day 1

Route, day T

Su (j°mt)

can tnen

t>e derived as follows:

The definition of as and ys were given in equation (8).

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Model Specification This analysis focuses on the day-to-day dynamics of commuters' departure time and route decisions for morning commutes without intervening stops (trip-chaining). The specification of the joint indifference band for the departure time switching mode consists of the following components: • • • • •

initial range of tolerable schedule; socioeconomic characteristics of the commuter; dynamic effects; myopic term; unobserved component.

The joint model specification can then be expressed as: IBD/t = [Witai + (1 - Wit)a2 + W/ r a 3 AGE/ + (1 — Wit)a4 AGE/ + Witas GENDER/ + (1 - Wit)a6 GENDER/ + Wita7 NFAIL/f a8 + (1 - Wit)a9 NFAIL/,fl10 + Witaii\it (jJiTRit/fjDTit)] + eit

initial bands socioeconomic component

dynamic component myopic component unobserved component

The definitions of the elements of the indifference band are summarised in Table 1. The detailed specification of the route switching model for the joint indifference band consists of the following three components: (1) initial range of tolerable schedule delay; (2) dynamic effects; (3) unobserved component. The joint model specification can then be expressed as: IB/, = \WitCi + (1 - Wit)c2 + Witc3 STDTR/f + (1 - Wit)c4 STDTR/, + WitC5 NFAIL/, + (1 - Wit)c6 NFAIL/J + Tit

initial bands dynamic component dynamic component unobserved component

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Table 1 Indifference band elements and definitions, departure time switching Element

Definition

AGE,

GENDER, NFAILf,

Wit

A,-r 0i, a2 . . . eit

flu

The age of commuter /; 1, if age <18; 2, if age G [18, 29]; 3, if age E [30, 44]; 4, if age E [45, 60]; 5, if age >60 The gender of commuter /; =1, if male; =0, otherwise The number of unacceptable early and late arrivals until day t The difference between travel times of commuter / on day t and t — 1 (min) The amount of departure time that commuter i has adjusted between day t and t — 1 (min) A binary indicator variable, equal to 1 if SDit > 0 (early-side), or equals to 0 if SD(-, < 0 (late-side) A binary indicator variable, equal to 0 if DTit = DTn-i, or = 1, otherwise Parameters to be estimated Error term for commuter / on day t

The definitions of the various elements of the indifference band are shown in Table 2.

Estimation Results Estimation procedure Tong (1990) applied the approach of Daganzo and Sheffi (1982) to a switching model of departure time and route decisions over T consecutive days and reduced the number of alternatives from 22r to 2T + 1. However, only models with at most four days (nine alternatives) of data could be estimated due to the limitations of existing MNP estimation software, such as CHOMP (Daganzo and Schoenfeld, 1978). The MNP estimation program developed by Lam and Mahmassani (1991) showed significant

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Travel Behaviour Research: Updating the State of Play Table 2 Indifference band elements and definitions, route switching Element

STDTR;, NFAILzf Wit Ci, c2 . . . c6 Tit

Definition The standard deviation of travel time up to day t (min) The number of unacceptable early and late arrivals up to day t A binary indicator variable, equal to 1 if SD,r > 0 (early-side), or equal to 0 if SD,f < 0 (late-side) Parameters to be estimated Error term for commuter / on day t

improvements in accuracy and ease of solution-finding over previous approaches. In this research, this procedure is applied to estimate the joint indifference band models described in the previous section. The central feature of this approach is an accurate and efficient Monte Carlo simulation procedure to evaluate the MNP choice probabilities in a vector processing environment (Lam and Mahmassani, 1991). The difficulty in estimating MNP model parameters, and evaluating the associated MNP choice function arises from the need to evaluate the multidimensional integral corresponding to a multivariate normal density function. The Monte Carlo simulation had been considered too demanding computationally for MNP model estimation (Lerman and Manski, 1981). However, on a vector or parallel computing architecture, the Monte Carlo frequency methods have been demonstrated to be competitive with the most efficient numerical approximation techniques for MNP model computation (Lam and Mahmassani, 1991). This efficiency is derived from its inherently parallel structure, whereas, numerical approximation methods are highly sequential in nature. The nonlinear optimisation approach, adopted in Lam's (1991) Maximum Likelihood Estimation procedure, is a BFGS quasi-Newton algorithm with central difference gradient evaluation. This procedure was successful in estimating the joint indifference band model for up to eight consecutive decision days.

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Behavioural interpretation To simplify the estimation, only the case with the same variance and covariance in ST and Se is discussed, that is, a\ = cr\ and 71 = 74 = 714 = 741 for departure time; v\ = a24 and y2 — 75 = 725= 752 for route. Also, since the survey data include 10 working days, estimations are performed for five, six, seven and eight consecutive decision days in order to examine parameter stability over time. The estimation results of departure time switching for five, six, seven and eight days (consecutive) with the error structure described above are shown in Table 3. The initial band for the late-side is smaller than for the early-side, as shown by the respective magnitudes of ai and a2 (23.25 and 17.94, respectively, for the five-day estimates). As such, these estimates, based on actual survey data, confirm the earlier finding obtained by Tong (1990) using data from laboratorylike experiments. The parameters that capture socioeconomic effects are a3 through a6; the estimated values have the correct signs and reasonable magnitudes. The estimates of a3 and a4 suggest that older commuters tend to tolerate greater schedule delay than younger ones. The estimates of as and a6 suggest that female commuters have a wider indifference band than males.

Table 3 Estimated parameters for four cases, departure time switching Five days Param. Constant(e) Constant(l) Age(e) Age(l) Gender(e) Gender(l) Nfail(l) Exp(l) Nfail(e) Exp(e) Ratio Thetal Theta 2 Loglikelihood

t value

23.25 2.40 17.94 5.13 7.35 5.49 4.41 2.87 -5.51 -3.65 -6.56 -2.97 5.13 2.70 0.34 3.35 3.41 3.85 0.11 2.19 3.84 3.46 16.98 2.72 9.97 4.56 -425, .21

Six days Param.

t value

23.24 3.98 17.89 2.18 7.44 3.74 4.30 2.12 -5.62 -4.80 -6.64 -2.06 6.04 5.07 0.95 2.25 5.10 4.58 0.53 5.12 4.80 3.52 15.22 3.06 9.17 5.20 -508. .69

Seven days Param.

; value

23.28 3.09 5.37 17.87 2.21 7.64 3.74 4.58 -5.62 -5.12 -2.36 -6.60 5.04 3.30 4.50 1.13 3.90 4.69 2.52 0.79 2.84 3.60 15.37 3.78 5.45 9.13 -597, .36

Eight days Param.

/ value

2.51 23.26 17.82 4.08 4.85 7.61 4.51 5.68 -3.74 -5.59 -6.57 -2.66 5.23 5.49 4.02 1.16 2.73 4.36 5.96 0.78 4.17 2.98 3.44 15.38 9.13 5.18 -680.45

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The late-side parameters are all smaller than the early-side, which may imply that commuters are expanding the late-side indifference bands more cautiously than the early-side bands in response to frustrations likely encountered through their commute experience. This can also be viewed as confirming that commuters are indeed more sensitive to late arrivals than to early arrivals (Tong, 1990). The parameters that capture the dynamic effect of commuters "learning" through previous experience are a-j and «8 for the early-side, and a9 and ai0 for the late-side. Commuters tend to engage in less departure time switching after experiencing conditions that require them to switch decisions on the previous t days. In other words, to the extent that previous switching is an indication of the inability to find a feasible alternative, it is natural to expect the indifference band to increase, resulting in less switching. This result is identical to earlier findings by Mahmassani and Chang (1986). The short-term effect of adjustment in response to the most recently experienced travel time change resulting from a departure time change is captured by parameter flll5 the estimated value of which has the correct sign and reasonable magnitude. If commuters have recently experienced a substantial increase in travel time resulting from a small adjustment in departure time, they are induced to tolerate greater schedule delay associated with a particular departure time decision. The estimates of the variance and covariance terms for departure time, a2 and y, are all significant at a reasonable confidence level, which confirms the need to explicitly incorporate serial correlation in the error specification. The value of a (thetal) in the five-day case is larger than for any of the other alternatives. Examining the value of y (theta2) reveals that the covariance terms are generally much smaller than the variance terms. Therefore, their influence is relatively small compared to the variance terms. It should be noted that all the covariance terms have positive signs, reflecting positive correlation between the unobserved disturbances, as expected. Table 4 shows the estimation results for the route switching indifference band with the error structure assumed previously. The initial band for late-side is also smaller than that for early-side (24.96 and 31.16, respectively, for the five-day case), which again confirms the earlier finding by Tong (1990). The parameters that capture the dynamic effect of commuters' "learning" through previous experience are c3 and c5 for early-side and c4 and c6 for late-side. Parameters c3 and c4 have positive signs, indicating that commuters are reluctant to continue switching route in response to experienced higher travel time fluctuation. This result is consistent with Tong's

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Table 4 Estimated parameters for four cases, route switching Six days

Five days Param. Constant(e) Constant(l) Stdtr(e) Stdr(l) Nfail(e) Nfail(l) Thetal Theta2 Loglikelihood

t value

31.16 24.96 3.41 8.92 4.17 3.19 20.18 21.75 -135.29

6.03 5.40 7.22 4.05 6.38 4.91 8.17 8.36

Param.

t value

4.17 30.68 7.89 24.79 6.55 7.68 7.57 5.38 7.70 2.98 5.91 4.39 10.69 21.50 6.40 16.58 -174.84

Seven days Param.

t value

30.53 25.00 6.14 7.52 3.45 5.27 21.29 4.50 -227 .81

4.90 4.40 7.81 5.67 3.54 4.08 4.06 4.48

Eight days Param.

t value

27.22 18.76 8.87 4.37 8.95 9.13 17.74 5.89 -233.12

5.62 9.61 9.21 5.67 5.29 8.03 4.16 5.09

(1990) earlier findings. Commuters tend to engage in less route switching if more switches are experienced in the previous t days. These results are very similar to the findings obtained for the departure time model. The estimates of a2 and y for route switching models are all significant at reasonable confidence levels, which confirms the need to incorporate serial correlation. The covariance terms exhibit positive signs indicating positive correlation between the unobserved disturbances, as expected. Comparing the results for route with those for departure time, the mean indifference band for departure time switching is much smaller than that for route switching both for early- and late-side components (23.25 < 31.16 and 17.94 < 24.96). The results indicate that when a commuter switches route, s/he is very likely to switch departure time as well. These estimates confirm the earlier finding by Stephan (1987).

Conclusion This study presented the analysis of two-week commuting trip diaries from a sample of auto commuters in Dallas. The analysis focused on the dayto-day dynamics of commuter trip timing and route decisions. Unlike the previous "laboratory-like" experiments, actual field data formed the basis of the present models. Instead of estimating early and late indifference bands separately, a joint IB was specified and estimated. In this study, a recent probit model estimation procedure using the Monte Carlo simul-

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ation to evaluate the MNP choice function and a BFGS nonlinear search algorithm, was applied successfully to estimate models with serially correlated data. Several substantive conclusions have been obtained in this study which, in many cases, corroborated the findings first noted in connection with the laboratory experiments, as discussed hereafter. 1. Commuters are more sensitive to late rather than early arrivals. 2. In the departure time model, older commuters tend to tolerate greater schedule delay than younger ones. Also, female commuters exhibit a wider mean indifference band than male commuters. The greater propensity for departure time switching of young males is consistent with the estimation results of the above-mentioned switching frequency models. 3. Commuters are inclined to tolerate greater schedule delay (associated with a particular departure time decision), if they have recently experienced a substantial increase in travel time resulting from adjustment in departure time. 4. Commuters are reluctant to continue switching route in response to greater experienced travel-time fluctuation, which is consistent with earlier findings obtained by Tong (1990). 5. The mean indifference band for departure time switching is much smaller than that for route switching, both for early- and late-side components, indicating that when a commuter switches route, s/he is very likely to switch departure time as well. These estimates confirm the earlier findings of Stephan (1987). 6. Commuters tend to increase their indifference band (i.e. switch less) in response to more failures; this is true for both departure time and route models. 7. The estimates of the variance and covariance terms are all statistically significant in both departure time and route models, which confirms the need to incorporate serial correlation in the specification.

References Caplice, C. (1990) Analysis of Urban Commuting Behaviour: Switching Propensity, Use of Information and Preferred Arrival Time. M.Sc. Thesis, The University of Texas at Austin.

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Daganzo, C.F. and Schoenfeld, L. (1978) CHOMP user's manual. Research Report UCT-ITS-RR-78-7, Institute for Transportation Studies, University of California at Berkeley. Daganzo, C.F. and Sheffi, Y. (1982) Multinominal probit with time series data: unifying state dependence and serial correlation models. Environment and Planning 14A, 1377-1388. Hatcher, S. (1991) Daily Variation of Trip Chaining, Departure Time and Route Selection of Urban Commuters. M.Sc. Thesis, The University of Texas at Austin. Jou, R.C. and Mahmassani, H.S. (1996) Comparability and transferability of commuter behaviour characteristics between cities: departure time and route switching decisions. Transportation Research Record 1556, 119-130. Jou, R.C., Mahmassani, H.S. and Joseph, T. (1992) Daily variability of commuter decision: Dallas survey results. Technical Report 1216-1, Center for Transportation Research, The University of Texas at Austin. Lam, S.H. and Mahmassani, H.S. (1991) Multinomial probit estimation: computational procedures and applications. Preprints of the 6th International Conference on Travel Behaviour. Quebec, May 1991, Canada. Lerman, S.R. and Manski, C.F. (1981) On the use of simulated frequencies to approximate choice probabilities. In C.F. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications. The MIT Press, Cambridge, Mass. Mahmassani, H.S. (1990) Dynamic models of commuter behaviour: experimental investigation and application to the analysis of planned traffic disruptions. Transportation Research 24A, 465-484. Mahmassani, H.S. and Chang, G.L. (1986) Experiments with departure time choice dynamics of urban commuters. Transportation Research 20B, 297-320. Mahmassani, H.S., Hatcher, S. and Caplice, C. (1997) Daily variation of trip chaining, scheduling and path selection behaviour of work commuters. In P. Stopher and M. Lee-Gosselin (eds.), Understanding Travel Behaviour in an Era of Change. Elsevier Science, Oxford. Mahmassani, H.S., Joseph, T. and Jou, R.C. (1993) A survey approach for the study of urban commuter choice dynamics. Transportation Research Record 1412, 80-89 Mahmassani, H.S. and Stephan, D. (1988) Experimental investigation of route and departure time dynamics of urban commuters. Transportation Research Record 1203, 69-84.

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Mahmassani, H.S. and Tong, C.C. (1988) Availability of information and dynamics of departure time choice: experimental investigation. Transportation Research Record 1085, 33-47. Stephan, D.G. (1987) Route Choice and Departure Time Decision Dynamics for Urban Commuters. M.Sc. Thesis, The University of Texas at Austin. Tong, C.C. (1990) A Study of Dynamic Departure Time and Route Choice Behaviour of Urban Commuters. Ph.D. Thesis, The University of Texas at Austin.

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Departure Time and Path Choice Models for Intercity Transit Assignment Agostino Nuzzolo and Francesco Russo

Abstract In this chapter, the problem of intercity and extra-urban transit assignment will be dealt with through a network approach which explicitly considers timetables, and a random utility choice model involving departure time and path. The spatial-temporal network used is diachronic, thus allowing dynamic assignment of the demand. In the first part, after a general analysis of transit assignment models, the timetable and network assignment model formulated by the authors is described, reporting the user's behavioural hypothesis on which it is based. In the second part, the departure time and path choice model required are analysed to determine the penalty function of anticipation and delay, which must be inserted in the network model, and two random utility logit and probit models are reported and calibrated for home-work and home-school trips. In the final part, two applications of the test network model are described.

Introduction Intercity transit services are characterised by medium-low frequency which can entail considerable periods of delay, or anticipation for users compared to the desired arrival and departure times. Therefore, real timetables have to be taken into account in the assignment models. The problem of intercity transit assignment, taking the timetable into account, has been dealt with in various ways in the literature through the enumeration of feasible paths. In this study, the problem will be dealt with through a network approach which explicitly considers timetables, and a random utility choice model involving departure time and path. The spati-

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al-temporal network used is diachronic and, thus, allows dynamic assignment of demand. In the first part, after a general analysis of the assignment transit models, the assignment model formulated by the authors is described, reporting the user's behavioural hypothesis on which it is based. In the second part, the departure time and path choice models are analysed to obtain the penalty function of anticipation and delay compared with the desired arrival or departure times. This must be inserted in the network model, and some random utility models (logit and probit) are reported for homework and home-school trips. In the final part, some applications of the assignment model are described.

Intercity Transit Assignment Models From the assignment model point of view, public transport systems can be classified according to some characteristics concerning service; the main ones being service frequency and punctuality as measured by vehicle arrival compared with the established timetable. In general, high frequency and low punctuality, typical in urban areas, leads to the random arrival of users at stops with a large margin of adaptation in the choice of path. The supply, path choice and assignment models, which are more suited to this type of service and have been developed in the literature, originated in the concept of the hyperpath (Nguyen and Pallottino 1986, 1988; Cascetta and Nuzzolo, 1988; Spiess and Florian 1989; Russo 1991). For services with medium-low frequency and high punctuality, typical of national, regional and in general extra-urban systems, the hypothesis of adaptive choice proves incongruous and is replaced with the hypothesis of a completely consumptive choice. In this case, two definable categories of models result: either with representation of the lines or the runs. By line, we mean, the spatial path followed by a transport mode, characterised by a sequence of stops, and by run, the service offered with an established time period at the stops. From the bibliographical analysis, it emerges that various works dealing with some specific problems concerning intercity assignment models have been published. However, there are few examples involving the complete treatment of assignment models, all of which have been published recently. They include, in the area of line approach, the models used in the study of fare structures of the Italian Railways (Cascetta et al., 1989, and in the updating of traffic predictions for the Italian Railways High Speed

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train (Tech. A.V.-Tpla. V., 1993), and finally, the assignment model on a national level developed in the PFT2-CNR (Nuzzolo and Russo, 1994). Regarding the approach for runs, it is worth recalling the procedure developed by the air transport companies in the 1980s (Etschmaier and Mathaisel, 1985), and specific studies by Sangiorgio et al. (1990) and Nuzzolo and Russo (1993). The timetable approach, which is referred to in this section, is the one on the network formulated by the authors for public transit extra-urban transport: the complete treatment, including also the flow calculation methods, is reported in Nuzzolo and Russo (1994, 1996). Subsequently, user behavioural hypotheses based on the model and the network models used are discussed.

Behavioural hypotheses of user choice The hypotheses imposed on user behaviour are: (a) With regard to the high level of service punctuality, path choice is only consumptive: the choice concerns contemporaneously path (boarding, alighting and interchange stops) and departure time. (b) In order to choose among many options the user considers as utility components: (i) access time from origin to first stop; (ii) waiting time at stops; (iii) onboard time; (iv) time and inconvenience for any interchange; (v) egress time from last stop to destination; (vi) fare; (vii) comfort related to the degree of crowding; and (viii) disutility for anticipation or delay compared to the origin or destination target time. (c) The user is a rational decision maker, who considers all paths connecting his Origin and Destination (OD), and chooses the alternative that involves the perceived minimum cost. This cost is a random variable and, therefore, the chosen alternative cannot be predicted with certainty, but only the probability can be calculated, for example, with a random utility model. The random utility model maintains its validity in spite of the punctuality of the trips and the user's hypothesised knowledge of the timetables, for the following reasons: • different users can evaluate differently the same attributes (for example, if the user is more or less aware of access and egress mode, or of the interchange time);

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Travel Behaviour Research: Updating the State of Play • some attributes evaluated by the user may be excluded from those defined in the preceding point (b), for example, vehicle characteristics, etc.; • some attributes can only be evaluated by the analyst in an approximated way (i.e. interchange, comfort, access and egress times, etc.).

The diachronic network model The network model used (Fig. 1) is similar to the one usually adopted to represent public transport supply in an urban area. The main modification lies in the representation of each run of each line with the explicit inclusion of the time variable. The network produced by such a modification is called the diachronic network. The diachronic graph consists of two subgraphs: one relates to run representation, and the other is dependent on the demand structure. For every stop j, there is a temporal axis on which for every run r, a node n] is positioned relative to the stopping time of run r. This node is connected by an embarkation link to node nrja, which is relative to the departure time of run r. It is also connected by a disembarkation link from node nrjd, relative to the arrival time of run r. Link (nrjd, nja) represents the pause at stop / of run r; link (nrja, nrjd} represents the connection between stop j and stop k by means of run r. Therefore, the demand subgraph consists of various subgraphs, at least one per zone centroid, in relation to the OD matrix structure, which is supposedly known for purpose and destination target time (DTT), or origin target time (OTT). In general, the distribution of the DTT, or OTT, can be made to be discrete with reference to a certain number of time intervals, where it may be accepted that demand distribution is concentrated at the final point of the interval. A time axis is then considered for every zone, and a time centroid, located in the axis on the final point of each interval, will correspond to each time interval. Therefore, each temporal centroid may be the origin and destination of user trips, and each trip can be with the DTT and/or OTT. Consider a matrix OD of dimensions [n0 * (/OTT + 1), «D * (/DTT + !)]> where n0 is the number of spatial origins, nD the number of destinations, /OTT and /DTT the number of intervals in which the time slices referring to origin and destination for the target departure and arrival times are divided. For each zone, it is possible to associate as many time centroids

Departure Time and Path Choice Models

temporal centroid axisD stop axis k

link

link

Figure 1 Example of diachronic network

389

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concerning origin nOTT, and destination «DTT> as there are specified time intervals with an additional one for nontarget trips. In order to connect the time centroid axis and the spatial centroids with the run subgraph, the access and egress links need to be introduced. Such links have one extremity on the time centroid axis, or on the spatial centroid, and the other extremity on the time axis of the stop, each of which guarantees connection with an accessible run in the zone. The first extremity of the generic access link (nr0), represents the time at which it is necessary to leave the origin in order to reach stop j (second extremity) in time to take the choice run r(nj). The time difference between the first extremity nr0 of the access link, and the time centroid of origin WOTT represents, exactly, the anticipation or delay connected to the use of the generic run r considered. A similar consideration also holds for the egress link. The qualifying characteristic of the diachronic network derives from the possibility of introducing penalty functions of anticipation and/or delay compared to user DTT and/or OTT, directly on the network. Furthermore, the different weights of delay and anticipation may be considered for different user categories and different purposes, using a time axis for each purpose or category. In the literature, such functions are expressed both in a linear and nonlinear form. Moreover, they can still be divided in continuous or discontinuous form, according to whether, or not, the introduction of an indifference time slice within which the user does not suffer any penalty, has been allowed for. The general indicative forms of the three functions are: linear

nonlinear

discontinuous

where ?ear = time difference between the destination target time and arrival at destination; f lat = time difference between the time of arrival at destination and the target time; A = width of indifference slice. Implementation of linear functions such as equation (1) is represented

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391

in Fig. 1. Where network algorithms are used which require the implementation of nonlinear functions, more complex forms of centroid subgraph must be introduced, inserting direct connecting links between each time centroid and the departures of all runs included in the selected interval. In the following section, the departure time and path choice models which allow for the calibration of penalty functions are examined. It must be noted that the additivity of link costs and, therefore, the use of linear penalty functions, are the conditions for using the traditional assignment on network algorithms.

Departure Time and Path Choice Models Existing departure time and path choice models can be classified in different ways: aggregated and disaggregated, according to whether the users are considered in aggregate, or disaggregate ways; behavioural and descriptive, according to whether we do, or not, make explicit hypotheses concerning the user's behaviour. Different types of behavioural models exist, the most commonly employed are part of the group of random utility models. The differences between various models in this group derive from the hypothesis concerning the distribution of the random term involved in user utility. However, the models used in practice mainly refer to two distributions: WeibullGumbel (WG) and Normal Multivariate (MVN), see, for example, Ortuzar and Willumsen (1994). The other classification concerning existing models is relative to path choice: between modes or within modes. The following belong to the first group: • Abkowitz (1981), includes 12 departure time choice alternatives each using car and bus, and specific linear and nonlinear terms for anticipation and delay. • Hendrikson and Plank (1984) include up to 28 alternatives obtained with four modes and seven different departure times, and allow for nonlinear terms of anticipation and delay. Various models that generally refer to the car mode belong to the second group:

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• Ben-Akiva et al. (1986) present three possibilities: leaving early to avoid the traffic, arriving early; leaving and arriving late, and taking an alternative longer path; these authors specify linear terms but introduce a discontinuity by means of an indifference time slice on arrival. • Alfa (1986), explicitly introduces the variable DTT (destination target time), and verifies the existence of correlation between the flexibility of arrival at work and the uniformity of the demand in the peak hour; he considered linear terms without discontinuity. • Mannering (1989), hypothesised a Poisson distribution of path changes including the nonchange option; he considers flexibility concerning the time at which one starts work. • Biggiero et al. (1992) consider a WG distribution and the width of the indifference slice was estimated compared to the DTT, thereby, using a discontinuous function. Calibrated ad hoc models for home-work and home-school travel will be reported below. They are departure time models with a path choice between competitive transit modes. Two classes of models were specified and calibrated: multinomial logit and probit, with the joint utility function of alternative "/'" as follows:

where Xkj is the kth attribute for alternative "/" and user "/", ry is the random term for alternative/, and 7, is the choice-set for "/"; the attributes considered are reported in Table 1. In the multinomial probit model (Daganzo, 1979), the random terms are distributed as multivariate normal, MVN (0, £). The model is uniquely defined by specification of the covariance matrix 2. Computation of probit choice probabilities was performed using Clark's formula. The data used were obtained through surveys performed in a region of southern Italy. The destination survey was based on a random sample with more than 100 useful interviews with workers and university students performed in a standard revealed preferences way. The questionnaire had three different sets of questions; the first concerned the user's socioeconomic characteristics, the second, the time and cost of the path chosen, and the last, the time and cost of the alternative paths by mode and run. The alternatives considered were a maximum of four for each mode— two that give destination or origin delay time, and two that give anticipation time.

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Table 1 The attributes of the utility function (time in hours, cost in Italian lire/1000) Attribute

Definition

Global modal time

Mean onboard time plus walking time or other access time to arrive at the mean-stop plus, if existing, time for interchange, plus the time for arrival at destination from the meanstop. Summation of time to arrive at the first stop from home and time to arrive from the last stop at destination. Mean onboard time plus time for interchange if this exists. Difference between the destination target time and arrival at destination, if occurring before DTT. Difference between the destination target time and the arrival at destination, if occurring after DTT Estimated as season-ticket holder cost Estimated as season-ticket holder cost weighted by an attribute that represents the income level. Early time greater and less than 10 min. Early time greater than an indifference slice of 10 min. Late time greater and less than 10 min. Late time greater than an indifference slice of 10 min.

Access and egress modal time

Onboard time Early time

Late time

Cost Cost/income

Early time discontinuous Early time with slice Late time discontinuous Late time with slice

Symbol GMT

AET

BMT ET

LT

C CI

ET+, ETET+ LT+, LTLT+

The alternatives were included in the choice set if the referred time (origin or destination) is inside the 12-hour slice around the user target time. The attributes examined can be divided into two main groups: (a) user specific attributes, obtained by surveys; and (b) level of trip service

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attributes for each mode, obtained from the official timetable. The trip purposes considered were home-work (W) and home-school (S), and the modes available were train and bus. The calibration was carried out with the maximum-likelihood method, using numeric derivatives for the probit model. The models goodness-offit was evaluated using the following statistics: • the log-likelihood function In L(/3) for the final coefficient values /3m; • the log-likelihood function In L(0) for a model with all coefficients equal to zero; • the log-likelihood function In L(/3C) for a model with constant only /3C; • the usual p2 index with respect to the equally-likely model, defined as,

• the equivalent index with respect to the constants only model, defined as,

In the calibration of the logit model, the specification was developed by focusing the attention on the various components of the travel and anticipation/delay times. In particular, we used the functional form described in the second section for the anticipation/delay time, the linear model and the discontinuous models with, and without, indifference slice. Various specifications on the part of the utility function concerning travel time were tested for each functional form of the anticipation and delay time. Furthermore, the travel cost was considered also in relation to the user's income group. The best results obtained for each functional form of the anticipation and delay time are reported in Table 2, together with the p2 statistic. All the specifications indicate the central role of the time penalty for anticipation or delay. Comparison between the onboard and penalty times lends more weight to punctuality in home-school travel. It may be presumed that this weight derives from the absence of flexibility for students. Indeed, they have a large penalty in the first lOmin (-14.97).

Table 2 Logit models for work and school Home-work

Models

Discontinuous linear attributes

Linear attributes and indifference slice

Continuous linear attributes

-2.42 -3.96

-2.62

-2.67

-1.89 -5.52

-5.05 -0.90*

-8.54

P2

-4.12

Discontinuous linear attributes

-1.82

-1.61

-6.66 -1.95

-4.39

-7.12* -14.97*

-5.79

-6.80 -6.64* -3.63*

-5.29

-0.83*

-0.78 -0.08 -7.39*

Linear attributes and indifference slice

-0.15 -5.26

0.39

*Not significant at the 95 percent level.

0.40

-0.09* -7.13

-0.72

-0.32 -0.83

-0.68

0.42

-0.40

0.39

0.39

Departure

Continuous linear attributes Attributes BMT ET ET+ ETLT LT+ LTC CI AET

Home-school

I a a a, Sr O 8 |

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Moreover, the specification confirms the different value of time (VOT) obtained for different travel purposes. The other interesting indication derives from the weight of access/egress time, which is very high for home-work and can condition the choice of mode if the stop is far away from the final destination. Finally, the use of more complicated functional forms than the linear ones of anticipation and delay time does not offer great advantages concerning model performance. Hence, the subsequent calibrations involving the probit model referred only to the linear model. Various models were calibrated in connection with the typical potentiality of the probit model to introduce different variances among the alternatives, and nonzero covariances. The first Si matrix used allows direct comparison with a logit model, with only the main diagonal different from zero and all the elements equal to 1.64. It provides an extremely similar model to the logit. Other X matrices were obtained from Si by increasing the variances, and with a certain level of covariance among similar alternatives. The best models obtained (as shown in Table 3), are those with covariance between train and bus, with anticipation relative to the DTT and with delay relative to the DTT. Table 3 Probit models for work and school with linear attributes Home-work

BMT/GMT ET LT C AET P2

Home-school

(early) ai} = 1.50 (late)

an = 3.28 ai} = 0.20 (early) au = 0.40 (late)

a a = 1.64 atj = 0.20 (early) au = 0.50 (late)

-0.18 -5.66 -3.58 -1.16 -6.95

-0.55 -5.58 -4.69 -2.39 -5.58

-0.41 -4.39 -4.21 -1.49 -5.37

a a = 1.64 atj = 1.20 (early) (Tit= 1.50 (late)

an = 3.28 an = 0.20 (early) ati = 0.50 (late)

ait = 1.64 an = 0.20 (early) o-ij = 1.50 (late)

aH = 1.64

-2.08 -4.31 -0.46 -0.31

-3.11 -1.66 -0.76 -0.02 -2.02

-2.81 -1.41 -0.64 -0.18

0.29

-0.26

0.21

Oy=1.20

0.51

0.46

0.46

When comparing logit and probit models, it is evident that the hypothesis of the nonzero covariance does not always give better results (see p2), and the results obtained are already quite good with the logit model. It is worth noting that in the case of the daily commuter model

Departure Time and Path Choice Models

397

(for work or school), the decision maker has better knowledge of the utilities of the various alternatives, which are perceived as independent. Considerable improvements are expected, from the introduction of a different matrix £ for different travel purposes such as shopping, leisure etc.

Test Applications The assignment model proposed was applied to an extra-urban transit network in a district in southern Italy, whose main characteristics are: ten serviced towns and one city for a total of 250,000 inhabitants; 20 traffic zones; 25 temporal centroids for each zone; and two trip purposes, work and study. As regards the railway mode, there are 37 runs: 15 direct, and 22 local; the bus mode consists of 14 lines with a total of 72 bus runs. The diachronic graph derived from this study, is made up of 2,288 nodes and 5,942 links, both of which are about 2.5 times the respective values of a graph with the same number of traffic zones, but developed traditionally for lines. The difference is given by the characteristics of the centroid subgraphs that, in spite of the considerable detail of introduced centroids (temporal and purposeful), maintain the network within manageable proportions. Linear functions, with the /3 value calibrated and reported in Table 2, were used for the penalty functions. An OD matrix available from other studies was assigned to the network by means of a Stochastic Assignment Loading (SNL). Paths were analysed and, thereby, verified their consistency with the behavioural hypotheses. The same procedure was applied to the national air network of Italy. With 22 main airports, the overall graph consists of 2,820 nodes and 5,956 links, again verifying the full dimensional applicability of the diachronic network model. Even from the point of view of time calculations, the applications gave positive results, because the time for SNL assignments was only a few seconds for both networks, using Pentium/160 computers.

Conclusions In this chapter, a model was presented that allows simulation of departure time and path choice in relation to established destination, or origin target times. The model is to be used in assignment models for intercity transit

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networks. Calibration was carried out using the extra-urban home-work and home-school trip surveys, and specifying logit and probit models. The results are satisfactory both in parameter values and statistical analyses. It is worth noting that the penalty weight of the anticipation/delay time is more important than the disutility of the other travel times. Thus, the penalty component has to be used in intercity transit assignment. The final part reports two applications of the assignment model using diachronic networks, with promising results for its development, having obtained chosen paths which provide a good representation of the behavioural hypotheses introduced and networks of a size which may be easily managed with contemporary PCs.

Acknowledgements The research, on which this chapter is based, was partially supported by the Ministry for University and Scientific Research and by the National Research Council of Italy (PFT2).

References Abkowitz, M.D. (1981) An analysis of the commuter departure time decision. Transportation 10, 283-297. Alfa, A.S. (1986) A review of models for the temporal distribution of peak traffic demand. Transportation Research 20B, 491-499. Ben-Akiva, M., De Palma, A. and Kanaraglou, P. (1986) Dynamic model of peak period traffic congestion with elastic arrival rates. Transportation Science 20, 164-181. Biggiero, L., Cascetta, E. and Nuzzolo, A. (1992) Analysis and modelling of commuters departure time and route choices in urban networks. Sixth World Conference on Transport Research, Lyon, July 1992, France. Cascetta, E. and Nuzzolo, A. (1988) Uno schema comportamentale per la modellizzazione delle scelte di percorso nelle reti di trasporto pubblico urbano. Internal Report, Dipartimento di Trasporti, Universita di Napoli. Cascetta, E., Nuzzolo, A. and Rostirolla, P. (1989) Optimal railway pricing: result of a model for the Italian case. Proceedings 17th PTRC Summer Annual Meeting, University of Sussex, September 1989, UK.

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Daganzo, C.F. (1979) Multinomial Probit: The Theory and its Applications to Demand Forecasting. Academic Press, New York. Etschmaier, M.M. and Mathaisel, D.F. (1985) Airline scheduling: an overview. Transportation Science 19, 127-138. Hendrikson, C. and Plank, E. (1984) The flexibility of departure times for work trips. Transportation Research ISA, 25-36. Mannering, F. (1989) Poisson analysis of commuter flexibility in changing routes and departure times. Transportation Research 23B, 53-60. Nguyen, S. and Pallottino, S. (1986) Assegnamento dei passeggeri ad un sistema di linee urbane: determinazione degli ipercammini minimi. Ricerca Operativa 38, 22-49. Nguyen, S. and Pallottino, S. (1988) Equilibration traffic assignment for large scale transit networks. European Journal of Operations Research 37, 176-186. Nuzzolo, A. and Russo, F. (1993) Un modello di rete diacronica per 1'assegnazione dinamica al trasporto collettivo extraurbano. Ricerca Operativa 67, 37-56. Nuzzolo, A. and Russo, F. (1994) An equilibrium assignment model for transit network. Preprints TRISTAN 2 Conference, Capri, May 1994, Italy. Nuzzolo, A. and Russo, F. (1996) Stochastic assignment models for transit low frequency services. Some theoretical and operative aspects. In L. Bianco and P. Toth (eds.), Advanced Methods in Transportation Analysis. Springer-Verlag, Berlin. Ortuzar, J. de D. and Willumsen, L.G. (1994) Modelling Transport. Second Edition, John Wiley & Sons, Chichester. Russo, F. (1991) Un modello di assegnazione alle reti di trasporto collettivo: aspetti teorici ed applicazione a casi reali. In A. Nuzzolo and F. Russo (eds.), Metodi e Modelli per la Pianificazione e la Gestione dei Sistemi di Trasporto Collettivo. F. Angeli, Milan. Sangiorgio, G., Bason, E. and Morgando, A. (1990) La pianificazione della rete dei trasporti pubblici extraurbani nell'area metropolitana torinese. Preprints Convegno AIRO, Napoli, September 1990, Italy. Sheffi, Y. (1985) Urban Transportation Networks. Prentice-Hall, Englewood Cliffs, NJ. Spiess, H. and Florian, M. (1989) Optimal strategies: a new assignment model for transit networks. Transportation Research 23B, 83-102. Tech. A.V.-Tpla. V. (1993) Rielaborazione ed aggiornamento delle previsioni di traffico A.V. Milano Napoli. Internal Report, F.S. Roma.

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22

The Impact of Dynamic Traffic Information: Modelling Approach and Empirical Results Eric C. van Berkum and Peter H.J. van der Mede

Abstract In 1993, a dynamic, information sensitive route choice modelling framework was proposed by Van Berkum and Van der Mede. This chapter presents a study to test and validate this modelling framework. The study concerns car-driver route choice when queue-length information is offered and uses data from a field study on the Route choice Information Amsterdam (RIA), the first Dutch variable message sign. It is shown that the proposed framework is suited to model route choices and responses to information in a dynamic environment. Furthermore, clear evidence for the importance of habit in route choice behaviour is presented. Also, this study demonstrates the effectiveness of ATIS. Even commuters who are very familiar with the traffic situation benefit from information. As a consequence of information, the amount of habit of these car drivers diminished, and their propensity to maximise utility increased. Consequently, information enables car drivers to form more accurate expectations of the traffic situation.

Introduction Several studies have shown that driver behaviour is inefficient due to erroneous route choice and timing of travel (King, 1986; Jeffery, 1986; King and Mast, 1987). Reasons for inefficient driving may be that drivers are not well informed about available alternatives, or about the current

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state of the road network. In that case, provision of information might induce more efficient driving. One of the questions raised, is to what extent can information technology contribute to the alleviation of congestion? A number of studies have been carried out to answer this question (e.g. Allen et al., 1991; Bonsall, 1992; Bonsall and Parry, 1991; Hamerslag and Van Berkum, 1991; lida, et al., 1992; Koutsopoulos and Lotan, 1989; Stevens and Hounsell, 1992), but no definite answer has been given yet. One of the reasons for this is that a comprehensive methodology to deal with travel behaviours in information environments has not been developed yet. Watling and van Vuren (1993) presented an overview of the modelling issues that need to be considered. They state that model development will provide a means for evaluating the potential benefits of the system, and essential insight into appropriate means for its implementation and, furthermore, improve our understanding of transportation networks. They listed general requirements for the design of such a model. For our work the following are relevant: • The model must reflect driver behaviours at a relatively high level. It must accommodate dynamic and habit effects. This includes the tripto-trip process by which drivers learn about network conditions. The behavioural rules should recognise that drivers may not change from their habitually chosen routes, regardless of the information provided. • The model should be able to represent a heterogeneous population of drivers. • The flexibility of a stochastic model is required to represent uncertainties that arise in data collection and transmission, journey time prediction, and the process by which a driver selects a route. • The model must represent between-days dynamics. This arises from the need to evaluate a system that should respond in its advice to such variations. The notion of networks reaching an equilibrium state is highly questionable in this context. It has been demonstrated that static steady-state models are not suited to simulate route choice behaviour in the presence of information systems (Ben-Akiva, 1985; Watling and van Vuren, 1993; Van Berkum and Van der Mede, 1993). Several authors have presented frameworks which describe the dynamic route choice process in situations with and without information systems. Mahmassani and Shen-te-Chen (1991) presented a dynamic route and departure time choice model in which a switching

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module plays a key role. The assumption is that on a trip-to-trip basis an individual only switches route when its benefit exceeds a certain boundary. This behaviour is described by the concept of bounded rationality (Simon, 1955). The application of the model is limited, in the sense that only a specific information system can be simulated. To simulate more diverse information systems, the model needs to be extended both on a behavioural and information level. Ben-Akiva et al. (1991) presented a framework in which former ideas of dynamic travel behaviour are put together (Ben-Akiva et al., 1984, 1986). Although their concepts are promising, they are not operational; elements of both approaches are used here to arrive at an operational model.

General Model Outline To deal with trip-to-trip route choice behaviour a dynamic modelling approach is imperative. Furthermore, a stochastic model where drivers base their decisions on (expectations of) perceived utility must be included. A dynamic notion of expectations involves a learning model where drivers learn from their experiences. The model should deal with the relationship between utility, information, uncertainty and ignorance, more thoroughly than has been done thus far. The representation of internal expectations about performance is a necessary component in a model that deals with information. The dynamic model emphasises the process, i.e. the development of choice behaviours over time, and is not directed towards some final solution (equilibrium). Both choice and learning from experience must be part of the model. In this context, learning may be described as updating knowledge from experience or exogenous information. Expectations about performance may change. It is assumed that expectations only change after experience. Also, it is assumed that the expectation depends on the previous expectation and the most recent experience. The extent to which this expectation changes from trip-to-trip depends on the weight given to the previous expectation and the most recent experience. If drivers are considered to be rational decision-makers, who maximise their expected utility, the expected utility maximisation model is the best available option. However, to a limited degree, decisions are only the result of conscious trade-offs (e.g. Rasmussen et al., 1987). In particular, choices made repeatedly over time (e.g. commuter route choice) will not require the high level of cognitive processing, which is implied by utility

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maximisation, all the time. Therefore, utility maximisation cannot be the only decision rule which operates. It is assumed that low-level cognitive processing exists, and can be modelled as habitual choice behaviour. The extent to which drivers make habitual choices is assumed to depend on the strength of habit for each alternative. Habit strength may change over time. It is assumed that the first time any choice is made, habit is absent (i.e. habit strength is zero). Furthermore, the buildup and decay of habit depend on when, and how often, a certain alternative is chosen. Thus, in situations without external information systems, one of two decision rules can be operational—expected utility maximisation or habitual choice. Whichever of these rules is operational depends on individual choice characteristics, e.g. how many times a certain route has been chosen in the past. Again, this depends on expectations and experienced trip performances. When descriptive traffic information is presented, the expected utility maximisation rule allows this information to enter into the individual choice process.

Summary The model simulates individual route choice behaviour of a number of drivers over time, i.e. from day-to-day, in transport environments with, and without, exogenous information systems. The model output is the result of individual behaviours. The overall structure of the model in situations with exogenous information is depicted in Fig. 1. Processes are depicted as rectangles and connected with bold arrows. Data are depicted as rectangles with blunt corners and their relation to processes with hollow arrows. To start the model an initial state must be assumed. This initial state defines "habit" and "expectations" at the first day, t = 1. Route choice is performed in the process "choice", which is based on "expectations", "habit" and "information", together with "credibility/compliance". An individual may either choose a route from habit, by maximisation of the perceived utilities of the different alternatives, or by complying with the advice given by system that provides prescriptive information. Expectations are determined by perceived utilities of choice options. Perceived utilities simulate individual expectations about the state of the network at a certain time. This kind of knowledge is referred to as expectations. Information may be descriptive or prescriptive. It can influence the choice process in two different ways. It may alter the expectations that someone had without the information. This is performed in

The Impact of Dynamic Traffic Information

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Figure 1 Overview of the model for environments with exogenous information

the "information evaluation" process. In the case of prescriptive information, it may directly influence the choice process, since an individual may, or may not, comply with the advise. The extent to which information plays a role in the choice process depends on the (perceived) quality of the information, described by "compliance/credibility". After a route has been chosen, "trip performance" takes place, resulting in an experienced travel time. Over time, expectations may change as a consequence of experiences. Adjustments of mean expected travel times, and travel time variances due to variations in experienced travel times, are made in "expectation update". "Habit update" computes new habit strengths after trips have been performed. The experienced travel time, and the route chosen, also update the perceived credibility of the information system. In case of prescriptive information, this means that compliance is updated. A complete mathematical specification of the model is beyond the scope of this contribution, but is given by Van Berkum and Van der Mede

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(1993). It depends on the specific application how the different parts of the model are specified. In the next paragraphs, an application of the model where the information system is a VMS showing queue-length information will be discussed.

Validation Study In a validation study, the effect of descriptive information on route choice was modelled. For this study, data were used from a longitudinal panel study which was part of an evaluation study of the first Dutch variable message sign (BGC, 1992, 1993). The highway system around Amsterdam involves a ring road with two tunnels, the Coentunnel and Zeeburgertunnel. During the morning peak congestion occurs at the entrance to the Coentunnel. In 1991, a variable message sign, or RIA-sign (Route choice Information Amsterdam), was installed. The sign provides drivers approaching Amsterdam from the north with information about congestion before the two tunnels. It shows queue information, i.e. the physical length (in kilometres) of queues at the approaches to the Coentunnel and/or Zeeburgertunnel. The information is generated automatically from data from the Motorway Control and Signalling System (MCSS+)(Rijkswaterstaat, 1992).

Data To learn about the effects of the sign on the route choice of individual drivers over time, a longitudinal panel study was carried out. Route choice behaviour of a group of car drivers was recorded over four waves (one before and three after introduction of the sign, see Table 1), each consisting of 15 workdays. Only car drivers who drove by the sign at least three times weekly during the morning peak were selected. In each wave panel, members recorded the following for each trip on the ring road in a travel diary: destination (postal code), departure time, arrival time at the RIA sign, arrival time at destination, chosen route, observed RIA information and experienced congestion on the ring road. During the first wave the RIA sign was not yet operating, and RIA messages were simulated from speed-flow data. To ensure relevant data for both routes, series were only analysed when such a series existed for both routes.

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Table 1 Characteristics of the four waves of the panel study Wave 1 (before study) 2 (1st post study) 3 (2nd post study) 4 (3rd post study)

Period

Participants

Trips

27.10.91-15.11.91 17.11.91-6.12.91 10.2.92-27.2.92 4.5.92-22.5.92

458 439 334 288

5,380 4,787 3,908 3,037

In wave 1, trips from 352 cases met requirements for analysis, and 3,042 trips were analysed. Statistics for all waves are listed in Table 2. To test for drop-out effects, analyses for wave 1 were also carried out only for participants remaining in wave 4. Results did not differ. So, drop-out did not influence the results of the study. Table 2 Data for all waves Wave 1 2 3 4

Panel size

Cases analysed

Trips analysed

Trips/ case

458 439 334 288

352 254 163 130

3,042 2,366 1,597 1,158

7.64 9.32 9.80 7.91

Model specification Panel members were asked to judge whether their route choice had been correct and whether they judged the RIA information to be correct. Only a very small fraction of drivers judged their route choice and the RIA information incorrect (wave 2, 0.5 percent; wave 3, 0.4 percent; wave 4, 0.2 percent). Thus, it seems that drivers found the information very credible. To generalise this finding, complete credibility of the information system was assumed. For each wave w the model is formulated as,

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where Pin = probability that individual i chooses route r on day t; Phin = probability that individual i chooses route r on day t because of habit; Pui™ = probability that individual / chooses route r on day t because of highest (perceived) expected utility; and Hit — habit strength for individual / on day t. All drivers in the study were regular commuters, who have encountered the choice situation many times. Therefore, maximum habit strength throughout all waves is assumed. So,

Substitution yields

Habit Habitual choice is conceived to be dependent on three parameters: maximum habit strength (Hmax), the speed with which habit strength builds up over choices (a), and the stability of habit strength when choices vary (y). To model habit, two assumptions are made. • After a certain route is chosen it becomes more likely that the same route will be chosen the next time. • The likelihood that a route is chosen depends on the number of times it was chosen previously. We define the probabilities of habit for all routes as,

This formula can be explained as follows: the amount of habit for route r changes when this route was chosen and experience was good. This is expressed by dir,t-i, where 8irt is 1 when route r was chosen at day t and

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zero otherwise. Parameter y reflects the importance of the previous choice. When y is large the distribution of habit over routes hardly changes. When y is small, the fact that a route was chosen significantly enlarges the proportion of habit of that route. Furthermore, the total amount of habit strength for individual / at day tis,

The importance of the last choice is part of the tendency to make habitual choices. The more important the last choice is, the more likely it is that the next choice will be the same. In this way, perseverance in choice behaviour is simulated. The importance of the last choice must be distinguished from the habit concept as a whole, which also depends on the number of times a certain route was chosen in the past. The more times the same route was chosen, the more likely it becomes that it will be chosen again. The evolution of habit over choices is assumed to depend on two parameters: the importance of the former choice (y), and the number of choices needed to reach maximum habit Hmax(a). To start the process an initial habit must be assumed.

Utility maximisation The dynamic formulations of the probability that route choice is based on utility maximisation is,

where Virt is the expected utility for individual i on day t for route r. The utility function was defined as follows. Next to expected travel time and perceived standard deviation of experienced travel times, expected queuelength is incorporated as a utility component. Thus, when no information is provided, the following utility function is assumed,

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where ttin = expected travel time by individual i for route r on day t; sirt = expected standard deviation of travel time; firt — expected queue length; and pk = utility parameters. Following the learning model by Horowitz (1984), the dynamic formulation of expected travel time is,

where ettirt = experienced travel time; and if/ = learning parameters. The dynamic formulation of expected queue-length is defined in a similar way,

where efirt = experienced queue length; and if/ = learning parameters. The dynamic formulation of the expected standard deviation in travel time is, ~3

When information is provided, the utility function becomes slightly different. In that case, expected queue-length firt is replaced by riairt, the queue-length according to the RIA sign. Since complete credibility of this information is assumed, queue-length expectations are completely replaced by the information from the sign. Drivers who are provided with queue information, adjust their expected travel times accordingly. Suppose a driver expects a travel time of 15 min and no congestion, but the RIA sign shows a queue of 4km on the route. It is likely that the driver will adjust expected travel time with this information. To model this, the expected travel time ttirt is updated with the information riairt, yielding

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where 0 = correction parameter for expected travel time using queuelength information; and riairt = queue-length on the RIA sign. Thus, when information is provided the utility function becomes

Obviously, the experienced queue-length equals the information about queue length, thus

Initial values The dynamic formulations of Phirt, ttirt, firt and sirt require initial values for each wave. These were determined separately for each individual. Since, drivers in the study were regular commuters it was assumed that initial values correspond with the actual choice behaviour and route performance during wave 1.

Probability of habit During the first wave no information was provided. The choice behaviour during this wave was assumed to be the same as prior to this wave. For each individual PPir was determined, denoting the proportion of choices route r was used during wave 1. Since waves 1 and 2 are consecutive, initial values for wave 2 were determined by

';,i5

No data on choice behaviour or experiences during the gaps between the waves were available. To arrive at initial values for the beginning of these waves, the end-values of wave 2 are taken as initial values for wave 3 etc.

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Attributes of the utility function Initial values for expected travel time, expected queue length and expected standard deviation in travel time were defined as follows: for each individual i the set of individuals with the same destination and period /,- is defined. Obviously it holds that / £ /,-. We define initial values for expected travel time for wave 1 as,

Similarly, initial values for expected standard deviation of travel time as,

and initial values for expected queue-length as

where A£r is the number of times individual i has chosen a route from the first until the rth day in wave w. Similar to the case of probabilities of habit we assume that the initial value for wave w is the last value of wave w - 1.

Estimation procedure Model parameters (H, y, i/r, /3i, /32 and /33) were estimated using a maximum likelihood procedure. Since we are interested in whether, or not, and how much, the values of parameters change over time as a

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consequence of the information provided, estimation was carried out for each wave separately. For wave w the log-likelihood function is

Results Parameter estimates For the model in which descriptive information is processed (waves 2 to 4), the factor 0 that updates expected travel time using queue-length information, was determined by regressing expected travel times on experienced travel times and corrected expected travel times. It was found that (/> = 130.0125. This means that "optimal" travel time expectations were reached by adding 0.0125 h (45 sec) to the originally expected travel time for each kilometre that queue-length was underestimated by drivers. The results of the maximum likelihood estimation for all waves are listed in Table 3. From the inspection of p2c it can be concluded that the

Table 3 Estimated parameters for all waves Parameters

H

y t 0i 02 03

Wave 1 (n = 3,042)

0.99 159 0.99 -90 -107 -1.95

Summary statistics A(c) -2031.4 A(**) -359.4 pi 0.82

Wave 2 (n = 2,366)

0.90 159 0.89 -90 -50 -2.22 -1617.6 -377.4 0.77

Wave 3 (n = 1,597)

0.89 159 0.87 -90 -50 -3.35 -1083.6 -237.9 0.78

Wave 4 (n = 1,158)

0.88 159 0.67 -80 -25 -6.75 -786.3 -213.4 0.73

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model fits well for all waves. Interpretation of the upper part of the table shows that during the first wave choice behaviour is almost completely dominated by habit (H — 0.99). For the next waves H decreases, but still dominates choice behaviour. In waves 2, 3 and 4 the decrease of H is 8, 11 and 12 percent compared to wave 1. Thus, utility maximisation plays only a modest role in the choice behaviour at hand. The distribution of habit strength over the two routes is stable over waves. The magnitude 159.1 of y shows that this distribution changes only after a large number of choices. The stability of y over waves might further indicate that changes in this distribution are independent of other model parameters. The weight given to the most recent experience in the learning process, (1 - i/f), increases over waves. After introducing information, this weight increases (in waves 2, 3 and 4 with 11, 13 and 33 percent compared to wave 1). In fact, during wave 1, if drivers are not choosing habitually, they seem to rely almost completely on general expectations about utility attributes built up over a longer time period. This finding could be considered to be a normal description of an equilibrium situation. In such situations drivers would not respond much to day-to-day variations in travel time, because these variations are experienced as incidents. It is interesting to note that when utility maximisation as a choice rule gains importance, the most recent experience in the learning process also gains importance. Three parameters of the utility function were estimated. The weight given of expected travel time in the utility function (/3i), is stable over the first three waves. This could be expected since travel time is considered the major criterion in trade off between routes. Unfortunately, /^ decreases from -90 to -80 from wave 3 to 4. One explanation for this might be that since /33 increases significantly, the absolute value of the utility increases significantly too. To compensate for this /3i decreases, such that total utility approximately stays the same. The weight for the expected standard deviation of travel time (/32) decreases strongly over waves (in waves 2, 3 and 4 the decreases of /32 are 54, 54 and 77 percent compared to wave 1). The role of this parameter is to model the weight of uncertainty about the travel time as a trade-off criterion. The decrease in this parameter might best be interpreted in the light of the finding that the weight given to the expected queue-length (/33) increases strongly over waves. In waves 2, 3 and 4 the increase of /33 is, 15, 72 and 246 percent, respectively, compared to wave 1. The importance of expected queue-length increases because drivers receive credible

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information on this. At the same time this information decreases the uncertainty drivers experience when making choices. To test the significance of each parameter set for each dataset likelihoodratio tests (Ortuzar and Willumsen, 1990) were performed for all 16 combinations of datasets and parameter sets. A parameter set denotes the set of parameters that were estimated for a wave. Tests shows that, in all waves except wave 3, the estimated parameter set has significantly better fit than all other parameter sets (^2(6) > 16.8, /?<0.01). For wave 3, parameter sets 2 and 3 do not differ significantly (x2(6) = 1-6, n.s.).

Simulation For each wave parameter, estimates were used to perform the MonteCarlo simulations. With these simulations route choice probabilities were generated. Experienced travel time is unknown when an individual chooses a different route in the simulation than was observed in reality. To overcome this problem, we assume that in these cases experienced travel time equals expected travel time corrected for queue-length information according to equation (13). From these simulations additional statistics were derived. Table 4 presents the number of cases in which observed and simulated route choices were the same or differed. For wave 1, the simulation yields the observed choice in 93.5 percent of the 3,042 choices. For waves 2, 3 and 4 these percentages are 92, 91 and 89.3 percent. Also from these statistics it may be concluded that the model fits well. Observed and simulated proportions of route 1 choices per day for all waves are presented in Fig. 2. Again, these figures indicate that the model

Table 4 Observed versus simulated route choices for all waves

Obs. 1 Obs. 2 Correct

Wave 1

Wave 2

Wave 3

Wave 4

Sim. 1 Sim. 2

Sim. 1 Sim. 2

Sim. 1 Sim. 2

Sim. 1 Sim. 2

1754 88

108 1092

93.5%

1292 100

90 884

92.0%

878 64

81 584

91.0%

621 69

55 413

89.3%

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proportion Zeeburgertunnel

0,65 0,6

0,65 0,5

0,46 0,4

1

11

21

31 day

observed

41

51

simulated

Figure 2 Observed and estimated proportion use of Zeeburgertunnel for wave 1 performs well for all waves, x2 goodness-of-fit tests between observed and simulated data for all waves show that daily aggregate simulated and observed route choices do not differ significantly, indicating a good model fit.

Effect of the variable message sign Does the information on the RIA sign lead to less experienced congestion? It might be argued that this type of information is useless, because in a situation like this, drivers already know what the queue lengths before the two tunnels are. It is conceivable that experienced drivers can predict these queue-lengths from the flows they observe, experience or other information sources. The model provides the opportunity to test this hypothesis. The study does not allow us to determine the benefits of information in terms of travel time. However, the difference in experienced queue lengths in the situation with and without information can be determined. For waves 2-4, simulations were performed using parameter estimates

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of the first wave and using utility function (11) instead of (16). The resulting choice behaviour mimics a situation in which no information is provided to drivers. This choice behaviour was compared to the observed and simulated choice behaviour with information. The results show that information has a considerable effect on experienced queue-lengths (Table 5). In wave 2, just after the RIA sign became operational, the simulations show that if no information had been provided, drivers would have experienced 2.1 percent more queues. In wave 3, this is 9.7 percent and in wave 4, 11.2 percent. So the effect of the information on experienced queuelength is evident. The above argument can also be reversed. What would drivers have experienced in the first wave, if at that time information had been provided? To answer this question we suppose that choice behaviour, in the first wave can be described by the parameters of the 2-4 waves, because these parameter values describe behaviour when information is provided. Table 5 Experienced queue-lengths (kms) from simulations with and without information

Wave 2 Wave3 Wave 4

Observed

Simulation with information

Simulation without information

Effect of information (%)

1,535 957 677

1,575 961 685

1,608 1,054 762

2.10 9.68 11.24

Discussion This study showed that a route choice model which incorporates the processing of information from a variable message sign is a usable tool to simulate real-life choice behaviours. Three kinds of results were obtained: model parameter estimates, simulation results and estimates of the effect of the VMS on experienced queue-lengths. First, the model fitted the data for all waves. Model parameter estimates showed that for the first wave choice, behaviour was almost completely dominated by habit. It seems

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that drivers who are very familiar with a choice situation are no utility maximisers. Also, the most recent experience with a route choice was of little importance in this situation. Drivers seem to have made up their minds: dynamic choice behaviour had become static. These results indicate that, in familiar choice situations, drivers might be unaware of changing circumstances, and their suboptimal choice behaviour is, to a large extent, a consequence of habit and, to a lesser extent, a consequence of faulty expectations. Traditional transport models that adhere to Wardrop's (1952) principles, in which drivers are assumed to choose the shortest route, are not valid for the equilibrium situations for which they were originally developed. After information was provided to drivers, their habit strength decreased, though it still dominated the choice process. Immediately after the RIA sign was turned on, habit dropped by nine percent. Also, in the following periods habit continued to decrease, though only a few percent. When habit decreased, the most recent experience in the learning process became more important. This effect became more pronounced over waves. During wave 4, new expectations are two-thirds of the prior expectations, plus one-third of the most recent experience. After information was provided, drivers became utility maximisers to a greater degree. However, the habit was never surpassed by utility maximisation. Although results indicate that utility maximisation was not the most prominent decision rule, some interesting results from the estimation of the weights for the utility components were obtained. The weight for expected travel time was stable over the first three waves. In the last wave, it dropped by about 10 percent. We hypothesised that this was due to the increased weight of information on queue-length in the utility function. The role of expected standard deviation can be translated into uncertainty about expected travel time. The importance of expected standard deviation in travel time decreased significantly over waves. This indicates that the provision of information diminished the uncertainty as a consequence of prior experiences. In a number of attempts to determine the influence of information on network performance (Koutsopoulos and Lotan, 1989; Hamerslag and Van Berkum, 1991; Cascetta et al., 1991), such a decrease was assumed as a way to model information provision. Although the present results confirm the validity of this approach, they also show that there is definitely more to information provision than merely uncertainty reduction. The importance of the expected queuelength, and when applicable the reported queue-length, in the utility function increased strongly after the VMS became operational.

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For all waves the model fits well. For the first wave, the model without information was used, while for the last three waves, the model with information was used. Within the setting of this study, it could not be determined whether, or not, information helped drivers to make a better choice with regard to experienced travel time. However, results on the difference in experienced queue-lengths showed that information had a considerable effect on the queue-lengths that the drivers experienced. Drivers would have experienced up to 11.2 percent more queues if no information had been provided. This result shows that the provision of information about queue-lengths, even in an accident-free environment with familiar drivers, has a substantial effect on experienced queue lengths.

References Allen, R.W., Ziedman, D., Rosenthal, T.J., Stein, A.C., Torres, J.F. and Halati, H. (1991) Laboratory assessment of driver route diversion in response to in-vehicle navigation and motorist information systems. Transportation Research Record 1306, 82-91. Ben-Akiva, M. (1985) Dynamic network equilibrium research. Transportation Research 19A, 429-431. Ben-Akiva, M. and Lerman, S. (1985) Discrete Choice Analysis: Theory and Application to Travel Demand. The MIT Press, Cambridge, Mass. Ben-Akiva, M., Cyna, M. and de Palma, A. (1984) Dynamic model of peak period congestion. Transportation Research 18B, 339-355. Ben-Akiva, M., de Palma, A. and Kaysi, I. (1991) Dynamic network models and driver information systems. Transportation Research 25A, 251-266. Ben-Akiva, M., de Palma A., and Kanaroglou, P. (1986) Dynamic model of peak period traffic congestion with elastic arrival rates. Transportation Science 20, 164-181. BGC (1992) A Better Look at RIA. DVK Report CXT92044, RAP, Rotterdam. BGC (1993) RIA: deelonderzoeken. Eindrapportage deel 2, BGC, Deventer. Bonsall, P. (1992) The influence of route guidance on choices in urban networks. Transportation 19, 1-23. Bonsall, P. and Parry, T. (1991) Using an interactive route-choice simul-

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ator to investigate drivers' compliance with route advice. Transportation Research Record 1306, 59-68. Cascetta, E., Cantarella, G.E. and Di Gangi, M. (1991) Evaluation of control strategies through a doubly dynamic assignment model. Transportation Research Record 1306, 1-13. Hamerslag, R. and Van Berkum, E.G. (1991) Effectiveness of information systems in networks with and without congestion. Transportation Research Record 1306, 14-21. Horowitz, J.L. (1984) The stability of a stochastic equilibrium in a twolink network. Transportation Research 18B, 13-28. lida, Y., Akiyama, T. and Uchida, T. (1992) Experimental analysis of dynamic route choice behaviour. Transportation Research 26B, 17-32. Jeffery, D. (1986) Route guidance and in-vehicle information systems. In P. Bonsall and M.G. Bell (eds.), Information Technology Applications in Transport. VNU Science Press, Utrecht. King, G.F. (1986) Driver performance in highway navigation tasks. Transportation Research Record 1093, 1-11. King, G.F. and Mast, T.M. (1987) Excess travel: causes, extent, and consequences. Transportation Research Record 1111, 126-134. Koutsopoulos, H.N. and Lotan, T. (1989) Effectiveness of motorist information systems in reducing traffic congestion. Proceedings of the IEEE Vehicle Navigation and Information Systems Conference, Toronto, May 1989, Canada. Luenburger, D.G. (1984) Linear and Non-linear Programming. AddisonWesley, Reading, Mass. Mahmassani, H.S. and Shen-Te-Chen, P. (1991) Comparative assessment of origin-based and en route real-time information under alternative user behaviour rules. Transportation Research Record 1306, 69-81. Ortuzar, J. de D. and Willumsen, L.G. (1990) Modelling Transport. John Wiley & Sons, New York. Rasmussen, J., Duncan, K. and Leplat, J. (1987) New Technology and Human Error. John Wiley & Sons, Chichester. Rijkswaterstaat (1992) Dynamic traffic management in The Netherlands. Rijkswaterstaat, Rotterdam. Simon, H.A. (1955) A behavioural model of rational choice. Quarterly Journal of Econometrics 69, 99-118. Stevens, A. and Hounsell, N. (1992) Simulation modelling of route guidance strategies. Proceedings 25th IS ATA Conference, Florence, October 1992, Italy. Van Berkum, E.G. and Van der Mede, P.H.J. (1993) The Impact of

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Traffic Information: Dynamics in Route and Departure Time Choice. Dissertation, Delft University of Technology. Watling, D. and Van Vuren, T. (1993) The modelling of route guidance systems. Transportation Research 1C, 159-182. Wardrop, J.G. (1952) Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, Part II 1, 325-362.

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Part V Methodological Advancements

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23

Bayesian Reliability of Discrete Choice Models Rodrigo A. Garrido

Abstract This chapter presents an index of predictive quality for discrete choice models as a function of their predictive success over a control sample, and the choice probabilities estimated by the model for each alternative. This index, called Bayesian Reliability (BR), allows to compare different model specifications even between nonnested structures. The index is easy to compute and has a clear and intuitive interpretation which provides the modeller with a valuable decision tool at both the model calibration and forecasting stages. The key properties of the index are shown and two practical examples are presented.

Introduction Discrete choice models give an estimate of the probability that an individual chooses an alternative from a mutually exclusive and collectively exhaustive set of options. For forecasting purposes, practitioners generally assume that an individual chooses the alternative to which the model confers the highest choice probability. On the other hand, researchers prefer to use a Monte Carlo probabilistic approach. In either case, it is known that models are not error-free, and this is mainly due to the existence of measurement and functional specification errors (see for example, Daly and Ortuzar, 1990). Therefore, the predicted choice will always be uncertain. Considerable effort has been put towards the study of goodness-of-fit indices for discrete choice models (among others see Tardiff, 1976;

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Hauser, 1978). However, very little attention has been given to the forecasting ability of this type of models. One of the most commonly used indices to measure a model's ability to replicate the choices on the calibration sample is the First Preference Recovery (FPR). FPR is the ratio between the number of observations successfully predicted and the total number of cases in a given sample, that is, the proportion of individuals that actually chose the alternative predicted by the model over the sample size. FPR has the advantage of being easy to compute and of having an intuitive interpretation (see for example, Foerster, 1979). Nevertheless, it has been shown that the FPR suffers severe shortcomings as an index of fit and that its values alone do not constitute evidence of good model's performance (see for example, Gunn and Bates, 1982; and the discussion by Ortuzar and Willumsen, 1994). Another very common index of fit among practitioners is the p2 index (Tardiff, 1976), but it has the problems of lacking an intuitive interpretation and hard to explain to nonexperts in the field, such as policy makers. This chapter presents a statistic that avoids the FPR's drawbacks and gives an index of the reliability of the model's predictions. A statistic of this sort must be able to assist in the specification and forecasting stages of modelling. Ultimately, the index presented here answers the following question: what is the probability that an individual actually chooses the same alternative predicted by the model?

Problem Statement The following definitions are needed for a mathematical description of the problem: • A: • • • • • •

m: EC. Pi\ p(X): p(X, Y): p(XIY):

Set of available alternatives (choice set) for the unit of analysis. Number of alternatives in A = {Al,A2, . . . , Am}. Event of choosing alternative Af. Event of predicting that alternative At will be chosen. Probability that event X takes place. Joint probability of X and Y. Conditional probability of X given that Y took place.

The problem of forecasting reliability can be expressed as the conditional probability of choosing an alternative A,-, given that a model predicted

Bayesian Reliability of Discrete Choice Models

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that it was going to be chosen, i.e. /?(£f,-/Pl-). The conditional probability sought can be computed with the aid of Bayes theorem,

(D

Of course the values of p(Et, Pt) and p(Pt) are needed to compute equation (1).

The estimation of p(Et, P,) From Bayes theorem we can write,

In this expression, the term p(Ei) corresponds to the choice probability estimated by the discrete choice model after an appropriate method of aggregation (see Ortuzar and Willumsen, 1994). The termp(P / /£' J ), represents the a priori information available to the modeller. Thus, if the characteristics of the population under study can be described by the parameters of a statistical sample, then p(Pj/Ei) can be estimated from a prediction success table T computed for that sample (see Hensher and Johnson, 1981; McFadden, 1976). The elements ttj of T count the number of observations in the sample (individuals), for which the model predicted that alternative A, would be chosen but the actual choice was the alternative AI (note that the diagonal elements show the number of times that each alternative was successfully predicted, that is, the FPR components). Therefore, the probability that alternative Aj is predicted, given that At was the actual choice, can be expressed as the ratio between the number of cases for which the first was predicted, but the latter was chosen and the total number of cases where At was selected,

where nt is the number of individuals who chose the alternative A{ in the sample. Substituting equation (3) into (2) we have,

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which contains, of course, the particular case i = j .

The estimation of p(Pt} By definition,

then, applying this summation over equation (4) we obtain,

Finally, substituting equations (4) and (6) into (1) we have the following result,

This expression will be termed hereafter Bayesian Reliability (BR) of the model with respect to the alternative Af. In some cases, it is useful to have an overall assessment of the model's reliability, that is, a single index for all the alternatives rather than one index for each. Indeed, a model presents a different reliability index for each alternative. Moreover, each alternative has a different effect on the overall reliability due to the influence or weight of their market shares. The expected value of the BR over the whole choice set can be used as an overall measure,

As mentioned earlier, p(Ei) is given by a calibrated discrete choice model.

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Comparison with a Null Model Given that BR is an index of the forecasting quality of a model's specification, it is useful to know the reliability of reference specification (see Hauser, 1978, for more on this topic), so that these reliabilities may be compared. This comparison can be used to measure how much better than the reference or null model (if it is better) is the specification under analysis. The simplest reference specification is a model that assigns individuals to alternatives randomly according to a constant choice probability (that is, each alternative is equally likely to be chosen). This model, shown in equation (9), is known as the equally likely (EL) model,

As the choice is considered random in this model, the expected value of the BR is,

In fact, if alternative Af was randomly selected to be the choice of a given individual then the probability that the individual actually chooses At is given by the a priori probability of choosing that alternative, which in this case is a random draw out of M options. Therefore, a well specified model should have a BR value greater than the value given by equation (10), otherwise, it would not be better than random selection. Example 1. Two modal-split models have been calibrated on a sample of car and bus users commuting from their homes to their job/study place (see Garrido, 1991, for details). The specification of the models (logit and probit) considered travel cost, travel distance, bus frequency and a modal constant as explanatory variables. The modeller must decide which model is the best in terms of their predictive quality and goodness of fit.

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The calibrated parameters are shown in Table 1 (V-statistics in parenthesis). The values have been scaled in order to allow a direct comparison between the logit and probit models. As expected, both models appear to be very similar, but the probit is slightly superior in terms of parameter significance and goodness of fit. However, this information is insufficient to make a good decision, so we will examine if the new measure can help. Table 1 Models calibrated for Example 1 Parameter/ (t ratio) Travel cost Travel time Bus frequency Modal constant P2 BR car BRbus Overall BR Number of car users Number of bus users

Logit model

Probit model

-0.0037 (-3.8) -0.0879 (-3.2) -0.1531 (-2.4) 1.1097 (2.8) 0.127 0.664 0.518 0.604 118 83

-0.0041 (-4.0) -0.0958 (-3.4) -0.1729 (-2.5) 1.2088 (2.8) 0.130 0.672 0.529 0.613 118 83

The BR's of the probit model are slightly higher than those of the logit model. Let us compare them against the null model. The BR of the EL model in this case is 0.5 (there are two alternatives), hence, the logit model is 32.8 percent more reliable than the EL for the prediction of car users' behaviour, and only 3.6 percent better than EL in the case of bus users. The probit model is 34.4 percent better than the EL model for car choice predictions, and 5.8 percent better in the case of bus choice predictions Therefore, in the absence of more information the probit model should be preferred.

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Example 2. The modeller wants to test the inclusion of the socioeconomic variable "age" in the specification found in Example 1. However, inclusion of the new variable caused the modal constant to become zero (not different from zero at more than the 99 percent confidence level). In some cases (e.g. logit models with linear-in-parameters utility function), the inclusion of the constant has the additional advantage of making the model replicate the market shares independent of the attributes used in the specification. However, in this case the inclusion of either the age attribute, or the modal constant, excludes the inclusion of the other one due to an extremely low statistical significance. Therefore, the decision is whether, or not, to include the attribute age instead of the modal constant (Table 2 shows the results). In Table 2, the model PRO-1 is the specification found in Example 1, and PRO-2 corresponds to the specification including age. The coefficients of age, and of the modal constant, have a very similar statistical signifi-

Table 2 Models calibrated for Example 2 Parameter

PRO-1

PRO-2

Travel cost

-0.0041 (-4.0) -0.0958 (-3.4) -0.1729 (-2.5) 1.2088 (2.8) 0.130 0.672 0.529 0.613 118 83

-0.0038 (-3.8) -0.0828 (-3.4) -0.1586 (-2.3) 0.0358 (2.9) —

Travel time Bus frequency Age

Modal constant p2 BR car BR bus Overall BR Number of car users Number of bus users

0.131 0.690 0.574 0.642 118 83

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cance and sign (both positive and significantly different from zero). This implies that the same variability of the data may be represented by either of them. The rest of the coefficients had only minor variations in magnitude and significance. Besides, the log-likelihood values are very alike (the p2 indices differ by less than 0.8 percent). Again, the above information is not enough for making an informed decision about the quality of both specifications. Nevertheless, the BR's can indeed enlighten the comparison. In fact, the BR's of the car and bus are greater in PRO-2 (and, therefore, so is the overall reliability), approximately 5 percent greater than those corresponding to PRO-1. The BR's of both models are greater than 0.5, hence, both outperform the EL model. In fact, PRO-1 is 34.4 percent more reliable than EL for car predictions, and 5.8 percent better off in the case of bus. PRO-2 is 38 and 14.8 percent more reliable than EL for the car and bus segments, respectively. Then, it may be concluded that PRO-2 is a better specification in terms of its predictive quality.

Conclusions An index of the predictive reliability of discrete choice models has been derived, which is both easy to compute and interpret. This index gives the conditional probability that an individual actually chooses the alternative with the highest modelled utility. The BR can be used, not only as a tool for model specification, but also for comparisons between nonnested models (which is a difficult subject for most measures, see the discussion in Ortuzar and Willumsen, 1994), because it is based only on the ability of a model to replicate a statistical sample. In fact, two or more estimated models can also be compared in view of their ability to forecast discrete choices in a different spatial or temporal contexts from the ones for which they were originally estimated. Finally, it has to be mentioned that the selection of the sample used for computing the table of predictive success depends on the objectives of the analysis. For example, a portion of the calibration sample would be useful as a tool for comparing different specifications of the same model, whereas, for testing model transfer ability, a new sample should be taken on the population of interest.

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Acknowledgments This research has been partially financed by the Bureau of Research of the Pontificia Universidad Catolica de Chile (DIUC) and the National Fund for the Scientific and Technological Development (FONDECYT). The author thanks Professor Juan de Dios Ortuzar and two anonymous referees for valuable assistance.

References Daly, A.J. and Ortuzar, J. de D. (1990) Forecasting and data aggregation: theory and practice. Traffic Engineering and Control 31, 632-643. Foerster, J.F. (1979) Mode choice decision process models: a comparison of compensatory and non-compensatory structures. Transportation Research 13A, 17-28. Garrido, R.A. (1991) Preferencias Declaradas en la Modelacion de Demanda por Nuevas Alternativas de Transporte. M.Sc. Thesis, Department of Transport Engineering, Pontificia Universidad Catolica de Chile. Gunn, H.F. and Bates, J.J. (1982) Statistical aspects of travel demand modelling. Transportation Research 16A, 371-382. Hauser, J.R. (1978) Testing the accuracy, usefulness and significance of probabilistic choice models: an information theoretic approach. Operations Research 26, 406-421. Hensher, D.A. and Johnson, L.W. (1981) Applied Discrete Choice Modelling. Croom Helm, London. McFadden, D. (1976) The theory and practice of dissaggregate demand forecasting for various modes of urban transportation. Working Paper 7623, Urban Travel Demand Forecasting Project, Institute of Transportation Studies, University of California at Berkeley. Ortuzar, J. de D. and Willumsen, L.G. (1994) Modelling Transport. 2nd edition, John Wiley & Sons, Chichester. Tardiff, T.J. (1976) A note on goodness-of-fit statistics for probit and logit models. Transportation 5, 179-190.

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24

Discrete Choice Models with Latent Variables Using Subjective Data Takayuki Morikawa and Kuniaki Sasaki

Abstract This chapter proposes a method for incorporating latent qualitative factors in travel-demand models. The framework for the proposed method is composed of a linear structural equation model and a discrete choice model. The linear structural equation model describes the process of the latent attributes generating subjective psychometric indicators of various aspects of travel attributes, and the relationship between the latent attributes and the observable objective variables. The discrete choice model expresses the observed choices explained by observable variables and the latent attributes. A practical calibration method of unknown parameters included in this system employs a two-step sequential maximumlikelihood estimation. First, a LISREL like program estimates the structural equation model to calculate the fitted values of the latent variables. Then, a discrete choice model, such as logit or probit with the calculated latent explanatory variables, is estimated. The practicality of the proposed method is demonstrated by an empirical analysis. The case study uses survey data of inter-city travel mode choice between rail and car. The data include six subjective indicators of travel attributes from which two latent attributes, ride comfort and convenience, are identified. The fitted values of these two latent attributes had outstanding explanatory power in the mode choice model. The proposed method is characterised by constructing the latent variables using objective variables, such as travel attributes and socioeconomic variables. This implies that the method can be used for predicting demand in conjunction with policy changes, because the predicted values of the latent variables can be calculated from objective variables.

Introduction Behavioural travel-demand models are usually estimated with observations of actual behaviour, or Revealed Preference (RP) data, using the

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method of discrete choice analysis (e.g., Ben-Akiva and Lerman, 1985). In recent years, however, there has been an increasing interest among transportation researchers in using psychometric, or market research type, data such as Stated Preferences (SP), perceptions and attitudes. Econometricians and market researchers have also been analysing consumers' choice behaviour in more psychometrical ways to obtain better predictive accuracy (e.g., McFadden, 1986). These approaches contrast with the traditional treatment of choice behaviour, which regards the decision maker as an "optimising black box". Adopting the view of most contemporary behavioural market researchers, the consumer decision process can be described as shown in Fig. 1. In this diagram, ovals refer to unobservable or latent variables, while rectangular boxes represent observable or manifest variables. The relationship between the observable attributes of alternatives and observed behaviour is represented by three groups of intervening factors: perceptions, attitudes and preferences.

Utility (Preference) Black Box Market Behavior (Choice)

Figure 1 Decision making process Perceptions are a consumer's perceived values of attributes of alternatives which are usually influenced by his or her socioeconomic characteristics, experiences and market information, while attitudes represent his or her evaluation of alternatives which is based on the subjective importance

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of attributes and the satisfaction with these attributes. Preference is also a latent factor and represents desirability of alternative choices, which is usually expressed by subjective expected utility. Traditionally, the latent factors enclosed by the dashed line have been treated as the black box. Following the basic structure of this diagram, this chapter develops a methodology for incorporating latent perceptual variables into discrete choice models using choice data and subjective ratings of travel attributes. The latent variables may include reliability, comfort, availability, etc. of travel alternatives, which are supposed to be important in making a choice, but difficult to include in models. In this chapter, formulation of a choice model system incorporating such latent variables is described, followed by alternative methods of estimating parameters of the system. An empirical analysis of mode choice is also presented.

Travel Behaviour Analysis with Subjective Factors Most operational travel behaviour models have used only obvious and objective explanatory variables, such as travel time, travel cost and sociodemographic attributes. However, latent and subjective factors, omitted from the models due to difficulty of measurement, clearly have significant influence on travel behaviour. In the choice of a travel mode, for instance, subjective factors listed below seem to be important. (1) Reliability (unknown variation of travel time). (2) Comfort (seating availability, ride quality, heating and ventilation, etc.). (3) Availability (locational and temporal ease of accessibility of the mode). (4) Information availability (about schedules, station locations, transfers, etc.). (5) Safety from accidents. (6) Security from crimes. (7) Privacy. (8) System image (general image of the mode). In a model omitting these factors, their effects may be embedded in an alternative specific constant and/or a random component of utility. Models that explicitly include these factors have the following two practical and theoretical consequences. First, the transportation system in developed

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countries is at the mature stage and requires more complex and detailed demand analysis for policies, such as demand management schemes and intellectualised transport facilities. For that purpose, models with only travel time and cost will be of little use. Second, it is found that parameter values of discrete choice models are not as transferable as expected at the early stage of the methodology. Especially, alternative specific constants are the most unstable both spatially and temporally. As stated earlier, a large part of the latent factors is embedded into the constants, causing the temporal and spatial unstableness of the values. In the travel behaviour literature, researchers have been constantly showing interest in incorporating such subjective factors into travel behaviour models. The Attitude-Behaviour model is the representative method of modelling travel behaviour with latent factor. Lovelock (1975) and Dobson (1975), for instance, reported the importance of latent factors in many contexts. Dobson and Tischer (1977) estimated logit models using perceptual and objective values of level of services and socioeconomic variables to show that perception affects travel behaviour. Recker and Golob (1976) used factor analysis to find latent factors that represent each market segment and estimated a logit model with indicators of the factors. Attitudes and their measurement were one of the major topics discussed in the third International Conference on Travel Behaviour in 1977. In this conference, relationship between attitudes, behaviour and measurement methods of attitudes, were discussed. Golob et al. (1979) showed a conceptual model of travel behaviour and discussed on the cognitive dissonance biases. Levin (1979) segmented the samples by their preference and investigated the relationships between the segments and attributes. Louviere (1979) proposed a mode choice model with the perceptions using a simultaneous equation system describing the relationship among attributes, perceptions and preference. Koppelman and Pas (1980) modelled the relationships between perception and attributes of alternatives, perception and preference, and preference and choice, then estimated the perception and feeling using factor analysis. They compared a choice model incorporating only the perception with that incorporating both the perception and feeling. Koppelman and Patrica (1981) estimated choice models incorporating alternative specific feeling and choice models incorporating a common feeling for all modes. Ben-Akiva and Boccara (1987) and Morikawa et al. (1990) proposed a choice model system incorporating various psychometric data using the concept of the MIMIC (Multiple Indicator Multiple Cause) model.

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Integrated Choice Behaviour Model and Perception Structure The model framework The model proposed in this chapter has the MIMIC-type structure that is illustrated by the path diagram in Fig. 2. As shown in the diagram, latent factors discussed in the previous section are incorporated in the choice model. Subjective ratings of attributes (Y in the diagram) and observed choice are treated as the indicators of latent variables, i.e. latent factor w* and utility, respectively. The subjective ratings are obtained for several attributes of each alternative. The model is formulated by structural and measurement equations. The structural equations specify the cause-andeffect relationship that the analyst is interested in and the measurement equations relate the observable indicators with the latent variables. The formulation below is for the binary choice context for the sake of simplicity, where all the variables are expressed as the difference of two alternatives. The asterisks (*) are attached to the latent variables (MNV denotes the Multivariate Normal distribution).

s, x

1

Observed Choice

Figure 2 The proposed model system

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Structural equations

where w* = utility of alternative; x = vector of observable explanatory variables; w* = vector of latent explanatory variables; s = vector of observable variables influencing w*; a, c, B = arrays of unknown parameters; v = random component of utility where v ~ jV(0,1); £ = vector of random components where £ ~ MVN(0, W). Measurement equations

where d = choice indicators; Y = vector of observed indicators (e.g., subjective ratings of attributes) of w*; A = matrix of unknown parameters; e = vector of random components where e ~ MVN(0, ®). This system can be viewed as an integration of two submodels. One is a binary probit model composed of equations (1) and (3), and the other is a linear structural equation model composed of equations (2) and (4). A linear structural equation model is discussed in more detail in the following section.

Linear structural equation model A linear structural equation model is useful in modelling causal path diagrams as shown in Figs. 1 and 2. It has the advantage that the system can include latent variables. Usually, all the variables in the structural equations are regarded as latent to generalise the specification. The generalised form of the system is shown below.

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Structural equation

Measurement equation

where 17 = vector of latent variables; Y= vector of indicators; B, A = matrices of unknown parameters; £ = vector of random components where £ ~ MVN(0, ^P); e = vector of random components where e~MVN(0, 0). In the above structural equation, the latent variables are regarded as endogenous. But the kih variable in 17 can be exogenous if we set the Ath row of B to be 0. This implies 17 can be viewed as a combined vector of w* and s in the framework given above. The linear structural equation model system is a generalised form of two multivariate analysis models. The structural equation alone is equivalent to a simultaneous multiple regression model and the measurement equation alone is equivalent to a factor analysis model. The maximum likelihood method is generally used to estimate the parameters, assuming that all the variables are normally distributed. LISREL is a representative computer program to estimate this model, hence, the model is often called the LISREL model (Joreskog and Sorbom, 1984).

Estimation of the Model System Sequential estimation In this section, we show the sequential estimation procedure of the whole model. First, we estimate the parameters of the LISREL model using some appropriate program, and then estimate those of the choice model conditional on the previous ones.

Derivation of the choice probability Assuming all the variables are normally distributed, the choice probability is derived as follows. The joint distribution of Y, w* and u* is

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where

Here, given the observable variables Y, x, 5, the conditional distribution of w* and u* is

where

and,

defining

Then the choice probability is given as,

where O is the cumulative distribution function of the standard normal distribution.

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Estimation method The following two-step sequential method can utilise readily available estimation programs and yield consistent, but not fully efficient, estimators. Step 1: Use a LISREL type estimator to estimate equations (2) and (4) and calculate the fitted values:

Step 2: Use a modified probit maximum likelihood estimator to estimate equation (9) using w* and co. Namely, estimate a and c using the following choice probability: (12)

Sequential estimation considering the cognitive dissonance "Cognitive dissonance" is known as discrepancy between attitudes and experiences, which one wishes to resolve by adjusting the attitudes for psychological consistency. In our context, respondents may overstate the ratings of their chosen alternative to justify their actual choice. Using such biased subjective data generally yields good fit of the model, but care should be taken when they are used to investigate the underlying structure of the decision making. The estimation procedure is based on the Sequential Estimation shown in the previous section.

Specification of the model To correct the potential biases caused by the effect of cognitive dissonance, the model is modified as follows. Structural equations Equations (1) and (2)

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Measurement equations Equation (3) and

(13) where y is an unknown parameter. The choice dummy is included to correct the bias in the measurement equation of perception.

Estimation method Basically the same estimation method as described above can be adopted. The choice dummy is treated as a (perfectly measured) latent variable, and then g becomes a part of A. Note that g should be omitted when estimating the choice model at the second step because it is supposed to capture the bias of cognitive dissonance.

Simultaneous estimation In this section, we propose the simultaneous estimation procedure of the whole model shown in the framework. This procedure has a different form from the sequential estimation methods in the previous sections. The basic concept of the estimation is maximising the joint probability of observing the choice and the perceptual indicators, conditional on the explanatory variables.

Derivation of the choice probability Assuming all the variables are normally distributed, the choice probability can be derived as follows. The joint distribution of Y, x, u* is the same as equation (7). Given w*, the conditional distribution of Y and u* is,

where

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Then the joint probability of Y and u* can be calculated by taking the mathematical expectation with respect to w*.

where is the probability density function of the standard normal distribution. In equation (15), we assume that the dimensions of Y and w* are n and m, respectively, and the components of Y and w* are independent among others. The maximum likelihood method is used to estimate the parameters to obtain consistent and asymptotically efficient estimates.

Simultaneous estimation considering discreteness of perceptual indicators The perceptual indicators are usually obtained in discrete scales such as: (i) very bad; (ii) bad; (iii) neutral; (iv) good; (v) very good. The estimation methods described thus far regard them as continuous variables. Stricter formulations should treat explicitly the discreteness of the indicators. The estimation procedure is based on the simultaneous estimation method shown in the previous section.

Model specification Structural Equations Equations (1) and (2) Measurement Equations Equation (3) and

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Equations (16) and (17) express the relationship between the latent perceptual indicators and observed discrete perceptual indicators.

Derivation of the choice probability Assuming all the variables are normally distributed, the joint distribution of y*, w* and u* is the same as in equation (7). Then, given w*, the conditional distribution of y* and u* is the same as in (14). The joint probability of Y and d is calculated by taking the mathematical expectation of y and d with respect to w*. Here, we assume that we obtained the /th category for the /th indicator.

This also assumes the independence among the components of y and w*. All the unknown parameters in the model are estimated by the maximum likelihood method.

Summary of the alternative estimation schemes 1. Sequential estimation: estimate the LISREL model and the discrete choice model sequentially. This is not statistically efficient but easy to carry out. 2. Cognitive dissonance: include the choice dummy variable in the perceptual measurement equation to remove the cognitive dissonance bias. The sequential estimation method is employed. 3. Simultaneous estimation: estimate the whole system simultaneously. This method is statistically efficient but requires more computational load because of the complex algorithm. 4. Discrete indicators: estimate the whole system simultaneously considering the discreteness of the subjective indicators. This is most

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desirable from the statistical and data characteristic points, but it requires more computational load than the simultaneous model.

Case Study Outline of the data used The empirical case study is on the inter-city mode choice context (rail versus car), for which data were collected in the Netherlands in 1987 by Hague Consulting Group. The data include the decision maker's sociodemographic and trip attributes. They also include the subjective evaluation of trip attributes on six items listed below. Note that the strings inside the parentheses are the variable names used in the following model specification: (a) (b) (c) (d) (e) (f)

relaxation during the journey (relax); reliability of the arrival time (relia); flexibility of choosing the departure time (flex); ease of travelling with children and/or heavy baggage (ease); safety during the journey (safe); overall rating of the mode (overall).

The first five perceptual indicators, (a)-(e), are given by the alreadymentioned 5-point scale; and the overall evaluation (f), is rated by a 10point scale, such as (1) worst to (10) best.

Specification of the model Two latent factors, ride comfort and convenience, are specified from a few trial models. Structural equations (perception part only)

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where aged is 1, if 40 years old or older; Ihtime is line-haul travel time including transfer time (hours); first is 1, if the rail trip is made by first class and zero otherwise; trmtime is the terminal travel time (hours); xfern is the number of transfers and freepark is equal to 1, if the parking fee is free at the destination and zero otherwise. The specification of the measurement equations of the perception part is shown in the next section. The utility function that is the structural equation of the choice model part is specified as follows:

where costpp is the travel cost per person (Guilder); business is 1, if the trip purpose is on business and zero otherwise; and female is equal to 1, if female and zero otherwise.

Estimation results Sequential estimation model (Tables 1 and 6) The estimation result of the LISREL-type model, that describes the structure of perception, is shown in Table 1 and that of the choice model in Table 6. The estimated parameters have expected signs and most of them are significant. The estimates in the measurement equations are generally more statistically significant than those in the structural equations. The observable endogenous variables in the structural equations do not explain the covariance of the endogenous variables. The two latent variables represent ride comfort/safety and convenience, respectively. These latent variables have significant and positive parameters in the choice model and consequently its goodness-of-fit measure is significantly better than the model without them. The sign of the parameter on line-haul time is reversed and its variance becomes large when incorporating the latent variables. This may be caused by the fact that the line-haul time is also included in the structure equation of comfort/safety. The rail constant loses its significance with the latent variables. This result may imply that the model with the latent variables has greater transferability.

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Table 1 Estimation result of LISREL part of sequential estimation model parameters-statistic) ("2*)

-0.232 (-1.4) -0.292 (-1.3) 0 B' —

0.406 (3.3)

(aged)

0

(Ihtime)

-0.522 (-2.1)

(trmtime)

0.286 (1.0) 0 0

0

-0.0471 (-0.6) 0.164 (1.6)

-0.0405

0

-(-o.i)

(first)

K*)

1

0.170 (0.8)

(relax)

0.722 (1.8)

1

(relid)

1.49 (4.3) (1.16 (5.2) (0.329 (2.0) 2.43 (5.9)

0

A=

0

(xfern)

0.686 (3.1) 1.64 (2.6)

(freepark) (aged x xfern)

(flex) (ease) (safe) (overall)

Cognitive dissonance model (Tables 2 and 6) It may indicate the existence of the cognitive dissonance bias that the parameter of the choice dummy in A is positive and significant, because this result means that the subjective indicator of the chosen mode is

Table 2 Estimation result of LISREL part of cognitive dissonance model parameters-statistic) -0.173 (-1.47) -0.370 (-1.5)

B' =

0.378 (1.8)

(aged)

0

(Ihtime)

0

-0.248 (-0.8)

(trmtime)

0.147 (0.5)

0

(first)

0 0

-0.0760 L (-0.2)

-0.00017 (-0.01) 0.130 (1.2) 0

1

1.00 (1.2) A=

0 0

(xfern) (freepark) (aged x xfern)

0.593 (2.0) 1.51 (1.6)

("2*)

d

0.224 (0-4)

0

(relax)

1

0

(relid)

0

(flex)

0

(ease)

0

(safe)

0.770 (4.5)

(overall)

1.98 (2.0) (1.12 (2.6) 0.295 (0.8) 2.31 (3.1)

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positively biased. The measure of goodness-of-fit is not better than the Sequential model by removing the bias. Simultaneous estimation model (Tables 3 and 6) Many of the parameter estimates of the LISREL model have different signs from the Sequential model. The estimators in the LISREL model are influenced not only by the perceptual indicators but also the choice indicator in the simultaneous estimation method. This means that the cognitive dissonance bias on the parameters in the LISREL model may be corrected implicitly. In this model, the latent variables seem to represent perceived accessibility, i.e. the convenience of train use and convenience of car use, respectively, judging from the significant variables. Table 3 Estimation result of LISREL part of simultaneous estimation model parameter/Ostatistic) r (Wl*) 1.35 (7.2) -1.25 (-9.2)

B' =

("*) 0.576 (2.7)

-

(aged) (Ihtime)

0

-3.26 (-8.7)

(trmtime)

- 0.0712 (-0.6)

0

(first)

0

0.300 L (0.9)

-0.886 (-4.5) 1.47 (5.6) 0

-i w

0

0

-

(xfern) (freepark) (aged x xfern)

A=

( i) (w*) 0.334 -0.185 (6.9) (-7.0) 0.354 -0.0414 (10.0) (-1.8) 0.412 0 (12.4) 0.401 0 (12.5) 0.281 -0.174 (9.0) (-8.1) 0.328 0.865 (6.7) (13.7)

(relax) (relia) (flex) (ease) (safe) (overall)

Discrete indicator model (Tables 4, 5 and 6) Specifying the thresholds as a free parameter yielded the different estimates on parameters mainly in the LISREL part and the parameters of latent variables in the choice model. This result may imply that assuming the discrete perceptual indicators as the relative scale is too strong. The latent variables seem to represent the safety and convenience of car use from the estimates. The intervals of estimated threshold value shown in Table 5 are not even but larger for the upper thresholds. This result implies that respondents expressed their perception mainly by the upper

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Table 4 Estimation results of LISREL part of discrete indicator model parameter/(/-statistic) r (W*)

(aged)

0

(Ihtime)

0

-1.71 (-8.4)

(trmtime)

-0.0448 (-0.1)

0

(first)

-1 51 (-3.8) 0.751 (5.9)

B' =

-0.185 (-1.4) 0.300 (1.9)

0 0

-0.0903 _ (-0.5)

0

-

-

(fa*) 2 22 (7.3)

-

(w*} -3.08 -0.855 (-7.6) (-3.7) -1.20 -0.904 (-5.8) (-4.8) 0.0215 0 (0.2) 2.53 0 (12.2) 0.764 -1.29 (-7.7) (2.8) 1.01 0.676 (5.8) (11.9) ( W*}

A=

(xfern) (freepark) (aged x xfern)

(relax) (relia) (flex) (ease) (safe) (overall)

Table 5 Estimation result of threshold values of discrete indicator model parameters-statistic) threshold —

-4.20 (-10.5)

-1.83 0.821 3.96 (-6.6) (5.3) (30.0)

score, since they have no absolute criterion of evaluation. Entirely, most parameters in the LISREL model are significant, and the parameter of the line-haul time in the choice model is negative and significant. This implies that the latent variables represent different factors from other models. We conclude that approximating the discrete perceptual indicators for continuous variables may result in biased parameter estimates.

Discussion and Summary This chapter proposes a methodology to incorporate latent and subjective factors into a choice model. It is based on the supposition that there exist some latent factors constructed by objective attributes and elicited by

Table 6 Estimation results of choice models Normal model Rail constant costpp Ihtime trmtime xfern Business Female w*

0.583 (2.0) -0.0268 (-4.2) -0.405 (-1.6) -1.57 (-4.2) -0.195 (-1.3) 0.942 (3.6) 0.466 (2.3)

M>2 P2

N

0.242 219

Sequential estimation model

Cognitive dissonance model

0.322 (1.0) -0.0338 (-4.1) 0.0751 (0.2) -1.18 (-2.6) -0.316 (-1.7) 1.33 (3.6) 0.652 (2.6) 0.882 (2.7) 1.39 (4.1) 0.352 219

0.566 (1.2) -0.0495 (-3.4) 0.178 (0.4) -1.91 (-2.7) -0.477 (-1.7) 1.92 (3.3) 0.958 (2.4) 1.52 (2.3) 2.08 (3.2) 0.347 219

Simultaneous estimation model 0.831 (17.8) -0.0316 (-5.0) 0.0791 (0.6) -0.891 (-2.7) -0.185 (-1.2) 1.26 (10.5) 0.535 (4.8) 0.422 (5.0) 0.324 (5.0) 0.252 219

Discrete indicator model

1.17 (4.8) -0.0721 (-5.9) -1.23 (-4.8) -1.29 (-9.7) -0.278 (-2.6) 1.93 (30.3) 1.77 (9.1) 2.00 (15.8) 1.50 (8.7) 0.424 219

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subjective evaluation. The approach is different from the existing ones that directly use subjective evaluation in the utility function. The proposed method uses subjective evaluation just as indicators of latent variables that themselves are functions of observable variables. This makes it possible to estimate the future values of the latent variables from the structural equation in the LISREL model. The subjective indicators are only used to calibrate the LISREL model, hence, the subjective indicators are not needed for forecasting. For example, policy analysis such as change in travel time can be conducted using this methodology. Subjective indicators should be carefully collected because they often involve various biases like cognitive dissonance. But they have some advantages in that respondents can answer subjective evaluation without much mental fatigue due to the subjective nature of their responses. Proper utilisation of such easy-to-answer data will be a prospective approach for modelling choice behaviour. We applied this methodology to inter-city mode choice data in an empirical case study. We found that two latent variables estimated by the Sequential Estimation model affected mode choice significantly. The other three estimation schemes also provide the following findings. One is that estimating the whole system simultaneously, in which the choice affects fitting of the LISREL model, is better than including the choice dummy in the measurement equation in the LISREL model, and attempting to improve the goodness-of-fit of the structural equation in the LISREL model. The estimation result of the Sequential Estimation model is somewhat different from the Simultaneous Estimation model. Further investigation is required to find the source of this discrepancy and recommend the most appropriate method. The other finding is that the estimation result of the Discrete Indicator model shows that the intervals of estimated thresholds of the subjective indicators are not equal. This model has the weakest constraint among the models we tested and yielded different estimates from the other three estimation procedures. Hence, the Discrete Indicator model is the most recommendable in the present circumstance although it requires heavy computational load—approximately one hundred times as heavy as the Sequential Estimation model. For this particular set of data, on the other hand, the goodness-of-fit of the structural equation in the LISREL model is poor because of the limited number of observable variables in the data. The fitted values of the latent variables calculated only from the structural equation are not necessarily reliable, leaving as a future research problem how to use this methodology more comfortably in forecasting. It is considered that the

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perception structure is heterogeneous among individuals, implying that proper market segmentation may improve the goodness-of-fit of the LISREL model.

References Ben-Akiva, M. and Boccara, B. (1987) Integrated framework for travel behaviour analysis. International Conference on Travel Behaviour, Aixen-Provence, May 1987, France. Ben-Akiva, M. and Lerman, S. (1985) Discrete Choice Analysis: Theory and Application to Travel Demand. The MIT Press, Cambridge, Mass. Dobson, R. (1975) Towards the analysis of attitudinal and behavioural responses to transportation system characteristics. Transportation 4, 267-290. Dobson, R. and Tischer, M.L. (1977) Comparative analysis of determinants of modal choice by central business district workers. Transportation Research Record 649, 7-14. Golob, T.F., Horowitz, A.D. and Wachs, M. (1979) Attitude behaviour relationships in travel demand modelling. In D.A. Hensher and P.R. Stopher (eds.), Behavioural Travel Modelling, Croom Helm, London. Joreskog, K. and Sorbom, D. (1984) LISREL VI-Analysis of Linear Structural Relations by Maximum Likelihood, Instrumental Variables, and Least Square Methods: User's Guide. Department of Statistics, University of Uppsala. Koppelman, F.S. and Pas, E.I. (1980) Travel-choice behaviour: models of perceptions, feelings, preference, and choice. Transportation Research Record 765, 26-33. Koppelman, F.S. and Patrica, K.L. (1981) Attitudinal analysis of work/ school travel. Transportation Science 15, 233-254. Levin, I.P. (1979) The development of attitudinal modelling approaches in transport research. In D.A. Hensher and P.R. Stopher (eds.), Behavioural Travel Modelling, Croom Helm, London. Louviere, J.J. (1979) Attitudes, attitudinal measurement and the relationship between attitude and behaviour. In D.A. Hensher and P.R. Stopher (eds.), Behavioural Travel Modelling, Croom Helm, London.

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Lovelock, C.H. (1975) Modelling the modal choice decision process. Transportation 4, 253-265. Recker, W.W. and Golob, T.F. (1976) Attitudinal modal choice model. Transportation Research 20A, 293-310. McFadden, D. (1986) The choice theory approach to market research. Marketing Science 5, 275-297. Morikawa, T., Ben-Akiva, M. and McFadden, D. (1990) Incorporating psychometric data in econometric travel demand models. Banff Invitational Symposium on Consumer Decision Making and Choice Behaviour, Banff, May 1990, Canada.

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25

The Stability of Parameter Estimates in Household-Based Structured Logit Models for Travel-to-Work Decisions Terje Tretvik and Staffan Widlert

Abstract A substantial body of empirical evidence now exists on the stability, or rather instability, of model specifications and parameter values of disaggregate choice models. A majority of the studies deal with rather simple model structures, often involving only mode choice. This chapter investigates the transferability between two cities in neighbouring Scandinavian countries of a complicated nested structure for travel-to-work decisions by households. The model accommodates joint travel decisions by two-worker households. Mode choice, car allocation and trip frequency are modelled by full-information estimation. The results from the transfer experiment show that the model developed for the Stockholm conurbation (1.5 million inhabitants) could be successfully transferred to the city of Trondheim (0.14 million inhabitants) with only a minimum of updating. A model with recalibrated constant terms on the mode choice level provided 90 percent of the improvement in log-likelihood that was obtainable between a naive transfer and the best local model. A model in which all parameters were reestimated on local data behaved in almost complete accordance with the best local model in all validation tests. The model with recalibrated constant terms only, showed just minor discrepancies with the best local model in prediction tests.

Introduction Disaggregate travel demand models are being used increasingly in traffic planning studies in the Scandinavian countries. One important problem is that it requires substantial effort in terms of money and time to develop models. It is expensive to carry out travel surveys to get data for model

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development, and the estimation work is often both difficult and somewhat unpredictable. During the foreseeable future, we will most likely have a situation where locally estimated models are not available in most places where travel demand studies are needed. It is therefore natural that transferring models between different places is of great interest. Many studies of model transferability have been conducted during the years, and statistical as well as more pragmatically-based criteria for the judgement of transfer results have been established (e.g., Atherton and Ben-Akiva, 1976; Koppelman and Wilmot, 1982; Gunn et al., 1985; Gunn and Pol, 1986). In many cases, only simple mode choice models have been transferred, and the results have differed substantially. The authors are unaware of any studies which have addressed the transferability of very complex models of household choices. In this chapter, we describe the results from transferring a complicated nested model structure for travel-to-work decisions by households. It was developed for the Stockholm conurbation (Algers et al., 1991) and transferred to the city of Trondheim. The study formed part of a project carried out jointly by SINTEF Transport Engineering in Norway and Transek AB in Sweden, and was funded by the Nordic Committee for Transport Research. The project also included transfer studies of systems of models for individuals' mode, destination and frequency choices for different trip purposes. These models considered local and regional trips, and the transfer was from a large Swedish city to a medium sized Norwegian city. Transferring national models for long distance trips was also included. The transferability experiment reported in this chapter is particularly interesting, since it deals with the transfer of a fairly complex system of household models. Not only is the model system transferred between different countries, but also between cities with very different size, urban structure and transportation system. The population of the Stockholm region is 1.5 million compared to a population of only 0.14 million in the city of Trondheim. In Stockholm, the public transport system includes buses, underground and commuter trains and the public transport share is high. In Trondheim, car traffic is much more dominant. In the following section, we describe the structure of the model which is transferred, and some of the differences in travel patterns between the two regions. In the third section, the original Swedish model is presented together with Norwegian models with varying levels of reestimations on local data. The fourth section contains the validations of the model transfers.

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The Household Work-Trip Model Structure in Both Cities

Model structure The tree structure for the model substructure that was the central focus of the transfer experiment is shown in Fig. 1. The figure shows the options for a household with two working members. Complexity is of course considerably reduced if a household has only one working member. If the household has more than two working members, two "main" workers are identified. The other working members are treated individually, as secondary one-person households. The two main workers are denoted A and B, and the coding procedures are such that A is usually a man and B usually a woman. A model for choice of secondary destinations during work-trips is shown at the bottom in Fig. 1. Secondary destinations are, for example, shops visited on the way to or from work. This model had to be estimated first, so that logsum variables could be included in the utility functions on the next level. The Stockholm work-trip model system also had a combined destination and car ownership choice substructure attached to the top, by a logsum variable. This substructure was not estimated for Trondheim, and thus, is not part of the transfer experiment. The trip frequency, car allocation and mode choice models are estimated simultaneously. In the frequency model, the alternatives are that the household makes no trips (0), only person A makes a trip (1 (A)), only person B makes a trip (1 (B)), or that both make a trip to work that day (2 (A and B)). On the car allocation level, if only A goes to work, he has the choice of using the car (A), if he has a licence, or not using the car (0). If he does not take the car he can choose on the mode choice level between car passenger (in another household's car or with a nonworking member from his own household), public transport, walk and bicycle. If only B goes to work she has a corresponding choice set. If both go to work, they have the following options on the car allocation level: 0 A B AB A and B

Nobody uses the car. A uses the car. B uses the car. Both use the same car (shared ride). Both drive different cars (only if the household has more than one car).

Frequency

A and B Carallocation Mode choice

1 X2 K3 K 4 K S K6 X 7K8 K9 K10M11J. . . 126X27X28X29130131X32X33X34X35X36

Secondary destination

Figure 1 The complete model structure for two-worker households

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461

Choices Table 1 shows a summary of actual mode choices in the Stockholm and Trondheim estimation datasets. In the top section of the table modal shares for single work-trips are shown. It is evidently clear that large behavioural differences exist between the two cities. Table 1 Mode choice alternatives Stockholm (%) One person travelled: Car driver Car passenger Public transport Bicycle Walk Subtotal Two people travelled'. Both car passenger Car passenger + public transport Car passenger + bicycle Car passenger + walk Both public transport Public transport + bicycle Public transport + walk Both bicycle Bicycle + walk Both walk Car driver + public transport Car driver + bicycle Car driver + walk Car driver + car passenger* Both car driver Shared ride** Subtotal Total

Trondheim (%) 320 30 321 30 62

(42) (4) (42) (4) (8)

549 86 116 100 93

(58) (9) (12) (11) (10)

763

(100)

944

(100)

0 5 0 2 66 11 15 0 4 5 104 21 28 0 35 56

— (1) — — (19) (3) (4) — (1) (1) (30) (6) (8) (10) (16)

2 2 0 2 8 6 7 15 6 5 73 30 35 13 79 74

— — — — (2) (2) (2) (4) (2) (1) (20) (8) (10) (4) (22) (21)

352

(100)

357

(100)

1115

1301

* Driven by a nonworking household member, or passenger in another household's car. ** Car driver + car passenger in the same car, and both travelled to work.

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While the Stockholm public transport share for these trips was 3.5 times higher than in Trondheim, the Stockholm shares for other modes were all lower than in Trondheim. In the bottom section of the table, the combined mode choices of persons A and B are depicted. Combinations involving public transport are evidently more common in Stockholm. Figure 2 shows the total individual mode choices, irrespective of whether one or two people went to work. The much higher public transport share in Stockholm is again coupled with a lower share for all the other modes. Thus, it is evidently clear that the two urban areas are very different with respect to mode choices.

Figure 2 Modal shares for individuals in Stockholm and Trondheim On the car allocation level, patterns of gender roles of different strength could be observed. For instance, if two people went to work, it was four times more usual in Stockholm and three times more likely in Trondheim that the man drove a car and the woman travelled by another mode, than the reverse allocation. If only one person went to work, in Stockholm the car driver share was 2.6 times higher among men than women, compared to 1.6 times higher in Trondheim.

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463

The Stockholm and Trondheim Models In Table 2, the model result which was imported from Stockholm is presented (Model 1) alongside the results from tree types of reestimation on Trondheim data (Models 2-4). First, the respective model estimation results will be discussed. Then, the models will be evaluated with respect to transferability issues.

The Stockholm Model Two Stockholm parameters are omitted from the table, because the corresponding variables had no variation in the Trondheim data. One was a dummy for winter, attached to bicycle and the other was a dummy for the home and work zone being the same, attached to public transport. These parameters are included, however, in the computation of the statistics for the Stockholm model reported at the bottom of the table. Level-of-service variables are for the home-work-home round trip. Values are zone-to-zone averages based on the coding and implementation of network models, but updated by information from travel surveys and other sources. The implied in-vehicle value of time is reasonable, and outof-vehicle components of travel time are more negative than the in-vehicle valuation. A car competition variable reflects competition with nonworking members of the household. Note that competition between working members is explicitly modelled at the allocation level. At the mode choice level, note that shared ride (defined before as both travelling to work in the same car) is treated as a separate alternative, and that the reference alternative with no alternative specific constant is car driver. The logsum parameter from the secondary destination models is significantly different from zero, indicating that the accessibility to different destinations on the way to and from work affects the choice of main mode. On the car allocation level, gender variables show that women, everything else being equal, have a lower probability of getting access to the car in households with two working members. This might be interpreted as different bargaining positions because of traditional roles of women and men. The logsum parameter shows that the accessibility gained by using the car is an important element when the household decides about the use of the car. In the frequency model, all alternatives except the one for both travel-

464

Travel Behaviour Research: Updating the State of Play Table 2 Comparison of model parameters Variables (f-ratios)

Mode choice Constant, car passenger Constant, public transport Constant, bicycle Constant, walk Constant, shared ride In-vehicle time, car and public transport Cost, car and public transport Walk time, public transport Wait time, public transport Travel time, walk and bicycle Dummy, 1 if car competition, car driver Dummy, 1 if city centre, car driver Dummy, 1 if car during work, car driver Dummy, 1 if secondary house hold, car driver Dummy, 1 if reserved parking, car driver Dummy, 1 if car in household, car driver Dummy, 1 if female, car passenger Dummy, 1 if female, public transport Dummy 1, if city centre, bicycle Dummy, 1 if < 35 years, bicycle Dummy, if academic bicycle Dummy, 1 if female, walk

Model 1: The Stockholm model

Model 2: Local est. of constant terms

Model 3: Local est. of all parameters

Model 4: The best local model

-4.2420 (-4.7) -1.0170 (-2.1) 1.4340 (2.0) 3.3300 (4.4) 0.1493 (0.2) -0.0178 (-3.3) -0.0524 (-5.2) -0.0510 (-3.3) -0.0202 (-2.7) -0.0616 (-10.4) -0.9952 (-2.7) -1.3460 (-3.7) 3.2170 (5.5) -1.6070 (-2.4) 1.2550 (2.5) 1.5900 (3.1)

-3.4160 (-23.9) 1.3610 (10.5) 1.2150 (9.2) 1.7210 (12.0) 0.8521 (3.3) -0.0178 (-) -0.0524 (-) -0.0510 (-) -0.0202 (-) -0.0616 (-) -0.9952 (-) -1.3460 (-) 3.2170 (-) -1.6070 (-) 1.2550 (-) 1.5900 (-)

-4.1640 (-9.6) -1.2790 (-4.2) -0.9238 (-4.1) -0.3421 (-1.4) -1.1020 (-4.1) -0.0201 (-5.1) -0.0404 (-6.7) -0.0324 (-3.7) -0.0096 (-1.7) -0.0589 (-16.0) -0.6097 (-3.7) -0.4800 (-2.3) 1.5150 (6.9) -1.1390 (-2.4) 0.8177 (3.9) 0.5667 (1.4)

0.4922 (2.1) -1.2070 (-2.4)

0.4922 (-) -1.2070 (-)

0.6181 (3.2) -0.4952 (-2.2)

-4.2650 (-9.4) -1.0520 (-3.5) -1.0570 (-4.7) -0.2615 (-1.1) -0.5054 (-2.2) -0.0199 (-5.1) -0.0403 (-6.7) -0.0333 (-3.8) -0.0097 (-1.7) -0.0589 (-15.9) -0.6657 (-4.0) -0.4856 (-2.3) 1.4800 (6.8) -1.1260 (-2.3) 0.8444 (4.0) 0.6196 (1.5) 0.8036 (3.4) 0.9977 (5.1) -0.5165 (-2.2) 0.4965 (2.7) 0.7383 (3.8) 0.5689 (2.6)

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Table 2 (Continued) Variables (f-ratios) Logsum from secondary destination Car allocation Dummy, 1 if only female travels, not car driver Dummy, 1 if both travel, no car drivers Dummy, 1 if both travel, female car driver Dummy, 1 if both travel, both car drivers Dummy, 1 if male academic, car driver Dummy, 1 if male flexitime, car driver Dummy, 1 if female flexitime, car driver Logsum from mode choice Frequency Constant, only male travels Constant, only female travels Constant, no trip Dummy, 1 if both academic, only male travels Dummy, 1 if Saturday, no trip Dummy, 1 if Sunday, no trip Dummy, 1 if male part-time, not trip Dummy, 1 if female part-time, no trip Dummy, 1 if two employed and small children, only female travels Logsum from car allocation Log— likelihood P2(0)

Model 3

Model 1

Model 2

0.2841 (4.0)

0.2841 (-)

0.9706 (3.5) 0.7410 (3.0) -0.5535 (-1.9) -0.2003 (-0.6) -0.7001 (-2.8)

0.9706 (-) 0.7410 (-) -0.5535 (-) -0.2003 (-) -0.7001 (-)

0.5570 (2.6) 0.3281 (1.4) -0.5231 (-2.2) 0.2645 (1.0) -0.5187 (-2.7)

0.6503 (6.7)

0.6503 (-)

1.0 (-)

-0.6958 (-7.6) -0.7162 (-7.3) -1.3100 (-10.8)

-0.6421 (-7.6) -0.8247 (-9.1) -1.9900 (-22.7)

-0.7807 (-7.9) -0.9753 (-8.9) -2.3030 (-16.0)

3.0930 (17.5) 3.8360 (16.1) 0.9434 (3.2) 0.2287 (1.7) -0.4713 (-2.8)

3.0930 (-) 3.8360 (-) 0.9434 (-) 0.2287 (-) -0.4713 (-)

3.2820 (17.5) 3.6170 (19.6) 0.9602 (2.0) 0.5308 (3.4) -2.072 (-1.0)

0.0323 (0.9) * 0.5103

0.0323 (-) -2845.8 0.4007

0.0733 (1.7) -2814.8 0.4072

0.0 (-)

Model 4 0.0 (-)

0.2506 (1.2) 0.8574 (3.7) -0.2955 (-1.6) 0.5607 (2.0) 0.2272 (0.8) 1.0 (-) -0.8626 (-8.5) -0.9612 (-10.3) -2.2550 (-17.9) 0.3984 (2.7) 3.3100 (17.7) 3.6310 (19.7) 0.9501 (1.9) 0.5094 (3.3)

0.0762 (1.8) -2791.6 0.4121

* The log-likelihood value obtained in Stockholm is not directly comparable to the ones obtained in Trondheim, since sample sizes were different. However, when the Stockholm model was applied to the Trondheim data, log-likelihood = -3315.9 and p2(0) = 0.3017.

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ling have alternative-specific constants. Weekday parameters reflect the lower work-trip rate on Saturdays and Sundays. The part-time dummies show that people working part-time often work fewer days. A dummy for households with children of age seven or under and two working members shows that women in such households have a higher probability of staying at home, for example when a child is sick. Since the logsum parameter is small and not significantly different from zero, accessibility was not found to significantly influence the frequency of work-trips.

Models estimated on Trondheim data Table 2 also contains the results from three estimations on local data, Models 2, 3 and 4, exploiting increasing amounts of information and freedom in the specification. In Model 2 only the five constant terms on the mode choice level are recalibrated, while Model 3 is a complete reestimation of all the parameters. Model 4 is labelled the best local model, since it includes a set of explanatory variables resulting from a search to best explain local choices.3 Table 3 summarises the improvements in log-likelihood between the models. It is evident that the reestimation of the constant terms brought about quite a considerable improvement in fit relative to a naive transfer, and that only moderate additional explaining power remained to be gained by Models 3 and 4. In fact, relative to the total improvement obtainable between Models 1 and 4, Model 2 managed 90 percent and Model 3 managed 96 percent.

Table 3 Differences in log-likelihood values between models Log-likelihood Model Model Model Model a

1: 2: 3: 4:

Naive transfer Reestimation of constants Reestimation of all parameters The best local model

-3316 -2846 (90%) -2815 (96%) -2792 (100%)

Improvement in log-likelihood 470 31 23

Specifying three separate cost parameters (car driving, parking and public transport) as well as separate parameters for in-vehicle time by car and public transport, produced a local model with a further 39 units improvement in log-likelihood. All these parameters came out significant and with the expected signs, but the implied values of time by car and public

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467

Ortuzar and Willumsen (1990) quote a t-statistic to evaluate the absolute difference between coefficients of a given model in contexts i and /. The null hypothesis that their difference is zero cannot be rejected at the 95 percent level if

Table 4 shows that only two constant terms in each model were significantly different from the ones in Model 1. This was obviously enough, however, to correct for the systematic differences in mode choices between the two cities, which were described in the previous section.

Table 4 T-statistics for the null hypotheses that constants are equal to the ones in the Stockholm model

Model 2 Model 3 Model 4

Constant car passanger

Constant public transport

Constant bicycle

Constant walk

Constant shared ride

0.9 0.1 0.0

4.7 0.5 0.1

0.3 3.1 3.3

2.1 4.6 4.5

0.8 1.4 0.7

A comparison of the other parameter estimates from Stockholm and Trondheim in Table 2 reveals that, with the exception of one insignificant dummy on the car allocation level, all got the same sign. Also, Trondheim parameters are in general smaller in size on the two lowest levels and larger in size on the top level. The logsum parameter from the secondary destination model came out not significantly different from zero in the Trondheim context, and was therefore constrained to zero. Thus, accessibility to secondary destinations did not vary in such a way in Trondheim that it had an effect on mode and car allocation choices. The logsum parameter from mode choice got a t-value of nearly 9, and values of 1.20 in Model 3, and 1.07 in Model 4. Thus, it was constrained transport differed enormously. The public transport cost parameter was 3.5 times larger than the car cost parameter, and the public transport time parameter only a third of the car time parameter.

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to 1 to avoid the problems of implied cross-elasticities with the wrong sign. Anyway, this means that the accessibility by modes had a large influence on car allocation. The Trondheim logsum parameter from car allocation became more than twice as big as the Stockholm parameter, and nearly significant. This implies that there is evidence of a certain feedback effect from accessibility to trip generation/suppression.

Validation of Model Transfers A number of measures based on log-likelihood values can be computed to assess the quality of a transferred model. For instance, Koppelman and Wilmot (1982) define transfer index (TI) as the degree to which the loglikelihood of the transferred model exceeds some base model, relative to the improvement provided by a model developed in the application context. If i denotes the original estimation area, j the application area and the base model is taken as the market shares model (constants only), TI can be defined as

T h i s ferred model is as accurate as the best local model. In Trondheim LL/c) = —3779, and the transfer index for Models 1-3 came out as 0.469, 0.945 and 0.977, respectively. Table 5 summarises the results from running validation tables on the category variables car ownership (three levels), age (four levels) and education (three levels). Mode and car allocation choices were aggregated to 15 alternatives, and the frequency choices consisted of four alternatives. The numbers in the table are counts of the number of cells in the validation tables having differences between predicted and actual choices of 0-1, 12 and 2+ standard errors. In a sense, the more cells that can be assigned to category A rather than B in Table 5, and the more that can be assigned to B rather than C, the better the model (Gunn et al., 1985). The 'score' is an attempt to summarise the results for each model adopted from Gunn and Pol (1986). This summary statistic has no strong interpretation, but it can be compared with more conventional measures based on log-likelihood values. Averaging the scores across all choice situations gives 1,27, 0.62, 0.57 and 0.52 for Models 1-4 respectively. Thus, based on these average values, Model 2 obtained 87 percent and

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469

Table 5 Summary results from validation tables Number of standard deviations A: 0-1

B: 1-2

Mode and car allocation Model 1 47 Model 2 79 Model 3 86 Model 4 91 Trip frequency Model 1 Model 2 Model 3 Model 4

choices 5 23 23 25

choices 34 46 40 43 15 10 12 9

Score

C:2+

(B + 2C)/(A + B + C)

69 25 24 16

1.15 0.64 0.59 0.50

20 7 5 6

1.38 0.60 0.55 0.53

Model 3 obtained 93 percent of the total improvement from Model 1-4. A basic requirement of a model is that it should be able to reproduce actual choices in the application context. Table 6 shows the results of enumerating the models on the Trondheim estimation sample. Clearly, Model 1 is in large error. The total number of trips is in fact

Table 6 Comparisons of model predicted mode shares and trip generation with actual numbers

Car driver Car passenger Public transport Bicycle + walk Total

Model 1

Model 2

Model 3

Model 4

Actual numbers

802.8 (56%) 134.4 (9%) 37.5 (3%) 469.2 (32%)

927.5 (56%) 190.4 (12%) 216.1 (13%) 318.2 (19%)

930.4 (56%) 183.3 (11%) 218.9 (13%) 325.2 (20%)

930.1 (56%) 180.8 (11%) 220.0 (13%) 327.3 (20%)

932 (56%) 181 (11%) 220 (13%) 325 (20%)

1443.9 (100%)

1652.2 (100%)

1657.8 (100%)

1658.2 (100%)

1658 (100%)

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Travel Behaviour Research: Updating the State of Play

underestimated by 13 percent, and the public transport share is far too low and the soft modes share is far too high. Most of the bias is corrected by Model 2, but only Models 3 and 4 are able to produce unbiased estimates of actual numbers. Finally, the models are evaluated by subjecting each of them to the following scenario: Cost, car driver In-vehicle time, public transport Wait time, public transport

+10 NOK —20 percent —50 percent

Figure 3 shows the predicted percentage change in the number of travellers by each mode. Only Model 3 behaved perfectly, i.e. in accordance with the answer book provided by Model 4. In addition to imitating the forecast percentage changes by Model 4 on all modes very well, it also mimicked an overall one percent reduction in the number of trips. Model 2 predicted no change in the number of trips, slightly overstated changes for car passenger and public transport and understated changes for car driver and

Figure 3 Predicted changes in the number of trips by different modes

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471

the soft modes. The errors were much larger for Model 1, especially for the public transport alternative.

Conclusions In this chapter, we described the main elements of an investigation of the transfer of a household based model structure from the relatively large Stockholm conurbation in Sweden to the much smaller city of Trondheim in Norway. The model considered mode, car allocation and trip frequency choices for work travel as a joint household decision. The results reported in this chapter are substantially better than the other transferability results obtained in the project. Those other results concerned much simpler individual based choice models. The results therefore give support to the hypothesis that complex specifications give better predictions in transfer than models with simpler specifications. Despite contextual differences, a model with just a recalibration of the constant terms on the mode choice level provided 90 percent of the improvement in fit between a naive transfer and the best local model. A model in which all parameters were recalibrated on local data behaved in almost complete accordance with the best local model in all validation tests.

References Algers, S., Daly, A. and Widlert, S. (1991) Modelling traveller behaviour to support policy making in Stockholm. In P. Stopher and M. LeeGosselin (eds.), Understanding Travel Behaviour in an Era of Change, Elsevier Science, Oxford. Atherton, T.J. and Ben-Akiva, M. (1976) Transferability and updating of disaggregate travel demand models. Transportation Research Record 610, 12-18. Gunn, H.F., Ben-Akiva, M. and Bradley, M.A. (1985) Tests of the scaling approach to transferring disaggregate travel demand models. Transportation Research Record 1037, 21-30. Gunn, H.F. and Pol, H. (1986) Model transferability: the potential for increasing cost effectiveness. In A. Ruhl (ed.), Behavioural Research for Transport Policy, VNU Science Press, Utrecht.

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Koppelman, F.S. and Wilmot, C.G. (1982) Transferability analysis of disaggregate choice models, Transportation Research Record 895, 1824. Ortuzar, J. de D. and Willumsen, L.G. (1990) Modelling Transport. John Wiley & Sons, New York.

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The Dependent Availability Logit Model and its Applications Wafaa Saleh and Michael G.H. Bell

Abstract Often discrete choice situations arise where the choice set is determined by the price of the options and the budgets of the decision makers. In this case, the availability of one option implies the availability of all the cheaper options, or conversely the nonavailability of one option implies the nonavailability of all the more expensive options, thereby introducing a dependency into availability in the choice set. This chapter proposes a model, referred to as the Dependent Availability Logit (DAL) model, where availability and choice is modelled jointly under the assumption of dependent availability. The Davidon-Fletcher-Powell quasiNewton method is used to fit the model, yielding maximum likelihood estimates and their standard errors. For illustrative purposes, the model is applied to a data set for the choice of mode of travel on an inter-city corridor in Egypt.

Introduction Recent years have seen significant advances in issues related to random utility models, discrete choice analysis and related statistical methods. In particular, choice models have been used extensively in social science and market research. Much of the modern choice theory stems from the assumption of utility maximisation, namely that the individual, when confronted with a specific choice set, chooses the alternative which maximises his utility. Utility is composed of two parts, a systematic part which accounts for the observed factors, and a random part, which accounts for the unob-

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served factors. The most widely used random utility model is the Multinomial Logit (MNL) model:

(1)

where P, is the probability of a randomly selected individual choosing alternative i from a choice set C, and v, is a function of the attributes defining the systematic component of the utility function of alternative i. The attributes may relate to the consumer as well as the options. The choice set is the set of alternatives available to the individual. The identification of the choice set relevant to and perceived by a particular individual in a particular situation is an important problem. Generally in discrete choice analysis, it is required that the choice set is given. A basic assumption behind the theoretical development and practical application of these models is that the analyst is able to correctly specify the set from which an individual decision maker chooses a given alternative. Some early studies considered that all the individuals choose from the same choice set (see Domencich and McFadden, 1975). An extension to the standard discrete choice analysis relaxes the assumption that the analyst knows the decision maker's true choice set. Analysts have sought to avoid mis-specification by allowing the choice set available to be limited by resource constraints (e.g. budget or time constraints), or physical availability (e.g. unavailability of a car). Rules have been proposed to reduce the choice set. For example, no transit line would be available if the access walking distance exceeds some specific distance. When the choice set is mis-specified, it will cause biases in estimated model parameters. Stopher (1980), Williams and Ortuzar (1982) and Swait and Ben Akiva (1986), are examples of studies which show numerically and empirically the effect of the choice set mis-specification. According to Stopher (1980), individuals who are captive to their alternative, but considered to have more than one alternative in their choice set, cause the estimated coefficients of the attributes (both alternative- and consumerrelated) to be smaller and less significant than in the true model (the model estimated on data excluding the captives). Furthermore, the modespecific constants were larger and more significant than in the true model. Williams and Ortuzar (1982) investigated the impact of the assumption that the individual has all the alternatives available in the choice set when,

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in reality, the process follows a probability law. Swait and Ben Akiva (1986) address the impact of ignoring, or mis-specifying, the effect of captivity on the predicted user responses to transport supply changes. In prediction, the larger the size of the alternative-specific constant and the smaller the size of the other coefficients (relative to each others), the less the predictive capability of the model. This chapter considers the mis-specification of the choice set, and presents a new approach which is computationally convenient and practically acceptable in certain circumstances. It assumes that availability of an alternative is constrained by some form of budget, such that individuals with the largest budgets have all options available, and options are progressively eliminated as the budget is decreased. When the budget itself is unknown, but can be related to some other known factor, this leads to the Dependent Availability Logit (DAL) model.

Choice Set Generation Manski (1977) formulated an axiomatic view of the choice process in terms of conditional probabilities. For every element ; of a finite set of alternatives (A),

where C is a choice set, and 7} is the set of choice sets containing alternative /. This decomposition can be used to formulate models which explicitly consider all the forms of full and partial captivity. Assuming that an individual chooses alternative ;', then the number of feasible choice sets containing that specific alternative is given as,

where T has 2(y~1) elements and A defines the full choice set with all alternatives, 1, . . . , / . If 7} is very large, consideration of all the available choice sets is computationally difficult. Usually, the transport analyst has to restrict the number of choice sets considered in any specific context. We can identify two main approaches.

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Simple captivity One possible way of dealing with the problem is to consider that the individual is either captive to his chosen mode or may choose from the whole set. The probability of being captive to i can be represented by,

where 0, 2* 0 is a parameter for alternative i, and 6 = S0,. This approach has been used by Gaudry and Dagenais (1979) to develop the Dogit model. The estimation of the parameters of the Dogit model is simpler than for the Multinomial Probit model, according to Gaudry and Gagenais (1979). The Dogit model has been applied empirically a few times. Gaundry and Wills (1978) calibrated the parameters of two different models; the first was a time-series urban transit mode of payment model, and the second an inter-city mode choice model. Swait and Ben-Akiva (1987a) used the Dogit model with disaggregate work mode choice data for the Brazilian city of Maceio. In their work, they followed Ben-Akiva (1977) by expressing the "captivity odds" parameters 0, as functions of independent variables where

where dT = (dt,. . . , dk, • . . , dK) is a vector of parameters, and xf is a vector of attributes of alternative /. This leads to what they called the Parametrised Logit Captivity model, which tries to add more flexibility by representing the constraints on the availability of the alternatives. However, their work was based mainly on the assumption that the traveller is either captive to his chosen mode of travel, or has the full choice set.

Independent availability logit model Swait and Ben-Akiva (1987b) propose a behavioural interpretation of the choice set generation process, based on the assumption that the availability of any specific alternative in the choice set is independent of the availability

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of any other alternative. The probability that the choice set is ct is given by

where 8kt= 1, if mode k is contained in choice set 1 and zero otherwise. The independent availability assumptions, although providing a plausible specification of the choice set generation for some situations, does make a strong assumption of independence regarding the availability of the alternatives. Saleh and Bell (1992) and Saleh (1993) proposed the DAL model, endowed with a hierarchical configuration of choice sets defined by budget constraints. The availability of one option is dependent on the availability of the cheaper options. The concept is applicable in many cases, both in the developed and developing world. Data from a survey for inter-city work trips in Egypt have been used to demonstrate the potential of the concept. In the analysis, the individuals were assigned manually to four choice sets according to their occupations, which is interpreted to be a proxy for their wealth. The estimation of the coefficients of the DAL model was performed using the ALOGIT package (see Daly, 1992). A limitation with the manual assignment is, that while occupations may be ranked reasonably reliable, the thresholds leading to the allocation of occupations to choice sets are not generally known. In this chapter, an extension to the DAL model is made by assuming a probability for the availability of the marginal option in each choice set. The Davidon-Fletcher-Powell (DFP) method is used to compute maximum likelihood parameter estimates and their standard errors.

The DAL Model There are many choice situations in which availability of one alternative is related to the availability of another. As an example, consider four models of car, A, B, C and D, with prices in a descending order. If an individual can afford to buy car A (the most expensive), it means his choice set includes all four alternatives; he chooses one (not necessarily the most expensive) according to his preferences. The unavailability of one model due to its price would exclude all the more expensive models from his choice set. There are many examples of this type, particularly

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relating to relatively expensive purchases. Inter-city mode choice in developing countries is just such an example. Let us assume that the traveller chooses from a choice set bounded by his budget, which could be time, money, effort, etc. Let us define Ci,. . . , Cj such that ck is a choice set which has k alternatives. The options are ranked with option 1 being the "cheapest" option, available to all, and option / being the "most expensive", available only to some. Define:

where af — 1 implies option i is available. Now define the probability of availability of any alternative i for an individual n as a function of the income of that individual, zn- In this case:

otherwise where a/ (i = 2 , . . . , / ) are coefficients to be estimated. Coefficient a, 5= 0 defines the probability that option / + 1 is available given that option i is available. The exponential function is used for convenience. We depart from equation (8) by assuming that eVfn is proportional to the probability that person n chooses i, given that i is available. The more conventional assumption, that eVfn is proportional to the probability that person n chooses /, given that i is in the given choice set, leads to intractable mathematics. In our case

which is a nonlinear function of the attributes of the modes as well as the attributes of individuals (income in this case). The main assumption of the DAL model is that the availability of any alternative in the choice set is determined by some budget constraint. Decision makers with the largest budgets have all options available to them and their number in the choice set decreases as the budget decreases. It is assumed that the probability of availability is related to some measurable quantity, like income.

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Applications of the DAL Model The Egyptian data Data were collected for inter-city work trips on an Egyptian corridor (Cairo-Alexandria) from December 1990 to January 1991. Only public transport modes have been considered in the survey. This is because, in Egypt, the private car represents a very low share of work trips, especially long journeys. Saleh (1993) provides a description of inter-city travel in Egypt, and Saleh and Crouch (1991) a description of the survey. The four modes of inter-city travel from Ahmed Helmi terminal are in a descending order according to their fare:

1. 2. 3. 4.

First class train, airconditioned (train 1); Inter-city shared taxi (taxi); Inter-city bus (bus); and Normal class train, not airconditioned (train 2).

The travellers were interviewed using a laptop computer on board the three modes (i.e. after the choice of the mode of travel). The private car was excluded from the survey.

Definition of income bands As discussed earlier, the formation of the choice set in the DAL model is determined by the price of the options and the budgets of the decision makers. The fare structure suggests a dependent pattern of availability. In this case, the normal class train (the cheapest mode) is assumed to be available to everyone. The higher the fare of the next mode in the hierarchy (bus) deletes this option from the choice set of those of lowest income. However, no data about income was collected in the survey. Occupation is used as an indirect measure of income. Thus, the respondents from the survey were clustered into four income-related groups on the basis of their stated occupations, as shown in Table 1.

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Travel Behaviour Research: Updating the State of Play Table 1 Income groups with respect to occupation

Income group

Occupation

1

Student Employee I Military Employee II Teacher Managers and higher government officials Labour Scientific and higher technical Private business

2 3

4

Choice sets and median incomes Table 2, shows a segmentation of the data according to income (or occupation), where the relationship between the number of users on each mode of travel are compared for each income group. In Table 2 modes are arranged according to the fare level; train 2 (not airconditioned) being the cheapest and train 1 (airconditioned) the most expensive; income groups are labelled so that group 1 is the poorest and group 4 the richest. From the figures, it appears that the median income for train 2 travellers is in the first income band; the median for the bus

Table 2 The relationship between patronage and occupation group (% in brackets) Income Group

1

Mode Train 2 Bus Taxi Train 1 Total

35 43 36 15

(27.1) (33.3) (27.9) (11.6)

129 (100)

2 22 27 19 9

(28.6) (35.0) (24.7) (11.7)

77 (100)

3

4

2 (7.7) 4 (15.4) 9 (34.6) 11 (42.3)

7 (9.3) 25 (33.3) 13 (17.4) 30 (40.0)

26 (100)

75 (100)

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lies at the first quarter of the second income band; the median for the taxi lies at the first eighth of the second income band, and the median for train 1 lies about three quarters into the third income band. Hence, if the modes were ranked by the travellers' median income, the ranking would be broadly the same as that for fare level, although one may wish to exchange bus and train.

Estimation Results The DFP method was used to search for a vector of parameters which maximise the likelihood function. The log-likelihood function for this multinomial choice model is,

Assume that the explained part of the utility function Vin is a function of m explanatory variables.

From equation (9), the first derivative of the probability with respect to |6W is,

or, in a compact form,

The derivatives of the log-likelihood function with respect to fim is then,

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which simplifies to

Similarly,

otherwise which leads to

or, in a more compact form,

The DFP algorithm requires the gradients of the log-likelihood function. In the case of the Egyptian data, there are three parameters; time, fare and waiting time, so m = 3. No mode specific constant is considered. In Table 3, the parameter estimates of the MNL model are given, assuming all modes are available to all individuals. The estimates of the coefficients, the respective standard errors (in parentheses), the log-likelihood, p2 index and the number of observations are given. It should be noted here that the sign of the time coefficient is positive due to trip-length distributions as there was different journey lengths considered in the survey. Table 4 presents the parameter estimates for the DAL model with four income groups (zn = 1, 2, 3 or 4). Table 4 shows that only for train 1 (the most expensive mode), the coefficient is statistically significant (t = 3.5640). That is, the availability

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Table 3 MNL coefficients for Egyptian data Variable

Coefficient (standard error)

Travel time Travel fare Waiting time Sample size (N)

0.0083 (0.0016) -0.1864 (0.357) -0.0117 (0.0044) 308 0.04547

Table 4 Estimation of the DAL coefficients Variable/Mode

Coefficient (standard error)

Travel time Travel fare Waiting time «! (bus) «2 (taxi) «3 (train 1) Sample size (N)

0.0076 (0.00215) -0.1728 (0.0344) -0.0148 (0.0045) 18.1314(2018.4381) 25.9664 (2926.6890) 0.7103 (0.1993) 308 0.8137

of the airconditioned train is constrained by the income of the travellers. The probability of train 1 being available to income group 4 travellers (za = 4) is 0.94, while for income group 1 travellers (za = 1) it is only 0.5. The other three modes appear to be available to all income groups.

Conclusion The chapter considers the mis-specification of the choice set and presents the DAL model. In the model, the choice set of an individual need not include all the available alternatives. Instead, the probability of availability

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of any alternative in the choice set is assumed to be determined according to some constraints. In maximising the log-likelihood function, the DFP method is used. The convexity of the proposed log-likelihood function has not been proven. However, in all cases studied, the DFP algorithm converged satisfactorily. The concept of the DAL model is applicable in many cases where it is believed that there is a relationship between the availability of different alternatives in the choice set. Results obtained from applying the DAL model to survey data of work trips in Egypt on the Cairo-Alexandria corridor are presented, which illustrates the potential of the DAL model.

Acknowledgements This research is funded by the ODA, to which the authors would like to express their thanks.

References Ben-Akiva, M. (1977) Choice models with simple choice set generating processes. Working Paper, Centre for Transportation Studies, MIT. Daly, A.J. (1992) ALOGIT 3.2 User's Guide. Hague Consulting Group, The Hague. Domencich, T. and McFadden, D. (1975) Urban Travel Demand: A Behavioural Analysis. North Holland, Amsterdam. Gaudry, M.J.I, and Dagenais, M. (1979) The Dogit model. Transportation Research 13B, 105-112. Gaudry, M.J.I, and Wills, M.I. (1978) Estimating the functional form of travel demand models. Transportation Research 12, 257-289. Horowitz, J. (1991) Modelling the choice of choice set in discrete-choice random-utility models. Environment and Planning 23A, 1237-1246. Manski, C.F. (1977) The structure of random utility models. Theory and Decisions 8, 229-254. Saleh, W. (1993) The Dependent Availability Logit Model and Its Applications to Inter-City Travel in Egypt. Ph.D. Thesis, Department of Civil Engineering, University of Newcastle-upon-Tyne. Saleh, W. and Crouch, F.O. (1991) Model travel behaviour on inter-city corridors in Egypt. Preprints Sixth International Conference on Travel Behaviour, Quebec, May 1991, Canada.

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Saleh, W. and Bell, M.G.H. (1992) The dependent availability logit model. 6th World Conference on Transport Research, Lyon, July 1992, France. Stopher, P.R. (1980) Captivity and choice in travel behaviour. Transportation Engineering Journal of ASCE 106, 427-435. Swait, J. and Ben-Akiva, M. (1986) Analysis of the effects of captivity on travel time and cost elasticities. In A. Ruhl (ed.), Behavioural Research for Transport Policy. VNU Science Press, Utrecht. Swait, J. and Ben-Akiva, M. (1987a) Empirical test of a constrained choice discrete model: mode choice in Sao Paulo, Brazil. Transportation Research 21B, 103-115. Swait, J. and Ben-Akiva, M. (1987b) Incorporating random constraints in discrete models of choice set generation. Transportation Research 2IB, 91-102. Williams, H.C.W.L. and Ortuzar, J. de D. (1982) Behavioural theories of dispersion and the mis-specification of travel demand models. Transportation Research 16B, 167-219.

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27

The Timing of Change for Automobile Transactions: Competing Risk Multispell Specification David A. Hensher

Abstract With the increasing number of panel datasets available in transport, the opportunity exists for the study of the timeframe a household uses in making transport decisions. Panels collect data at regular intervals, and record information related to occurrences over the period since the last wave. Some panels record the precise time of an event during a panel wave. The opportunity to record event histories complete with identification of the states associated with a phenomenon, such as automobile ownership together with the duration spent in each state, provides powerful data for modelling the "when" component of change through time. The ability to trace the timing of change and to model it, will give transportation planners one missing element of forecasting—the timing of change. This chapter develops a number of competing risk multispell models to obtain insights into the time spent in each of three states of automobile transactions (no change, replace used with used vehicle, and replace used with new vehicle), the factors which affect the probability of leaving a state, staying with a state, the effect of past history on current behaviour, and whether, or not, the population segments into distinct groups with different change probabilities. A dataset of 12 years of annual observations (1974-1985) of a sample of Sydney households is used to illustrate the application of event history models.

Introduction A knowledge of the length of time that a household keeps an automobile, the timing of a change in the fleet, the type of ensuing transaction (e.g. replace a used vehicle with a new vehicle, replace a used vehicle with a

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used vehicle), and the influences on the timeframe and transaction type are important issues in forecasting and, hence, transport planning. They are of interest to many planning agencies. For example, government authorities need to identify the time it takes for a household to dispose of older, less fuel-efficient, vehicles under various pricing and structural contexts, since this lag is important in the development of forecasts of the impact of policies designed to meet emission reduction targets. An understanding of the reasoning behind the turnover, or lack of turnover, of vehicles in households is also important to automobile manufacturers. It provides some guidance on how the demand for new vehicles is changing over time and what the likely influences on the timing and speed of change might be. Scrappage rates of vehicle classes can be developed from this framework. The growing availability of transport panel data has expanded the opportunities to develop models to identify the temporal relationships (i.e. timing and duration), between automobile acquisitions and disposals, and the influences on the timing and duration of automobile ownership. Transport panels typically have a limited life with repeated waves every 6 or 12 months over 4-6 years (see Raimond and Hensher, 1997, for a review; also see Axhausen, 1992; Golob and Golob, 1989; Murakami and Watterson, 1990; Van Wissen and Meurs, 1989). Some panels identify the precise date of key events (e.g. vehicle replacement), enabling the richness of the timing and duration of events to be identified. The Sydney automobile panel offers this richness. In each of the four waves of the Sydney automobile panel (Hensher et al., 1992), spaced 12 months apart, details were sought on the annual profile of the automobile fleet composition and utilisation, and the socioeconomic description of each household member. However, data on a selected set of items were obtained over a longer period using a retrospective recall strategy to identify the initial conditions for the panel. This data is sufficiently rich to allow us to develop a 12-year panel (1974-1985) on a limited number of socioeconomic and automobile variables. The aim of this chapter is to utilise the restricted 12-year panel to investigate alternative ways of modelling the automobile transactions decision from a sample of 200 households in Sydney. Three states or a maximum possible nine changes of state (i.e. transactions or transitions) are investigated. The states are: no change (SI); replace a used vehicle with a used vehicle (S2); and replace a used vehicle with a new vehicle (S3). Other feasible states infrequently observed in the dataset (and excluded herein) are: dispose of a vehicle (S4); acquire a used vehicle (S5);

The Timing of Change for Automobile Transactions 489 and acquire a new vehicle (S6). The modelling of movement from multiple origin states to multiple destination states, and the desire to preserve the distinction between the OD transitions, as well as permitting repeated presence in each transition type, adds considerable complexity, although significant realism over the majority of transportation applications of the tools outlined in this chapter. The chapter is organised as follows. The next section provides an overview of methods suitable for modelling event histories, followed by a discussion of the context in which the models will be implemented. A set of estimated models are then reported and interpreted, followed by a number of main conclusions.

An Event History Approach to Studying the Timing and Duration of Change Introduction

Real choice opportunities and ensuing decisions are inherently dynamic. When we observe a choice there is a history of events that have preceded the current outcome. By deduction, the role of the forces that shaped the timing and duration of an event history are likely to have an important role in the continuing evolution of decision making. If the analyst can "capture" the structure of an event history through some formal quantitative procedures, the ability to predict the timing of future change and, hence, the amount of time spent in a particular event state, is likely to be substantially enhanced. Given the inherent uncertainties in any assessment of future event paths, all outcomes are probabilistic. An event history can be profiled in a timeline as illustrated in Fig. 1, where each Xt represents the point in time that a specific endogenous (e.g. transaction) on exogenous variable changes its state. In principle, the time dimension can be graduated to any level of refinement; in practice, however, the recording of events is often truncated to a number of finite discrete time periods. When the discretisation is sufficiently fine, such that a ratio-scale treatment is feasible in the time dimension, a continuous time specification of an event history model is possible. This is essential if we are to study the duration of events. Event histories can be characterised as a time-sequenced set of events. For each unit of analysis, event histories provide information about the exact duration until a state transition, as well as, the occurrence and

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Figure 1 Timeline for automobile transactions

sequence of events. For example, such data can provide information on the amount of time a household held a particular vehicle, the exact dates of acquisition and disposal, and the nature of the transaction at the time of disposal (e.g. replacement or disposal only). This information can be identified for each vehicle in a given period of time. A duration model in its statistical form is referred to as a hazard function. Formally, the hazard function can be expressed in terms of a cumulative distribution function, F(i), and a corresponding density function, f ( t ) . The cumulative distribution is written as,

where Prob denotes the probability, T is a random continuous time

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variable, and t is some specified time. Equation (1), for example, identifies the probability of replacing a vehicle before some transpired time (assuming no left censoring). The corresponding density function is

and the hazard function is,

where h(t) is the conditional probability that an event will occur between time t and t + dt, given that the event has not occurred up to time t:

Information relating to duration dependence, as derived from the first derivative of the hazard function with respect to time (i.e. its slope), provides insights into the duration process being modelled. Plotting the hazard function against time gives important empirical information for the parameterisation of the baseline hazard (Hensher and Mannering, 1994). The probability of ending a duration, or spell, in a particular state may be dependent on the length of the duration. There may also be important determinants of duration (e.g. socioeconomic characteristics) that should be included in the modelling approach. These covariates are included in hazard-based models using two alternative methods—proportional hazards and accelerated lifetime. Proportional hazards models operate on the assumption that covariates act multiplicatively on some underlying, or baseline, hazard function. The proportionality is due to the decomposition of the hazard rate into one term dependent on time, and another dependent only on the covariates (Prentice and Gloeckler, 1978). To accommodate time-varying covariates, we assume that they are well approximated by their mean over the interval. This gives a clue to the interval size given the particular application (Hensher, 1997). A relatively general form of the hazard is specified as,

where \b(t) is an arbitrary baseline hazard, and exp(z0(f)/3) is the parametric component including time-varying covariates associated with an

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origin state o. A discrete set of time intervals are observed. The conditional probability rule in equation (4) translates into the following function given equation (5):

where y(t] — ln(/J+1 Xb(u)du), and u is any function in terms of time. The model allows for a continuous "failure" time T0, and (right) censoring c0, but with observations taking place only at t0, t = 0, 1, 2, . . . , / — 1, or in the final interval (/, o°) . If the baseline hazard is assumed to be well approximated by its mean over the time interval, it is completely captured by the single term y(t). Left censoring may exist if an event was well underway when the panel commenced. Right censoring exists since the endpoint of the last episode of an individual cannot be observed. We allow for right censoring in model estimation. An alternative approach for incorporating covariates in hazard-based models is the accelerated lifetime model. This model assumes that the covariates rescale time directly (i.e. accelerate time). Assuming that the covariates act in the form exp(/3Z), as was the case for the proportional hazards model, the accelerated lifetime model in terms of hazard functions is given by,

Accelerated lifetime models, along with proportional hazards (PH) models, enjoy widespread use (see Kalbfleisch and Prentice, 1980). The selection of accelerated lifetime, or PH models, is often determined on the basis of distributional assumptions (i.e. the assumed distribution of durations— Weibull, Normal, Gamma, etc.). We concentrate on the PH model for the rest of this chapter.

Competing risks and multispell models The dominating emphasis in empirical analysis of event history data, particularly in transportation, but also in economics (e.g. Lancaster, 1979) and marketing (e.g. DuWors and Haines, 1990), involves the study of a single initial or origin state, a single final or destination state, and a single period of time between successive events, often referred to as a single episode or spell. In the marketing literature it is called a nonrepeated

The Timing of Change for Automobile Transactions 493 event. An example of the singular dimensionality would be studying the time before a traveller switches from a free public route to a tolled private route (Hensher, 1997). Multistate (or competing risks) and multispell situations are common in transportation, but they impose substantial complexity on the estimation of models. The combination of complexity, and the general absence of packaged software for multistate and multispell models, has limited applications, despite the realism. LIMDEP (Econometric Software, 1993), for example, currently handles only a single initial state, a single destination state and a single spell. Hamed and Mannering (1992) and Paselk and Mannering (1992) are two important applications using a single state single spell framework. The application of interest herein, involves three origin states (no change, Ol; replace used with used vehicle, O2; and replace used with new vehicle, O3), and three destination states (the same three states), to give nine possible OD states or transitions. In reality, the only five transitions likely to be observed are O1-D1, O1-D2, O1-D3, O2-D1 and O3-D1. Furthermore, we want to preserve the distinction between each pair of states and allow for repeated transitions from one state to another, or repeated occurrence of events. In the past, many researchers have assumed that a competing risks model with n possible outcomes, had a likelihood function that could be separated into n distinct pieces. Under such an assumption, estimation could proceed by estimating separate hazard models for each of the n outcomes. Gilbert (1992) introduced a competing risks specification and separate estimation for three transitions in a study of automobile ownership duration. Separately estimating competing risks hazards inherently assumes independence among risks. This is frequently done (e.g., Katz, 1986 and Gilbert, 1992), but may not always be appropriate because it ignores potentially important interdependence among risks. Treating competing risks independently is analogous to assuming recursivity in more traditional simultaneous equations problems, which can be solved using three-stage least-squares and similar methods (Hensher and Mannering, 1994). Some researchers also regard the various spells as being analysed as independent events, and apply the methods developed to handle single spells. This is problematic if the populations are heterogeneous, which would result in a mixing that may lead to a time dependency and incorrect inferences. Since transport applications are characterised by high levels of interdependency between variables, the homogeneity assumption is quite improbable. Incorporating observed and unobserved heterogeneity is ne-

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cessary, or at least, should be tested. Segmentation by socioeconomic characteristics is partially useful. It is unable, however, to handle the sources of unobserved heterogeneity (and its probable correlation with duration dependence). The importance of introducing time-varying covariates and unobserved heterogeneity into a PH model is appreciated when it is understood that the PH model, in the presence of time invariant covariates, assumes that the ratio of the hazard for any two sampled members of a population should be constant throughout the observation (i.e. it is independent of time). Accounting for interdependence among competing risks is not an easy task, but was undertaken by Diamond and Hausman (1984), Han and Hausman (1990), Sueyoshi (1992) and Meyer (1986, 1990). Diamond and Hausman (1984) developed a model with strict parametric assumptions on the nature of interdependence. Han and Hausman (1990) extend this work by providing a flexible parametric form of interdependence, but with time constant covariates, and Meyer (1986) and Sueyoshi (1992) extended the Han-Hausman model to the time-varying covariates case. This approach allows one to statistically test whether, or not, the more common assumption of independence among competing risks is valid. Meyer (1986) combined nonparametric distributions for both components of the hazard function. Two important issues in the study of event histories are: (i) ways of capturing the unobserved heterogeneity in the sampled population (not investigated by Gilbert, 1992); and (ii) the dependency of duration and states over time. These important phenomena accommodate elements of the dynamics of event histories which influence the nature of transitions. They can be introduced in single spell single state models, as well as in the more complex multistate multispell models. To introduce these ideas, it is useful to define the information requirements of an event history, and then introduce the essential formulae required to parameterise a competing risks multispell duration model as extensions of equations (5)-(7). Hensher and Mannering (1994) reviewed the broader literature on duration modelling and applications in transportation, but limited the discussion to single state and single spell methods. An event history of a sampled household over some observed time period requires information on: (i) the initial state; (ii) the number of spells in the observation period; (iii) the points in time at which some state transition has occurred or a specific event has taken place; (iv) state occupancies corresponding to the above points in time; (v) an indicator that identifies whether, or not, a particular spell is censored; and (vi) the

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set of covariates, measured at the beginning of each spell. Covariates take on three forms: time invariant (e.g. sex); time dependent (e.g. age); and time varying (e.g. life-cycle stage). If in estimating the hazard rate, one aggregates the unobserved differences across the sampled population, an apparent duration dependency occurs. This is potentially spurious duration dependence. At the level of the hazard rate to be analysed, it is no longer possible to differentiate whether the hazard rate falls with increasing duration for each household, or if this is simply a methodological artefact due to neglected differences between households. While some, hopefully much, of the differences can be accounted for by a set of observed time invariant and/or time-varying covariates, there is likely to remain a potentially significant source of unobserved heterogeneity which needs special treatment. In general, heterogeneity is handled by a mixing distribution over separate (but jointly estimated) hazard functions. A popular way of incorporating heterogeneity is as a random multiplicative factor that shifts the baseline hazard:

where 00 is a random variable associated with initial state o with a distribution defined by the analyst, representing the distribution of the unobserved heterogeneity within the population of sampled households. The random variable must be limited to positive values (given that the hazard rate is not negative). If we set E(6) = 1, then on average one obtains A fe (f). Parametric specifications have been investigated, especially the gamma, normal and logistic mixing distributions. Heckman and Singer (1984) proposed a nonparametric finite mixture model to accommodate the highly sensitive nature of the parameter estimates associated with the covariates to alternative distributional assumptions. A nonparametric specification for the heterogeneity profile (or finite mixture model) is defined by a set of support values (typically up to ten), which are estimated jointly with the probability mass for each point. Unlike the parametric specification of 60, a fraction of the population can have a zero hazard rate. There is considerable debate in the literature as to whether the baseline hazard, or the mixture distribution, should be nonparametric. For example, Trussell and Richards (1985) suggest that a nonparametric baseline and a parametric mixture distribution are equally plausible. This topic is ripe for extensive empirical inquiry. We investigate the implications of parametric and nonparametric specifications of unobserved heterogeneity in

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our empirical application. We impose the assumption that there is no omitted variable bias, due to the correlation of any observed covariates and unobserved heterogeneity. The possibility of dependency could be tested by specifying Q0 as a function of the covariates. This greatly complicates the model, including the possibility of identification problems. The hazard model for a competing risk model can be defined as:

and

where 8odk is the baseline hazard for a multistate model, z0(t0) defines time-varying covariates, z0 defines time-dependent covariates, and fk(t0) is defined by equation (10) as a Box-Cox transformation over time to capture general duration dependence. Setting K = 1 and hence, AI = 0 gives a Weibull distribution; setting K = 1 and AI = 1 gives a Gompertz distribution. Other functional forms are possible. For example, setting K = 2, AI = 1 and A2 = 2 produces a quadratic duration dependence. Lillard (1993) chose a piece-wise linear spline to represent the dependence of hazards on calendar time. cod9 is a weighted unobserved heterogeneity index, where 6 is common across all transitions o to d, and the weight, cod conditions the unobservable scalar to have a differentiating role in different transitions or different spells. Equation (9) is a very general specification of a hazard function allowing for time varying covariates, unobserved heterogeneity and duration dependence. Setting Pod = cod =fk(t) = 0 gives an exponential form for the hazard function. Parametric or nonparametric assumptions can be imposed on 6 as discussed above. Equation (9) is the kernel of the specification of a multistate multispell model with allowance for time-varying covariates, unobserved heterogeneity and duration dependence. The challenge now is to estimate a number of hazard functions under the most interesting alternative specifications. In the context of the household's timing and duration of automobile transactions, four empirical model specifications are investigated:

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Ml Parametric baseline hazard, time-varying covariates, no unobserved heterogeneity, duration dependence. M2 Parametric baseline hazard, time-varying covariates, unobserved heterogeneity, duration dependence. M3 Parametric baseline hazard, no time-varying covariates, no unobserved heterogeneity, duration dependence. M4 Parametric baseline hazard, no time-varying covariates, unobserved heterogeneity, duration dependence. In models M2 and M4, we investigate one parametric distribution—log normal—and a nonparametric finite mixture model for unobserved heterogeneity. Duration dependence is evaluated under Weibull, and Gompertz distributions.

An Empirical Study of Automobile Transactions Data and modelling results A sample of 200 households from the Sydney automobile panel (Hensher et al., 1992) who provided complete information over a 12-year period on a limited number of socioeconomic and vehicle characteristics (Table 1), were used in the empirical application. The data for the years 1981-1984 were obtained from an annual re-interview; the other data (1980-1974) were collected retrospectively at the conclusion of the panel. Given the problems associated with retrospective data, the number of items of data obtained were somewhat limited, but adequate for the current purpose. The sample sizes for each transition are: 1 to 2 = 197; 1 to 3 = 137; 2 to 1 = 212; 3 to 1 - 140; 1 to 1 = 163; 2 to 2 = 23; 3 to 3 = 14; 2 to 3 = 0, and 3 to 2 = 0. This gives 886 spells. The importance of understanding the timing and duration of automobile transactions is well documented (e.g. Kitamura, 1987, 1989; Smith et al., 1991). Despite this recognition, the empirical efforts are few. The only substantive study is by Gilbert (1992), although the interest in automobile transactions modelling is growing. Gilbert treated each transition as independent events and ignored unobserved heterogeneity. The current study is the only known application of competing risk multispell models in transportation, in which the transitions are estimated jointly with allowance for unobserved heterogeneity. The purpose is to identify the influences on the probability that a sampled household will undertake a

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Travel Behaviour Research: Updating the State of Play Table 1 The data set used in model estimation41

No.

Acronym

Definition

1 2 3

END YR STATE

4 5 6 7

HSIZE NHINC LIFA LIFBCD

8

LIFEF

9 10 11 12 13

LIFG LIFH LIFIJ RGHH REGHS

14

REGOT

15

LOCAL

End of case identifier (1,0) Year (74,75,76,. . . , 85) State (1 = no change; 2 = replace used with used vehicle; and 3 = placed used with new vehicle) Household size Number of Income earners in household life-cycle A (1,0) young adults (<35), no children life-cycle BCD (1,0) two heads, children up to 12 years old life-cycle EF (1,0) one or two heads, children over 16 years life-cycle G (1,0) older adults, no children life-cycle H (1,0) retired persons over 65 years old life-cycle IJ (1,0) single head 1 or more vehicles are private registered (1,0) 1 or more vehicles are household business registered (1,0) 1 or more vehicles are other company registered (1,0) Prime county of manufacture (1 = local; 0 = other)

Mean (sd)

2.96 (1.44) 1.67(0.64) 0.053 0.196 0.191 0.228 0.226 0.107 0.705 0.171 0.127 0.491

* 12 years of data for a sample of Sydney (Australia) households, 2,400 lines of data or 200 households.

particular type of transaction over the period 1974-1985, given the observation of one of three states in each time interval. The three states are: no change, replace a used vehicle with a used vehicle; and replace a used vehicle with a new vehicle. Out of 2,400 observations across 200 households and 12 years, we have 2,011 (83.8 percent) states of no change, 235 (9.8 percent) replacements with a used vehicle, and 154 (6.4 percent) replacements with a new vehicle. In this chapter, we limit the empirical assessment to joint estimation of transitions 1 to 2, and 1 to 3. The average duration of the transition from no change to replace with a used vehicle is 3.90 years; the equivalent mean for a replacement with a new vehicle is 4.41 years. There are five time-varying covariates: household size (HSIZE); number of income earners (NHINC); household stage in the life-cycle (LIF); number of vehicles in each registration category (REG); and the prime country of vehicle manufacture (LOCAL). Within the limits of the data, a number of broad issues are worthy of investigation. In particular,

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we want to evaluate the role that, changing household life-cycle and vehicle registration status, plays in the households automobile replacement decision. To what extent are households loyal to the used car market, or are willing to trade up to new vehicles? Automobile manufacturers are particularly interested in this question, as might be proponents of alternative fuelled vehicles in the early formative years. Since it is almost certainly likely that there be some important missing covariates, allowance for unobserved heterogeneity will be important to the results. The set of models estimated under different assumptions on the form of duration dependence, and unobserved heterogeneity for a given set of significant time-varying covariates, are summarised in Table 2. The set of possible model forms is extensive. We have limited Table 2 to a sufficiently broad range of situations to illustrate the diversity of results. The Weibull and Gompertz distributions provide a good array of alternative interpretations of behavioural response over time for duration dependence (see Hensher and Mannering, 1994, for further details). Under a Box-Cox specification of duration dependence (equation 10), we set K equal to 1, and A equal to 0 and 1, respectively for Weibull and Gompertz distributions. The Weibull distribution is a generalised form of the exponential distribution. The Weibull distribution imposes the monotonicity restriction on the hazard. We are able to identify whether loyalty to the used car market is time-dependent, or time-independent. The Gompertz distribution, derived from the extreme-value distribution, is truncated at zero, so that no negative values are possible. Unobserved heterogeneity is evaluated as a parametric log-normal distribution and a nonparametric mixture specification. We have assumed ten intervals on each side of the mean to approximate the log-normal distribution. Since the distribution is asymmetric, the intervals will be of different lengths on each side of the mean. A nonparametric cumulative density function, with three support points on the unit interval, is specified with all of the support points and cumulative probabilities fixed. Allowing free estimation of a range of support points, except the first and last points and the last cumulative probability, gave spurious results. Further investigation is warranted.

Discussion of illustrative results The hazard of replacing a vehicle with a used vehicle (transition 1 to 2), or with a new vehicle (transition 1 to 3), varies quite noticeably between

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Travel Behaviour Research: Updating the State of Play Table 2 Illustrative model results for alternative specifications Variables

DD = Weibull 1 to 2

DD = Weibull 1 to 3

DD = Gompertz 1 to 2

DD = Gompertz 1 to 3

-2.820 (-8.65) 0.314 (9.50) 1.00 -0.105 (-0.72) 0.598 (1.31) 0.083 (0.30) -0.085 (-0.33) 0.095 (0.37) 0.103 (0.36) -0.126 (-0.42) -0.414 (-1.80) -1057.74 -1052.30

-3.424 (-9.71) 0.399 (7.94) 1.00 -0.082 (-0.53) -0.083 (-013) 0.098 (0.35) -0.038 (-1.31) 0.191 (0.67) -0.483 (-1.34) 0.052 (0.16) -0.153 (-0.64)

UH = 0

constant gamma lambda nhinc Ufa lifbcd lifef lifg lifij regot reghs LL(0) LL(C)

-3.139 (-9.33) 1.069 (9.22) 0.00 -0.117 (-0.77) 0.624 (1.46) 0.125 (0.45) -0.045 (-0.17) 0.112 (0.44) 0.101 (0.33) -0.195 (-0.67) -0.392 (-1.7) -1029.30 -1021.46

-4.301 (-10.4) 1.723 (8.2) 0.00 -0.109 (-0.71) -0.021 (-0.04) 0.128 (0.46) -0.373 (-1.3) 0.215 (0.75) -0.497 (-1.37) -0.011 (-0.03) -0.129 (-0.56)

UH = 0

constant gamma lambda LL (0) LL (C)

-3.278 (-18.5) 1.025 (9.49) 0.00 -1069.32 -1030.86

-4.462 (-13.95) -2.963 (19.09) 0.298 (9.54) 1.652 (8.52) 1.00 0.00 -1061.8 -1061.3

-3.582 (-16.04) 0.379 (8.27) 1.00

UH = log- constant normal gamma lambda nhinc lifa lifbcd lifef lifg lifij regot reghs factor loading LL(0) LL(C)

-3.03 (-7.31) 1.112 (8.82) 0.00 -0.127 (-0.81) 0.638 (1.42) 0.156 (0.55) -0.037 (-0.14) 0.128 (0.50) 0.090 (0.29) -0.223 (-075) -0.375 (-1.49) -0.103 (-0.61)

-4.086 (-8.47) 1.947 (8.10) 0.00 -0.150 (-0.85) -0.008 (-0.01) 0.214 (0.70) -0.370 (-1.15) 0.251 (0.82) -0.547 (-1.44) -0.085 (-025) -0.052 (-0.20) -0.341 (-1.24)

-2.878 (-2.46) 0.325 (7.24) 1.00 -0.117 (-0.78) 0.609 (1.32) 0.085 (0.31) -0.094 (-0.36) 0.093 (0.36) 0.122 (0.43) -0.131 (-0.44) -0.427 (-1.78) 0.035 (0.05)

-3.535 (-2.51) 0.403 (5.40) 1.00 -0.085 (-0.53) -0.060 (-0.09) 0.103 (0.36) -0.377 (-1.26) 0.191 (0.65) -0.473 (-1.29) 0.045 (0.13) -0.157 (-0.66) 0.070 (0.09)

-2132.55 -1016.11

-1047.72 -1047.45 -2.806 (-16.3) 0.403 (11.1) 1.00 -0.278 (-3.09) -1060.13 -1046.30

-3.357 (-12.2) 0.649 (10.7) 1.00 -0.785 (-3.91)

UH = lognormal

-3.187 (-10.4) Constant 1.057 (9.36) gamma 0.00 lambda factor loading -0.084 (-0.45) -1218.63 LL (0) -1025.85 LL(C)

-4.293 (-9.4) 1.778 (8.03) 0.00 -0.239 (-0.78)

the transition types and the distributional assumptions on duration dependence and unobserved heterogeneity. Beginning with no unobserved heterogeneity, the shape parameter (gamma) for duration dependence for both distributions is significantly positive in all models across both trans-

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Table 2 (Continued) Variables UH = non- constant parametric gamma lambda nhinc Ufa lifbcd lifef lifg lifij regot reghs factor loading support point LL (0) LL (C)

DD = Weibull 1 to 2

DD = Weibull 1 to 3

DD = Gompertz 1 to 2

DD = Gompertz 1 to 3

-2.594 (-3.34) 1.144 (8.95) 0.00 -0.135 (-083) 0.651 (1.42) 0.183 (0.63) -0.023 (-0.09) 0.139 (0.54) 0.092 (0.29) -0.244 (-0.82) -0.381 (-1.44) -1.053 (-0.79)

-2.484 (-1.84) 2.104 (8.56) 0.00 -0.184 (-1.00) 0.0126 (0.02) 0.310 (0.95) -0.334 (-1.02) 0.293 (0.94) -0.553 (-1.45) -0.146 (-043) -0.033 (-0.12) -4.014 (-1.45)

-1.796 (-3.50) 0.422 (9.61) 1.00 -0.131 (-081) 0.707 (1.52) 0.238 (0.84) -0.017 (-0.06) 0.203 (0.76) 0.095 (0.32) -0.278 (-094) -0.447 (-1.77) -2.152 (-3.17)

-0.180 (-0.27) 0.768 (12.3) 1.00 -0.193 (-0.99) 0.148 (0.24) 0.544 (1.70) -0.200 (-0.65) 0.519 (1.72) -0.459 (-1.22) -0.351 (-1.127) -0.176 (0.67) -7.614 (-6.20)

0.841 (4.58)

0.805 (17.99) -1052.30 -1033.38

0.805 (17.99)

0.841 (4.58) -1021.46 -1020.33

UH = non- Constant -3.276 (-0.00) parametric gamma 1.025 (8.85) 0.00 lambda factor loading -0.002 (-0.00) support point 0.004 (0.01) LL (0) -6724.37 -1030.87 LL(C)

-4.457 1.652 0.00 -0.005 0.004

(-0.016) -1.923 (-5.21) (5.65) 0.402 (10.3) 1.00 (-0.01) -2.187 (-3.17) (0.01) 0.819 (17.4) -1065.36 -1047.64

-0.681 (-1.20) 0.682 (12.5) 1.00 -6.705 (-6.10) 0.819 (17.4)

itions, suggesting that for both distributions, the hazard is an increasing function of time. When we control for unobserved heterogeneity, the shape parameter has a stronger influence on the hazard, increasing the expected time in a state, ceteris paribus. Adding in a set of time-varying covariates to remove the role of life cycle stage, number of income-earning household members, and the registration status of the household vehicles (a proxy for financial obligation in vehicle transactions), has very little impact on the scale (i.e. constant) and shape parameters. The exception appears to be for the model with a Weibull duration dependence and nonparametric unobserved heterogeneity. Here, we find that the scale parameter changes quite substantially for both transitions suggesting some influence of time-varying covariates. However, a closer examination highlights the change in the middle support point, which was statistically significant in the full model and insignificant in the absence of the covariates. The reason for this is unclear. One might postulate that the nonparametric distribution in the presence of the covari-

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ates, is "about right" but completely unsuitable when it has to carry more information. The only three covariates approaching acceptable statistical significance are: REGHS (household has at least one household-business registered vehicle) in transition 1 to 2; LIFBCD (households in life-cycle stage of two heads and children up to 12 years old); and LIFG (households with older adults and no children) in transition 1 to 3 for Gompertz duration dependence, and nonparametric unobserved heterogeneity. The negative sign on REGHS suggests that the hazard of replacement with a used vehicle decreases, ceteris paribus, where households have access to a household-business registered vehicle relative to a privately registered vehicle. The life-cycle effects are both positive, implying that a household in either of these life-cycle stages, ceteris paribus, has a higher hazard of replacement with a new vehicle. A useful way of comparing the alternative specifications is to tabulate the hazard as a function of time. Given the statistical insignificance of the covariates we limit this to the models containing the scale, duration shape and unobserved heterogeneity parameters (Table 3). The predicted hazards in parenthesis relate to parametric unobserved heterogeneity. Table 3 Estimated hazard functions Time (years) 1 2 3 4 5

6 7 8 9 10

DD = Weibull 1 to 2

DD = Weibull 1 to 3

DD = Gompertz 1 to 2

DD = Gompertz 1 to 3

0.038 (0.037) 0.077 (0.076) 0.116 (0.115) 0.156 (0.155) 0.196 (0.195) 0.237 (0.235) 0.277 (0.275) 0.318 (0.315) 0.358 (0.355) 0.399 (0.396)

0.012 (0.009) 0.036 (0.029) 0.071 (0.056) 0.114 (0.090) 0.165 (0.130) 0.223 (0.175) 0.287 (0.226) 0.358 (0.282) 0.435 (0.343) 0.518 (0.408)

0.052 (0.051) 0.070 (0.079) 0.094 (0.102) 0.126 (0.129) 0.170 (0.173) 0.229 (0.230) 0.309 (0.311) 0.416 (0.417) 0.560 (0.558) 0.755 (0.753)

0.028 (0.023) 0.041 (0.039) 0.059 (0.052) 0.087 (0.072) 0.127 (0.113) 0.185 (0.162) 0.270 (0.235) 0.395 (0.346) 0.577 (0.523) 0.843 (0.721)

The Weibull and Gompertz specifications are monotonically increasing in duration, implying that the longer a household goes without exiting a duration, the more likely it is to exit soon. The effect is stronger for transition 1 to 3, than transition 1 to 2. The turnover is greater for used vehicles than new vehicles. For transition 1 to 2, the hazard is higher for the Weibull distribution for 2-6 years with the Gompertz producing a

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greater hazard for 7-10 years. For transition 1 to 3, the Gompetz has the higher hazard up to two years, and after seven years, with the Weibull higher in the middle-time durations. When allowance is made for unobserved heterogeneity, we find some reordering of relativities and some significant adjustments in the hazard for transition 1 to 3. Allowance for unobserved heterogeneity reduces the hazard with the gap increasing as duration increases. The difference for transition 1 to 2 is not noticeable at all. This leads one to conclude that failure to control for unobserved heterogeneity tends to lead to an overestimation of the hazard for transitions involving replacement of a vehicle with a used vehicle, but its has no affect in the new car market.

Conclusions Event history data, embedded in some panel or activity diary datasets in transportation offer an opportunity to investigate the underlying structure of duration that a household is in a particular state, and the timing of a change into another state. The literature on multistate multispell modelling in continuous time offers a future prospect for improving our understanding of "when" changes are likely to occur. The consequences for improved forecasting of change into the future is clear. Existing methods of modelling travel behaviour, including recent dynamic discrete choice models, are limited in the advice they give on the timing of change. Knowing if a change will occur is handicapped if we lack a procedure for identifying when it will occur. There is a lot more research required to increase our empirical knowledge of the implications of alternative assumptions on how duration dependence, unobserved heterogeneity and baseline hazards are specified. The illustrative empirical study highlights the role of these various dimensions in establishing a capability for predicting the timing of change. This chapter is a contribution to this effort in transportation. The greatest challenge, however, will continue to be the establishment of sufficiently rich data sources capable of assisting the transport analyst in the search for improved methods of forecasting the duration and timing of change, and the establishment of efficient software capable of modelling the myriad of competing risks and multiple spell event histories in transportation.

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Acknowledgements The comments, advice and assistance of Juan de Dios Ortuzar, Phillip Colla, Fred Mannering, David Brownstone, Bill Greene and Dan Steinberg are greatly appreciated. This chapter was written while the author was a Visiting Professor at the Institute of Transportation Studies, University of California at Irvine.

References Axhausen, K.W. (1992) British travel behaviour panels. Mimeo, Department of Civil Engineering, Imperial College of Science and Technology. Diamond, P. and Hausman, J. (1984) The retirement and unemployment behaviour of older men. In H. Aaron and G. Burtless (eds.), Retirement and Economic Behaviour, Brookings Institute, Washington, DC. DuWors, R.E. and Haines, G.H. (1990) Event history analysis measures of brand loyalty. Journal of Marketing Research XXVII, 485-493. Econometric Software Inc. (1993) LIMDEP 6.0. Econometric Software, New York and Sydney. Gilbert, C.C.M. (1992) A duration model of automobile ownership. Transportation Research 26B, 97-114. Golob, T.F. and Golob, J.M. (1989) Practical considerations in the development of a transit users panel. International Conference on Dynamic Travel Behaviour Analysis, Kyoto, July 1989, Japan. Hamed, M.M. and Mannering, F.L. (1992) A note on commuters' activity duration and the efficiency of proportional hazards models. Mimeo, Department of Civil Engineering, University of Washington. Han, A. and Hausman, J. (1990) Flexible parametric estimation of duration and competing risk models. Journal of Applied Econometrics 5, 1-28. Hannan, M.T. and Tuma, N.B. (1979) Methods of temporal analysis. Annals of Review of Sociology 5, 303-328. Heckman, J. and Singer, B. (1984) A method for minimising the impact of distributional assumptions in econometric models for duration data. Econometrica 52, 271-320. Hensher, D.A. (1997) The timing of change: discrete and continuous time

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panels in transportation. In T.F. Golob and R. Kitamura (eds.), Panels in Transport Planning, Kluwer Academic Publishers, Amsterdam. Hensher, D.A. and Mannering, F.L. (1994) Hazard-based duration models and their application to transportation analysis. Transport Reviews 14, 63-82. Hensher, D.A., Smith, N.C., Milthorpe, P.M. and Barnard, P.O. (1992) Dimensions of Automobile Demand: A Longitudinal Study of Automobile Ownership and Use. North Holland, Amsterdam. Kalbfleisch, J. and Prentice, R. (1980) The Statistical Analysis of Failure Time Data. John Wiley & Sons, New York. Katz, L. (1986) Layoffs, recall and the duration of unemployment. Working Paper 1825, National Bureau of Economic Research, Cambridge, Mass. Kitamura, R. (1987) A panel analysis of household car ownership and mobility. Journal of Infrastructure Planning and Management of the JSCE 3381IV-7, 13-27. Kitamura, R. (1989) A causal analysis of car ownership and transit use. Transportation 16, 155-173. Lancaster, T. (1979) Econometric methods for the duration of unemployment. Econometrica 47, 939-956. Lillard, L.A. (1993) Simultaneous equations for hazards: marriage duration and fertility timing. Journal of Econometrics 56, 189-217. Meyer, B. (1986) Semi-parametric estimation of hazard models. Mimeo, Northwestern University. Meyer, B. (1990) Unemployment insurance and the distribution of unemployment. Econometrica 58, 757-782. Murakami, E. and Watterson, W.T. (1990) Developing a household travel panel survey for the Puget Sound region. Transportation Research Record 1285, 40-46. Paselk, T.A. and Mannering, F.L. (1992) Use of duration models for predicting vehicular delay at U.S./Canadian border crossings. 71st Annual Transportation Research Board Meeting, Washington DC, January 1992, USA. Prentice, R.L. and Gloeckler, L.A. (1978) Regression analysis of grouped survival data with applications to breast cancer data. Biometrics 34, 5767. Raimond, T. and Hensher, D.A. (1997) Panel surveys and other longitudi-

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nal techniques: an annotated bibliographic review. In T.F. Golob and R. Kitamura (eds.), Panels in Transport Planning, Kluwer Academic Publishers, Amsterdam. Smith, N.C., Hensher, D.A. and Wrigley, N. (1991) Modelling discrete choice outcome sequences with panel data: an application to automobile transactions. International Journal of Transport Economics XVIII, 123150. Sueyoshi, G. (1992) Semi parametric proportional hazards estimation of competing risks models with time-varying covariates. Journal of Econometrics 51, 25-58. Trussell, J. and Richards, T. (1985) Correcting for unobserved heterogeneity in hazard models: an application of the Heckman-Singer model to demographic data. Sociological Methodology 15, 242-276. Van Wissen, L.J.G. and Meurs, H.J. (1989) The Dutch Mobility Panel: experiences and evaluation. Transportation 16, 99-119.

28

Forecasting Car Occupancy: Literature Review and Model Development Gerard de Jong, Andrew Daly, Hugh Gunn and Ursula Blom

Abstract Most conventional models of multimodal travel demand focus on individuals, and on discrete choices which typically include car drivers and passengers along with other modes. As environmental and energy policies, and the wish to reduce investment in infrastructure, all benefit from increasing the relative attractiveness of the car-passenger mode, so has interest grown in promoting the attractiveness of the car-passenger mode, either through formal car pools, or informal arrangements. High-occupancy lanes, car-pool incentives and specially provided car-pool collection points, are only three of the management tools now used to achieve this end. Planning and forecasting the impact of such management tools on total traffic calls for models more sophisticated than those used in most previous studies. This chapter will review research in the Netherlands and elsewhere and describe possible explanatory models and associated forecasting systems. This chapter deals with different segments of the car-passenger market (including individual occasional passengers, group travel by friends, relatives or colleagues and car pools of various sorts). It reviews the issues of both the availability and attractiveness of the car-passenger mode for different segments. Recent work in the Netherlands is put in the context of published material on the subject. The chapter concludes with recommendations for new model forms, to be explored to replace the conventional treatment of the mode in models of mode and destination choice.

Introduction In the official long-term transport policy documents in the Netherlands, car-pooling is regarded as one of the means of controlling and reducing mobility and improving accessibility. The objective stated in this chapter is to raise the mean car-occupancy for home-to-work travel from 1.2 to

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1.6 persons per car. Several policy measures have been suggested to promote car-pooling: • • • • •

Car-pool schemes (area- or employer-based matching programmes). High-occupancy vehicle (HOV) lanes. Parking restrictions, car-pool subsidies and fiscal incentives. Provision of collection points. Publicity campaigns.a

Some of these measures, including the provision of collection points, matching programmes and fiscal incentives, have already been implemented. In 1993, the first European HOV lane (on the A1/A6, running from the Southeast to Amsterdam) was opened. However, after one year it was closed, due to problems of the legal status of a car-pool lane. To predict the impact of the above car-pool promotion measures on traffic—a prerequisite to any assessment of the cost and benefits of such measures—new models will have to be developed. The possibilities of using present model systems, such as the Dutch National Model System (NMS), (see, DVK and HCG, 1992), for predicting car-pooling, are limited. Basically, this is because mode choice in these models includes car drivers and passengers, but excludes information on car pools, also the availability of car-pooling as an option in mode choice is not dealt with explicitly. Nevertheless, such models can provide a very valuable basis for predicting car-pooling, since they can provide inputs at the origindestination level and provide a framework in which the demand for carpooling can be combined with other travel demand and confronted with supply of capacity. This chapter contains the results of a study on the possibilities for developing models that can predict the impact of car-pool policy measures in the Netherlands. The study was commissioned by the Transport Research Centre of the Dutch Ministry of Transport, Public Works and Water Management. The objective of the study was to define model structures which can be used to predict the long-term impact of car-pool policy measures. As discussed above, it is considerably more efficient to start from the existing NMS compared to developing completely new models. Therefore, a

Model structures for the effect of publicity campaigns on car-pooling will not be proposed in this paper. Explicit quantitative modelling of this is notoriously difficult. The models proposed however do assume that people are informed about car-pool options and their attributes, as may be achieved through publicity campaigns.

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the model structures defined in this chapter will be extensions of the NMS (therefore also of the New Regional Models (NRM), which are consistent with the NMS). As regards the impact of the policy measures, the main interest will be in: • the number of poolers, the number of pools and the vehicle occupancy; • the net change in car kilometres (by zone), which influences emissions, and in car kilometres (by link and time of day), which influences congestion; • the use of the other modes, especially public transport. Apart from the influence of policy measures, car-pooling will also be affected by other factors, unrelated to car-pool promotion policy. The envisaged model should be able to predict both the amount of "autonomous" car-pooling and the extra amount which results from the policy measures, as well as the monetary and nonmonetary cost they impose (for evaluation purposes). In the second section, we make some remarks on classifying car-poolers. The third section contains a short literature review of methods and models for forecasting car-pooling. In the fourth section, we sketch the structure of a model to be developed in the Netherlands, emphasising which components can be derived from the literature and which have to be built new. Finally, in the fifth section, we give some conclusions.

Some Remarks on Classifying Car-Poolers In this chapter, following the car-pool definition study by Menting et al. (1991), car-pooling is defined as the regular shared use of a passenger car or minibus. This is a very broad definition. The only restrictions are: • regularity, excluding occasional ride-sharing. We define lift-giving and receiving as the more general terms, which include both car-pooling (regular), and occasional lift-giving/receiving; • type of vehicle, excluding full-size buses and such. In the NMS and the NRM, buses are already dealt with in the public transport mode. A distinction between passenger car and minibus (van)

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is unnecessary, providing the vehicle occupancy is registered. Occasional ride-sharing, though not a part of car-pooling, has to be accounted for in the envisaged model, since this will affect the vehicle occupancy rate. This is necessary for evaluating the impact of HOV lanes and related policy measures. In the above definition, car-pooling includes both alternate driving and riding (the car-pool members pool their cars) and arrangements in which the driver is (nearly) always the same person. The basic distinction within the car mode(s) in a model, which has to predict on a national or regional scale, appears to be the following: A. Car drivers (either driving alone or driving a multiple occupancy car). B. Car passengers who are not car-poolers (occasional lifters). C. Car passengers who are car-pooling, but not as a direct result of policy measures to promote car-pooling (those who would car-pool anyway; the car-poolers of the base scenario, which in this context is the scenario with all dedicated policy measures except the carpool promotion measures listed in the first section). D. Car passengers who are car-pooling as a direct result of policy measures to promote car-pooling. The envisaged model (the NMS extended by new car-pool modules) should be capable of predicting the number of travellers in each of these four categories. It is recommended that not only individual travellers are studied, but also the number of persons per pool or vehicle: • 2-person pools or vehicles; • 3-person pools or vehicles; • 4+ person pools or vehicles. Within all A-D categories, travel purposes need to be distinguished, as already done in the NMS mode/destination choice model. For the C-D categories, home-to-work will probably be the most important purpose by far, followed by business travel. Travel for nonwork purposes is considerably less regular than home-to-work travel, and since car-pooling was defined to be regular car sharing, is less suited for forming car pools. Occasional lift-giving is more likely here. Whether the car pool consists of members of the same, or different households, is not really important at the output level. On the other hand,

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it may be of great importance within the model, since household car-pool formation is behaviourally quite different from car-pooling with colleagues, or forming car pools with complete strangers. Also, it is not so important, as an output, who drives and which vehicle (is it always the same person with the same car, or is there a rotation of drivers and/or cars?) Again this distinction can be important inside the model itself. The NMS predictions refer to an average working day in the long run, as should the outcomes of the car-pool module be developed. The fact that some car pools have different frequencies (e.g. 1-5 times a week) should be taken into account in producing forecasts for the average working day. The car-pool module should also represent the influence of the "survival duration" of the car pools in giving the long-term equilibrium outcome. If possible, car-pool forecasts should distinguish between time-of-day periods (morning peak, evening peak, off-peak), to fit with the NMS timeof-day module, and to give vehicle occupancies for different periods (HOV lanes may have different regulations for different time-of-day periods). Of course, this distinction will correlate with that for trip purpose.

Review of Reported Methods and Models In this section, we review the literature on methods and models which can be used to predict the amount of car-pooling. In her state-of-the-art review, Kostyniuk (1982) used three categories of models (ride-sharing unit formation models, disaggregate travel choice models and traffic equilibrium models). To some extent we follow this procedure and distinguish between five types of methods/models for car-pooling. 1. Transfer of participation rates; 2. Trip table analysis; 3. Mode choice models; 4. Mode choice models combined with supply models; 5. Car-pool formation models. Each of these types will be discussed separately in the following paragraphs. In the next section, we discuss which elements from the literature can be useful for our purpose and which topics do not yet seem to have been covered in the literature.

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Transfer of participation rates The simplest method to predict the amount of car-pooling in an area, or among the employees of a firm, is the transfer of participation rates based on the car-pooling potential derived from other areas or firms. The impact of similar measures on similar sites is found through before and after studies. The rate of success (per employee or resident) is then transferred to the new site, for which similar measures are under consideration, and multiplied by the number of employees or residents at this new site. The transfer method can only be used for estimating the impact of policy measures which were implemented elsewhere. The most important disadvantage of this method is that the assumption that sites are similar in every relevant respect will almost invariably be invalid. Testing this assumption in practice means building one of the models to be discussed in the following sections.

Trip table analysis The basic idea of a trip table analysis for car-pooling is that necessary conditions for the formation of a car pool are: • trip origins and destination for the potential members which are not too far away from each other (spatial constraint); • trip departure and arrival times for the potential members which are not too far apart (temporal constraint). Kendall (1975) developed a model for estimating the maximum potential for car-pooling from trip tables by making specific assumptions for what "not too far" in the above conditions means. The boundaries for the zones in his trip tables had been established a priori. He set the maximum time interval at 30 min. All workers with common origins and destinations who depart within the same time interval, were counted as potential carpoolers. The resulting car-pooling potential was 60 percent of the hometo-work trips in the morning. This method does not take into account whether, or not, there is (i) any incentive for potential car-poolers to form a car pool; (ii) potential car-poolers can find car-pool mates they would be willing to accept (compatibility); and (iii) a once-formed car pool will survive for any period of time. Therefore, it is not a method for predicting the likely amount of car-pooling, but rather a way to find an upper limit,

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which might be relevant for emergencies, such as a public transport strike, or smog alarm. The trip table method can be extended by expressing the distance in space and time between the potential members' trips in terms of travel costs and time. By using different values-of-time for different trips/groups, costs and time can be made comparable. If the generalised costs of car-pooling are lower than those of driving alone, the trip mode will be car-pooling. The same mechanism can also be expressed in terms of maximum economic circuity (Berry, 1975). Such a model is more appropriate for predicting the likely amount of car-pooling than the above potential models. Nevertheless, it does not address car-pool formation, compatibility of car-poolers and car-pool duration.

Mode choice models Most European mode choice models contain as choice alternatives car driver, car passenger, public transport and, sometimes, slow modes. Then a problem in simulating car-pool policy is that the model cannot tell whether, or not, the car driver is driving alone. In the USA, a number of mode choice models has been developed including car-pooling. One of these is the model developed by Cambridge Systematics, Inc (CSI) for the US Federal Energy Administration and the Department of Transportation (CSI, 1976, 1978). Apart from submodels for car ownership, trip generation and nonwork mode-destination choice, the models contain a mode choice model for home-to-work travel with the following alternatives: • drive alone; • car pool; • public transport; with another submodel for the size of the car pool. All submodels are disaggregate logit models, except for the car-pool size model, which is a linear regression model. Following this CSI model, several mode choice models, with car-pooling as one of the alternatives, were developed in the USA. In most cases, they were estimated on household surveys containing actual choices. But it is also possible to derive some, or all, the parameters of a mode choice model from Stated Preference (SP) data. This is especially relevant for investigating the demand for forms of car-pooling which presently do not exist. The Shirley Highway model (COMSIS, 1989) was estimated on obser-

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ved choice data for the Shirley Highway Corridor, which includes operating HOV lanes. Between the suburbs in Virginia and downtown Washington, DC, the Shirley Highway contains a 2-lane reversible roadway with preferential treatment for HOVs (at the time: 4+ occupant vehicles for use in the peak periods). The dataset consists of 2,225 morning peak work trips entering Washington for 1984. For the level-of-service variables networks were used. Several logit mode/occupancy models were estimated using the following choice set: • • • • •

car-driver (alone); 2-occupant car; 3-occupant car; 4+ occupant car; public transport.

The observed choices were found to be best explained by a logit model with a car pool and car nest: • car • public transport

drive alone carpool

2-occupant car 3-occupant car 4+ occupant car

In this model, the highest propensity to shift to 4+ occupant car can be found among 3-occupant car travellers. In the multinomial logit model, the HOV facility draws from the other modes in proportion to the mode shares of all other alternatives (this is a manifestation of the IIA property). Mode choice models with car-pool alternatives for the Netherlands are reported in Daly et al. (1990). They estimated several mode choice models on data for Amsterdam. The "central" specification contained the following choice alternatives: • • • • •

car driver (alone); car-pool driver; car-pool passenger; public transport; slow modes.

This model is somewhat more elaborate than the "European" mode choice model without car-pooling, or the CSI work mode choice model with

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carpooling. If the car driver and the car-pool driver are merged, the "European" mode choice model emerges; if the car-pool driver and passenger become one alternative, the model structure is the same as in the CSI mode choice model (except for the presence of the slow modes). These two hypotheses that alternatives could be merged were tested using the Cramer-Ridder test (Cramer, 1991). The hypotheses that there are four alternatives (merging) were both rejected. Several nested logit models (e.g. car-pool driver together in a nest with car-pool passenger or car-pool passenger together with public transport) were tested against this five-alternative multinomial logit model. None of the nested models performed significantly better than the multinomial model, thus, giving no support to the hypothesis that some of the alternatives made closer substitutes than others. All of the mode choice models discussed so far were logit models (multinomial or nested). Brownstone and Golob (1991) developed a ordered probit model for the choice between: • always a car pool (on the work trip in a two weeks survey); • sometimes a car pool; • always drive alone. The model was estimated on the first wave (n = 2189) of a panel in the greater Los Angeles area. All members are commuters, mostly working full-time. The employment locations are not well served by public transport, so this mode could be excluded from the analysis. An ordered model can only be used if there is some natural way to order the alternatives. In their paper the order is: always a car pool, sometimes a car pool, drive alone. It is not quite clear what the order might be if public transport and slow modes were available. In a later paper (Golob, 1992), the model is extended using two waves from the panel (about 1,500 commuters). The new model is dynamic, with variables in one period affecting variables in the other. Furthermore, indicators of attitudes and perceptions are added to the model explaining mode choice. When compared to the models in the previous sections, the disaggregate models with mode choice provide much richer specifications and can be used to evaluate more policy options. Nevertheless they have two important disadvantages: 1. Car-pool formation and compatibility of members are not explicitly modelled; this means that the car-pool passenger alternative is avail-

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able for all and the car-pool driver for all who have a car available; in practice several constraints exist which may rule out car-pooling, especially the matter of finding suitable car-pool partners. 2. There are no feedbacks in the model; increased car-pooling might reduce congestion on the roads, which may make driving alone more attractive than it originally was.

Mode choice models combined with supply models The second of the two above-mentioned problems can be overcome by embedding the mode choice model in a larger traffic model, which also contains the supply of service. The CSI model discussed in the third section has been used to evaluate HOV lane strategies in traffic corridors. The mode choice model (with car-pooling as an option) is then used as an incremental logit model, which predicts changes from the existing mode split. The traffic volumes from the demand model are confronted with supply and the new travel times are then compared with the initial ones. If necessary, several iterations can be made to reach equilibrium. Similar traffic models, often with a simplified demand structure, have been applied in the USA for studies aimed at assessing the effectiveness of HOV facilities.

Car-pool formation models Bonsall's microsimulation model (Bonsall, 1980, 1982) was designed to predict the performance of organised car-sharing schemes. When the investigation started, these schemes did not exist in the UK, since it was feared that car insurance would be invalidated if any money the driver accepted for the operating cost could be construed as payment for a service. Therefore, the model was based on SP data. From the start, it was recognised that the performance of such a scheme was a function of reconciling individual suppliers (drivers) and consumers (passengers) within a formalised market mechanism (the matching service). Unlike the models of the previous two sections, the compatibility of the car-pool members (in terms of location, journey time and personality) is considered here. The decision makers in the simulation model are individuals from a synthesised population. In the model, their behaviour with regard to a

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defined car-pooling scheme is simulated. Within the model there are three submodels: 1. A submodel for an individual's decision to apply to join a car-pooling scheme. 2. The creation of "match lists" for each applicant (done by some organisation). 3. A submodel for the decision of an applicant whether or not to start a car pool with the proposed partners (those on the match list). The making of the match list is not a choice model; it is a purely mechanical process, which for a real scheme would be the task of some car-pool organisation. The decision to apply and the decision to form a car-pool arrangement are represented by individual choice models. An individual's decision whether, or not, to apply is formalised as a series of seven binomial logit models, one for each type of application: 1. 2. 3. 4. 5. 6. 7.

Alternate driving and riding; Giving lift in the morning and evening; Giving lifts in the morning only; Giving lifts in the evening only; Receiving lifts in the morning and evening; Receiving lifts in the morning only; Receiving lifts in the evening only.

The coefficients in these models were estimated from a SP survey (one of the first in transportation research). Respondents received application forms for a hypothetical car-pooling scheme. Explanatory variables in the application model are home-to-work distance, normal mode, age, car availability, licence holding, professional status, gender, time-of-day and presence of a telephone. For each applicant in the simulation, a match list is created with proposed car-pool members. Each "active" applicant (those who applied to drive) then has to decide whether, or not, to accept this proposal and form a car pool. First, the applicant can reject proposed partners who are unacceptable to him or her (satisficing constraint). After this, the model assumes that the applicant will start car-pooling, if the arrangement has a positive net utility to the applicant and to all the other parties in the arrangement. If several arrangements yield a positive net utility to this active applicant, s/he will choose the one with the highest net utility.

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Thus, for the passive applicants, the arrangement is possibly not the best available. Bonsall (1980, 1982) argues that this, in the short-term at any rate, may not be a problem since he thinks optimality is a very unlikely outcome for this process. The utility functions are linear regression equations with utility influenced by attributes of the applicant and the proposed arrangement, including the fee paid, location, diversion, shifts in departure and arrival time, gender, age and availability of a telephone. The coefficients were again estimated from SP information: respondents, who had already answered that they wished to apply, were asked to put monetary values on arrangements with prespecified attribute values (a socalled "transfer price experiment"). The microsimulation model can be used to predict the number of applicants to and participants in an organised car-pooling scheme, as well as the reduction in private vehicle and public transport passenger kilometres. In Bonsall (1982), such predictions are compared with observed outcomes for a car-pooling scheme in Yorkshire. The predictions turned out to be remarkably accurate. Furthermore, most of the prediction errors which were found, were due to inadequacies in the calibration data, and not to errors in the models. The author remarked that he believed that errors in the decision submodels were kept in check by the realistic constraints imposed by the rigid structure of the model. At the time, Bonsall's model was quite novel in a number of respects: use of SP data, use of a synthesised population base and modelling of the probability of application and acceptance of an arrangement. As far as we are aware, Bonsall's microsimulation is still the only model in which the formation of a car pool is dealt with (except for the models that will be described below). It does not predict whether, or not, the car pool will survive and, if so, for how long after it has been established. Furthermore it is especially designed to predict the impact of organised car-pooling. It does not tell us how many car pools are formed without the use of an organised matching system, although it might be extended or modified to do so.

Sketch of an Envisaged Model for the Netherlands Structure of the model The first two methods, described in the previous section, can only be used to give a first impression on the likely amount of car-pooling in some region or firm. Disaggregate mode choice models with one, or more, car-

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pool alternatives can handle many more variables, through which reasons for car-pooling and several policy instruments can be included. Such models can be made part of a larger traffic model, including assignment to the road network, so that changes in congestion, as a result of changes in car-pooling intensity, can be fed back into mode choice until equilibrium is reached. This mechanism has already been developed in the NMS. We believe this approach is not sufficient for forecasting the impact of car-pool promotion measures on home-to-work travel. Both the mode choice submodels in the NMS, and mode choice models with car-pool alternatives in the literature do not make clear whether, or not, carpooling is an available option for an individual traveller. Therefore, we propose that new car-pool formation models—which also deal with carpool survival—be developed for home-to-work travel and added to the NMS. The existing NMS submodels for licence holding, car ownership and tour frequency need to be changed. In the envisaged simulation system, these variables will not be affected by car-pool promotion measures (car availability on the other hand can be affected). The potential market for car-pooling can come from the NMS mode-destination models. After application of the car-pool formation and duration models to this market size, the predicted number of car-poolers for home-to-work can be fed back into the NMS and further processed, including assignment. For the non-car-poolers in home-to-work travel, a more conventional mode choice model will be used, but with an added distinction between "drive-alone" and "driver giving an occasional lift". For the other travel purposes we do not propose such a car-pool availability model because: • car-pooling, defined as regular shared car use, will occur most frequently in home-to-work travel, while most policy measures also focus on this particular purpose; • for the other purposes the availability and acceptability of a car pool is less of a problem (colleagues travelling to a meeting, friends or household members making the same journey regularly for a social or recreational purpose). For the non-home-to-work purposes, we propose to develop a mode choice model containing the following modes: • car driver driving alone; • car drivers giving an occasional or regular lift; • occasional or regular car passengers;

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• public transport; • slow modes. These alternatives could be further subdivided by distinguishing members of the same household from nonmembers, or by defining car pools of various sizes. A special car-pool size submodel can be added. It does not seem possible, or particularly useful, to distinguish between car-poolers and occasional lifters within the other purposes. In, for instance, an HOV lane, both groups are treated the same way. Mode choice will be combined with destination choice (which can also be affected by some car-pool measures, such as car-pool lanes and parking policy). After assignment, new travel times can be derived, which would be inserted back into timeof-day and mode-destination choice and car-pool availability.

Building blocks for the model In this section, we discuss for which elements of the envisaged simulation model the existing literature on car-pool models provides valuable clues, and for which elements we have to build new models, possibly by using material from other fields. As discussed earlier we intend to use the NMS, both for identifying markets for car-pooling and for providing means for including the feedback effects of limited road capacity. Other conclusions derived by comparing the literature with the needs according to the structure sketched above are: • For the submodel for car-pool formation in home-to-work travel (insofar as it concerns organised pools), we can follow the work of Bonsall. This submodel could explain application, matching and acceptability. • For the mode choice models, extended to include car-pool alternatives (both for home-to work and other purposes), we can exploit models like those of CSI, COMSIS and Daly et al. (1990). • The following "holes" in the literature were found: - In Bonsall's acceptability model the decision making involved several persons. Bonsall chose a workable solution, but this and several other solutions might be investigated by using game theory (e.g. Friedman, 1990; Roth and Oliveira-Sotomayor, 1990). - Bonsall's model only deals with organised car-pool schemes. In practice, most car-poolers found each other without the help of an organisation, and often they are not members of the same

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household. Therefore, we need a model for "private" car-pooling. For this we might follow the economic theory of search, especially labour market search theory (e.g. Lippman and McCall, 1976). - We need to predict the long-term impact of car-pooling. The car pools which result from the car-pool formation models may not last very long. A once-formed car pool may break up, while new car pools will be formed over time. Car-pool formation and dissolution have to be placed in an explicit time framework. For this we can make use of either system dynamics (e.g. Meadows et al., 1992) or microeconometric duration models (e.g. Lancaster, 1990), or both. The suggestions for searching for analogies and applications in game theory, search theory, system dynamics and duration models are elaborated on in HCG (1993).

New Developments As a first step towards the envisaged car-pool model for the Netherlands, a system dynamics model for car-pooling by commuters was developed (de Jong et al., 1995). It contains six levels: 1. 2. 3. 4. 5. 6.

Number Number Number Number Number Number

of of of of of of

commuters commuters commuters commuters commuters commuters

driving alone. in 2-person car pools. in 3-person car pools. in 4-person car pools. in public transport. using slow modes.

The model also contains equations for the car-pool formation rate (which depends on the difference between the actual car-pool share and the desired share based on the relative utility of car-pooling), and the stop rate (which depends on the car-pool duration), and a number of feedback effects. The model parameters are based on the estimation of logit models, mean values in the sample survey of commuters and the outcomes of initial simulation runs. Another step for commuters only, was the development of a disaggregate car-pool model based on search theory and duration analysis. The model structure follows the labour market search model of Flinn and Heckman (1982). In this model, an individual will accept an encountered

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car-pool match if the expected utility from this match (taking account of the possibility of termination) exceeds the expected utility from continuing to search (which implies search cost). This model gives a steady-state equilibrium for the number of car-poolers cpe:

where TT\ : hazard of the non-car-pool duration model (which explains how long it takes before someone starts car-pooling; the hazard gives the exit probability from the non-car-pool state); 7T2: hazard of the car-pool duration model (which explains how long a car-pool survives; the hazard gives the exit probability from the car-pool state); and N: total number of carpoolers and non-car-poolers in the sample. The two hazards were estimated as functions of exogenous personal and level-of-service attributes, using a sample of 2,000 Dutch commuters (de Jonget al., 1995). Simulations with the estimated model gave plausible policy effects (impact of car cost, car-pool travel time, travel time in public transport, etc.), but for the base case, the model predicted a decline in the share of carpoolers in the sample from 15-5 percent, which seems unrealistic. Since we expected that the reason for this large decrease in the carpool share was to be found in the non-car-pool duration model, different reformulations for this submodel were tried. A particular useful reformulation in this respect turned out to be the split population duration model. In the standard duration model for non-car-pooling, it is assumed that eventually every person will start car-pooling. Of course, this is not what is in the dataset, and in estimation of the standard duration model on real-world data, the model coefficients will imply very long durations until car-pooling and very small hazards. In the split population duration model (originally developed by Schmidt and Witte, 1989 to explain recidivism), some fraction of the population will never car-pool. This fraction is determined in a probit model, which is added to the model for the noncar-pool duration. In estimation of the model (on the same dataset of Dutch commuters as the other models in this section), this fraction turns out to be quite large (78 percent). But for the remaining 22 percent potential carpoolers, the hazards for the transfer to car-pooling are much larger than in the standard duration model. The full search/duration model now consists of hazard functions for car-pooling and non-car-pooling and a probit model for the fraction that will never car-pool. Several simulation methods have been tried with this set of functions

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(HCG, 1996). One method predicts an equilibrium that is reached in one year and gives an increase in the number of car-poolers of 1.5 percent. Unfortunately, this equilibrium is unstable and the method contains an inconsistency. Another method predicts a decline in the number of carpoolers of 26 percent, but on an unrealistic timescale of 10 years. Consequently, the car-pool models are still discussed and improvements necessary. The most effective methods to promote car-pooling, according to the different implementations of the model, are raising the cost of driving alone and employer subsidies for car-poolers. Increases in the travel time for driving alone and decreasing the time and cost for car-poolers also lead to a larger car-pool share.

Conclusions A number of elements which are needed to build a model which can predict the number of car-poolers in the Netherlands, in the medium to long run, can be derived from the existing literature on car-pool models. Disaggregate mode choice models, extended to include car-pool alternatives, can be used here. Feedback effects on mode choice, working through travel times in congested networks, can be represented by embedding the mode choice models in a demand-supply traffic model, such as the NMS. The major handicap of mode choice models for simulating the demand for car-pooling is that they do not properly take account of the availability of car-pooling as a choice alternative. Travellers may prefer car-pooling but may be unable to find car-pool partners (yet). This issue is especially important for home-to-work travel. We propose to develop microsimulation models for the formation and duration of commuter car pools—both for organised and spontaneous car-pooling. These models can be based on the car-pool simulation models Bonsall developed in the UK, with extensions using concepts in game and search theory, and duration modelling. As a first step towards a car-pool formation/dissolution model, a system dynamics model and search/duration model have been developed.

Acknowledgement The authors wish to thank Frank Hofman of the Transport Research Centre and three anonymous referees for their valuable comments. The

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study was financially supported by the Directie Individueel Personenvervoer of the Directoraat-Generaal voor het Vervoer.

References Berry, W.L. (1975) On Economic Incentives for Commuter Car-Pooling. Ph.D. Thesis, Graduate School of Business Administration, Harvard University. Bonsall, P. (1980) Micro-simulation of organised car sharing: description of models and calibration. TRRL Supplementary Report 564, Transport and Road Research Laboratory, Crowthorne. Bonsall, P. (1982) Micro-simulation: its application to car sharing. Transportation Research 16A, 421-429. Brownstone, D. and Golob, T.F. (1991) The effectiveness of ride-sharing incentives: discrete-choice models of commuting in Southern California. ITS Working Paper 90-7, Institute of Transportation Studies, University of California at Irvine. Cambridge Systematics, Inc. and Alan M. Voorhees and Associates (1976) Car-pool Incentives: Analysis of Transportation and Energy Impacts. Report FEA/d-76/391, US Federal Energy Administration, Washington, DC. Cambridge Systematics, Inc (1978) Analytic Procedures for Estimating Changes in Transit Demand and Fuel Consumption. Final Report to the US Department of Energy, Washington, DC. COMSIS Corporation (1989) Models of Mode and Occupancy-Choice in the Shirley Highway Corridor. Final Report to the Federal Highway Administration, Washington, DC. Cramer, J.S. (1991) Pooling states in the multinomial logit model. Journal of Econometrics 47, 267-272. Daly, A.J., de Jong, G.C. and Brohm, G. (1990) Vervoerwijzekeuzemodellen met car-pooling. In J.M. Jager (ed.), Colloquium Vervoersplanologisch Speurwerk-1990; Meten-Modelleren-Monitoren, Nieuwe Ontwikkelingen in Onderzoeksmethoden. CVS, Delft. DVK and HCG (1992) The Netherlands National Model 1990. Dienst Verkeerskunde and Hague Consulting Group, Rotterdam. Flinn, C. and Heckman, J. (1982) New methods for analysing structural models of labour force dynamics. Journal of Econometrics 18, 115-168. Friedman, J.W. (1990) Game Theory with Applications to Economics. Oxford University Press, Oxford.

Forecasting Car Occupancy

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Golob, T.F. (1992) Use of a commuter panel to evaluate the effectiveness of incentives to reduce solo driving: results from a study in Southern California. Proceedings 20th PTRC Summer Annual Meeting, University of Manchester Institute of Science and Technology, September 1992, UK. Hague Consulting Group (1993) Predicting the impacts of car-pooling policies: outcomes of a fundamental research project. HCG Report 3291, The Hague. Hague Consulting Group (1996) Een carpoolmodel voor woon-werk verkeer; aanvullende analyse I + II. HCG Reports 6046-1 and 6083-1, The Hague. De Jong, G.C., Bradley, M.A. and Hofman, F. (1995) System dynamics and search/duration models for car-pool formation and dissolution. Proceedings 23rd European Transport Forum, University of Warwick, September 1995, UK. Kendall, D.C. (1975) Car-pooling: Status and Potential. Report DOTTSC-OST-75-23, US Department of Transportation, Washington, DC. Kostyniuk, L. (1982) Demand analysis for ride-sharing: state-of-the-art review. Transportation Research Record 876, 17-26. Lancaster, T. (1990) The Econometric Analysis of Transition Data. Cambridge University Press, Cambridge. Lippman, S.A. and McCall, J.J. (1976) The economics of job search: a survey; Part I: optimal job search policies. Economic Inquiry 14, 155189; Part II: Empirical and policy implications of job search. Economic Inquiry 14, 347-368. Meadows. D.H., Meadows, D.L. and Randers, J. (1992) De Grenzen Voorbij: een Wereld-wijde Catastrofe of een Duurzame Wereld. Spectrum/Aula, Utrecht. Menting, L.J., Rooijers, A.J., van Oord, P. and Kropman, J.A. (1991) Carpoolen: definitiestudie als uitgangspunt voor beleidsontwikkeling en onderzoek. Verkeerskundig Studiecentrum, RUG en Instituut voor Toegepaste Sociale Wetenschappen. Roth, A.E. and Oliveira-Sotomayor, M.A. (1990) Two-Sided Matching: A Study in Game-Theoretic Modelling and Analysis. Econometric Society Monographs 18, Cambridge University Press, Cambridge. Schmidt, P. and Witte, A.D. (1989) Predicting criminal recidivism using 'split population' survival time models. Journal of Econometrics 40, 141-159.

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29

Coordination of Road Pricing Policies in Hong Kong William H.K. Lam and Rui J. Ye

Abstract A coordinated planning of road pricing policies is required, especially in conditions of very constrained resources and rapid expansion of urban areas, such as Hong Kong. In this chapter, an optimisation method is used to enable the coordination of road pricing policies to be planned systematically. The optimisation procedures would identify road usage charges that would minimise total network cost given physical network constraints. The developed model advances this subject and helps the authorities to rapidly, and consistently, evaluate road pricing policy schemes. The Hong Kong 2006 planning data and road network are used for application of the optimisation method.

Introduction Highway planning should point the way for major changes in both road network and pricing policies, and ensure that today's decisions will not prove inconsistent, and irreconcilable, with long-term goals. Hong Kong is expanding rapidly. To accommodate this expansion, approximately three billion dollars have been invested annually for the construction of new highways and transport infrastructure in Hong Kong. There are a large number of potential road projects to chose from, but also practical constraints in terms of financial and construction industry capacities. Therefore, to obtain the maximum benefits from the investment for the region, new transport infrastructure projects must be carefully planned. The conventional approach failed to deal satisfactorily with the impact of road

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Travel Behaviour Research: Updating the State of Play

pricing policies on the investment in highway facilities, as this was normally formulated with a fixed set of road usage charges. The conventional approach to highway planning consists of four steps. First, a number of alternative highway networks and a set of road usage charges are proposed. Second, the land use planning data and the transport model are applied to estimate the traffic demand on each alternative road network. Third, the performance of the alternative highway networks is evaluated against preselected planning goals. Finally, the preferred network is analysed and designed in detail. The deficiency of the conventional approach lies in the difficulty of selecting suitable road usage charges for testing. The amount of computational effort involved made it impractical to test a wide range of road usage charges. But if the effects of varied road usage charges are not examined, the real optimal road network could be overlooked. A Land Use Transport Optimisation (LUTO) model was developed (Choi, 1986) to solve the problem of a joint optimisation of land use and transportation development. LUTO has been used for the strategic land use and transport development planning in Hong Kong (Choi, 1986; Leung and Lam, 1991). Since the task of transport planning is to determine cost-effective solutions for minimising traffic congestion, a cost-effective solution to transport problems should consist of a land use pattern, a transport system and a set of road usage charges, that together bring the demand and supply into balance. However, the road usage charges, considered in previous studies, have been seen as fixed parameters in the model, and the role of road usage charges as an alternative to highway investment has been ignored. Based on the LUTO planning data, this chapter examines how road usage charges affect travel demand and network performance. Tunnel tolls and petrol taxes are the direct charges for road usage. In fact, these road usage charges are being used in Hong Kong and directly affect the traffic demand. In previous related studies, Beckman (1965) commented that "tolls are economically optimal if they induce an efficient use of the available road capacity". Dafermos and Sparrow (1971) showed that by using congestion tolls, individuals are forced to choose their travel paths, thus leading to a system of optimal resource allocation and toll patterns for a simple network with two paths. Similarly, Lam (1988) demonstrated how road tolls affect the decision of transport investment and the role of road pricing in network design. In fact, it is necessary to consider the road pricing policies simultaneously when designing a road network. Otherwise, what is designed may prove an expensive but inefficient solution. Road usage charges have been

Coordination of Road Pricing Policies in Hong Kong

529

widely used to reduce congestion, provide a basis for investment decision, assist traffic control, and so on. A distance-based charge, such as a distance license has been used in New Zealand (Starkie, 1988); an Area License Scheme (ALS) has been implemented in Singapore since 1975 (McCarthy and Tay, 1992; Holland and Atson, 1978); in Norway, the revenues from road tolls have been linked directly to road improvements (Tretvik, 1992); and an electronic road pricing system has been examined in greater detail in Hong Kong (Dawson and Brown, 1985) and will be fully implemented in Singapore in the near future. Conventional studies on the static space dimension of road pricing are represented by the traditional marginal-cost pricing theory. It has been long recognised that road users travelling on congested roads should pay a toll equal to the difference between marginal social and private costs in order to achieve a system optimum flow pattern (Beckmann, 1965; Dafermos and Sparrow, 1971; Smith, 1979). Smith et al. (1994) showed that for any transportation network with regular link cost functions, and any positive travel-demand, all fully positive systemoptimal link-flows associated with a given demand are supportable by nonnegative link tolls if the route flows that induce the link-flow pattern are strictly positive. Recently, Yang and Lam (1996) considered the optimal road tolls under conditions of both queuing and congestion in static networks by applying a bilevel programming approach. This chapter presents an optimisation method, which will enable the analysis of coordinated tunnel toll and petrol tax charges, by optimising an "objective function" while the travel demand in terms of origin-destination (OD) matrix is not fixed and would vary with changes in road usage charges. A case study is shown based on the Hong Kong road network adopted in the LUTO studies. We will use the optimisation method to derive an optimal set of toll charges for the 10 toll links and the desirable petrol tax in Hong Kong. In the next section, the search algorithm is formulated and the optimisation method described. An application of the optimisation method will be presented in which the total network travel costs are used as a measure for evaluating road usage charges in Hong Kong. Finally, our conclusions and recommendations are given for further study.

Search Algorithm Given a road network with m toll links and df petrol tax, let ht denote the increase (or decrease if negative) of the charge of ith toll link and of

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Travel Behaviour Research: Updating the State of Play

petrol tax with respect to a reference charge Y° = (y?,y2, • • • , y™, df). Hence, for each (hi, h2,. . . , hm, hm+i), there corresponds a usage charge in which the toll charge of the ith toll link is given by yf = y° + hf and the petrol tax is given by d f = d f + hm+i. For each usage charge, Y = (yi + y 2 ,. . . ,ym,dk), let /(Y) be the total network travel cost. The objective is to find an optimal set of usage charges Y* such that/(Y*) is a minimum. In order to guarantee optimality, or arrive at a small neighbourhood of the minimum point, a grid-point search algorithm would be required, particularly when the trip matrix is not fixed. The algorithm was introduced by Cheung and Ng (1995) and is adopted in this study. The proposed algorithm contains the following three basic steps. Step 1: Full local exploration Let Yk be the kth approximation of yf and dk to the minimum, and h the step-length. We evaluate the objective function/(Y) at two sets of points about Y:

if f(Yk+1) =£/(Y fe ) for some choice of / and j, then the function values at an additional set of 2(n — 2) points about Yk+l will be evaluated, namely,

If /(Y* +1 )^/(Y* +1 ) for some choice of r, replace Yk+1 by Yk+\ and continue with partial local exploration. In case that no point around Yk has a lower function value, reduce the step-length and repeat the full local exploration at Yk. The process will terminate when the step-length is less than a prescribed tolerance. Step 2: Partial local exploration Let b = Yk+1 — Yk, and evaluate / at the following set of points about Yk+l:

(5)

Coordination of Road Pricing Policies in Hong Kong

531

where e,•. = — 1 or 1, according to the sign of the ith coordinate of b; if b - V2h and n = 2, or if b = v3h and n = 3.

If /(Y5) ^f(Yk+l) for some choice of /, then make exploratory move as depicted in Step 3 along the Ys - Yk direction. Otherwise, reduce the step-length and start full exploration again at Yk+l. Step 3: Exploratory movement Let M = Ys - Yk, and evaluate / at the following set of points:

where / = ! , . . . , « ; and b is not along the direction of M. ltf(Yk+2) ^f(Ys), replace Yk by Ys, and Ys by Yk+2. Then repeat the procedure above until it no longer decreases. Afterwards, restart the full local exploration at Ys.

Optimisation Method The previous studies merely investigated how road usage charges affect the total network travel time where the OD matrix is fixed. In this case, the trip distribution and modal split are assumed constant, and only the choice of route is varied. However, travel costs not only affect route choice, but also the modal split and trip distribution in long-term planning of highway networks. In this chapter, we will investigate how road usage charges, such as toll charges and petrol tax, affect the modal split, trip distribution and route choice and, hence, how to attain optimal highway network planning by means of these fiscal measures on road usage. The transport model used in the LUTO system is a feasible tool for evaluation of the performance of road usage charges in highway network planning. When a set of road usage charges is given, we can use the LUTO transport model to assess their effects on travel demand in terms of OD matrices, link-flow pattern and so on. The total highway network travel cost will be used as the performance measure for evaluation of the varied road usage charges.

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Travel Behaviour Research: Updating the State of Play

Given a set of road usage charges Yk, LUTO can be employed to obtain the objective function value (Yk). However, it takes about 100 min for LUTO to run in a PC486. Therefore, if we have many variates, i.e. road usage charges needing optimisation, computing time will be enormous and unacceptable. In view of this, a heuristic optimisation method is proposed to optimise the road usage charges when the modal split and OD matrices are not fixed. The flow chart of the heuristic approach is displayed in Fig. 1, and the optimisation model is presented in Fig. 2. The optimisation procedure of road usage charges is discussed in detail as follows: Set number of iteration k = 1. Step 1: Run LUTO with reference road usage charge Yk to obtain: Output: Link choice proportion (result of traffic assignment); behavioural cost matrices; and objective function value F(Yk). If k = 1, go to Step 3. Step 2: Check |F(Y*) - F(Yk+1)\: If \F(Yk) - F(Yk+l)\ ^ (given stopping criterion) go to Step 5; otherwise, go to Step 3. Step 3: Run the optimisation model Step 3.1: Grid-point search. Step 3.2: Update behavioural cost. Step 3.3: Run the SLUT submodel of LUTO (including trip generation, distribution and modal split). Step 3.4: Traffic assignment. Step 3.5: Objective function evaluation. Step 3.6: If objective function no longer decreases, go to Step 3.7; otherwise, go back to Step 3.1. Step 3.7: Stop; output optimal road usage charges Yk+l. Step 4: Update reference road usage charges Yk with Yk+1 and set k k + 1, go to Step 1. Step 5: Stop, output results.

Coordination of Road Pricing Policies in Hong Kong

Link choice proportion

Behavioral cost

If IF(Y,K)-F(Y,K+1)K=a

Yes

No Optimization model

Optimal toll charge; petrol tax

Note: a = given stopping criterion

Figure 1 Optimization procedure of road usage charges

533

534

Travel Behaviour Research: Updating the State of Play

....... "}

Grid— Doint s earch

i

Value of : Toll charge; Petrol tax \

,

Update: Behavioral cost s/

SLUT \/

Assignment \/

Objective function evaluation \/

Yes

If the objective function no longer decreases V

No

Stop

Figure 2 Flowchart of optimisation model

Coordination of Road Pricing Policies in Hong Kong

535

In Step 1, by running the LUTO transport model, we can obtain the objective function value F(Yk) corresponding to the reference road usage charges. The link-choice proportion, which is the proportion of trips by OD pair through the particular links, will be fixed at each iteration and used for the optimisation process, as shown in Step 3. The behavioural cost matrices includes all zone pairs' behavioural cost by mode, i.e. the behavioural generalised cost of travel from zones / to / by private car, good vehicles and public transport. In Step 3 (the optimisation model), we use a grid-point search algorithm for searching the optimal road usage charges. Step 3.2 is the key point in the optimisation process. Subject to the road usage charges output from the grid-point search, we can update the behavioural costs accordingly. Let Bcost(i,j) be the behavioural generalised cost of trips from zones i to / by mode. For instance, Bcost(i,j) by private car consists of three components—toll charge, parking charge and operating cost related to distance. Therefore, Bcost(iJ) can be obtained as follows:

where Ta = toll charge on link a; 5ija = 1, if trips from zone / to j through toll link a, otherwise 0; P7 = parking charge at zone /; Df = distance factor (including petrol tax); d(i, /) = travel distance from zones / toy; Tf= time factor; t(i, j) = travel time from zones i to /. Using equation (9), we can update the behavioural cost by private car with various road usage charges. In Step 3.3, run the SLUT submodel, which is part of the LUTO transport model including trip generation, trip distribution and modal split. The updated OD matrices by modes can then be obtained corresponding to the updated behavioural cost. In Step 3.4, use the link choice proportion output from Step 1 to assign OD flows onto each link and so obtain the link-flow pattern. It should be noted that in the optimisation model, the link choice proportion is fixed, while the behavioural costs and the OD matrices change accordingly to the various road usage charges. Hence, this leads to a simplified optimisation procedure. This procedure can save much computing time used in the assignment process and achieve a reasonable result. This will be shown in the following case study.

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Travel Behaviour Research: Updating the State of Play

Case Study The 2006 LUTO planning data and road network, for the case of the Hong Kong airport not being relocated, are used for the application of the proposed optimisation method. It consists of 51 zones and 345 links of which only 10 links have toll charges. The locations of the ten toll links are shown in Fig. 3, while their reference tolls are listed in Table 1. Table 1 Road tunnels and reference tolls Road tunnel No.

Name of road tunnel

Tunnel toll (HK$) Private car

1 2 3 4 5 6 7 8 9 10

Aberdeen Western Harbour Cross Harbour Eastern Harbour Tseng Kwan O Tate's Cairn Lion Rock Route 16 Route 5 Route 3

6.00 21.00 14.00 9.00 6.00 6.00 6.00 6.00 6.00 6.00

Note: All values are expressed at the 1981 price level. In this case study, only the road usage charges for private cars will be changed, while those for goods vehicles are fixed. Given the initial point, namely, the reference toll charges for private car (6.0, 21.0, 14.0, 9.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0), the reference petrol tax factor (df) is 1.0. Using the LUTO model, we obtained total network travel cost (initial estimate /(Y°, d°)) of 1808.00 thousand vehicle hours. The results of alternative road usage charging schemes are shown in Table 2. If there is no change in toll charges, only the toll links and petrol tax can be varied, the proposed optimisation method yields a total network travel cost of 1802.85 thousand vehicle hours. It is found that the total network travel time is, generally, in the descent direction, while the total generalised cost of travel is not convex in response to the change of petrol tax. In other words, if the objective is to minimise the total highway network travel time, the highest acceptable petrol tax should be chosen.

Coordination of Road Pricing Policies in Hong Kong

LEGEND

SHENZHEN (CHINA)

537

N

ROAD LINK TUNNEL AND/OR BRIDGE 1

TOLL LINK 1

Figure 3 Location of toll links of Hong Kong

Similarly, it would be optimum to raise tolls to a level where no one can afford to travel. Therefore, the optimisation of network travel time may be an inappropriate objective function, particularly when the travel demand is adaptable to road pricing policies.

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Travel Behaviour Research: Updating the State of Play Table 2 Optimal road tolls and petrol tax

Name of road tunnel

1. Aberdeen 2. Western Harbour 3. Cross Harbour 4. Eastern Harbour 5. Tseng Kwan O 6. Tate's Cairn 7. Lion Rock 8. Route 16 9. Rock 5 10. Route 3 Proportion of Change in Petrol Tax Total network travel cost (in 1,000 vehicle hour) Total network travel time (in 1,000 vehicle hour)

Tunnel toll (HK$) Reference charges of LUTO Private car

Optimal charges of Scheme 1 Private car

Optimal charges of Scheme 2 Private car

Optimal charges of Scheme 3 Private car

6.00 21.00 14.00 9.00 6.00 6.00 6.00 6.00 6.00 6.00

6.00 21.00 14.00 9.00 6.00 6.00 6.00 6.00 6.00 6.00

11.70 28.18 25.52 17.55 8.00 8.53 8.07 9.28 11.42 11.70

6.00 23.18 24.96 16.46 6.00 8.40 8.41 3.07 3.00 6.00

1.00

1.40

1.00

1.90

1808.00

1802.85

1802.66

1782.97

1206.73

1155.54

1189.49

1070.92

Notes: LUTO = Land Use and Transport Optimisation; Scheme 1 = Change petrol tax only; Scheme 2 = Change road tolls only; Scheme 3 = Change both road tolls and petrol tax.

In view of this, it is more appropriate to minimise the total network travel cost. Using the proposed grid-point search method, the total network travel cost of 1782.97 thousand vehicle hours was attained with the following road usage charges: Y** - (6.0, 23.18, 24.96,16.46, 6.00, 8.40, 8.41, 3.07, 3.00,6.00), and df* = 1.96

Conclusion The facts illustrated by this case study are important from the point of view of highway planning. Direct road usage charges, such as toll pricing and petrol tax, can improve the highway network performance. However, the imposition of an appropriate set of tunnel tolls and petrol tax, can

Coordination of Road Pricing Policies in Hong Kong

539

reduce the total network travel cost more effectively than just optimising either tunnel tolls or petrol tax separately. It is necessary to consider road usage charges simultaneously when planning a highway network. A heuristic optimisation approach is proposed in this chapter. The LUTO transport model and grid-point search algorithm are the basic tools for the optimisation procedure. It merits attention that the trip matrices are not fixed and would be varied with changes in road usage charges. This makes the heuristic optimisation approach promising for solving real problems. On the other hand, the system objective should be carefully determined as different objectives would result from different road pricing policies. These phenomena should be further illustrated for cases of (1) maximising revenue; (2) minimising total marginal cost of travel; and (3) minimising total vehicular emissions. With the advance of electronic road pricing technology, zone pricing systems will be feasible in practice and their effects on network performance should be further studied.

Acknowledgements This research was funded by the Research Grant Council under Project No. 340.917. The views presented in this chapter are those of the authors only.

References Beckmann, M.J. (1965) On optimal tolls for highways, tunnels and bridges. In L.C. Edie, R. Herman and R. Rothery (eds.), Vehicular Traffic Science. American Elsevier, New York. Cheung, B.K.S. and Ng, A.C.L. (1995) An efficient and reliable algorithm for non-smooth non linear optimisation. Neural, Parallel and Scientific Computations 3, 115-128. Choi, Y.L. (1986) Land use transport optimisation (LUTO) model for strategic planning in Hong Kong. Asian Geographer 5, 155-176. Dafermos, S. and Sparrow, F.T. (1971) Optimal resource allocation and toll patterns in a user-optimised transport network. Journal of Transport Economics and Policy V, 198-200. Dawson, J.A.L. and Brown, F.N. (1985) Electronic road pricing in Hong Kong: a fair way to go? Traffic Engineering and Control 26, 522-529.

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Holland, E.P. and Atson, P.L. (1978) Traffic restraint in Singapore. Traffic Engineering and Control 19, 14-22. Lam, W.H.K. (1988) Effects of road pricing on system performance. Traffic Engineering and Control 29, 631-635. Leung, T.Y.C. and Lam, W.H.K. (1991) Transport strategy for Hong Kong. Proceedings National Transport Conference of the Institution of Engineers. Brisbane, May 1991, Australia. McCarthy, P. and Tay, R. (1992) Road pricing in Singapore: too much of a good thing? Selected Proceedings of the 6th World Conference on Transport Research. Lyon, July 1992, France. Smith, M. J. (1979) The marginal cost taxation of a transportation network. Transportation Research 13B, 237-242. Smith T.E., Eriksson, E.A. and Lindberg, P.O. (1994) Existence of optimal tolls under conditions of stochastic user-equilibria. In B. Johansson and L.G. Mattsson (eds.), Road Pricing: Theory, Empirical Assessment and Policy. Kluwer Academic Publishers, Boston, Mass. Starkie, D. (1988) The New Zealand road charging system. Journal of Transport Economics and Policy XXII, 239-245. Tretvik, T. (1992) The toll road alternative: variations in choice behaviour and values of time. Selected Proceedings of the 6th World Conference on Transport Research. Lyon, July 1992, France. Yang, H. and Lam, W.H.K. (1996) Optimal road tolls under conditions of queuing and congestion. Transportation Research 30A, 319-332.

List of Participants TORGIL ABRAHAMSSON Royal Institute of Technology, Sweden ODILE AND AN Universite Lumiere Lyon 2, France DAVID BANISTER University College London, England JOHN BATES John Bates Services, England MICHAEL BELL University of Newcastle upon Tyne, England URSULA BLOM Dutch Ministry of Transport and Public Works, Holland MARK BRADLEY Hague Consulting Group, USA ANDREW DALY Hague Consulting Group, Holland GERARD DE JONG Hague Consulting Group, Holland DANIELE DUBOIS Centre National de Recherche Scientifique, France KURT FALLAST Graz University of Technology, Austria

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List of Participants

LASSE FRIDSTROM Norwegian Institute of Transport Economics, Norway TOMMY GARLING Goteborg University, Sweden RODRIGO GARRIDO Pontificia Universidad Catolica de Chile, Chile CECILE GODINOT Universite Lumiere Lyon 2, France FAUSTINO GOMES CISED Consultores, Portugal HUGH GUNN Hague Consulting Group, Holland DAVID HENSHER University of Sydney, Australia ROBERT HERMAN University of Texas at Austin, USA BILL HILLIER University College London, England NICK HOUNSELL University of Southampton, England SERGIO JARA-DIAZ Universidad de Chile, Chile RONG-CHANG JOU Feng Chia University, Taiwan UWE KUNERT Deutsches Institut fur Wirtschaftsforchung, Germany WILLIAM LAM Hong Kong Polytechnic University, China ANNE MADSLIEN Norwegian Institute of Transport Economics, Norway HANI MAHMASSANI University of Texas at Austin, USA

List of Participants SHOJI MATSUMOTO Nagaoka University of Technology, Japan TAKAYUKI MORIKAWA Nagoya University, Japan OTTO NIELSEN University of Denmark, Denmark AGOSTINO NUZZOLO "Tor Vergata" University of Rome, Italy JUAN DE DIOS ORTUZAR Pontificia Universidad Catolica de Chile, Chile RAM PENDYALA University of South Florida, USA ALAN PENN University College London, England PASCAL POCHET Universite Lumiere Lyon 2, France CHARLES RAUX Universite Lumiere Lyon 2, France LUPERFINA ROJAS Universidad de la Serena, Chile FRANCESCO RUSSO University of Reggio Calabria, Italy KUNIAKI SAKAKI Nagoya University, Japan WAFAA SALEH University of Newcastle upon Tyne, England GERD SAMMER University of Agricultural Sciences at Vienna, Austria TERJE TRETVIK SINTEF Transport Engineering, Norway ERIC VAN BERKUM Goudappel Coffeng, Holland

543

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List of Participants

PETER VAN DER MEDE Goudappel Coffeng, Holland PIERRE VAN ELSLANDE INRETS, France JOSE MANUEL VIEGAS CESUR, Portugal FRITZ WERNSPERGER Salzburg Provincial Government, Austria STAFFAN WIDLERT Swedish Institute for Transport and Communications Analysis, Sweden LUIS WILLUMSEN Steer Davies Gleave, England JIANMING XU University College London, England RUI YE Hong Kong Polytechnic University, China

JIN-RU YEN National Taiwan Ocean University, Taiwan

INDEX

Abelson, R. P. 4 Abkowitz, M. D. 391 Abrahamsson, T. 199-218 accidents 49-64 statistical data 50 typology 52-5 accuracy-effort trade-off 11 age 302, 314 Ahn, C. 36 air route characteristics 149-52 market segmentation 149, 158 air route choice factors affecting 143 importance of 141 models of 154-7 survey 144-54 air trip characteristics 152-4 ticket price 155-6, 158 transfer times 157 airport access time 156-7 Ajzen, I. 165, 169 Alexander, G. J. 61 Alfa, A. S. 392 Algers, S. 458 Allen, R. W. 402 ALOGIT 477 Ampt, E. S. 69 analytic hierarchy process (AHP) 182, 18694

Andan, O. 67-85 Anderson, J. R. 13 APRIL 252, 256, 258, 260 arrival time 367-72 Atherton, T. J. 458 Atson, P. L. 529 attitudes and behaviour 169, 438 Australia 488, 497-503 automobile see car Axhausen, K. W. 6, 282, 488

axial map 341 Bagozzi, R. P. 36 Banai-Kashani, R. 182 Banister, D. 339-61 Barnard, P. O. 264, 270 Bates, J. J. 24, 26, 31, 89-102, 426 Bayesian Reliability (BR) 428-32 Becker, G. 20-3, 25-6, 28 Beckman, M. J. 528-9 behaviour and attitudes 169, 438 stated and actual 84 see also travel behaviour Bell, M. G. H. 473-84 Belson, W. A. 36 Ben-Akiva, M. 4-5, 13, 117, 125, 154, 191, 224, 227, 392, 402-3, 436, 438, 458, 474-6 Berry, W. L. 513 Bhat, C. R. 167, 168 bias systemic 5 valuation 97 Biel, A. 6, 10, 12 Biggiero, L. 392 Blalock, H. M. 36 Blom, U. 507-23 Boccara, B. 438 Bonsall, P. 402, 516, 518, 520, 523 Box, G. E. P. 129, 134, 137 Boyce, D. E. 201, 203, 207 Braakhekke, W. G. 36 Bradley, M. A. 97, 98, 117, 141-59 Brog, W. 264, 265, 282, 304, 322, 325 Brown, F. N. 529 Brownstone, D. 515 Bunch, D. S. 171 Bussiere, Y. 304 Caliper 231

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Camerer, C. 4, 5 Caplice, C. 366 Caporael, L. 11 car gender allocation 462, 463 ownership 40, 287 use costs 81, 83 car change accelerated lifetime 491-2 duration 489-97 empirical study 497-503 hazards 499-503 scrappage rates 488 timing 487-503 car-driving model 309-14 see also demotorisation; motorisation rates car-pooling 507-23 classification 509-11 Dutch model 518-23 formation 516-18 literature review 511-18 model design 508 transfer 512 Carey, M. 203 Cascetta, E. 386, 418 causal analysis 35-47 causal structures specification 39-42 see also structural heterogeneity Caves, R. E. 144 Cellier, J. M. 51 Chaiken, S. 13 Chang, G. L. 366, 380 Chapleau, R. 304 Chen, Y. 218 Cheung, B. K. S. 530 Choi, Y. L. 528 choice behavioural hypotheses 387-8 between-mode and within-mode 99, 1358 destination 38 discrete 474 habitual 404, 408-9 implementation 7, 12-13 mis-specified 474-5 probability 441-2, 444-5 set generation 475-7 see also mode choice choice models 473

calibration 392-7 with departure time and path 385, 391-J results 413-17 simulation 415-16 specification 407-8 theoretical basis 4-13 validation 406-14 see also discrete choice models; mode choice model Cirillo, C. 102 Clark 392 cognitive dissonance 443-4, 449-50, 453 cognitive maps 6 cognitive psychology 61-3 computers, portable 90, 108, 120, 127 congestion adaptation strategies 74-5, 78-80, 83 attitude and reaction to 73-6 indices 256, 257 and travel time reliability 251, 253 consumption basic commodities 20-1 time requirement 21-2, 23 CONTRAM 254-5, 258-9 CONTRAMI 254-5 Copley, G. 100-1 costs of car use 81, 83 freight 129, 134 total highway network travel 531, 538 Cote, J. 304 Cox, D. R. 129, 134, 137 Cramer, J. S. 515 Crouch, F. O. 479 CSI model 516, 520 Dafermos, S. 528-9 Daganzo, C. F. 230, 370, 374, 377, 392 Dagenais, M. 476 Dalton, N. 341, 346 Daly, A. J. 97, 98, 117, 425, 477, 507-23 data fusion 224-5 Davidson-Fletcher-Powell (DFP) method 477 Dawes, R. M. 12 Dawson, J. A. L. 529 de Jong, G. 128, 507-23 De Keyser, V. 59 decisions interdependent 7-9 lexicographic rule 11 meta- 8-9

Index process 436 rules 10-11 demand analysis 123-5 forecasting 68 and road pricing 528 demography 300-1, 311, 315 demotorisation 314-15 Denis, M. 62 Denmark 222, 225-32, 240-3 departure times switching 366-82 DeSanctis, G. 162, 167 DeSerpa, A. 21-3, 26, 31 destination choice 38 development density 346-8, 353, 358, 3601 Dial, R. B. 229 Diamond, P. 494 Dim, L. 315 discrete choice models 163, 181-2 forecasting reliability 426-32 sequential estimation 441-4, 446, 44850, 453 simultaneous estimation 444-6, 450-1, 453 Dobson, R. 438 Dogit 476 Domencich, T. 474 Drissi-Kaitouni, O. 201, 203-6, 208, 213, 217-18 driving inefficient 401-2 nature of 59-60 Dubois, D. 49-64 duration dependence 494, 499-501 duration models 490-1, 521-2, 523 DuWors, R. E. 492 dynamic generalised ordinal probit (DGOP) model 163-77 Edwards, W. 4 Egypt 479 Einhorn, H. J. 10 elderly people non-homogeneous 301 travel behaviour 299-315 Elwood, J. M. 36 Ericson, K. A. 8 Erl, E. 322, 325 errors human 51 of perception 58

estimation 108-10 with different error structures 90 parameters 37-47, 413-17 structured 224 unstructured 223 Etschmaier, M. M. 387 Evans, A. 21-4, 26, 31 Evans, S. 207 event history 489-97 expectations 403, 405, 414 Fallast, K. 264, 317-37 Farah, M. 24 Farhangian, K. 205, 218 Fell, J. C. 49 First Preference Recovery (FPR) 426 Fischhoff, B. 5 Fishbein, M. 165, 169 Fisk, C. 201, 203, 205 Fleury, D. 64 Flinn, C. 521 Florian, M. 386 Foerster, J. F. 426 Fowkes, A. S. 94, 97 France Grenoble 300-15 Lyon conurbation 70-82 road tolling 69-70 freight demand analysis 123-5 heterogeneous market 124, 138 own account transportation 124 freight shipment between-mode choices 136-8 cost term 129, 134 disaggregated model 138-9 results 128-38 SP exercise 127-39 tariffs 124 wholesale 125-8 within-mode choices 135-6 Fridstrom, L. 123-39 Friedman, J. W. 520 full-information maximum likelihood (FIML) 43 Gallez, C. 307, 314 gaming-simulation techniques 72 Garling, E. 9 Garling, T. 3-13, 84, 282 Garrido, R. A. 425-32 Garvill, J. 7

547

548

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Gaudry, M. J. I. 129, 134, 476 generation 302, 309, 314 Germany 265-74 Gilbert, C. C. M. 493, 494, 497 Gloeckler, L. A. 491 Godinot, C. 67-85 Golledge, R. G. 4, 6, 9 Golob, J. M. 488 Golob, T. F. 36, 264, 438, 488, 515 Gomes, F. G. 279-97 Gommers, M. 128 goods, role of 27 goods-leisure trade-off 24-5 Goodwin, P. B. 36, 68 Gopal, S. 9 Gosling, G. D. 144 Green, P. 90 Greene, D. L. 311 Greene, W. H. 43 Greenwood, E. 36 Grether, D. M. 5 Groves, R. M. 282 Guillemard, A. M. 302 Gunn, H. F. 426, 458, 468, 507-23 habit probability of 411 strength 414, 417-18 Hague Consulting Group 107, 127, 142, 145, 447 Raines, G. H. 492 Hamed, M. M. 493 Hamerslag, R. 402, 418 Han, A. 494 Hansen, M. M. 144 Hanson, J. 343 Hanson, S. 38 Harvey, S. 68 Hatcher, S. 366 Hauser, J. R. 426, 429 Hausman, J. 494 Hayes-Roth, B. 8, 9, 10 Hayes-Roth, F. 8, 10 hazard of car replacement 499-503 car-pooling 522 function 490-1 model 496 proportional 491-2 rate 495 and time 502 Heckman, J. 495, 521

Hendrickson, C. 391 Hensher, D. A. 24, 26, 31, 275, 427, 487503 Herman, R. 161-78 heterogeneity, unobserved 494-6, 497, 499-501 highway planning 528 Hillier, B. 339-61 Hills, B. L. 61 historic period 302, 314 Hoc, J. M. 60 Hoch, S. 7 Hogarth, R. M. 10 Holland, E. P. 529 Hong Kong 527-39 Horn, W. 36 Horowitz, J. L. 410 Hounsell, N. B. 251-61, 402 HOV lanes 508, 510, 511, 514, 516 Hu, P. S. 264 Huff, J. O. 38 Huws, U. 162 lida, Y. 402 income 479-81 and mode choice 26, 30 see also wages and salaries indifference band 367-8 behavioural interpretation 379 early-side 368-71 joint 366, 372-81 late-side 371-2 route switching 380-1 information action failure 57 acquisition, representation and use 6-7, 9-10 decision failure 56-7 detection failure 55-6 dynamic 402-19, 406-19 evaluation 405 interpretation 64 overall failure 57-8 processing failure 49-64 technology 402, 406-19 see also knowledge intelligible space 361 interactive measuring procedures 325 interviews card ranking 113-18 computerised 108, 112-14, 115-18, 118, 145

Index NMB study 327 presence of interviewer 120 ranking versus rating 119-20 telephone 282 Italy 397 Jacobs, J. 361 Jansson, O. W. 315 Japan 182 Jara-Diaz, S. R. 19-31 Jeffcoate, G. O. 253 Jeffery, D 401 Johnson, B. 22 Johnson, L. W. 427 Jones, J. C. 162 Jones, P. M. 68, 69, 72 Joreskog, K. 43, 441 Jornsten, K. 218 Jou, R.-C. 365-82 Juster, F. T. 27, 31 Kahneman, D. 4, 5, 7, 10 Kalbfleisch, J. 492 Katz, A. I. 162 Katz, L. 493 Kersten, H. M. P. 264 Kessler, D. 302 Kimber, R. M. 255 King, G. F. 401 Kinoshita, E. 182 Kitamura, R. 36, 162, 168, 497 Kloas, J. 273 knowledge categorisation of 61-3 processing 50-8 see also information KONTIV surveys 274 compared 268-70 design of 265 Koppelman, F. S. 438, 458, 468 Kostyniuk, L. 511 Koutsopoulos, H. N. 402, 418 Kroes, E. P. 68, 99 Kunert, U. 263-75

Lam, S.H. 172, 366, 377, 378 Lam, W. H. K. 527-39 Lancaster, T. 492, 521 land use 346-8, 353, 360-1 retail 347, 361 Land Use Transport Optimisation (LUTO) 528, 531-5, 539

549

learning 83-4, 403 Leblanc, F. 68 LeBlanc, L. 205, 218 Lee-Gosselin, M. E. 69 Leonard, D. R. 254 Leplat, J. 49, 60 Lerman, S. R. 4, 5, 13, 117, 125, 154, 378, 436 Lesgold, A. 8 Leung, T. Y. C. 528 Levin, I. P. 438 Levy, A. 4 lexicographic answers 110-12, 116-17 Lichtenstein, S. 5 Liebrand, W. B. G. 11 likelihood ratio test statistic 191-2 Likert 165 LIMDEP 493 Lindberg, E. 5 Lindh, C. 106 Lippman, S. A. 521 LISREL 43, 441, 443, 446, 448-51, 453 Loewenstein, G. 4, 7 logit models 108, 271, 396 binary 126, 154 dependent availability (DAL) 475, 47784 independent availability 476-7 multinomial (MNL) 163, 392-7, 474 nested 515 parametrised captivity model 476 random utility 386 Lotan, T. 402, 418 Louviere, J. J. 438 Lovegrove 60 Lovelock, C. H. 438 Lundgren, J. 201, 203-6, 208, 213, 217-18 Lundqvist, L. 207, 216 Lunenfeld, H. 61 Lyon, P. K. 36 McCall, J. J. 521 McCarthy, P. 529 McClintock, C. G. 11 McFadden, D. 24, 25, 28, 427, 436, 474 McKelvey, R. D. 163-4, 170 McNulty, T. M. 5 Maddala, G. S. 39 Madre, J. L. 307, 314 Madslein, A. 123-39 Mahmassani, H. S. 161-78, 365-82, 402 Malaterre, G. 59, 60

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Mannering, F. L. 392, 491, 493, 494, 499 Manski, C. F. 378, 475 March, J. G. 4 Mason, A. 302 Mast, T. M. 401 Mathaisel, D. F. 387 Matsumoto, S. 181-94 May, A. D. 254 Mazet, C. 59, 60, 63 Meadows, D. H. 521 Menting, L. J. 509 Method of Successive Averages (MSA) 231, 247-8 Meurs, H. J. 36, 264, 488 Meyburg, A. H. 282 Meyer, B. 494 microeconomic model 19-31 microeconomic theory 5-7 Middlebrook, P. N. 37, 38 Miller, G. A. 7 MINT progam 107, 127, 145 mobility determinants of 271-2 general indicators 285-6 trends 273-4 modal shift 78-9, 83 due to NMB 327-36 and journey purpose 333-6 sex and age effects 333 modal split 287 mode choice 38 analysed 28-30 income effect 26, 30 inter-city 447-51 loyalty to 293, 296-7 reasons for 290 Stockholm and Trondheim 461-2 mode choice models 19-31, 513-16, 520 disaggregated 518-19 discrete 24-6 with supply models 516 mode use elderly people 304-6 gender differences 304, 312 models estimability 37-47 household 458 transferability 458-71 Moning, H. J. 264 Montgomery, F. O. 254 Montgomery, H. 11 Morikawa, T. 224, 227, 435-54

motorisation rates elderly people 306-9 generation 309 see also car-driving Multiple Path Matrix Estimation (MPME) 222, 233-40 calculation time 239-40 compared to SPME 231-2 evaluation of 242-3 and traffic counts 234 multispell models 493-7 Murakami, E. 488 N'doh, N. N. 144 Neboit, M. 58 Netherlands 141-59, 447-51, 507-23 Amsterdam 406-19 National Model System (NMS) 508-10, 519-20 New Regional Models (NRM) 509 network diachronic 385-6, 388-91 modelling 202, 254-8 performance 528 travel cost 531, 538 travel time 536-7 new motorised bicycle (NMB) 317-37 concept 319-21 infrastructure for 321-2 Newell, A. 7 Ng, A. C. L. 530 Nguyen, S. 218, 386 Nielsen, O. A. 221-48 Nilles, J. M. 162, 168 Norsk Gallup Institutt AS 127 Norway 68, 124-39 Trondheim 459-71 Nuzzolo, A. 385-98 Oliveira-Sotomayor, M. A. 520 Oliver, W. 8 Oort, C. 22 optimisation method 529, 531-5 Orfeuil, J. P. 304 origin-destination (OD) matrices 199-218 bilevel 200-1 CPU-times 213, 215, 217, 218 descent-based 205-6, 208-16, 217-18 distorted problem 202, 208, 213-17 distribution and assignment 206-7 equilibrium problem 202, 208, 209-13, 214, 215, 216-17

Index estimation problem 200, 204-7 gradient-based methods 201, 206 minimum-information 202-3, 204, 207, 211-12, 215 see also Multiple Path Matrix Estimation (MPME); Single Path Matrix Estimation (SPME) Ortuzar, J. de D. 24, 102, 182, 224, 231, 391, 415, 425-7, 432, 467, 474 Ouwersloot, H. 102 Paillat, P. 302 Pallottino, S. 386 panel data 406, 488, 497-503, 515 parking choice 181-94 distance to destination 189 probability 183, 189-93 parking choice model 183-4 AHP 189-92, 194 data 185-6 RP 193, 194 Parry, T. 402 Pas, E. I. 438 Paselk, T. A. 493 Patrica, K. L. 438 Payne, J. W. 5, 10 pedestrian flows 346-8, 357, 360 pedestrians 340-1 Pendyala, R. M. 35-47, 162 Penn, A. 339-61 perceptions, attitudes and preference 436-7 Plank, E. 391 planning opportunistic 8 plan formation 7 properties of 8 Plott, C. R. 5 Pochet, P. 299-315 Pol, H. 458, 468 Polak, J. 68, 69 Portugal 280-97 Powell, W. B. 230-1, 239 preferences inconsistent 4 ordinal variable 90 see also revealed preference (RP); stated preference (SP) Prelec, D. 4 Prentice, R. L. 491-2 price versus travel time 109 price resistance 80 probit models 396, 430

551

dynamic generalised ordinal (DGOP) 163-77 multinomial (MNP) 163, 366, 377-8, 382, 392-7 random utility 386 public transport 386-91 funded from road pricing 70 see also air trip; trains Pushkarov, B. 340 Raimond, T. 488 Rasmussen, J. 49, 51, 403 rat runs 347 Raux, C. 67-85 ray diagram 94-7 Reason, J. 51, 57 Recker, W. W. 438 repeated measurement problem 102 retail 347, 361 revealed preference (RP) 68, 144, 222, 435 Richards, T. 495 Rietveld, P. 102 risk 59, 60 competing 492-7 interdependence 494 risk-taking 57 RLD Integrated Model System (IMS) 158 road categories 62-3 road pricing 527-39 APRIL 252, 256, 258, 260 attitudes and reaction to 77-82 duration based toll 77 effect on travel demand 528 and network performance 528 optimisation method 529, 531-5 scenario design 82 search algorithm 529-31, 535 urban 67-85 use of funds from 70 Roberts, M. 24 Rojas, L. E. 181-94, 193 Ronis, D. L. 7, 13 Rosch, E. 61, 62 Roth, A. E. 520 route choice 403-19 route switching 380-1, 382 Russo, F. 385-98 Saad, F. 59, 60, 61 Saaty, T. L. 182-3 Sahni, B. S. 36 salaries and wages 30, 172, 174-5, 177

552

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Saleh, W. 473-84 Salomon, I. and M. 162 Sammer, G. 264, 317-37 Samuelson, P. A. 11 Sandberg, L. 6 Sasaki, K. 435-54 schedule delay 367, 382 Schmidt, P. 522 Schoenfeld, L. 377 search algorithm 529-31, 535 search theory 521 selfishness 6, 11-12 Sheffi, Y. 230-1, 237, 239, 370, 374, 377 Shefrin, H. M. 7 Sheldon, J. 68, 99 Shen-te-Chen, P. 402 Sherali, H. D. 224 Shirley Highway Model (COMSIS) 513-14, 520 Simon, H. A. 4, 6, 7, 8, 11, 403 simulation gaming 72 realism 71 validity 69 simultaneous equation model 40 Singer, B. 495 Singh, B. 36 Single Path Matrix Estimation (SPME) 222, 225-32 calculations using 227-9 choice of assignment model 229-31 compared to MPME 231-2 evaluation of 241-2 principle of 225-7 site dictionary 283-4 Sjoberg, L. 10 Slavin, H. 231 Slovic, P. 5 Small, K. A. 68 Smeed, R. J. 253, 257 Smith, N. C. 497 Smith, T. 12 Smith, T. E. 529 Snell, J. 5 Snickars, F. 203 social motives 11-12 Sorbom, D. 43, 441 spacial configuration analysis 341-62 and movement 344-9 multiplier effect 346-7, 356, 360-1 pedestrian flows 346-8, 357, 360 relative asymmetry 342-3

vehicular flows 349, 353-4, 357-8 Sparrow, F. T. 528-9 Spiess, H. 201, 203-6, 208, 213, 217-18, 386 Srinivasan, V. 90 Starkie, D. 529 stated adaptation 69 experimental learning process 83-4 potentials and limits 82-4 quality of participation 81-2 respondents behaviour 75-6 simulation realism 71, 76 stated preference (SP) 68-9, 222, 436, 513, 516-17 air route choice 141-59 classification procedure 326 design 93-7 adaptive 97-9 effect on results 105-21 estimation 108-10 freight 123-39 low expectations of 91-2 NMB study 322-7 participation 92, 97 situational approach 322-5 theory and practice 89-102 tolerance level 98 see also analytic hierarchy process (AHP) Steer Davies Gleave 252 Stephan, D. G. 366, 381, 382 stepwise modelling 271 Stevens, A. 402 Stochastic User Equilibrium (SUE) 230-1, 237-9, 239-400, 247-8 Stopher, P. R. 264, 474 structural heterogeneity and model estimability 37-47 simulation experiment 39-45 subjective factors 437-41, 453 Sueyoshi, G. 494 supply and demand model 353-6 surveys 224-5 diachronic data 300, 303 diaries 366 household 300, 303 large-scale household 263-4 Lisbon and Porto 281-2 pilot study 282 purpose of 279-80 under-reporting 264, 265 versus counts 222-3 see also KONTIV surveys; panel data;

Index revealed preference (RP); stated adaptation; stated preference (SP) Svenson, O. 11, 12 Swait, J. 474-6 Sweden 106-21 Stockholm 200, 201, 207-17, 459-71 switching model 377 system dynamics 521, 523 Tamin, O. Z. 223-4 Tardiff, T. J. 425-6 Tay, R. 529 Taylor, M. A. P. 275, 279 technology 366, 402, 406-19 telecommuting 161-78 factors affecting adoption 167-9, 174-6, 177 and salary 172, 174-5, 177 for transport substitution 162 telecommuting adoption model 163-77 estimation results 172-7 survey data 165-6 utility thresholds 169-71 variance-covariance structure 171-2 Terza, J. V. 164 Terzis, G. 98, 102 Thaler, R. H. 4, 7 Thorndyke, P. W. 9 time airport access 156-7 for consumption 21-2, 23 conversion to goods 21 mode-specific coefficient 26 in models 20-2, 29 penalty 394, 398 total highway network travel 536-7 valuation 93-7 value of (VOT) 396 working 22, 26 see also travel time timetables 385, 387 Tischer, M. L. 438 Tng, H. 167 Tong, C. C. 366, 377, 379-80, 382 traffic assignment models 226, 229-31, 237-9 intercity 386-91 limitations 340 traffic counts 225 links 200 missing 244-6 and MPME 234

553

quality 246 and trip matrices 221-48 versus traffic surveys 222-3 traffic management 354 Train, K. 24, 25, 28 trains 93-7, 106-21 transfer index (TI) 468 transfers air travel 157 car-pooling 512 Lisbon and Porto 293 transport system management (TSM) 365-6 travel behaviour elderly people 299-315 long term trends 263-75 with subjective factors 437-41 see also behaviour travel time coefficient of variation (CoV) 253-4, 260 variability 259, 261 sources 253, 255-6 utility function 394 versus price 109 see also time travel time reliability choice of variables 256 and congestion 251, 253 methodology 255-6 results 257-8 supply effects 252-61 Treat, J. R. 49 Tretvik, T. 457-71, 529 TRIO software 129, 134 trip frequency 293 trip length 259, 261, 336 trip matrices 221-48 trip motives 290, 510 trip table 512-13 trip-chaining 270, 376 Truong, P. 24, 26 Trusell, J. 495 Tversky, A. 4, 7, 9, 10 uncertainty judgements 9-10 United Kingdom 68, 159 City of London 347, 354 Dept of Transport 252 London 254-5, 343-4 London Underground 100 United States 165-6, 366-82 unobserved heterogeneity 494-6, 497, 499501

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utility and constraints 20-3 and consumption 20-1 experienced and predicted 5 maximization 403-4, 409-11, 418 subjective expected 437 thresholds 169-71 utility function attributes of 412 with information 410-11 travel time 394 truncated conditional indirect 19 utility models 30, 473-4 random 386, 391 valuation bias 97 soft variables 99-101 van Berkum, E. C. 401-19 van der Mede, P. H. J. 401-19 Van Elslande, P. 49-64 van Vuren, T. 231, 239, 402 Van Wissen, L. J. G. 488 van Zuylen, H. J. 231 Vargas, L. G. 182 variables hard 93, 99 soft 93, 99-101 vehicular flow analysis 349, 353-4, 357Veldhuis, J. 158 Videla, J. 26, 30 Viegas, J. M. 279-97 Viton, P. 24, 26 Wachs, M. 302 wages and salaries 30, 172, 174-5, 177 see also income Walmsley, D. J. 6

Wardrop, D. 418 Watling, D. 402 Watterson, W. T. 488 Weibull, J. W. 203 Wermuth, M. 264 Wernsperger, F. 317-37 wholesalers freight choice 125-8 stratified random sample 126 Widlert, S. 99, 102, 105-21, 128, 457-71 Wigan, M. 270 Wilde, G. J. S. 60 Williams, H. C. W. L. 474 Wills, M. I.(or J.) 128, 476 Willumsen, L. G. 182, 223-4, 231, 251-61, 391, 415, 426-7, 432, 467 Wilmot, C. G. 458, 468 Winston, G. C. 26 Witte, A. D. 522 work-trip model Stockholm 463-8 structure 459-60 transferred 466-71 Wright, S. 36 Xu, J. 339-61 Yang, H. 224, 227, 529 Yap, C. S. 167 Yates, S. 13 Ye, R. J. 527-39 Yen, J.-R. 161-78, 163, 172 Young, J. 264 Zakay, D. 10 Zavoina, W. 163-4, 170 zone-internal traffic 244 Zupan, J. 340