Advances in Doctoral Research in Management

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Author: Luiz Moutinho | Graeme Hutcheson | Paulo Rita

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Volume

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Advances in Doctoral Research in Management

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Volume

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Advances in

D oct o r a l R e s earch

in Management Editor Luiz Moutinho University of Glasgow,UK

Associate Editors Graeme Hutcheson Manc h e s t Un e r i v e rt sy,i U K

Paulo Ritra ISCTE Business School, Lisbon, Portugal

World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

ADVANCES IN DOCTORAL RESEARCH IN MANAGEMENT Vol. 1 Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-256-044-0

Typeset by Stallion Press Email: [email protected]

Printed in Singapore.

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Advances in Doctoral Research in Management (ADRM) is a refereed academic research book series which publishes an annual volume devoted to disseminate excellence in doctoral research in management. It publishes seminal and challenging international doctoral research that could be seen as a benchmark in academic effectiveness which embraces the whole spectrum of academic research philosophies (from phenomenological/ ideographic to positivistic/nomothetic research).

Aims and Scope • To provide a robust refereed outlet for doctoral researchers in the management/business ﬁeld. • To encourage doctoral candidates to disseminate their work and receive positive and constructive feedback on their research projects. • To create a “focused forum and stage” in which some of the new and (potentially important) future research paradigms will be presented and tested among academics. • To become a most relevant academic publication in terms of the introduction of methodological issues, techniques and approaches which will ultimately beneﬁt doctoral students, their supervisors and other researchers. The planned scope will entail the following perspectives: • The annual volume’s coverage is cross-disciplinary since it entails all doctoral research output in the broad areas of management and business. • The main management disciplines from which it is expected to derive submissions will include marketing, strategy, international business, operations management, organisational behaviour, human resource management, organisational systems, ﬁnance, managerial economics and technology management.

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Editor Luiz Moutinho (University of Glasgow, UK)

Associate Editors Graeme Hutcheson (Manchester University, UK) Paulo Rita (ISCTE Business School — Lisbon, Portugal)

Editorial Review Board Enrique Bigne (University of Valencia, Spain) Eduard Bonet (University of Barcelona, Spain) Hilary Bradbury (Case Western Reserve University, USA) Charles Chien (Feng Chia University, Taiwan) Kaye Chon (The Hong Kong Polytechnic University, Hong Kong) Tom Elfring (Free University of Amsterdam, The Netherlands) Evert Gummerson (Stockholm University School of Business, Sweden) John Kraft (University of Florida, USA) Michel Laroche (Concordia University, Montreal, Canada) Robert Lawson (University of Otago, New Zealand) Barbara Lewis (Manchester School of Management, UK) Roderick Martin (University of Southampton, UK) Josef Mazanec (Vienna University of Economics and Business Administration, Austria) Robert Morgan (University of Cardiff, UK) Keith Punch (University of Western Australia, Australia) Hiroaki Sandoh (Kobe Gakuin University, Japan) Stephen Shugan (University of Florida, USA) Richard Thorpe (University of Leeds, UK) Keith Whitﬁeld (University of Cardiff, UK) Arch Woodside (Boston College, USA)

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ABOUT THE EDITORS

Luiz Moutinho Professor of Marketing, University of Glasgow. He completed his PhD at the University of Shefﬁeld in 1982 and held posts at Cardiff Business School, University of Wales College of Cardiff, Cleveland State University, Ohio, USA, Northern Arizona University, USA and California State University, USA, as well as visiting Professorship positions in New Zealand and Brazil. Between 1987 and 1989 he was the Director of the Doctoral Programmes at the Confederation of Scottish Business Schools and at the Cardiff Business School between 1993 and 1996. He was Director of the Doctoral Programme at the University of Glasgow, School of Business and Management between 1996 and 2004. He is the Editor of the Advances in Doctoral Research in Management (ADRM), and the Journal of Modelling in Management. One of Professor Moutinho’s primary areas of academic research is related to modelling processes of consumer behaviour. He has developed a number of conceptual models over the years in areas such as tourism destination decision processes, automated banking, supermarket patronage, among other areas. The testing of these research models has been based on the application of many different statistical computer modelling techniques ranging from multidimensional scaling, multinomial logit and linear structural relations to neural networks, ordered probit and tabu search. He has published 19 books: Problems in Marketing — Analysis and Applications (2004), second edition, co-authored (lead author) with Charles S Chien. Published by SAGE. Strategic Marketing (2003), co-authored with Laszlo Jozsa (Elsevier) Strategic Management in Tourism (2000). Published by CABI.

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About the Editors

Contemporary Issues in Marketing, co-authored with Martin Evans (MacMillan Business 1999) Strategic Planning Systems in Hospitality and Tourism, co-authored with Paul Phillips (CABI 1998). Quantitative Analysis in Marketing Management, co-authored with Mark Goode and Fiona Davies (Wiley 1998). Financial Services Marketing — A Reader, co-edited with Arthur Meidan and Barbara Lewis (The Dryden Press 1997). Applied Consumer Behaviour (1996), co-authored with Martin Evans and Fred van Raaif. Published by Addison-Wesley. Expert Systems in Tourism Marketing (1996), co-authored (lead author) with Paulo Rita and Bruce Curry. Published by the International Thomson Business Press. Tourist Marketing and Management Handbook (1995), Student Edition, co-edited with Stephen F Witt. Published by Prentice-Hall International. Cases in Marketing Management (1995), second edition. Published by Addison-Wesley. Computer Modelling and Expert Systems in Marketing (1994), co-authored (lead author) with Bruce Curry, Fiona Davies and Paulo Rita. Published by Routledge. Tourism Marketing and Management Handbook (1994), second edition, co-edited with Stephen F. Witt. Published by Prentice-Hall International. Cases in Marketing of Services — An International Collection (1993), co-edited with Arthur Meidan. Published by Addison-Wesley. Applied Marketing Research (1992), co-authored (lead author) with Martin Evans. Published by Addison-Wesley. Problems in Marketing: Analysis and Applications (1991). Published by Paul Chapman Publishing. Managing and Marketing Services in the 1990’s (1990), co-edited with Richard Teare and Neil Morgan. Published by Cassell plc, England. Cases in Marketing Management (1989). Published by Addison-Wesley. Tourism Marketing and Management Handbook (1989), co-edited with Stephen F. Witt. Published by Prentice-Hall International. He has over 350 refereed international publications. In addition to presenting papers at many international conferences, he also has had a vast number of articles published in journals such as

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About the Editors

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Journal of Business Research, Journal of Marketing Management, European Journal of Marketing, Journal of Strategic Marketing, Service Industries Journal, Journal of EuroMarketing, Journal of International Consumer Marketing, International Journal of Advertising, International Journal of Bank Marketing, Journal of General Management, European Management Journal, Journal of Professional Services Marketing, International Journal of Retail and Distribution Management, Irish Marketing Review, Journal of Marketing Channels, International Journal of Service Industry Management, Quarterly Review of Marketing, Marketing Intelligence and Planning, Journal of Retailing and Consumer Services among others. He is also a member of the Editorial Board of several international academic journals. Professor Moutinho has also received a number of awards for excellence in academic research in the USA, UK and Portugal. Luiz Moutinho has been a full Professor of Marketing since 1989 and was appointed in 1996 to the Foundation Chair of Marketing at the University of Glasgow. He holds Visiting Professorships at the University of Vilnius, Lithuania, Bled School of Management, Slovenia and Feng Chia University, Taiwan. Has run teaching courses and research seminars in Denmark, France, Holland, USA, Brazil, Mexico, Spain, Portugal, Italy, Croatia, Slovenia, Hungary, Greece, Lithuania, Finland, Taiwan, Australia, New Zealand, Austria, Mozambique and Mongolia.

Graeme D Hutcheson Dr Graeme Hutcheson is currently director of the MSc in Educational Research programme and postgraduate methodology training in the School of Education at Manchester University. He obtained his doctorate at Manchester University and subsequently worked at Strathclyde and Glasgow Universities. His current specialism is in the teaching and application of generalised linear models, and more generally, in the application of research methodology to social science data. He has worked in a number of areas including psychology, education, linguistics, artiﬁcial intelligence (AI), marketing and management. He is the author of numerous journal articles and books, including a book on generalised linear models (The Multivariate Social Scientist. Introductory Statistics using Generalised Linear Models).

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About the Editors

In collaboration with Professor Moutinho from Glasgow University, Dr Hutcheson has taught research methods and data analysis at a number of institutions across the world.

Selected publications Hutcheson, G. D., Henderson, M. M. and Davies, J. B. (1995). Alcohol in the workplace: costs and responses. Department of Education and Employment Research Series No. 59. Henderson, M. M., Hutcheson, G. D. and Davies, J. B. (1996). Alcohol and the workplace. WHO Regional Ofﬁce for Europe, World Health Organization Regional Publications, European Series, 67. Hutcheson, G. D. and Sofroniou, N. (1999). The Multivariate Social Scientist: Introductory Statistics using Generalized Linear Models. Sage Publications. Hutcheson, G. D., Baxter, J. S., Telfer, K. and Warden, D. (1995). Child witness statement quality: general questions and errors of omission. Law and Human Behaviour, 19(6), 631–648. Hutcheson, G. D. and Moutinho, L. (1998). Measuring preferred store satisfaction using consumer choice criteria as a mediating factor. Journal of Marketing Management, 14, 705–720. Moutinho, L. and Hutcheson, G. D. (2000). Modelling store patronage using comparative structural equation models. Journal of Targetting, Measurement and Analysis for Marketing, 8(3), 259–275. Davies, F., Moutinho, L. and Hutcheson, G. D. (2001). Exploring key neo marketing directions through the use of an academic think tank: A methodological framework. European Journal of Marketing, 36, 4. Sofroniou, N. and Hutcheson, G. D. (2002). Conﬁdence intervals for the predictions of logistic regression in the presence and absence of a variancecovariance matrix. Understanding Statistics: Statistical Issues in Psychology, Education and the Social Sciences, 1(1), 3–18.

Paulo Rita Dr Paulo Rita is currently Director of the Management Research Centre (MRC) and Associate Professor of Marketing at ISCTE Business School — Lisbon, Portugal. He obtained his PhD in Marketing at Cardiff Business School, University of Wales, UK, and subsequently a Post Doctorate on Web Marketing at the University of Nevada, Las Vegas, USA.

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He was Director of the Doctoral Programme in Marketing at ISCTE Business School in 2000–2001. He is Associate Editor of the Advances in Doctoral Research in Management (ADRM). His current research interests are focused on Web Marketing and E-Commerce, Intelligent and Decision Support Systems in Marketing, Neuromarketing and Consumer Behaviour, and Marketing for Hospitality and Tourism. Dr Rita has published three books, including Expert Systems in Tourism Marketing (1996) co-authored with Luiz Moutinho and Bruce Curry (published by the International Thomson Business Press), and Computer Modelling and Expert Systems in Marketing (1994) co-authored with Luiz Moutinho, Bruce Curry and Fiona Davies (published by Routledge). In addition to presenting over 50 papers at international conferences, he also has had six book chapters and 23 articles published in journals such as Service Industries Journal, European Journal of Marketing, Journal of International Consumer Marketing, Annals of Tourism Research, International Journal of Contemporary Hospitality Management, Marketing Management, among others. He is also a member of the Editorial Board of ﬁve academic journals, and has supervised three PhD theses and 21 master dissertations, and examined six PhD theses and 22 master dissertations. Dr Rita has taught Research Methods at both Doctoral and Master programmes, E-Business and Information Management (Master programmes) Web Marketing & E-Commerce (Postgraduate courses, Executive education) Marketing Decision Support and Expert Systems (Postgraduate courses), Marketing Management & Strategy (Master programmes, Executive education), Consumer Behaviour (Master programmes), Tourism Marketing (Postgraduate courses), International Marketing (Postgraduate courses) in Portugal, Spain, Czech Republic, Mozambique, Cape Verde and Brazil.

Selected publications Águas, Paulo, Paulo Rita, Jorge Costa (2006). Performance as a classiﬁcation criterium of tourist origins and destinations, Service Industries Journal, 26(3) (April). Moutinho, Luiz, Paulo Rita, Shuliang Li (2006). Strategic diagnostics and managerial judgement: a hybrid knowledge-based approach, Intelligent Systems in Accounting, Finance and Management.

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Pires, Guilherme, John Stanton, Paulo Rita (2006). The Internet, consumer empowerment and marketing strategies, European Journal of Marketing. Rita, Paulo (2000). Marketing, Internet et services en ligne: une application à l’industrie du tourisme, Marketing Management, No. 4, 32–40. Rita, Paulo (2000). Tourism in the European union, International Journal of Contemporary Hospitality Management. Costa, Jorge, Paulo Águas, Paulo Rita (2000). A tourist market portfolio for Portugal, International Journal of Contemporary Hospitality Management. Moutinho, Luiz, Paulo Rita, Bruce Curry (1996). Expert Systems in Tourism Marketing. International Thomson Publishing. Moutinho, Luiz, Bruce Curry, Paulo Rita, Fiona Davies (1994). Computer Modeling and Expert Systems in Marketing, Routledge. Rita, Paulo, Luiz Moutinho (1994). An expert system for promotion budget allocation to international markets. In Muzzaffer Uysal (ed.) Global Tourist Behavior. International Business Press. Moutinho, Luiz, Paulo Rita (1994). Expert systems in tourism. In Stephen Witt and Luiz Moutinho (eds.) Tourism Marketing and Management Handbook (Second Edition). Prentice Hall International. Rita, Paulo, Luiz Moutinho (1994). Promotion budget allocation for national tourist ofﬁces using an expert system. In Stephen Witt and Luiz Moutinho (eds.) Tourism Marketing and Management Handbook (Second Edition). Prentice Hall International. Rita, Paulo (1994). Acquiring expertise for a knowledge-based system in tourism marketing. In Vicky Wass and Peter Wells (eds.) Principles and Practice in Business and Management Research. Gower. Rita, Paulo, Luiz Moutinho (1994). An expert system for promotion budget allocation to international markets, Journal of International Consumer Marketing, 6(3), 101–121. Rita, Paulo, Luiz Moutinho (1994). An expert system for national tourist ofﬁces, Annals of Tourism Research, 20(1), 143–145. Rita, Paulo, Luiz Moutinho (1992). Allocating a promotion budget, International Journal of Contemporary Hospitality Management, 4(3), 3–8.

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ACKNOWLEDGEMENTS

The editors express kind thanks to the reviewers, who assisted with the reviews involved in this book. Chris Burke (University of Wales, Bangor, UK) Margarida Cardoso (ISCTE Business School — Lisbon, Portugal) David Carson (University of Ulster, UK) Arnaldo Coelho (University of Coimbra, Portugal) Carlos Lucas de Freitas (Instituto Superior Técnico — Lisbon, Portugal) Llyod Harris (University of Cardiff, UK) Kunhuang Huarng (Feng Chia University, Taiwan) Michael Humphreys (University of Nottingham, UK) John Kraft (University of Florida, USA) Michel Laroche (Concordia University, Canada) Barbara Lewis (University of Manchester, UK) Wouter De Maeseneire (Erasmus University, Rotterdam, The Netherlands) Donald MacLean (University of Glasgow, UK) Robert McIntosh (University of Strathclyde, UK) Rui Menezes (ISCTE Business School — Lisbon, Portugal) Robert Morgan (University of Cardiff, UK) James O’Kane (University of Northumbria, UK) Clara Raposo (ISCTE Business School — Lisbon, Portugal) Richard Thorpe (University Leeds, UK) James Wilson (University of Glasgow, UK) Arch Woodside (Boston College, USA) Tiffany Hui-Kuang Yu (Feng Chia University, Taiwan)

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CONTENTS

Aims & Scope

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Editorial Board

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About the Editors

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Acknowledgements

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Editorial

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DOCTORAL RESEARCH PAPERS Knowledge Transfer: A Review to Explore Conceptual Foundations and Research Agenda Sajjad M. Jasimuddin Negotiating Incommensurability in Marketing Theory Mark Tadajewski, Jaqueline Pels, Michael Saren

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Explaining Ecological Product Purchase Using Consumers’ Psychographic Characteristics Elena Fraj, Eva Martínez, Teresa Montaner

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Extensions of Logistic Growth Model for the Forecasting of Product Life Cycle Segments Mladen Sokele, Vlasta Hudek

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Contents

Defensive Strategies and Consumers’ Bounded Rationality: An Artiﬁcial Market Simulation Josef A. Mazanec, Ulrike Schuster, Jürgen Wöckl A User Evaluation of Web Recommender Systems Ulrike Bauernfeind The Determinants of Relationship Marketing: An Application to Thermal Spas Joaquim Antunes Supermarket Site Assessment and the Importance of Spatial Analysis Data Armando B. Mendes, Margarida G. M. S. Cardoso, Rui Carvalho Oliveira

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DOCTORAL RESEARCH NOTES A Framework for Corporate Crisis Management: Applications to SMEs in Australia Mohammed Aba-Bulgu, Sardar M. N. Islam

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Option Games, Asymmetric Information and Merger Announcement Returns Hongbo Pan, Xinping Xia

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RESEARCH METHODOLOGY PAPERS Analysing Data Using GLM Models Graeme D. Hutcheson The Issue of Missing Values, their Presence and Management: A Relevant Demonstration of Data Analysis in Marketing Using CaRBS Malcolm J. Beynon

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EDITORIAL

Part 1 After having been involved with doctoral research for many years (I have been Director of Doctoral Programmes for 17 years), I can clearly say that I have developed a passionate linkage with this particular scholarly activity. So much so that, a few years ago, I had the idea of launching a Journal of Doctoral Research in Management, although I never had any particular inclination to take on a job as an editor of an academic refereed outlet. Despite many views reinforcing the idea that doctoral research is normally published in specialised academic channels, and according to the different topics and management areas of research, I have persevered and grateful to World Scientiﬁc Publishing (WSP) for believing in the project. WSP offered to publish my idea of the Journal but in the format of a book series, although all the editorial and refereeing policies would be the same as traditional robust academic journal. Hence, the scholarly launch of Advances in Doctoral Research in Management (ADRM)! Because ADRM is striving for very high standards in terms of paper reviewing and the subsequent refereeing process, as well as a relatively moderate submission rate which can be understandable in the case of a new academic publication, the previously planned inception into the academic market of ADRM for 2005 had to be delayed and re-scheduled for 2006. But ﬁnally, my project comes to fruition and I really hope that the quality of submissions and the level of acceptance by the doctoral research community are both going to be sustainably higher in the future and that ADRM can play an important dissemination role in terms of the most outstanding doctoral research in management. I would like to thank a number of people at World Scientiﬁc Publishing, namely Kim Tan for trusting my ideas right from the beginning; Chean Chian Cheong, my Editor, for the excellent work carried out at the Editorial Ofﬁce of ADRM; and Hooi Yean Lee and Serene Fong of the marketing xvii

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department for all their help and support to the project. I have also to thank Sylvia Kerrigan for her initial tremendous aid as an Editorial Administrator at the University of Glasgow. In addition, I can only show my gratitude to both of my Associate Editors, Graeme Hutcheson and Paulo Rita, for all the encouragement, assistance, advice and friendship all of which have been proven critical and essential for the successful launch of ADRM. A ﬁnal big thank you to all the authors, reviewers and Editorial Board members who have endorsed ADRM with their contributions! I sincerely hope that the intended audience of ADRM — doctoral researchers and academics — provide us with the necessary feedback related to the scientiﬁc robustness of ADRM so that this book series can be constantly improved. To all, please accept my sincere gratitude. Professor LUIZ MOUTINHO Editor, ADRM

Part 2 In the knowledge-based society, knowledge transfer is the key issue of an organisation’s competitive advantage. The topic of knowledge transfer within the knowledge management discipline is an emerging research ﬁeld with many issues yet to be explored. Knowledge transfer is widely emphasised as an important issue for competitive advantage of an organisation. However, there is little or no research on determinants of choice of knowledge transfer media, and the integration of knowledge transfer and storage are two potential research areas. Jasimuddin attempts to provide a roadmap of the existing literature in knowledge transfer. The purpose of the paper is to identify valuable directions for new research into knowledge management, particularly knowledge transfer. In this regard, the rationale for selecting a particular knowledge transfer mechanism is one of the key organisational problems that ﬁrms encounter, and that warrants further addressing. The important point is that it will be easier to conceptualise and utilise knowledge if we can recognise the appropriate mechanism to transfer knowledge. The paper undertakes a comprehensive review of the relevant knowledge management literature so as to understand the existing literature within the area and to position the research questions within the context of that literature. This discussion is actually

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taking a ﬁrst step towards developing some arguments about determinants of mechanism selection of knowledge transfer, and the connectivity of knowledge transfer and storage in order to broaden our understanding of the notion of knowledge transfer. It is also hoped that such an effort will engender interest in the topic of knowledge management, and knowledge transfer in particular, and, in so doing stimulate other researchers to address some of the research questions in more direct studies. Furthermore, the research framework presented here provides linkages between different topics and sub-topics reviewing numerous studies which helps to assist prospective researchers in identifying areas where considerable progress has been made and also in organising the considerable number of the existing studies. Tadajewski, Pels and Saren review the recent paradigm debates in marketing and reﬂect on the current pluralism of paradigms. It make the case that a future important direction for marketing theory is multiple paradigm research; an avenue that has been widely explored in organisation studies, but as yet has had little extended treatment in marketing or consumer research. As a ﬁrst movement in this direction they review the debates that have taken place in organisation studies showing how the so-called “paradigm mentality” has been seen to hamper constructive debate across paradigms, whereby researchers from different paradigms can fail to agree on inter-paradigm standards of evaluation so that theory choice between the divergent outputs of two different paradigms cannot easily be resolved. Then they question the veracity of the early incommensurability thesis apparent in Kuhn’s writing and the subjectivism that follows from Feyerbend’s interpretation of incommensurability, negotiating these arguments by drawing upon the Kuhnian concept of taxonomical lexicon, to suggest that learning alternative paradigms is similar to learning another natural language. By way of a conclusion they also reﬂect on the possibilities and possible problems associated with undertaking doctoral research using a multiple paradigmatic team brought together to contribute the distinct insights that each paradigm brings to the project. Fraj, Martinez and Montaner identify the characteristics of the consumer willing to purchase ecological products and consider their disposition to buy these products even when their price is higher than the non-ecological products. They consider in their study variables relating to ecological behaviour such as values, lifestyle, personality and attitude. Their results conﬁrm that the psychographic variables used differentiate the consumer proﬁle who is willing to purchase ecological products at different prices. These results reveal

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that companies face a wide demanding market and considering the environmental principles consistently in their global and marketing strategies may give them a sustainable competitive advantage which is critical today, given that consumers increasingly appreciate ecological issues. Proper forecast of product market diffusion enables optimal planning of resources, investments, revenue, marketing and sales. Quantitative forecasting methods for this purpose rely on sigmoidal growth models such as logistic growth and the Bass model, which are acceptable for the ﬁrst adoption interval of product life cycle (PLC). Modelling of other PLC segments requires complex models that need large set of input data that limits their application for the forecasting purposes. Sokele and Hudek present extensions of the logistic growth model that combine the principle of sigmoidal growth and the concept of interpolation splines. In addition, the adaptation of the logistic model is shown to be congruent with the Bass model. Applications of developed models for the forecasting of PLC segments are analysed and examined, together with possible ways of interaction between different products. Developed models and interaction types enable forecasting of the entire PLC with a minimum set of input data, or assessment of qualitative forecasting results. In the case of a minimum set of input data, the introduced logistic spline model is proposed for the forecasting of product life cycle segments with monotone growth or decline. The whole product life cycle modelling, that includes a combination of growth and decline, should be achieved by combining logistic splines and sigmoidal envelopes described within the interaction between products on a market. Mazanec, Schuster and Wöckl explore new ways of exposing defensive strategy recommendations to varying market conditions. This experiment analyses the consequences of changes in three factors: (1) a consumer population pursuing noncompensatory brand choice rules; (2) distinctive versus indistinctive (nonsegmented) preference structures; and (3) low versus high responsiveness to advertising. The consumer’s response is simulated on an Artiﬁcial Consumer Market (ACM). The ACM assists in constructing the surface of the incumbent’s proﬁt function under a ﬁxed-entry scenario and for experimentally varied market characteristics. The expected inﬂuence of consumers’ noncompensatory choice rules on defensive strategy is clearly demonstrated. Quite remarkably, this most amazing of the original gametheoretic results from “Defender” receives new support from ﬁndings gained with a completely different methodology of agent-based simulation.

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Decision-aid systems like web recommenders are an appropriate means to reduce this abundance of information by ﬁltering out relevant items according to the user’s previously stated preferences. Therefore, the impact of recommender systems is scarcely researched. Bauernﬁend proposes a model covering the factors impacting consumer satisfaction with recommender systems in her article. The model itself is designed empirically tested using three recommender systems. Respondents will be asked to simulate a real system user interaction and to evaluate the recommender systems afterwards. The objective will be to identify factors having the most signiﬁcant impact on recommender system satisfaction. The conceptualisation relates to the Technology Acceptance Model (TAM). Trust, hedonic beneﬁts and experience are important constructs belonging to the research model depicting this particular interaction with a website. Relationship marketing has become a decisive approach for the new marketing context organisations face. It is deﬁned as an interactive process which allows an organisation to establish stable, long-lasting relationships with their customers. The study by Antunes is centred on the analysis of the different roles performed by the determinants of relationship marketing and the environmental factors in the satisfaction and customer loyalty. The importance of satisfaction, trust and commitment as mediating variables are analysed in the process of relationship marketing. The empirical study is carried out with 346 people who patronise Portuguese thermal spas, using quota sampling process. In order to validate this theoretical model and to test the hypotheses a structural equation model is used. The role of the mediating variables: satisfaction, trust and commitment in the relationship marketing process, is unmistakable. These variables are considered fundamental to bather loyalty. Trust in the organisation plays a crucial role as it is a prerequisite to commitment. This model has the particularity of including a simultaneous analysis of relationship marketing variables and environmental factors and their direct and indirect effects on the loyalty of spa customers. In this way this study validates the various dimensions of relationship marketing and its inﬂuence on bather satisfaction and loyalty. It contributes with the development of new measurement instruments (the scales used), validated through different statistical methods. As it is a fairly recent area of knowledge, an added difﬁculty, it has an innovating character.

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Mendes, Cardoso and Oliveira in their paper explored the supermarket site assessment problem. This work proposes a 3-step method for stores’ site turnover forecast. In order to deal with demographic and competition data related to each supermarket, they use neighbourhood delimitation techniques. Three alternative delimitation techniques and two allocation procedures are compared. Results are evaluated based on the proportion of sales turnover variance that the alternative predictors are able to explain. Finally, they compare the relative importance of spatial data predictors in site assessment evaluation, using Dominance Analysis. As a result, the relevance of spatial analysis predictors clearly emerges being only dominated by the “sales area”. At ADRM, we are also planning to introduce a section on doctoral research notes. These full double- or triple-blind refereed papers which can be (i) shorter versions of an extended monograph; (ii) doctoral research papers already submitted as a research note; or (iii) a conventional doctoral research paper which has been shortened following a decision by the ADRM editors and with the full acquiescence of the author(s). In this ﬁrst issue of ADRM, we are including one of these such doctoral research notes. Bulgu and Islam developed a general framework for the design of corporate crisis management strategies. The focus here is on the identiﬁcation and analysis of stages of corporate crisis management, the analysis of the implications of various communication strategies, as well as the identiﬁcation and analysis of appropriate promotional strategies during various phases of business interruption. The authors apply this conceptual model and subsequent considerations to the realm of small and medium size enterprises (SMEs). They claim that it is essential to understand the impact of the reconstruction of tangible and intangible assets. Under the circumstance of industry-wide uncertainty, the paper by Pan and Xia models the intuition that returns to the acquiring ﬁrm rely on the different stock market valuations between managers and investors of merging ﬁrms which result from the asymmetric information on the merging synergism between them. In their paper the authors present a dynamic model of mergers based on stock market valuations of merging ﬁrms with industry-wide uncertainty. The model incorporates asymmetric information and determines the terms and timing of mergers by solving cooperative option games between

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acquiring shareholders and target shareholders. The model predicts that (1) returns to acquiring shareholders can be negative if the managers of participants are much more optimistic over merging synergism than outside investors; (2) returns to acquiring shareholders are negatively correlated with the size of the acquirer; and (3) returns to target shareholders are negatively correlated with the size of the target. At ADRM, we will strive to introduce in each volume, a selected number of research methodology papers that could trigger new research insights and beneﬁt doctoral researchers. In this ﬁrst volume, we are presenting two of such articles. In the ﬁrst of these research methodology papers, Hutcheson introduces a focus on analysing data using generalised linear models (GLMs). He discusses several generalised linear modelling techniques according to the type of response variable under study. The analytical presentation starts with the modelling approach used for continuous data — OLS regression (simple and multiple), followed by modelling binary data (simple logistic regression). The proportional odds model for ordered categorical data and multinomial logistic regression for unordered categorical data are also presented. Missing values are an often-alleged incumbency to the effectiveness of successful data analysis. Their presence able to be explained or not may be the issue, the very least acknowledges. In this second research methodology paper, Beynon discusses the extant issues of the presence of the missing values in data analysis, with particular attention to their management, including imputation. Following this discussion, the nascent Classiﬁcation and Ranking Belief Simples (CaRBS) system for data analysis (object classiﬁcation) is presented which has the distinction of not requiring the a priori consideration (management) of any missing values present. Moreover, they are treated as ignorant values and retained in the analysis, a facet of CaRBS being associated with the notion of uncertain reasoning. A problem on the classiﬁcation of standard and economy food products is considered, with knowledge on their inherent nutrient levels used in their discernment. The visualisation of the intermediate and ﬁnal results offered by the CaRBS system allows a clear demonstration of the effects of the presence of missing values, within an object classiﬁcation context. We sincerely hope that you will ﬁnd ADRM a useful and academically robust source and outlet for doctoral research in management, and we look forward to receiving your comments, constructive feedback, suggestions and,

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above all, submissions so that we can continually enhance the quality and scope of Advances in Doctoral Research in Management. Luiz Moutinho Graeme Hutcheson and Paulo Rita

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DOCTORAL RESEARCH PAPERS

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1 KNOWLEDGE TRANSFER: A REVIEW TO EXPLORE CONCEPTUAL FOUNDATIONS AND RESEARCH AGENDA Sajjad M. Jasimuddin School of Management and Business University of Wales, Aberystwyth Cledwyn Campus Ceredigon SY23 3DD, UK [email protected] Received October 2004 Accepted October 2005 The topic of knowledge transfer within the knowledge management discipline is an emerging research ﬁeld with many issues yet to be explored. Knowledge transfer is widely regarded as important for enhancing the competitive advantage of an organisation. Researchers have shown much interest in various aspects surrounding knowledge transfer, including factors affecting knowledge transfer, knowledge transfer for innovation, and knowledge transfer process. However, there are little or no research on determinants of choice of knowledge transfer media and the integration of knowledge transfer and storage. This paper attempts to provide a roadmap of the existing literature in knowledge transfer. Its purpose is to identify valuable directions for new research into knowledge management, particularly knowledge transfer. This is done by reviewing the relevant literature to develop research questions. The research framework presented here provides linkages between different topics and sub-topics reviewing numerous studies, which will help researchers sketch future research phenomenon and, in so doing stimulate other researchers to address some of the research questions in more directed studies.

Keywords: Knowledge management, knowledge transfer, organisational memory, innovation, knowledge transfer mechanism.

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1.

Introduction

The term “Knowledge Management” refers to the efforts of managing knowledge of an organisation so as to enhance its competitive advantage. As a key concern in the “post-industrial” society, organisations need to emphasise the importance of the creation, acquisition, transfer, retention, retrieval, and use of organisational knowledge, which seems to be the major tasks of knowledge management. The majority of the existing knowledge management literature tends to focus on various issues including knowledge typology (Polanyi, 1958; Nonaka, 1994; Spender, 1995; Blackler, 1995; Jasimuddin, 2005a), knowledge transfer (Albino, 1999; Argote and Ingram, 2000; Smith and McKeen, 2003; Connell et al., 2003; Pan and Scarbrough, 1999; Huber, 2001), knowledge creation (Nonaka, 1994; Nonaka and Takeuchi, 1995; Nonaka and Kanno, 1998; Jenkins and Balogun, 2003), and knowledge storage and retrieval (Walsh and Ungson, 1991; Olivera, 2000; Stein and Zwass, 1995; Sherif, 2002; Anand et al., 1998; Scarbrough, 1995; Jasimuddin et al., 2005a). Most speciﬁcally, knowledge transfer has been identiﬁed as a major focus area for knowledge management (Hendriks, 1999). In a survey result, McAdam and McCreedy (1999) show that knowledge transfer is considered as the key element of knowledge management by the majority of the respondents. Knowledge transfer is widely emphasised as a strategic issue for the competitive advantage of an organisation (Cohen and Levinthal, 1990; Albino, 1999; Argote and Ingram, 2000). Realising the signiﬁcance of knowledge transfer as an important research topic, Holtshouse (1998, p. 227) suggests that research on how to transfer knowledge between seekers and providers is one of the three priority areas for further research. Researchers within the knowledge management ﬁeld have shown interest in various issues surrounding knowledge transfer, including factors inﬂuencing knowledge transfer (Argote and Ingram, 2000; Hendriks, 1999; Kalling, 2003; van den Hoff and van Weenen, 2004), knowledge transfer for innovation (Hogberj and Edvinsson, 1998; Gilbert and Cordey-Hayes, 1996) and knowledge transfer process (Szulanski, 1996; Huber, 1991). However, it is also acknowledged as a major challenge among the researchers (Argote, 1999; Argote et al., 2000). Argote (1999), for example, argues that successful knowledge transfer is still difﬁcult to achieve. This has prompted the author to review the existing knowledge management literature in order to focus on several issues relating to the notion of

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knowledge transfer. The goal of this paper is to identify research opportunities relevant to knowledge transfer. This is done by reviewing the relevant literature to develop research questions. Therefore, this paper is organised as follows. First, the importance of knowledge transfer in an organisation is discussed. Next, a navigation process of the emerging theories of knowledge transfer is presented. Then the available literature is reviewed to explore the future research agenda concerning knowledge transfer and to set out research questions. Finally, conclusions are made.

2.

The Notion of Knowledge Transfer

Knowledge transfer is the process by which such transfer is accomplished between the contributor and the user of knowledge through some communication channels. Despite the fact that knowledge transfer within the knowledge management discipline is a relatively recent topic, several researchers, most notably Hendricks (1999), Nonaka and Hedlund (1991), Szulnaski (2000), and Kalling (2003), have produced a variety of its deﬁnitions. Argote et al. (2000, p. 3), for example, deﬁne knowledge transfer in organisations as “the process through which one unit (e.g., group, department, or division) is affected by the experience of another”. In parallel with this, knowledge transfer involves the exchanging of knowledge from one person to another (Lind and Persborn, 2000; Bender and Fish, 2000; Albino et al., 1999; Jasimuddin, 2005b). The knowledge transfer among employees in an organisation is considered to be a crucial process in business (Szulanski, 1996; Kalling, 2003; van den Hoff and van Weenen, 2004; O’Dell and Grayson, 1998; Osterloh and Frey, 2000). Gibert and Cordey-Hayes (1996) argue that the organisation’s success depends upon its ability to improve its capabilities by assimilating new technology through knowledge transfer. The Gibert and Cordey-Hayes’s argument (1996) is developed by Cohen and Levinthal (1990) who suggest that knowledge transfer is a critical factor for a ﬁrm’s ability to respond to changes, innovate and achieve competitive success. In the emerging knowledge-based society, the ability to transfer knowledge within an organisation has been found to contribute to the performance of the organisation in both manufacturing (Galbraith, 1990) and service sectors (Darr et al., 1995). Parallel to this, Barrett et al. (2004, p. 1) contend along similar lines noting that the major emphasis of organisations is placed on the processes of knowledge transfer, which are increasingly seen as crucial

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to organisational success. Reﬂecting this view, Argote et al. (2000, p. 1) argue that knowledge transfer is becoming increasingly important in organisations, pointing out that organisations which are able to transfer knowledge effectively from one employee to another are more productive and more likely to survive than organisations that are less adept at knowledge transfer. Due to its potentialities to enhance competitive advantage, it is argued that the question that becomes prevalent is not whether, but how quickly an organisation can accomplish knowledge transfer among its members. Although remarkable increases in organisational performance is evident by knowledge transfer, such transfer is also acknowledged as a major challenge among the researchers and practitioners. Several scholars (i.e., Arogate, 1999; Argote et al., 2000; Szulanski, 1996, 2000) assert that the effectiveness of knowledge transfer varies considerably among organisations. Szulnaski (2000), for example, points out that intraﬁrm transfers of knowledge are often labourious, time consuming, and difﬁcult. Our understanding of the theory of knowledge transfer is still in its most emergent stages. Similarly, Smith and McKeen (2003) contend that the knowledge transfer theory is still in its most rudimentary stages. This has encouraged the researcher to focus on issues surrounding successful knowledge transfer. The issues relating to the notion of knowledge transfer are discussed in the following sections.

2.1. Motivators and barriers of knowledge transfer Van den Hoff and van Weenen (2004) argue that determining the factors that promote or impede the knowledge transfer per se constitutes an important area of knowledge management research. It is found that the majority of the existing literature tends to focus on factors inﬂuencing knowledge transfer. In reviewing the literature, a very broad range of the forces that may inﬂuence the knowledge transfer in organisations is found available. A growing body of empirical studies conducted by scholars (e.g., O’Dell and Grayson, 1998; Szulanski, 1996; Connelly and Kelloway, 2001; Hendricks, 1999; Pan and Scarbrough, 1999; Davenport and Prusak, 1998; Kelloway and Barling, 1999; Cross et al., 2001; Rush, 2001; McDermott and O’Dell, 2001; Argote and Ingram, 2000; Kalling, 2003; van den Hoff and van Weenen, 2004; Smith and McKeen, 2003) provide some light on factors that stimulate or inhibit knowledge transfer. Having reviewed the literature, the forces that possibly inﬂuence the knowledge transfer initiatives can be categorised under ﬁve broader groups, namely, cognitive factors, motivational

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and psychological factors, managerial factors, technical factors, and social factors. However, Szulanski (1996), for example, claims that the biggest barrier to knowledge transfer is negligence on both ends of the transfer, followed by the absorptive capacity of the user and the lack of social ties between the actors as the second barrier and the third barrier respectively.

2.2. Knowledge transfer for innovation Viewing knowledge transfer as a major focus area for knowledge management, the limited but growing literature on various aspects concerning the knowledge transfer for innovation are currently found available. Academics namely, Hogberj and Evinsson (1998), Gilbert and Cordey-Hayes (1996), Nonaka and Takeuchi (1995), and Hall (2001) recognise the importance of knowledge transfer and making that knowledge available for innovation. The relevant literature reveals that the existing knowledge in an organisation may be utilised for further development of knowledge which is popularly termed as knowledge creation (Hall, 2001; Gilbert and Cordey-Hayes, 1996; Nonaka and Takeuchi, 1995) or to reuse for decision making and other business purpose (Walsh and Ungson, 1991; Connell et al., 2003).

2.3. Knowledge transfer process Most researchers in the knowledge management ﬁeld tend to view knowledge transfer either as “an act of transmission and reception” or to think in terms of “a process of reconstruction”. Putting it differently, Albino et al., (1999) argue that the knowledge transfer process can be conceptualised in terms of an operational level of analysis (the information system), a conceptual level of analysis (the interpretative system) or a combination of both. From an operational point of view, the knowledge transfer is a communication process with information processing activities in which a contributor can transfer knowledge to others conveyed by an appropriate mechanism (Lind and Persborn, 2000; Bender and Fish, 2000; Albino et al., 1999; Kalling, 2003), whereas from the conceptual viewpoint, the knowledge transfer is strictly connected to the concept of learning organisation (Gilbert and Cordey-Hayes, 1996; Huber, 1991; Baranson and Roark, 1985; Steensma, 1996). According to Davenport and Prusak (1998, p. 1), knowledge transfer process involves both the transmission of information to a recipient and absorption and transformation from one person to another person.

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3.

Narrowing Down a Researchable Topic to Explore Future Research Agenda

Prior to conducting any research, a researcher needs to review the existing literature to avoid duplicating previous work (Bailey, 1997; Smith and Biley, 1997), and to show how and why the current study could add to knowledge. Reﬂecting this view, Webster and Watson (2002, p. xiii) argue that a review of prior literature is an essential feature of any academic research in order to create a foundation for advancing knowledge and facilitating theory development. Taking as an example the broad area of knowledge management, the relevant management literature has been surveyed so as to show how a research topic can be narrowed down to a workable size (see Figure 1). The map provides a reasonably thorough coverage of core themes and issues in knowledge management. It pulls the issues together in order to narrow down to a research topic and subsequently explore research gaps that still exists in the knowledge management’s repertoire. As mentioned earlier, the majority of the existing knowledge management literature tends to focus on knowledge typology, knowledge transfer, knowledge creation, and knowledge storage and retrieval. In the meantime, knowledge transfer has been identiﬁed as the critical element of successful knowledge management implementation. The fact is that scholars have already shown interest in factors inﬂuencing knowledge transfer, knowledge transfer for innovation, and knowledge transfer process. The narrowing down process is elaborated to identify unexplored issues for future research. Although the knowledge transfer process seems to be explained in terms of an operational level of analysis, a conceptual level of analysis, or a combination of both, the research topic can be narrowed down by looking at only one perspective, for example, the operational level of analysis in which the knowledge transfer is a communication process. However, the majority of the literature on knowledge transfer has ignored the issues with respect to how knowledge is transferred in organisations and why a particular mechanism is chosen to knowledge transfer. We believe that the knowledge transfer process seems to accomplish well when an appropriate mechanism of knowledge transfer is selected. Viewing knowledge transfer within the operational perspective, there is a research gap in understanding why people select one particular means to carry out the transfer of knowledge. Against this backdrop, the factors that may inﬂuence the determination of a particular mechanism of knowledge transfer warrant further research.

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Knowledge Management

Knowledge Transfer

Knowledge Typology (Polanyi, 1958; Nonaka, 1994; Spender, 1995; Blackler, 1995; Jasimuddin, 2005a)

(Albino et al., 1999; Connell et al., 2003; Hendriks, 1999; Szulanski, 1996; Argote et al., 2000; McEvily and Zaheer, 1999; Kalling, 2003; Argote and Ingram, 2000; Huber, 2001; Darr and Kurzberg, 2000; Pan and Scarbrough, 1999; Smith and McKeen, 2003; Jasimuddin, 2005b)

Factors Influencing Transfer (Argote, 1999; Argote and Ingram, 2000; Hendriks, 1999; Kalling, 2003; van den Hoff and van Weenen, 2004; Szulanski, 1996; Smith and McKeen, 2003)

Knowledge Creation (Nonaka, 1994; Nonaka and Takeuchi, 1995; Nonaka and Kanno, 1998; (von Krogh, 1998; Jenkins and Balogun, 2000)

Transfer Process (Albino et al., 1999; Hunschild and Miner, 1997; Baum and Ingram, 1998; Darr and Kurzberg, 2000; Darr et al., 1999; Larsson et al., 1998; McEvily and Zaheer, 1999; Connell et al., 2001)

Operational level of Analysis

Knowledge Storing and Retrieval (Walsh and Ungson, 1991; Olivera, 2000 Stein, 1995 Sherif, 2002; Anand et al., 1998; Stein and Zwass, 1995; Hansen, 1999; Scarbrough, 1995; Marsh and Morris, 2001; Jasimuddin et al., 2005a)

Transfer for Innovation Hogberj and Evinsson, (1998), Gilbert and Cordey-Hayes, (1996), Hall, (2001)

Conceptual level of Analysis

(Albino et al., 1999; Bender and Fish, 2000; Kalling, 2003)

(Albino et al., 1999; Gilbert and CordeyHayes, 1996; Huber, 1991; Steensma, 1996)

Knowledge Transfer Mechanism (Nonaka and Takeuchi, 1995; Hansen et al., 1999; Davenport and Prusak, 1998; Pan and Scarbrough, 1999; Bhatt, 2001; Huber, 2001, Roberts, 2000; Jasimuddin et al., 2004; Dixon, 2000; Alavi and Leidner, 2001)

Intra-organizational Transfer (Szulanski, 1996; Kalling, 2003; van den Hoff and van Weenen, 2004; O’Dell and Grayson, 1998; Osterloh and Frey, 2000; Connell et al., 2003)

Knowledge currently in use (Argote and Ingram, 2000; Cohen and Levinthal, 1990; Hansen, 1999; Hogberj and Evinsson, 1998; Hendriks, 1999; Connell et al., 2003)

Inter-organizational Transfer (Albino et al., 1999; Hunschild and Miner, 1997; Darr and Kurzberg, 2000; Darr et al., 1999; Larsson et al., 1998; McEvily and Zaheer, 1999; Connell et al., 2001)

Knowledge of the past (Marsh and Morris, 2001; Argote and Ingram, 2000; Walsh and Ungson, 1991; Olivera, 2000; Stein, 1995 Sherif, 2002; Ackerman and Malone, 1990; Anand et al., 1998; Goldstein, 1991; Huber, 1991)

The determinants in selecting an appropriate mechanism of knowledge transfer and the linkage between knowledge transfer and knowledge storage Figure 1. Topics of knowledge management research.

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Meanwhile, knowledge transfer is important both within an organisation, i.e., intra-organisational (Szulanski, 1996; Kalling, 2003; van den Hoff and van Weenen, 2004; O’Dell and Grayson, 1998; Osterloh and Frey, 2000) and between different organisations i.e., inter-organisational (Albino et al., 1999; von Hipple, 1988; Darr and Kurzberg, 2000; Larsson et al., 1998; McEvily and Zaheer, 1999). The research may concentrate on intraorganisational knowledge, inter-organisational knowledge, or a combination of both. Focusing on the knowledge within an organisation, the majority of the existing literature on knowledge transfer tends to focus on current knowledge, i.e., the knowledge which is now being used by the organisational members. There have been few studies where academics have stressed the importance of past knowledge in knowledge transfer process (Goldstein, 1991; Marsh and Morris, 2001; Walsh and Ungson, 1991; Stein, 1995; Jasimuddin et al., 2005a). It is argued that past knowledge is a kind of knowledge which is available in various locations of an organisation. The most important point is that the moment it is applied or as soon as some inputs are added to it, it also becomes current knowledge. Knowledge is distributed asymmetrically across the organisation. Distributed knowledge has to be integrated through knowledge transfer process and then stored into a knowledge repository for future use. The Web-based technology allows for storage of the transferred knowledge. Unfortunately, the importance of integrating storage of knowledge within knowledge transfer processes has been ignored in the knowledge transfer literature.

4.

Future Research Agenda

Having identiﬁed the importance of the two unexplored issues, namely knowledge transfer mechanisms and the integration of knowledge transfer and storage, these issues will be elaborated and research questions will be set out in the following sections.

4.1. Knowledge transfer mechanisms There have been few studies where researchers have addressed the importance of knowledge transfer mechanisms (e.g., Nonaka and Takeuchi, 1995; Hansen et al., 1999; Davenport and Prusak, 1998; Argote, 1999;

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Newell et al., 1999; Roberts, 2000; Dixon, 2000; Scarbrough et al., 1999; Bhatt, 2001; Huber, 2001; Alavi and Leidner, 2001). To date, the mechanisms of knowledge transfer that are mentioned in the relevant literature can be classiﬁed into two dominant camps. Focusing on knowledge-as-acategory perspective, two very different mechanisms for knowledge transfer have emerged, labelled as soft mechanism and hard mechanism. This view is an extension of Hansen et al. (1999), who contend that the personalisation strategy is an approach where knowledge is closely tied to the person who create and share mainly through direct person-to-person interaction; while in the codiﬁcation strategy, knowledge is carefully codiﬁed and technology plays a central role in the knowledge transfer. Although the present literature on knowledge transfer has discussed in isolation the mechanisms used in transferring knowledge, it fails to address the rationale underlying the selection of a particular mechanism to transfer knowledge. Viewing knowledge transfer within an organisation from the operational perspective, there is a research gap in understanding why people select one particular mechanism for knowledge transfer. Our understanding is that the knowledge transfer process seems to accomplish well when a suitable mechanism of knowledge transfer is selected. While discussing mechanisms of knowledge transfer, several researchers (most notably, Kalling, 2003; Day, 1994; Albino et al., 1999; Connelly and Kelloway, 2001; Hansen et al., 1999; Jasimuddin et al., 2005c; Zack, 1999) argue that the mechanism selection of knowledge transfer goes with the tacitness of knowledge. But they have not considered other factors that might inﬂuence the selection of a particular mechanism to carry out the transfer of knowledge. While considering the transfer of tacit knowledge between individuals in a synchronised way, the personalisation approach is prescribed (Connell et al., 2003; Lam, 1997; Storey and Barnett, 2001; Davenport and Prusak, 1998; Huysman and De Wit, 2004; Brown and Duguid 1998). On the other hand, the transfer of explicit knowledge can be facilitated through the adoption of codiﬁcation approach using technologies (Scarbrough et al., 1999; Alavi and Leidner, 1999; Bhatt, 2001; Huber, 2001). But the tacitness of knowledge cannot be the only factor that can inﬂuence the choice of knowledge transfer media. There must have been other variable(s) that may also affect the selection of a particular mechanism. Against this backdrop, the identiﬁcation of factors that inﬂuence the selection of a mechanism

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for successful knowledge transfer warrants further research. Reﬂecting this view, the following research question can be set out: What are the determinants of an appropriate mechanism selection for knowledge transfer within an organisation?

4.2. The integration of knowledge transfer and knowledge storage The fact is that knowledge that resides in human brain has less value to an organisation if it is not transferred to other organisational members to use. Organisational knowledge that is transferred among the members within an organisation without storage also has limited value. The value of knowledge increases when it is transferred, retained, and reused among the organisational members. Douglas (2002, p. 74) comments along similar lines noting that “knowledge that is in the head of a person has limited value, while the value of knowledge can increase exponentially when it is networked, stored, and reused, and quickly integrated into business practices and processes”. Most of the studies mentioned earlier on are involved in knowledge transfer but have unintentionally ignored the issues concerning the storage of transferred knowledge and the transfer of stored knowledge (Jasimuddin, 2005c). Gray and Chan (2000, p. 13) contend that knowledge that is created but not stored in a knowledge repository, that is, either simply forgotten or passed on to a knowledge user directly without being stored, represents a waste of resources, because a prospective user will have to solve old problems again (Stein, 1995). There is a heightened interest in the storage of organisational knowledge which is commonly termed as Organisational Memory (Marsh and Morris, 2001; Walsh and Ungson, 1991; Olivera, 2000; Stein and Zwass, 1995; Sherif, 2002; Jasimuddin et al., 2005a). For example, Stein and Zwass (1995) deﬁne organisational memory as “the means by which knowledge from the past is brought to bear on present activities, thus resulting in organisational effectiveness”. Despite the fact that there is, however, vast literature relating to the knowledge transfer and knowledge storage in an organisation, it is noticable that the two literatures have largely developed independently of each other. Most of the studies mentioned above seem to have consciously or unconsciously failed to link knowledge transfer with knowledge storage. However, a few studies (e.g., Gray and Chan, 2000; Argote and Ingram, 2000; Douglas, 2002; Connelly and Kelloway, 2001; Kalling, 2003) that already

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exist are isolated descriptions of the signiﬁcance of having the integration of the knowledge transfer and the knowledge storage. The fact is that organisations should recognise the need for and advantages of the integration of knowledge transfer and knowledge storage, in order to reuse knowledge for present and future business needs. Reﬂecting this view, Ruggles (1998) points out that organisational members contribute their expertise electronically to their organisation so that it can be accessed by other members of the organisation. This is further supported by Connelly and Kelloway (2001) who observe that many organisations attempt to facilitate knowledge transfer among their employees through the creation of a database or “knowledge repository”. Gray and Chan (2000, p. 13) reinforce this point of view by suggesting that knowledge stored in a repository can be reused for solving future problems. Similarly, Argote and Ingram (2000, p. 152) contend that the knowledge repositories play a dual role in knowledge transfer in organisations: “On the one hand, the knowledge repositories are changed when knowledge transfer occurs. Thus, changes in the knowledge repositories reﬂect the outcomes of knowledge transfer. On the other hand, the state of the knowledge repositories affects the processes and outcomes of knowledge transfer”. In line with Connelly and Kelloway (2001) and Argote and Ingram (2000), it is arguable that “knowledge storage” needs to be incorporated within the knowledge transfer process so as to ensure successful knowledge management implementation. Whilst there is clear indication of the interactions between knowledge transfer and knowledge storage, however, there is a research gap in understanding the relationships between knowledge transfer and storage. It is believed that the knowledge transfer process seems to accomplish well when knowledge is transferred, stored and retrieved for future reuse in complementary ways. Since the process of integrating knowledge transfer and knowledge storage is largely unexplored, future study may ﬁll partially that gap. Reﬂecting this view, the following research question can be set out: What is the relationship between knowledge transfer and knowledge storage? Determinants of choice of knowledge transfer media, and the integration of knowledge transfer and storage are two potential research areas that have not been explicitly addressed in top management journals. Using the insights

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from the existing studies, this paper proposes the above two research questions relating to knowledge transfer that demand empirical work.

5.

Conclusion

In a knowledge-based society, knowledge transfer is the key issue of an organisation’s competitive advantage. Academics and practitioners have shown a signiﬁcant interest in understanding knowledge transfer in the management literature (Kogut and Zander, 1992; Prahalad and Hamel, 1990; Starbuck, 1992; Nonaka, 1994; Nonaka and Takeuchi, 1995; Szulanski, 1996). However, there are many gaps in our understanding of the topic of knowledge transfer within the knowledge management ﬁeld and some questions still remain unresolved. The purpose of this paper is to identify valuable directions for new research into knowledge management, particularly knowledge transfer. In this regard, the rationale for selecting a particular knowledge transfer mechanism is one of the key organisational problems that ﬁrms encounter, and that warrants further addressing. The important point is that it will be easier to conceptualise and utilise knowledge if we can recognise the appropriate mechanism to transfer knowledge. As discussed previously, there is also a vast literature in knowledge management that has addressed the issues of knowledge transfer and knowledge storage independently of each other. However, the majority of the literature on knowledge transfer has neglected issues concerning the connectivity of knowledge transfer and knowledge storage for successful implementation of knowledge management initiatives. The paper undertakes a comprehensive review of the relevant knowledge management literature so as to understand the existing literature within the area and to position the research questions within the context of that literature. This discussion has actually taken a ﬁrst step towards developing some arguments about determinants of selecting a mechanism for knowledge transfer, and the connectivity of knowledge transfer and storage in order to broaden our understanding of the notion of knowledge transfer. It is also hoped that such an effort will create interest in the topic of knowledge management, and knowledge transfer in particular, and, in so doing stimulate other researchers to address some of the research questions in more directed studies. Furthermore, the research framework presented here provides linkages between different topics and sub-topics reviewing numerous studies. It will help to assist researchers in identifying areas where

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considerable progress has been made, and in organising the considerable number of existing studies and thereby exploring potential areas for future research. However, the framework is not meant to be the deﬁnitive roadmap of knowledge management research. Although this paper focuses on the literature relating to knowledge transfer, the proposed navigating map provides insights for researchers to set out research questions in other disciplines.

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2 NEGOTIATING INCOMMENSURABILITY IN MARKETING THEORY Mark Tadajewski∗ Department of Accounting, Finance and Management University of Essex, Wivenhoe Park Essex, C04 3SQ, UK [email protected]

Jaqueline Pels Universidad Torcuato Di Tella, Saenz Valiente 1010 (1428 ATG) Capital Federal, Argentina

Michael Saren Management Centre, University of Leicester University Road, Leicester, LE1 7RH, UK Received May 2005 Accepted January 2006 This paper reviews the recent paradigm debates in marketing and reﬂects on the current pluralism of paradigms. It makes the case that a future important direction for marketing theory is multiple paradigm research; an avenue that has been widely explored in organisation studies, but as yet has had little extended treatment in marketing or consumer research. As a ﬁrst movement in this direction, we review the debates that have taken place in organisation studies showing how the so-called “paradigm mentality” has been seen to hamper constructive debate across paradigms, whereby researchers from different paradigms can fail to agree on inter-paradigm standards of evaluation so that theory choice between the divergent outputs of two

∗ Corresponding

author. 21

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M. Tadajewski, J. Pels & M. Saren different paradigms cannot easily be resolved. We then turn to the incommensurability thesis. We question the veracity of the early incommensurability thesis apparent in Kuhn’s writing and the subjectivism that follows from Feyerabend’s interpretation of incommensurability, negotiating these arguments by drawing upon the Kuhnian concept of taxonomical lexicon, to suggest that learning alternative paradigms is similar to learning another natural language. By way of a conclusion, we reﬂect on the possibilities and problems associated with undertaking doctoral research using a multiple paradigmatic team brought together to contribute the distinct insights that each paradigm brings to the project.

Keywords: Marketing theory, multiple paradigm research, paradigm incommensurability, pluralism, politics.

1.

Introduction

It is becoming routine to describe marketing theory in terms of its plurality (Thompson et al., 1998). Over the past twenty years this plurality has been seen to emerge as a response to the limitations of logical empiricism as the epistemological basis for marketing theory (Arndt, 1985a, 1985b). In response to the supposed strictures imposed by this philosophy of science and the comparative neglect of subsequent advances in philosophy, a small, but vocal group of marketing scholars, made the compelling case for a relativist turn in marketing theory and sought to demonstrate that a philosophical movement towards critical relativism would broaden the basis on which the foundations of marketing theory could be developed (cf. Anderson, 1983; Hunt, 1984). More recently, the focus of attention has again shifted, except this time ontological appeals are more prevalent, with Easton (2002) calling for critical realism as the appropriate stance from which we can generate marketing theory. These are technical and complex issues that continue to be debated and will, no doubt, remain contested for many years to come (e.g., Brown, 2005; Davies and Fitchett, 2005; Donaldson, 2005; Lowe et al., 2004; Lowe et al., 2005). While we can only gesture towards these changes here, they point to a sea change in the way that we view the production of knowledge. No longer limited to logical empiricism, the marketing theorist is confronted by a diverse literature that offers a plurality of paradigms applicable to a variety of research topics (Davies and Fitchett, 2005; Tadajewski, 2004). Paradigms, for Kuhn (1962), represented a set of assumptions that inﬂuenced our way of viewing the world and they are, in Kuhn’s parlance, theoretical structures comprised of a network of conceptual, theoretical and instrumental commitments that provide models for future research. These

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“local epistemologies” provide the foundation upon which we base our research (Grimes and Rood, 1995). The recent emergence of a plurality of seemingly incommensurable, “mutually exclusive” paradigms (Burrell and Morgan, 1979/1992) has led some to make the case that the use of a single paradigm to produce theory, as has been common to date, may result in intellectual provincialism with the researcher biased, either consciously or unconsciously, against alternative accounts of the phenomena they investigate (Gioia and Pitre, 1990). Here, the paradigm we subscribe to becomes an ideological force directing the way we view the world and our relationship to it (Deetz, 1996; Hirschman, 1986; Jackson and Carter, 1991, 1993). This “paradigm mentality” encourages us to limit possible dialogue between incommensurable paradigms and fosters the polarisation of theory production (Reed, 1990, 1992, 1993, 1999; McKelvey, 1997, 1999, 2003a, 2003b). From these initial movements towards greater epistemic pluralism in marketing sprang research based on phenomenology, hermeneutics, critical theory, post-structuralism and post-modernism. More recently, we are witnessing a new shift in this epistemological turn with various calls for research that supplements, but does not replace, mono-paradigm research, that is, for research that adopts multiple paradigms in a single study (Davies and Fitchett, 2005; Foxall, 2002; Hirschman, 1987; Lowe et al., 2004; Lowe et al., 2005; Tadajewski, 2004, forthcoming; Tynan, 2002; Wilk, 2001). The rationale behind this use of multiple, rather than mono-paradigm analysis in developing marketing theory, is that it is seen to facilitate conversations across research paradigms, and in so doing provides a more comprehensive view of the foci phenomena than would ordinarily be available. Despite the widely acknowledged support for multiple paradigm analysis among a burgeoning cadre of organisational theorists, marketing theorists have yet to examine the theoretical warrant for this approach in any detail. In an effort to introduce the various forms that multiple paradigm research can take, it is worthwhile brieﬂy reviewing this area. In acknowledgement of the theory-laden nature of intellectual inquiry, we examine the theoretical support for the proposal that multiple paradigm analysis can be undertaken, that is, the incommensurability thesis is questioned and a case is made that Kuhn, in actual fact, suggests a means by which we can evaluate the content of different paradigms (cf. Hunt, 2003; McKelvey, 1997, 1999, 2003a, 2003b). While this task of negotiating the incommensurability thesis is not unproblematic due to the nature of the politics that underwrite the paradigm

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debate more generally, i.e., arguments made in the organisation studies literature in relation to the apparent tendency towards “paradigm imperialism” (Jackson and Carter, 1991). “Paradigm imperialism” signiﬁes the attempts made to subsume less well supported or developed paradigms beneath the “dominant” paradigm in organisation studies — functionalism (see, Donaldson, 1985, 1988). Making the case for multiple paradigm research and providing the theoretical warrant by which theory-adjudication can be undertaken would, it appears, constitute a means to enact discursive closure (cf. McKelvey, 2003a, 2003b; McKinley, 1995). In acknowledging this, we realise in more pragmatic terms that discipline wide, social and intellectual consensus is perhaps unrealistic given the values incommensurability that under-grid intellectual labour (see, Hoyningen-Huene and Schaber, 2003). Registering this, we simply want to point to the deﬁciencies of our existing understanding of the treatment of the incommensurability thesis in the literature to date and by highlighting how Kuhn moved away from his earlier strict incommensurability thesis suggest one possible theoretical innovation — team-research pluralism — that we believe can be useful in the development of a comprehensive understanding of marketing related phenomena. Before we proceed with our examination of the incommensurability thesis, given that the aim of this paper is to provide the theoretical justiﬁcation for pursuing multiple paradigm research by drawing upon the work of the later Kuhn, we do not presume to attempt to outline the empirical research that is a result of this theoretical work due to space limitations. In this way, this paper represents a contribution towards the paradigm debate in that it develops the extant understanding of the incommensurability thesis beyond that currently in circulation in either marketing, management, ﬁnance or organisation studies. As a response, we provide a detailed discussion of an issue alluded to, but not yet expounded in a forthcoming paper, where Brodie et al. maintain that “the issue [of] paradigm incommensurability [is]. . . overstated” (Brodie et al., forthcoming).1 Having outlined our aim, we now turn to examine the potential contribution of multiple paradigm analysis and then outline the problematic of the incommensurability thesis in detail.

1 The

interested reader looking for further discussion of the empirical research is directed towards Brodie et al. (forthcoming), Pels et al. (2004), Tadajewski (2005b) and Tadajewski and Wagner-Tsukamoto (forthcoming).

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Intellectual Politics

Of course, as we have already gestured, the growth in the number of available paradigms has not been uncritically welcomed in either marketing or, for that matter, a theoretically diverse discipline such as organisation studies (see, Donaldson, 1985, 2005; McKelvey, 2003a, 2003b). In terms of a pertinent marketing example, we might consider the comments made by Greenley (1995), who implies that a certain lack of credibility can be attached to new and emerging paradigms; credibility that can only be established by recourse to epistemological warrant that coheres with his own philosophical cosmology. This kind of criticism is echoed in organisation studies where a number of recent commentators have argued that pluralism can be equated with the genealogical, conceptual and methodological fragmentation (Pfeffer, 1993), but these opinions remain marginal commentary on a process of paradigmatic expansion that is widely attributed with enhancing the theoretical richness and diversity of debate across a range of subjects from organisational culture (Daymon, 2000; Martin, 1992; Schultz and Hatch, 1996), work organisation (Hassard, 1991, 1993), multidivisional organisations (Clegg, 1991), work and technology design (Grint, 1991), performance appraisals (Gioia et al., 1989) advanced manufacturing technology (Lewis, 1997; Lewis and Grimes, 1999), total quality management (Kelemen, 1995), organisational structure (Gioia and Pitre, 1990), small-ﬁrm strategy (Graham-Hill, 1996), organisational politics (Bradshaw-Camball and Murray, 1991) and power (Gaventa, 1980). Likewise, we ﬁnd Kuhn (1989, 1991a) echoing, in his last publications, and in material that has not to our knowledge been used to philosophically and theoretically contribute to advance the paradigm debate, that paradigmatic fragmentation is beneﬁcial, arguing that it increases the problemsolving abilities of a scientiﬁc community. The review and contribution of this latter material is important, for even if we do not hold Kuhn’s contribution in high regard — and certainly not all do — it is still highly relevant if we are quick to bemoan the strictures that Kuhn’s early work is said to enact, because he is seen to reinforce incommensurability and restrict theorycomparison and theory-choice, that we actually examine what Kuhn does have to say on issues such as the incommensurability thesis. Only then can we move past assertions that the paradigm debate(s) are philosophically bereft and that this has prevented the debate from moving beyond Kuhn’s original 1962 statements regarding theory-choice and paradigm incommensurability (see, McKelvey, 1997, 1999, 2003a, 2003b; McKinley and Baum, 2002).

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In contrast to this premise, we follow Jones (2002, 2003), who makes the very important case that all too often we are quick to move beyond certain theoretical contributions without pausing to see how they might be read otherwise. This, of course, signals some distance from positivistic readings of texts which assume that there might be one correct interpretation of such material; a position problematised by the interpretive turn and the associated view that what is interpreted does not ultimately represent an essential and inviolable nature, but is to some extent guided by those motives and needs that guide research. Thus, in our view, and again not all will agree (see, Collins, 2000, 2002), once we move past the need for apodictic foundations for our knowledge base, and once we see our practices as contingent products whose encounter with changing epistemic conditions necessitates continual adjustment, clariﬁcation, and justiﬁcation, then the role of theory in the process of critical reﬂection on practice appears secure. “. . . what would be the value of the passion for knowledge if it resulted only in a certain amount of knowledgeableness and not, in one way or another and to the extent possible, in the knowers’s straying aﬁeld of himself? There are times in life when the question of knowing if one can think differently than one thinks, and perceive differently than one sees, is absolutely necessary if one is to go on looking and reﬂecting at all.” Foucault (1984/1992, p. 8) As the quote from Foucault above indicates, the role that we see for philosophy and social theory here is that of a sensitising device that enables us to better understand and negotiate our own ingrained biases towards a single paradigmatic perspective (see, Gioia and Pitre, 1990; Lewis, 1997; Tadajewski, 2004). Thus, we see the possible contribution of multiple paradigm research as the facilitation of dialogue across paradigms. But before we turn to the exposition of our empirical interests, and the way that these appear to offer a fruitful object for multiple paradigm analysis, we must confront what Feyerabend (1975, 1978) thought was the “swamp” of the philosophy of science — incommensurability. The incommensurability thesis is of such importance, various commentators have argued, given the structures that it enacts on our ability to produce, debate and compare alternative forms of knowledge (Aldrich, 1992; Gioia and Pitre, 1990; Grimes and Rood, 1995; Hassard, 1991; Reed, 1990, 1992, 1993, 1999; Willmott, 1993). Paradigm

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incommensurability becomes problematic for the multiple paradigm analyst because each different framework will necessarily rest on a diverse range of ontological, epistemological and axiological foundations (see, Hirschman, 1986). Taking Burrell and Morgan’s framework as our exemplar here, in view of its popularity among marketing theorists (Arndt, 1985a; Hudson and Ozanne, 1988; Morgan, 1992, 2003), the differences between paradigms becomes clear when we compare what are broadly called the “positivist” and “interpretive” paradigms (cf. Szmigin and Foxall, 2000). The “positivist” paradigm, for example, is the orthodox stance from which research is undertaken in marketing (Easton, 2002). The premises underpinning research conducted according to the tenants of this paradigm are that, ontologically, the world assumes a concrete existence that remains independent of the observers’ perception. Epistemologically, “positivist” research takes a reductionist orientation to its research object in that it is assumed that the foci of attention, no matter what the domain of study, can be broken down into its various constituent parts and subject to analysis, with a desirable output of this analytic strategy being knowledge that takes the form of general laws which can be extrapolated across environments. In the process of knowledge discovery, the researcher is seen to be an external observer vis-à-vis the phenomena of interest which remains phenomenologically distanced via the careful application of the scientiﬁc, hypothetico-deductive method. Research undertaken using this paradigm is usually subject to empirical corroboration or refutation of the hypotheses under examination (Hunt, 1976, 2002, 2003). In contrast, the “interpretive” paradigm questions the ontological status of reality that “positivist” researchers accord it, by emphasising that the social world exhibits a precarious ontological status. Everyday life, Burrell and Morgan suggest, is accorded the status of a miraculous achievement. In terms of research, emphasis is placed not on ascertaining the empirical structure of reality, those natural laws that frame everyday life, instead the social world is investigated at the level of social experience with social reality seen to be inter-subjectively created by the interaction of interpreting human beings. Knowledge cannot be apprehended from the standpoint of an external, objective position, rather the interpretive researcher is fully implicated in the co-constitution of their research project. Typically, their description of co-participant lived experience is generally, but not exclusively, elicited through the use of qualitative methods (Burrell and Morgan, 1979/1992; Lewis and Grimes, 1999). For Burrell and Morgan, the axiological, ontological and epistemological bases for these two paradigms are so distinct that they are “mutually

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exclusive” (Burrell and Morgan, 1979/1992; cf. Alvesson, 1994). Kuhn (1962), on the other hand, and in a different context, has postulated that paradigms are incommensurable because there was no neutral way that they could be compared on a point-by-point basis. What this has meant for practice of producing marketing theory is that much theory is currently being produced on an either/or basis (Hudson and Ozanne, 1988). Either we use one paradigm, or we adopt another, with the productive dialogue that might otherwise be fostered between different paradigms apparently stultiﬁed (Davies and Fitchett, 2005; Lowe et al., 2004; Gareth Morgan, 1983). This is problematic because it limits the theoretical foundations from which we approach the subject of interest, i.e., the way particular research problems are framed will often restrict and potentially bias the research, all of which constrain our ability to construct comprehensive theory (Lewis and Grimes, 1999): a feature of the paradigm debate that is widely lamented (e.g., Donaldson, 1985, 1988, 1995, 2003, 2005; Lewis and Grimes, 1999; McKelvey, 1997, 1999, 2003a, 2003b; Pfeffer, 1982, 1993; Reed, 1985, 1990, 1992, 1993, 1999). In an attempt to deﬂate the incommensurability thesis and clarify a “seriously neglected” topic of research (Bristor, 1985, p. 300; see Brodie et al., forthcoming; Davies and Fitchett, 2005; Lewis and Kelemen, 2002; Kilduff and Kelemen, 2003; Tadajewski, 2004, forthcoming; Weaver and Gioia, 1994), we turn ﬁrst to the incommensurability thesis in Feyerabend (1975, 1978). This is done in order to highlight the belief that paradigm choice becomes a matter of subjective “taste” for Feyerabend. Following this, we detail Kuhn’s (1962, 1970, 1977, 1989) understanding of the incommensurability thesis as one which ultimately allows him to assume a meta-theoretical view of paradigm debate (see, Phillips, 1977). These views are subject to scrutiny, and a case is made that we can debate the merits of different paradigms when a group of researchers with a variety of paradigm afﬁliations are involved in a joint research project. This, we suggest, is possible even when we acknowledge the politics involved in this process (cf. Burrell and Morgan, 1979/1992; Donaldson, 1985; Jackson and Carter, 1991; Gareth Morgan, 1985, 1990).

3.

Incommensurability

According to Feyerabend, the idea that science will be dominated by one paradigm during a period of normal science is wrongheaded (see, Preston, 1997 for a full review). Moreover, the thesis propounded by Kuhn that

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research is governed by one set of paradigmatic values borders on scientiﬁc monomania (Feyerabend, 1970). It is perhaps not surprising that, given this sentiment, Feyerabend refuses Kuhn’s conception of the normal science/revolutionary science/normal science distinction. Via a careful excavation of the historical record, Feyerabend problematises this distinction by making the case that the historical record demonstrates that science has been characterised by a history of pluralism: a plurality of competing theories with any one individual theory being constantly subject to criticism from the point of view of other theories. This is not only the case during scientiﬁc revolutions when Kuhn (1962) suggests that all fundamental ontological and epistemological assumptions are subject to radical revision and disavowal. There needs to be no crisis in the extant practice of science — a view which Feyerabend equates with Kuhn — for scientists to be motivated to produce competing theory that could destabilise the existing paradigm. It is only when there are competing theories that the weaker points of the currently popular theory can be assessed and subject to empirical study. Taking the Copernican revolution as his exemplar, Feyerabend questions the assumption that Ptolemaic thought was even in any difﬁculty. It certainly was not falsiﬁed in the Popperian sense (e.g., Popper, 1963) he asserts, but instead Copernicanism served as a counterpoint for Ptolemaic theory by demonstrating the limitations of it (Feyerabend, 1975). While these debates between Kuhn and Feyerabend (and also Popper) are interesting in and of themselves, the point that Feyerabend was attempting to justify, in this instance, was his principle of tenacity, i.e., the argument that scientists should defend the theories that they subscribe to, even in the face of often compelling evidence refuting them (Feyerabend, 1975). By doing this, science would be characterised by a plurality of competing theories — theoretical pluralism. The virtue of theoretical pluralism is, for Feyerabend, unrelated to the question of whether this state-of-affairs will necessarily lead to the progress towards truth Popper sees as desirable. Nor is Feyerabend convinced that pluralism can be equated with a progressive movement in knowledge development because, like Kuhn, Feyerabend sees these competing theories as incommensurable with one another. This is not to suggest that incommensurability is necessarily seen as wholly problematic for knowledge development; far from it. Feyerabend (1970) is explicitly concerned with avoiding the kind of intellectual stagnation that the paradigmatic dominance of one research style could encourage, and signals his belief that theoretical pluralism is of central import in the task of questioning established conceptions of theory

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and practice, so that understanding is not circumscribed by the “tyranny of unexamined systems” (Feyerabend, 1970, p. 203). Assuming a similar position to Kuhn, Feyerabend makes the case that because theories emanating from different paradigms are incommensurable, our only recourse for theory adjudication are aesthetic judgements, our own personal theoretical tastes and subjective preference (Feyerabend, 1970, 1975). Of course, this proposal is a function of the liberalist sentiment that Feyerabend was prone to support, which, while relatively appealing, becomes extremely problematic when we factor in the politics of knowledge production (see, Belk, 1995; Burrell and Morgan, 1979/1992; Donaldson, 2005; Jackson and Carter, 1991). Clearly, Feyerabend’s proposal can be interpreted as somewhat unreﬂexive, presupposing as it does that all scholars will be free to voice their own opinion in the appropriate channels of academic distribution — peer reviewed publications. As Belk (1995) reminds us, this is a problematic assumption. We therefore need to see if some appropriate means of negotiating the incommensurability thesis presents itself, but also whether we can ﬁnd some method of assuaging the concerns of ofﬁcial gatekeepers regarding the validity of multiple paradigm research. In this regard, Kuhn offers us some further purchase on the incommensurability thesis, and moreover, suggests a process of negotiation that undermines the incommensurability thesis and paves the way for multiple paradigm research using a team of researchers afﬁliated with different paradigms. It is to Kuhn’s shifting position that we now turn.

4.

Kuhnian Incommensurability

Kuhn’s initial formulation of incommensurability suggested the idea that there is no “neutral algorithm of theory-choice, no systematic decision procedure which, properly applied, must lead each individual in the group to the same decision” (Kuhn, 1970a, p. 200). This view raises the question that if paradigms are indeed rivals as Kuhn (1962) likes to assert, such rivalry would seem to require a shared perspective that identiﬁes them as rivals and this demands that there will be some semantic and methodological continuity — a degree of translation — and therefore of reference or meaning between theoretical terms. While we will go into this issue in some depth later, let us brieﬂy gesture towards the direction in which we are heading here. Perhaps the most important issue arising out of the incommensurability thesis is if there are important and incommensurable differences between

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paradigms, then how is it possible for Kuhn himself to understand and explicate the transition from Newtonian to Einsteinian physics (Kuhn, 1962). Davidson takes a somewhat wry glance towards Kuhn’s history of science noting Kuhn’s own ability to translate what scientiﬁc practice was like before a scientiﬁc revolution using a post-revolutionary idiom (Davidson, 2001). Nor has this difﬁculty escaped Bernstein (1983) who argues that despite all the discussion of incommensurability Kuhn was well aware that there might be some commonality between paradigms, even though Kuhn objected to the manner that philosophers of science had attempted to defend this common point of reference. While still reluctant to go beyond his subscription to methodological incommensurability Kuhn’s own philosophical inconsistency increasingly makes itself apparent, particularly in his discussion of taxonomical lexicons.

5.

Taxonomical Lexicons

In his later work, Kuhn (1990) further undermines the incommensurability thesis. Drawing the relationship between language learning and paradigm education even closer, Kuhn stresses the similarities between the practice of science and leaning and using an everyday language. Engaging in scientiﬁc research, he suggests, raises similar issues to those we face in day-to-day interaction such as rules pertaining to correct use of vocabulary, grammar, translation and so forth. As an example, Kuhn points out that in a manner similar to the incommensurability we experience when we attempt to translate one word in English to Japanese where no equivalent may exist, it is equally possible for the scientist to learn and entertain two distinct languages, with their concomitant theories. This is possible, Kuhn opines, because our theories share the characteristics of natural languages, and in as much as we move from one language to another, so too can the same strategy be achieved when we talk about different theories in different language communities. These languages are not directly translatable word-for-word but, by being able to understand both lexicons, we can begin to translate the ideas from one language into the other. While admittedly Kuhn gives us little indication of how a scientist may actually move from one language to the other, he nonetheless emphasises that we learn new scientiﬁc languages as we undergo our initial process of socialisation (i.e., doctoral training etc.) which continues as we progress through the academic lifecycle. In introducing this new, more dynamic process of paradigm education and the less

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deterministic relationship between the (paradigm) language and the way a scientist can view the world, the dogmatic scientist that Popper (1970) bemoans is invested with a latitude of agency by which they can evaluate their framework in some limited fashion (Kuhn, 1990, 1991a; Sankey, 1994, 1997). This agency is limited precisely because Kuhn sees these languages as clustered around a certain class of taxonomic terms which form the basis for the seeable and sayable in scientiﬁc research; they enforce a certain view of the world albeit one that is more plastic than was the case with the original (1962) paradigm concept and incommensurability thesis. If the scientist is to understand the meaning of the particular group of taxonomic terms and successfully converse with the targeted scientiﬁc community, they will quite naturally have to learn the language of their interlocutors. Here, Kuhn (1989, 1991a) is trying to grope towards the idea that unlike the previous revolutionary, gestalt shift where the practice of science was entirely dependent on incommensurable paradigms, now scientiﬁc practice becomes dependent on the learning of shared languages which, in turn, form the basis for the scientiﬁc theories invoked in their name. Rather than incommensurability being the complete absence of any available means to translate the lexicon of a different language into the other, Kuhn proposes that we are better off thinking about incommensurability as a kind of untranslatability of speciﬁc aspects of the language we are using. Drawing from Wittgenstein, he suggests that the limits of language set the parameters of our world. They deﬁne what is it possible to know and understand (Kuhn, 1983a, 1991a). This understanding of different languages presents us with a translation problem. We cannot simply translate the language of one taxonomical lexicon into that of another, instead, what this requires is that we learn a new language entirely — even if the terms may appear the same — because the meaning system in which these terms are embedded will differ (Sankey, 1997). What Kuhn suggests here is not that incommensurability poses intractable problems, but that scientists actually try to learn languages that would otherwise appear foreclosed to them, assuming of course that paradigm subscription were really as ideologically binding as some believe (e.g., Hirschman, 1986). There is more pragmatism to knowledge production and on occasion we have no choice but to shift paradigms (Tsoukas and Knudsen, 2003). In this case, what Kuhn suggests is desirable here, are (marketing) scientists who are lexically bilingual and understand the historical development of the debates they comment upon — as Kuhn (1962) did — and can help themselves, and others, to understand alternative modes of thought

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(Kuhn, 1989). Talking about the transmission of theoretical concepts from one generation to another, Kuhn says we inherit our current theory and practices from our immediate predecessors and these concepts are “a historical product, embedded in the culture to which current practitioners are initiated by training” (Kuhn, 1991b, p. 122). It should come as no surprise that these concepts in the later Kuhn’s work are not wholly incommensurable; we can understand them and there will be some degree of translation. This is possible by virtue of the lexicons that we learn through doctoral training and which enable researchers to become adept at the hermeneutic decoding of a range of taxonomical lexicons in much the same way as anthropologists and historians immerse themselves in alien cultures. Again, we may run into incommensurability by virtue of the systematic differences which exist between two different taxonomies, as Kuhn demonstrates with his example of Ptolemaic and Copernican celestial taxonomies which ultimately share a similar domain of investigation and yet are based on different lexicons and whose adherents thereby view their objects of inquiry differently (see, Tadajewski, 2005a). What he suggests, using the Ptolemaic and Copernican example, is that the changes between these different lexicons are in fact far more subtle and restricted than he had previously thought, being primarily related to changes in certain elements of the lexical code. The main challenge for the historian in this example is the identiﬁcation of the part of the lexical code that has been modiﬁed. This is as far from the gestalt shift of the early Kuhn as is conceivable. Far from being embedded in one paradigm, and on occasion shifting to another totally different “world”, a paradigm shift is no longer seen by Kuhn to be a move from one paradigm to another in one direction. Rather, we retain the ability to shift forwards and backwards, from one lexicon to the other and back again (Kuhn, 1987), with the consequence that his incommensurability thesis has itself been transformed from the way it is generally depicted in marketing theory where a strict incommensurability is generally assumed (e.g., Lowe et al., 2004; Lowe et al., 2005), to his later revision — the more nuanced semantic incommensurability (Sankey, 1994).

6.

Semantic Incommensurability

In diluting his methodological incommensurability thesis so that some comparison of frameworks is possible, Kuhn moves us closer to comparing different paradigms. His point in his later works is not that incommensurable

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languages are untranslatable, but instead that this process is extremely complex (Sharrock and Read, 2002). In making this case, Kuhn asks us to consider the differences between incompatibility, incomparability and incommensurability (Kuhn, 1983b). No longer does he place the (implicit) stricture on theory comparison that this must take place through the use of a theory neutral algorithm or be otherwise reducible to a common language as he did in his earlier work (e.g., Kuhn, 1962, 1970a). Instead, Kuhn continues to assert a weak version of semantic incommensurability, whereby there may be some limited meaning variance between extant and historical taxonomical lexicons in which a certain class or group of terms may be untranslatable within the wider language (Kuhn, 1989). Nonetheless, even if this is so, it still remains the case, says Kuhn (1990, 1991a) drawing upon the natural language analogy, that despite the untranslatability of certain terms on a one-to-one correspondence, it is still possible to understand the general thrust of the statement made (Kuhn, 1991a). A failure to translate one language into another does not necessarily mean that we fail to understand what has been said (Sankey, 1994). Simply, that this process of translation and understanding is complicated, since if an attempt is made to provide, as evidence of untranslatability various examples, as Kuhn does, of expressions of the untranslatable language, then such an attempt will undermine the claim of untranslatability because providing examples in one’s own language necessarily shows that translation can take place (Davidson, 2001). In practice, what this and much of the preceding close reading of early, middle and late Kuhnian thought appears to suggest is that in actuality scientists have a substantial number of ways by which they can compare competing theories. These will range from the various values that Kuhn (1977, p. 322) discusses (accuracy, consistency, scope, fruitfulness and simplicity) to the use of older theory that can also be used to assess the approximate contribution of new ways of seeking knowledge — Kuhn’s so-called “standards of responsibility” (1989, p. 12). Such values, Kuhn suggests, are not exhaustive, but given in order to indicate those that he thinks are collectively important for determining theory choice in the natural sciences and form the collective values that are seen to be present in “good” theory (Kuhn, 1977). This again returns us to Kuhn’s view that there are certain values underwriting the debates between different paradigm communities that can be used to adjudicate between the choices offered by different theories. For Kuhn, this allows us to move back from relativism and regain some of the inter-subjective ground that the original incommensurability thesis removed from beneath

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our feet (Kuhn, 1970a). What this enables is a certain degree of productive dialogue although ultimately, Kuhn laments, this dialogue can be stultiﬁed. As an example, Kuhn cites the debates between Einstein and Bohr, which he believes highlights the fundamental epistemological and ontological differences that may delimit debate. His use of the paradigmatic transformation of classical physics to quantum physics is of interest here, precisely because what it highlights contradicts what Kuhn proposes, in that it gives us an exemplar case of the kind of productive dialogue that can be encouraged by paradigm debate. Indeed, Bohr and Einstein discussed every step in this debate: “Einstein raised an objection; Bohr was mortiﬁed, thought intensely, found an answer, told Einstein, and Einstein accepted the answer. Einstein raised another objection; Bohr was again mortiﬁed, though intensely — and so on” (Feyerabend, 1999, p. 267). All of this leads Feyerabend, and the later Kuhn, to move towards the view that, in actuality, while the incommensurability thesis may continue to pose difﬁculties for the philosopher of science, particularly if they are interested in retaining the idea of wholly rational theory choice, incommensurability “disappears when we use the concepts in the way that scientists use them, in an open ambiguous and often counter-intuitive manner. Incommensurability is a problem for philosophers not for scientists” (Feyerabend, 1993, p. 211; emphasis in original). Incommensurability of scientiﬁc values, moreover, can be subject to a process of negotiated attempts to understand and comprehend the output of different paradigms in that, “anything which can be said in one language can, with imagination and effort, be understood by a speaker of another. What is a prerequisite to such understanding, however, is not translation but language learning” (Kuhn, 1989, p. 11). The beneﬁt that Kuhn sees accruing from such a process of debate and negotiation is “the shock generated by substituting . . . [alternative] conceptual spectacles for own [with the result that] . . . We have learned, against our own deep-seated ethnocentric resistance, to take shock for granted” (Kuhn, 1991a, p. 21). Thus, in contrast to recent comments made by a number of organisation theorists that conceptual ambiguity and deﬁnitional ambiguity precludes paradigm comparison and evaluation leading them to call for the development of a rigid conceptual dictionary (cf. McKinley, 1995, 2003; McKinley and Mone, 1998), we suggest, following Feyerabend, that the uncritical acceptance of rigid criteria for evaluation emplaces strictures on theory development that will not ultimately be productive. As Van Maanen maintains: “the more we try to be precise and exact, the less we are able to say” (Van Maanen, 1995, p. 139).

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Incommensurability, on this reading, can be negotiated by a process of iterative debate. What our foregoing examination of Kuhn and Feyerabend’s discussion means is that it is theoretically justiﬁable to engage in research based on multiple paradigms in a single study — justiﬁcation that has not yet been provided in the literature. Importantly, by outlining the philosophical basis for multiple paradigm research, we have provided the basis for the legitimisation of multiple paradigm analysis as a tenable and credible research strategy; something that has long been seen as desirable in theory building in marketing and consumer research (Foxall, 2002; Hirschman, 1986; Lutz, 1989; Tadajewski, 2004; Tynan, 2002; Wilk, 2001). As a gesture beyond the very theoretical discussion so far, we want to brieﬂy discuss the way in which we are presently trying to overcome the incommensurability thesis in practice. We see this project as representing the kind of reﬂexive conversation that Morgan (1983) and Lewis and Grimes (1999) broadly support.

7.

Toward Multiple Paradigm Marketing Theory

It has long been noted that marketing and consumer researchers need to remain open to a range of paradigmatic positions, by refusing to close down what might otherwise be a potentially fruitful discussion because of paradigmatic disagreement. Our own personal experience with multiple paradigm research leads us to a very different conclusion to that of Czarniawska (2003) who appears to suggest that academic debates across paradigms are usually unbeneﬁcial because researchers are unwilling to tolerate the views of researchers from alternative paradigms (see, Belk, 1995; Donaldson, 2005; McKelvey, 1997, 1999, 2003a, 2003b; McKinley, 1995). We think this overstates the actual difﬁculties of inter-paradigm discourse and in an ongoing research project we have used a research team whose members subscribe to different, but complimentary paradigms. For the purposes of our research, we have begun to undertake sequential multiple paradigm research which holds that the available paradigms are mutually complimentary and that the representations developed from one paradigm can be used to inform the research undertaken from an alternative paradigmatic stance. This process is said to provide sequential levels of understanding that build up on each other, or otherwise cast a critical perspective on the previous analysis (Gioia et al., 1989; Lewis and Grimes, 1999; Lewis and Kelemen, 2002; Schultz and Hatch, 1996). Of course, the refrain can be offered that Kuhn has previously

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argued that there are certain methodological principles that are valid within the paradigm community and that the dialogic process that we support will be stultiﬁed by the lack of transcendental methodological guidance. As we have already indicated, Kuhn no longer supports this assumption despite the widespread belief within the management, marketing and organisation studies literature to the contrary (e.g., McKelvey, 1997, 1999, 2003a, 2003b). In contrast, Kuhn outlines a series of values that he believes can be useful heuristics when comparing theories from different paradigms. Theories are valued, Kuhn (1970a) maintains, because they can yield predictions which should, for Kuhn, be accurate and preferably quantitative; they permit the continued development of puzzle-formation and problem solution; they are relatively simple vis-à-vis a competing theory and they are plausible in relation to existing knowledge. Continuing in this vein, Kuhn (1977) supplements these values, adding: scope (the theory can be extended beyond its existing domain) and fruitfulness (encourage new ways of seeing as yet unknown facts). Now, in outlining these values, we are in no way suggesting that they can determine theory-choice, that is, determine once and for all which theories drawn from different paradigms is (or are) correct. Rather, the methodological injunction to select theories on the basis of their simplicity requires the individual to make a decision regarding which theory they select and these are necessarily underdetermined by the available empirical evidence. Thus, we need to recognise that these values leave a range of options open regarding how these are interpreted, and the weight given to each value is likely to differ according to the primary paradigm that is subscribed to. In terms of our project, those involved subscribe to a variety of epistemological positions which, in turn, reﬂect their own substantive interests ranging from positivist research concerned with transactional marketing and interpretive research primarily oriented to the study of relationship marketing activities and while it makes for interesting debates — as the paradigm debate literature itself stands as testament — nonetheless some degree of inter-subjective consensus can usually be reached. This is perhaps not so surprising, despite the occasional tendency of researchers to talk past one another, common ground is generally obtainable as Nola and Sankey (2000: 27) maintain: “Thus Kuhn does not mention that inductivists and Bayesians put high store on high degree of hypotheses by evidence . . . Again constructive empiricists put high value on theories that are empirically adequate; in contrast realists wish to go further and value not only

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this but truth, or increased verisimilitude, about non-observational claims. Given what Kuhn says elsewhere we may view him as not endorsing the realists’ value of truth, though the constructivists’ value of empirical adequacy is one he could adopt. Finally some methodologists’ would downplay some of the values Kuhn endorses, such as external consistency or social utility.” Again, to state our claim most explicitly, the values that Kuhn provides are only a guide to theory choice. In certain respects they are extremely functionalist. They are, however, only a ﬁrst movement towards developing a more comprehensive heuristic through which multiple paradigm analysis can be guided. At this moment, they provide a touchstone to enable discussion across paradigms and enable us, to paraphrase Foucault, to stray aﬁeld of ourselves as researchers to look at our research foci in new ways. In our various attempts to effectively communicate across our respective paradigms, a number of common-sense recommendations, which may offer some guidance for those undertaking multiple paradigm analysis in future, have presented themselves, which we believe will contribute to the successful completion of (given the nature of this medium of communication) doctoral research. The ﬁrst and most important point is that for multiple paradigm analysis to be successful, each of the team members should, ideally, be competent researchers’ in their own paradigmatic style. Their ability to demonstrate this in the research output is of primary importance in convincing the appropriate gatekeepers that the output generated from this research strategy has been produced in a manner commensurate with each paradigm adopted (see, Davies and Fitchett, 2005). Of equal importance, or perhaps more so, each team member should, regardless of their academic position, appreciate and respect each others’ opinions and have a desire to contribute to the research inquiry. This is in addition to being willing to listen and recognise how they may best compliment each other and will require that they share, at some fundamental level, a mutual understanding of the nature of the research problem, but not, as we might generally expect, for this to be framed in a paradigmatic relative terminology. What we believe is a more fruitful way of framing research questions is to state them in terms of problem orientation. By adopting a problem orientation researchers can contribute their own insights as they relate to the problem at hand, drawing from the contributions offered by each paradigm similar to the sequential strategy outlined in detail by Schultz and Hatch (1996) without the potential correct responses being

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delimited by the use of any paradigm speciﬁc terminology. It is by recognising the potential for paradigm interplay and the facilitation of dialogue between paradigm communities that the kind of reﬂexive conversation indicated by Morgan (1983) is theoretically warranted and multiple paradigm analysis therefore justiﬁable, as the foregoing examination of the incommensurability thesis has illustrated. In contrast to the frequent reiteration that the Kuhnian incommensurability thesis precludes the possibility for multiple paradigm analysis, this chapter has shown that Kuhn himself provides the theoretical warrant for multiple paradigm analysis, and offers some (admittedly vague) criteria for reﬂexive conversation between different paradigm communities. It only remains for these criteria to be debated and further extended by being put into practice: a project which, we submit, represents an important future avenue for theory development in marketing.

8.

Conclusion

The project we have outlined in this paper is likely to be contentious, given the diverse argumentation surrounding the incommensurability thesis. We violate, with reason, the paradigm incommensurability thesis in recognition that the incommensurability thesis as it was represented in the work of the early Kuhn no longer stands. What this means for those interested in marketing theory is that multiple paradigm research can be supported theoretically, but not necessarily put into practice in a wholly unproblematic fashion. Registering this, we have demonstrated Kuhn’s own distancing from the original incommensurability thesis and, following this, the type of multiple paradigm study that marketing scholars are beginning to undertake. We should not, however, underplay the political nature of knowledge production within marketing or its sister disciplines. This said, the appearance of journals such as Marketing Theory and the increasing turn towards alternative paradigmatic positions evinced by the Journal of Consumer Research and, of equal importance, this vehicle for doctoral students, all suggest that research which negotiates established convention is likely to be further developed by virtue of the opportunities provided by these prestigious outlets.

Acknowledgement The authors would like to thank the helpful comments of both reviewers on an earlier draft of this paper.

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3 EXPLAINING ECOLOGICAL PRODUCT PURCHASE USING CONSUMERS’ PSYCHOGRAPHIC CHARACTERISTICS Elena Fraj∗ , Eva Martínez and Teresa Montaner Departamento de Economia y Direccion de Empresas Facultad de Ciencias Economicas y Empresariales Gran Via, 2. Zaragoza, Spain ∗ [email protected] Received July 2004 Accepted May 2005 This paper identiﬁes the characteristics of the ecological product consumer, and considers their disposition to buy those products even when the price is higher than non-ecological products. Variables relating to ecological behaviour such as values, lifestyle, personality and attitude (Straughan and Roberts, 1999; Kotchen and Reiling, 2000; Chan, 2001; Laroche et al., 2001) are considered. To achieve our purpose, a survey with a random sample of 573 consumers was designed. Several exploratory and conﬁrmatory factor analyses were conducted and a logistic regression analysis was applied on the obtained data. The results conﬁrm that the psychographic variables used differentiate the proﬁle of the consumer who is willing to buy ecological products at different prices.

Keywords: Ecological consumer behaviour, psychographic variables, ecological purchase, willingness to pay more, logit analysis.

1.

Introduction

Consumers committed to nurturing a healthy environment encourage companies to replace their usual practices with others that are more respectful to the environment. Company executives are interested to know such

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consumers’ behaviour, especially what they like and what they think. To satisfy that interest, researchers of consumers’ behaviour have decided to study the ecological consumer. Nevertheless, this is not an easy task since the ﬁrst problem they ﬁnd is the difﬁculty in deﬁning this type of behaviour due to the several dimensions that are involved (purchase, use, consume, reuse, disposal). Furthermore, there is no fully ecological behaviour since there is no fully ecological product. Thus, Kaiser and Wilson (2000) explain that the concept of ecological behaviour includes “all those actions which contribute to protect and preserve the environment”. For this reason, various conducts have been considered by the literature when analysing the proﬁle of the ecological consumer (Kinnear et al., 1974; Grunert and Røhme, 1992; Stone et al., 1995; Sánchez et al., 1998; Kotchen and Reiling, 2000; Chan, 2001; Laroche et al., 2001; Fraj and Martínez, 2002; Fraj et al., 2004). Actions like recycling energy and water saving, political activism and commitment to environmental organisations, and purchase, consumption and willingness to pay more for ecological products, reﬂect a consumer concerned for the environment. This paper examines several factors intervening in the ﬁnal development of the ecological consumer’s behaviour. These factors refer to the following groups of variables: demographic, socio-economic, psychographic and environmental knowledge. For the ﬁrst two groups, there is no consistent relationship in their use to explain the ecological consumer’s behaviour and, although they would solve some speciﬁc questions, they would be useless to identify this market segment properly (Kassarjian, 1971; Daniere and Takahashi, 1999; Laroche et al., 2001). For this reason, researchers have realised that the analysis of the ecological behaviour requires some other variables, like psychographic ones, in an attempt to guarantee the understanding of this type of behaviour (Bigné, 1997; Laroche et al., 2001; Fraj and Martínez, 2002). The analysis of values and lifestyles, personality and attitudes has been one of the most important aims of social and behaviour researchers over the last decades. The aim of the present study is to analyse the proﬁle of the ecological consumer who would be willing to buy ecological products even if they were more expensive than non-ecological ones. With this purpose, this study is organised as follows: we will ﬁrst review the main literature on the subject, which will be the base for the development of the hypotheses in the study; secondly, we will explain the methodology and the analyses performed; thirdly, we will describe the results obtained; and ﬁnally, the main conclusions will be presented.

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Review of the Literature and Hypotheses

Taking the existing literature as a starting point, this section describes the most relevant ﬁndings for every psychographic variable (values and lifestyles, personality and attitude) which will allow us to develop our study hypotheses. Therefore, this section establishes the hypotheses on the association of values and lifestyles with ecological behaviour; the hypotheses on the relationship between personality features and that behaviour; and the hypotheses on the relationship between environmental attitudes and behaviour.

2.1. Values and lifestyles Values and lifestyles are the most used variables by researchers to identify the ecological consumer’s proﬁle. Alonso (1999) observed that, among the consumer’s new habits, ecological values and respect for nature have a crucial relevance. The author explains that consumer tries to care for natural areas as a part of their leisure time and feels concerned about their eating habits and physical appearance. On the other hand, De Young (1985–1986) observed that an austere and moderate lifestyle would be associated with a positive behaviour towards glass and paper recycling. Equally, Lievers et al. (1986) proved that people with conservative and religious values and lifestyles participate actively in society. McCarty and Shrum (1993) found that values such as goal achieving, self-respect, others’ respect and self-fulﬁlment encouraged individuals to consider recycling. Schwartz (1992, 1994) observed that those values existing in dimensions like self-transcendence and self-exaltation had an inﬂuence on the ecological behaviour. Thus, those values in the dimension of self-exaltation (power and capacity) were less inclined to environmental actions. Schultz and Zelezny (1999) related Schwartz’s values with environmental attitudes, ﬁnding that the value of power (a value of the self-exalted ones) was negatively associated with the eco-centred vision of attitudes. Thøgersen and Ölander (2002) reach the same conclusions. These authors report strong ties between universal values (contained in the dimension of self-transcendence) and the adoption of sustainable behaviour patterns. However, this relationship was not so signiﬁcant for those values reﬂecting power (self-exaltation). Therefore, values and lifestyles may act as determining factors for the ecological behaviour. Thus, consider the following relationships about the

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inﬂuence of values and lifestyles on the ecological behaviour: H1a : Individuals with high versus low self-fulﬁlment values show a higher ecological behaviour. H1b : Individuals with little versus great interest for power show a higher ecological behaviour. H1c : Individuals with an austere or moderate versus easy-going lifestyle show a higher ecological behaviour. H1d : Individuals with high versus low interest for ecological matters show a higher ecological behaviour. H1e : Individuals who are concerned versus unconcerned for their health and body show a higher ecological behaviour.

2.2. Personality Personality is another psychographic variable which affects the consumer’s behaviour. Personality is a speciﬁc and unique variable for each individual, conditioned by the individual’s value system. The most relevant results on this issue found in the literature refer to personality features such as extroversion, solidarity with the others, responsibility and order, emotional stability and imagination. Anderson and Cunningham (1972) and Webster (1975) analyse social responsibility according to people’s availability to help others with no proﬁt motive in mind. These authors concluded that those consumers with a high degree of social responsibility are more inclined to buy environment-friendly products. Later, Ramanaiah et al. (2000), in order to analyse the personality proﬁle of individuals with a certain degree of environmental responsibility, found that this type of people distinguish themselves by their extrovert character, their open-mindedness and their solidarity with the others. Díaz and Beerli (2003) observed that people who were less involved in glass recycling showed less responsibility and emotional receptiveness. And those who did not recycle were characterised by being scarcely grouporiented and thinking that they could do nothing to improve the environment (external locus of control). Fraj and Martínez (2005b) found that personality was positively related to the fact that individuals buy ecological products, attend different environmental conferences and join pro-environmental groups. They obtained that consumers who were aware and conscientious had bought ecological products or had switched products for ecological reasons. Moreover, those

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who were extrovert and care about the others were more likely to attend some ecological conference and join an environmental group. Nevertheless, literature on personality and ecological behaviour is limited. Consequently, some of the hypotheses we present have an exploratory character. Firstly, although we might expect that those individuals with an extrovert character would tend to have a respectful behaviour towards the environment due to their sociability and their need of approval from the people around them (Costa and McCrae, 1992), in the Big-Five Factor scale this characteristic mainly reveals vanity and the result might be just the opposite. In other words, this type of extroversion would reﬂect conceited individuals, more interested in attracting people’s attention than in being respectful to the environment. Secondly, those individuals who are supportive and concerned about others will also be concerned about the future of society and thus the planet’s sustainability, which will make them behave in an ecological way. Thirdly, emotionally stable individuals will adopt an ecological behaviour in a positive way since they will feel better of themselves. Fourthly, responsible and meticulous individuals will try to achieve all their goals and observe the rules, thus they will tend to follow ecological behaviour patterns. Finally, educated people with a high interest for new experiences will be characterised by their open and liberal mind and will probably follow new trends of consumption and ecological behaviour. H2a : Individuals with a less extrovert and vain personality show a higher ecological behaviour. H2b : Individuals with a personality characterised by solidarity with the others show a higher ecological behaviour. H2c : Individuals with an emotionally stable personality show a higher ecological behaviour. H2d : Individuals with a personality characterised by order and responsibility show a higher ecological behaviour. H2e : Individuals with an imaginative and intellectual personality show a higher ecological behaviour.

2.3. Attitude Now, we will review the last element of the classic structure, which refers to the relationship between attitudes and ecological behaviour. We have

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found several studies in the literature which obtained relevant results from different perspectives. For example, Ling-Yee (1997) concluded that a more ecological attitude was connected with a higher environmental involvement. Kotchen and Reiling (2000) also stated that highly favourable attitudes towards the respect for the environment lead consumers to pay some extra money which may redound to the environment’s improvement. Laroche et al. (2001), in the same vein, suggested that those who were willing to pay more for ecological products had no objection to having an environmental behaviour; on the contrary, they considered it as an important thing. On the other hand, although not many studies have followed the tridimensional approach of attitude to relate it with ecological behaviour, some of them have proved that affective commitment has a positive inﬂuence on the relationship between verbal commitment (behaviour intention) and ecological behaviour, and that verbal commitment has a greater inﬂuence on that behaviour, since it is its nearest antecedent (Kaiser et al., 1999). In this respect, Chan (2001), in his study of the determinants of ecological product purchase in China, found that affection had a positive inﬂuence on environmental attitude which also inﬂuenced ecological product purchase. Fraj and Martínez (2005a) found that ecological behaviour was mainly determined by environmental affect. It seemed that ecological behavior was better explained by affect than by environmental attitude, and, at the same time, affect appeared quite signiﬁcant in determining environmental attitudes. From these researchers’ perspective, and for each element which constitutes attitude, we establish that those individuals concerned and interested in environmental issues, those who are willing to change their shopping and consume habits and those who are already following these behaviour patterns will all show a responsible behaviour towards the environment, as hypothesised below. H3a : Individuals with a more affective attitude (concern, interest) to the environment show a higher ecological behaviour. H3b : Individuals with a higher attitude of verbal commitment to the environment show a higher ecological behaviour. H3c : Individuals with a higher attitude of actual commitment to the environment show a higher ecological behaviour. To contrast these three groups of hypotheses we will explain the methodology used and the empirical analyses performed.

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3.

53

Methodology

3.1. Data collection The information was obtained from a survey performed in March and April 2001 with a random sample of 595 individuals in a city of Spain of these, 573 were valid (96%). Table 1 contains the sample’s technical speciﬁcations. We verify that for a trust level of 96%, an inﬁnite population1 and for the rest of parameters deﬁned in the sample calculation, there is a sample error of 4.2% in the 573 valid surveys. Prior to the ﬁnal questionnaire we performed a pre-test so as to detect any problem before the design of the ﬁnal survey.2 The ﬁnal questionnaire was divided into three main sections with the following questions: ﬁrst, questions on the recycling behaviour with some products, on the purchase of three types of ecological products (food, cleaning products and electrical appliances) and the willingness to buy them at the same price as the non-ecological ones and at a higher price; secondly, questions on psychographic variables and the individuals’ degree of knowledge and information of environmental issues; ﬁnally, we asked about the individuals’ socio-economic and demographic variables. From the demographic and socio-economic characteristics of the sample we may conclude that about 57% of the respondents are women, mostly between age of 15 and 55, 40% with higher education, 36.6% have a family income of 1,000–1,800 euro and most respondents belong to 2/3-member families. Table 1. Universe Sample size Sample error Proportions Trust level Sample design Fieldwork date Pre-test

1A

Technical speciﬁcations. Population over 14 573 surveys +/− 4,18% p = q = 0,5 95,5% Simple random sample March 2001 135 surveys / January 2001

large population (over 100,000) as the subject of a survey is usually considered as an inﬁnite population. 2 In the pre-test we reworded some items from the original scales and some were eliminated because we found they were not relevant in our cultural context.

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3.2. Variable measurement Several scales were used to measure the variables. First, the second version of the VALS (Values and Lifestyles Scale) scale obtained from an international inventory (SRI) was used to measure values and lifestyles. It is a methodology tested in several countries which includes several American lifestyles in 35 items (Kahle et al., 1986; Novak and MacEvoy, 1990; Schwartz, 1992). Nevertheless, this scale encompasses general values and lifestyles which do not reﬂect ecological tendencies (Appendix 1). Consequently, we have also used the scale on lifestyles proposed and used by Sánchez et al. (1998a), which is designed to measure lifestyle in speciﬁc studies of ecological behaviour. The scale contains 18 items including questions on the importance of having a healthy life and being respectful towards nature (Appendix 2). Secondly, personality is analysed with the approach of the ﬁve features considered in Goldberg’s Big-Five Factor Structure (1990). These characteristics are: extroversion, agreeableness and solidarity with others, conscientiousness and responsibility, emotional balance and imagination and intelligence. Each of these characteristics is measured with 10 items, thus the scale contains a total of 50 (Appendix 3). It belongs to the International Personality Inventory (IPI) and it is a scale which has been frequently used, although not speciﬁcally to determine ecological behaviour (Saucier and Goldberg, 1996; Sadowsky and Cogburn, 1997; Bonner, 2000; Witt, 2002). Thirdly, attitude has been measured with a subscale of the revised EAKS (Environmental Attitude and Knowledge Scale) scale proposed by Maloney et al. (1975). It gathers the three elements of attitude (Appendix 4): affective (affective commitment), intentional (verbal commitment), cognitive (environmental knowledge), to which they added behaviour (actual commitment). Despite being an old scale, it is one of the most widely used in the literature of the ecological consumer’s behaviour, although sometimes only one of its dimensions is considered (Alwitt and Pitts, 1996; Ling-yee, 1997; Kaiser et al., 1999a, 1999b; Chan, 1999; 2001; Fraj and Martínez, 2002). The three scales measure the individuals’ level of agreement or disagreement in a seven-point Likert scale. Before designing the ﬁnal survey we applied a qualitative validation by analysing the level of cross-cultural equivalence (Usunier, 2000) in the scales which came from other cultures (VALS; The Big-Five, EAKS). This analysis consisted of examining the construct’s operative, scalar and linguistic equivalences (Bhalla and Lin, 1987). This analysis allows comparing the results

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obtained in our study with those from other international studies which may have used the same measurement instruments. Ecological behaviour is measured in this study through ecological product purchase, since it is the individual’s expression of their interest and concern for environmental improvement. Consequently, we considered three types of product: two perishable (food and cleaning products) and one lasting (white-goods). Given that in many stores of our country ecological products are not fully available, the respondents were questioned about their willingness to buy this type of product at the same price as non-ecological ones and at 10%, 15% and 20% higher prices. The individuals had to answer whether they were willing or not to buy each product. The description of the frequencies on the studied variable showed that, at the same price, all the consumers would be willing to buy ecological products. When the price was 10% higher, nearly 70% of the respondents were willing to buy them. Nevertheless, this percentage decreased when the price was 15% or 20% higher.

4.

Results

4.1. Scale validation analysis To validate the scales, several exploratory factor analyses were carried out with the statistical applications SPSS and EQS 5.7b for Windows. These analyses allowed us to analyse ﬁrst the scales’ reliability and unidimensionality and secondly their ﬁt, ﬁnal reliability and validity (Grande and Abascal, 1999; Del Barrio and Luque, 2000). In this respect, for the VALS scale we obtained four dimensions which reﬂected a reduced version of the original (Table 2): the ﬁrst one formed by ﬁve items on the individuals’ liking for the latest fashion (FASHION); the second one had ﬁve items and referred to the adventurous spirit of those people who are keen on knowing new things and undertake new experiences which allow self-fulﬁlment (AVENT); the third one was formed by two items and was related to the value of power and authority reﬂected in the individuals’ aspiration to organise and lead other people (LEADER); and the fourth one, with two items, shows the respondents’ interest for engineering and communication issues (KNOWLEDGE). The dimensions in the VALS scale showed an excellent reliability, but the composite reliability coefﬁcient was below the optimum in the case of LEADER and KNOWLEDGE, maybe as a result of the reduced number of

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E. Fraj, E. Martínez & T. Montaner Table 2.

CONSTRUCTS Latest Fashion (FASHION)

Conﬁrmatory analysis for the values and lifestyles scale “VALS”. — — — — —

Adventurous Spirit (AVENT)

— — —

— — Leader Spirit (LEADER)

— —

Engineering and communications knowledge (KNOWLEDGE)

—

—

Reliab.(a) αc = 0.85 fc = 0.80

E.V.A(b) 0.45

αc = 0.84 fc = 0.79

0.43

0.73 0.84

αc = 0.76 fc = 0.67

0.5

0.66 0.83

αc = 0.71 fc = 0.63

0.46

ITEMS I follow the latest trends and fashions. I dress more fashionably than most people. I must admit that I like to show off. I like to dress in the latest fashions. I want to be considered fashionable.

(λ) 0.74

I like a lot of variety in my life. I like trying new things. I like the challenge of doing something I have never done before. I am always looking for a thrill. I like doing things that are new and different.

0.63

I like being in charge of a group. I like to lead others. I am very interested in how mechanical things, such as engines, work. I like to look through hardware or automotive stores.

0.76 0.56 0.83 0.76

0.63 0.64

0.84 0.82

Note: The table shows the standardised loads for each indicator of each construct (λ), all of them above 0.50 and signiﬁcant, the Cronbach’s alpha reliability coefﬁcients (αc ) and composite reliability (fc ), and the coefﬁcients from the extracted variance analysis (E.V.A). (a) Cronbach’s alpha is very sensitive to the number of indicators in the scale. The more indicators in a scale, the more reliable it will be (Peter, 1979). Composite reliability coefﬁcient is used as another measurement of the scales’ internal consistence. Its optimum threshold is on 0.7 (Hair et al., 1999) and its interpretation may be ﬂexible (Del Barrio and Luque, 2000). (b) The coefﬁcient from the extracted variance analysis allows to know the global variance of the items explained by the latent variable. Its value should be ideally above 0.50 (Del Barrio and Luque, 2000).

items, although the extracted variance analysis is better than in FASHION and AVENT. However, ﬁt measurements are within the adequate parameters (χ2 = 220.92 g.l. = 71; GFI = 0.95; RMSEA = 0.06; CFI = 0.95; NFI = 0.99; AGFI = 0.92).

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Explaining Ecological Product Purchase Table 3. CONSTRUCTS Ecological Patterns (ECOEV)

57

Conﬁrmatory analysis for the lifestyles scale “Lifestyles”. ITEMS — I prefer consuming recycled products. — I throw garbage in selective containers. — I participate in environment conservation tasks. — I worry about the human activity consequences on the climatic change and act consistently.

(λ) 0.6 0.65

Healthy food (ALISANA)

— — — — —

Healthy way of life (SALUDEV)

— I try to reduce stress. — Regularly, visit the dentist. — I try to take an arranged and methodical life. — I try to ﬁnd the balance between work and my private life.

I control the salt ingestion. I try not to eat pre-cooked food. I eat red meat moderately. I try to eat food without additives. Periodically, I check my health voluntarily.

Reliab. αc = 0.82 fc = 0.76

E.V.A 0.44

0.64 0.57 0.59 0.69 0.63

αc = 0.76 fc = 0.71

0.33

0.62 0.58 0.68

αc = 0.71 fc = 0.66

0.32

0.82 0.82

0.57

Note: See note in Table 2.

As for the scale of ecological “Lifestyles”, we obtained three dimensions (Table 3) on several ecological behaviours with four items (ECOEV), on healthy eating habits with ﬁve items (ALISANA) and on a healthy, balanced and relaxed lifestyle with four items (SALUDEV). In this scale the three dimensions present good reliability but the variance analysis coefﬁcient is below the threshold. Nevertheless, we did not consider the elimination of more items because the last conﬁrmatory factor analysis does not recommend it. Furthermore, as in the previous case, these data’s goodness of ﬁt is within the established parameters (χ2 = 261 g.l. = 62; GFI = 0.94; RMSEA = 0.08; CFI = 0.91; NFI = 0.90; AGFI = 0.91). In the case of “The Big-Five” personality scale, we obtained the ﬁve expected dimensions (Table 4): extroversion, with three items, (EXT); solidarity with the others, with six items, (SOL); responsibility and order, with eight items, (RES); emotional stability, with four indicators, (EMO); and intellect and imagination, with six indicators, (INT). The ﬁnal reliability of the personality scale is excellent according to Cronbach’s alpha. In this case, the dimensions SOL, EMO and

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E. Fraj, E. Martínez & T. Montaner Table 4.

Conﬁrmatory analysis for the personality scale “The Big-Five”.

CONSTRUCTS EXTROVERSION & VANITY (EXT_)

ITEMS — Am the life of a party. — Start conversations. — Keep in the background. (+)

(λ) 0.76 0.62 0.67

Reliab. αc = 0.82 fc = 0.66

E.V.A 0.39

AGREEABLENESS (AGR_)

— Am interested in people. — Sympathise with others’ feelings. — Have a soft heart. — Take time out for others. — Feel others’ emotions. — Make people feel at ease.

0.73 0.86

αc = 0.89 fc = 0.85

0.49

0.83 0.76 0.78 0.66

— — — — — —

Am always prepared. Pay attention to details. Like order. Follow a schedule. Am exacting in my work. Leave my belongings around. (+) — Make a mess of things. (+) — Often forget to put things back in their proper place. (+)

0.58 0.69 0.77 0.60 0.64 0.61

αc = 0.85 fc = 0.81

0.35

EMOTIONAL STABILITY (EMO_)

— — — —

0.67 0.84 0.66 0.88

αc = 0.81 fc = 0.79

0.49

INTELLECT OR IMAGINATION (INT_)

— — — —

0.69 0.73 0.66 0.62

αc = 0.84 fc = 0.78

0.81

CONSCIENTIOUSNESS (CONS_)

Am easily disturbed. (+) Get upset easily. (+) Change mood a lot. (+) Get irritated easily. (+)

Have a rich vocabulary. Have a vivid imagination. Have excellent ideas. Am quick to understand things. — Use difﬁcult words. — Am full of ideas.

0.65 0.58

0.61 0.69

Note: See note in Table 2; (+) Indicates that the sense of the scale has been changed so that all the items may have the same sense.

INT present an AVE of 0.5 or above, and it is inferior for EXT and RES. Equally, we neither remove nor add any indicators from these dimensions because the model would worsen. In this case, although some parameters are within the recommended levels, others do not reach that level (χ2 = 1327 g.l. = 314; GFI = 0.84; RMSEA = 0.08; CFI = 0.85; NFI = 0.99;

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AGFI = 0.81). This may be explained by the inﬂuence of the sample size and the number of indicators (Hair et al., 1999; Del Barrio and Luque, 2000). Finally, the attitudes scale “EAKS” gathers the intentional component, with two items (VC), the behavioural one, also with two items (AC) and the affective one, with ﬁve items (AF). All of them refer to aspects related with the individuals’ disposition to reduce air pollution, the activities to achieve that purpose and the feeling of frustration and anger experienced by individuals about environmental problems (Table 5). Regarding the ﬁnal reliability of the scale, considering that VC and AC dimensions include two items each, their internal consistence is enough. On Table 5.

Conﬁrmatory analysis for the environmental attitude scale “EAKS”.

CONSTRUCTS AFFECT COMMITMENT (AF)

ITEMS — It frightens me to think that much of the food I eat is contaminated with pesticides. — It genuinely infuriates me to think that the government doesn’t do more to help control pollution of the environment. — I become incensed when I think about the harm being done to plant and animal life by pollution. — I get depressed on smoggy days. — When I think of the ways industries are polluting, I get frustrated and angry.

(λ) 0.59 0.75

VERBAL COMMITMENT (VC)

— I’d be willing to ride a bicycle or take the bus to work in order to reduce air pollution. — I would be willing to use a rapid transit system to help to reduce air pollution

ACTUAL COMMITMENT (AC)

— I make a special effort to buy products in recyclable containers. — I have switched products for ecological reasons

Note: See note in Table 2.

Reliab. αc = 0.83 fc = 0.78

E.V.A 0.42

0.76 0.72

αc = 0.7 fc = 0.62

0.45

0.72 0.76

αc = 0.63 fc = 0.62

0.45

0.83

0.61 0.77

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the other hand, the extracted variance analysis is around 0.5 in the VC and AC dimensions, and it is below that value for AF. In this case, the data ﬁt has been nearly perfect (χ2 = 67.20 g.l. = 24; GFI = 0.97; RMSEA = 0.06; CFI = 0.97; NFI = 0.96; AGFI = 0.95). Moreover, successive factor analyses were also conducted to guarantee all these constructs convergent validity. This validity is proved because indicators present signiﬁcant factor loadings (over 0.5) (Anderson and Gerbing, 1988). We will proceed to contrast the hypotheses by applying several logit analyses, in the next section.

4.2. Logit analysis In order to contrast the three groups of the established hypotheses, on values and lifestyles, personality and attitudes, we have included the dimensions resulting from the previous analysis as variables which may explain the individuals’ disposition to buy ecological products. This expression of ecological behaviour has been measured by four price categories for the three considered products (food, cleaning products and white-goods): the same price, 10% higher, 15% higher and 20% higher. Because in the literature the inﬂuence of these variables on different ecological behaviours has not been studied as a whole but individually, a logit analysis has been applied for each group of variables. Tables 6, 7, 8 and 9 show the results on the relationship of each group of variables with ecological product purchase. The variables which have proved to be signiﬁcant in the ﬁrst regression3 (Table 6) have been FASHION at the same price for food and even paying 15% and 20% more for three ecological products. This reveals some relationship between the disposition to buy ecological products at different price ranges and the importance to follow the latest trends and fashion. The individuals’ adventurous spirit and satisfaction of trying out new things (AVENT) also shows a relationship with this behaviour although with 3 Within

the resulting factors of the VALS scale in conﬁrmatory analysis, none of them reﬂects an austere or moderate lifestyle, thus H1c cannot be contrasted. However, other factors whose inﬂuence on ecological behaviour will be analysed, although no hypotheses have been established since there is no literature on the matter. These factors are: the tendency to follow the latest fashion trends (FASHION) and the interest for engineering and communication issues (KNOWLEDGE).

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Table 6.

Logit analysis results about values and lifestyles (VALS).

Price Level Ecological Food

C

At the same price 10% 15% 20%

2.508∗∗ 0.018 −1.114∗∗ −3.167∗∗

FASHION 0.084∗ 0.043∗∗ 0.044∗

ADVENT −0.191* 0.075∗∗ 0.050*

LEADER

KNOWLED.

−0.074*

%

−2LL

G

χ2

95.3 74.9 61.6 81.5

209.213 625.24 736.9 525.98

7.325* 11.29* 11.61* 10.40*

8.273* 14.72∗∗ 7.96∗∗ 12.39∗∗

96.5 73.6 68.5 84.9

650.88 691.22 471.01

9.80* 4.32* 8.47*

4.92* 12.11∗∗ 6.40*

96.3 70.7 66.8 80.6

683.27 709.89 549.01

19.92 4.22* 9.61*

5.50* 5.89* 3.91*

Ecological cleaning products 3.316∗∗ 0.166 −1.555∗∗ −2.485∗∗

0.055∗∗ 0.052∗

0.043*

Ecological white-goods At the same price 10% 15% 20%

3.265∗∗ −0.003 −1.24∗∗ −1.957∗∗

0.038∗ 0.037∗

0.044*

Note: C = constant; the estimated regression coefﬁcients (β) are presented under each variable; −2LL = −2 Log of the verisimilitude function; χ 2 = Chi-square of the model to contrast the global signiﬁcance of the coefﬁcients; G = Chi-square on the signiﬁcance of Hosmer-Lemeshow goodness of ﬁt contrast to see whether the model conforms to the observed data; * = 5% signiﬁcant and ∗∗ = 1% signiﬁcant.

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VALS

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Price Level Ecological Food

C

At the same price 10% 15% 20%

0.816 −1.537∗∗ −2.058∗∗ −4.056∗∗

ECOEV

ALISANA

0.183∗∗

SALUDEV

%

−2LL

G

χ2

0.168∗∗

95.3 78.1 63.2 81.5

204.77 574.47 721.16 505.62

12.94* 8.184* 13.66* 9.70*

12.71∗∗ 65.49∗∗ 23.71∗∗ 32.75∗∗

96.5 78.2 68.3 84.9

169.66 576.22 676.54 449.88

8.56* 7.81* 17.06 4.14*

3.70* 79.57∗∗ 26.79∗∗ 27.67∗∗

96.3 75 68.2 80.1

173.66 612.6 679.9 508.5

5.46* 10.82* 5.27* 10.12*

6.28* 76.17∗∗ 35.89∗∗ 44.83∗∗

0.101∗∗ 0.160∗∗

Ecological cleaning products At the same price 10% 15% 20%

1.967∗∗ −2.166∗∗ −2.533∗∗ −4.312∗∗

0.094* 0.175∗∗ 0.114∗∗ 0.160∗∗

1.59* −1.897∗∗ −2.895∗∗ −4.945∗∗

0.190∗∗ 0.080∗∗ 0.114∗∗

0.039*

Ecological white-goods At the same price 10% 15% 20%

Note: See note in Table 6.

0.054∗∗

0.132* 0.112∗∗

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Lifestyles

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Logit analysis results about the Lifestyles.

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Table 7.

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Logit analysis results about personality (The Big-Five). The Big-Five

Price Level Ecological Food

C

At the same price 10% 15% 20%

1.057 −0.233 −1.223∗∗ −2.963∗∗

EXT

AGR

CONS

EMO

0.058* −0.068*

INT

%

−2LL

0.058∗∗ 0.054∗∗ 0.062∗∗

95.3 75.1 62.1 81.5

211.37 628.62 733.38 528.61

5.70* 7.10* 2.77* 10.40*

6.12* 11.35∗∗ 11.48∗∗ 9.75∗∗

0.076∗∗ 0.037* 0.049*

96.5 73.4 68.1 84.9

162.54 637.32 698.12 472.2

5.095* 6.60* 10.05* 4.82*

10.82∗∗ 18.48∗∗ 5.205* 5.35*

0.062∗∗ 0.051∗∗ 0.077∗∗

96.3 70.3 66.6 81

174.3 672.34 701.54 534.91

5.16* 12.12* 14.48* 12.96*

5.67* 16.44∗∗ 12.25∗∗ 18.42∗∗

G

χ2

Ecological cleaning products −0.415 −0.026 −1.635∗∗ −2.902∗∗

0.076∗∗ −0.086*

0.114*

Ecological white-goods At the same price 10% 15% 20%

1.175 0.28 −1.081∗∗ −2.256∗∗

Note: See note in Table 6.

−0.103∗∗ −0.104∗∗ −0.128∗∗

0.062*

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Table 8.

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Price Level Ecological Food

C

AF

At the same price 10% 15% 20%

0.921 −0.364 −1.67∗∗ −3.408∗∗

0.112∗∗

VC

%

−2LL

G

χ2

0.195∗∗ 0.301∗∗

95.3 75.1 64.2 81.5

205.99 595.89 714.66 495.11

7.87* 14.30* 5.525* 5.48*

11.50∗∗ 44.06∗∗ 30.21∗∗ 43.25∗∗

0.281∗∗ 0.196∗∗ 0.282∗∗

96.5 76.8 68.1 84.9

596.17 675.19 444.56

22.06 5.12* 1.61*

59.6∗∗ 28.14∗∗ 32.99∗∗

0.306∗∗ 0.247∗∗ 0.267∗∗

96.3 73.8 69.1 80.6

175.76 627.17 671.38 517.27

12.58* 8.77* 9.80* 7.81*

4.18* 61.61∗∗ 44.41∗∗ 36.05∗∗

AC

0.269∗∗

Ecological cleaning products At the same price 10% 15% 20%

3.316∗∗ −1.172∗∗ −1.95∗∗ −3.54∗∗

0.088*

Ecological white-goods At the same price 10% 15% 20%

1.815 −0.801∗∗ −2.205∗∗ −3.114∗∗

Note: See note in Table 6.

0.076*

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(EAKS)

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Logit analysis results about the environmental attitude (EAKS).

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Table 9.

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a different sign according to the price. Thus, while individuals who face new experiences and exciting challenges in an attempt to achieve self-fulﬁlment would not be willing to buy ecological products at the same price, they would pay 10% more in all the products and even 20% more in the case of food. This behaviour might reinforce these individuals’ interest for the environmental improvement or their commitment towards environmental protection. In this sense, H1a , which stated that “individuals with high self-fulﬁlment values will show a higher ecological behaviour”, would be valid for those cases. On the other hand, the value which reﬂects the individuals’ interest or curiosity for engineering or communication issues (KNOWLEDGE) only presents relationship with the disposition to buy ecological food when paying 10% more. This is a negative relationship, which means that people concerned for these issues would not be willing to pay more for ecological products. H1b is not conﬁrmed because no signiﬁcant coefﬁcient for the value of power factor (LEADER) was found. In the second regression (Table 7), where the variables from the Lifestyles scale have been considered, the results obtained about the individuals who follow an ecological lifestyle and like to buy ecological products and participate in environmental improvement actions (ECOEV) are remarkable, since this variable is positively related in all the behaviours and for all the products. Thus, H1d , “individuals with high interest for ecological matters will show a higher ecological behaviour”, would be clearly conﬁrmed. On the other hand, in some cases lifestyles related with having healthy eating habits (ALISANA) and having a healthy lifestyle (SALUDEV) have also showed a positive and signiﬁcant relationship. Consequently, those people who try to have healthy eating habits would be willing to buy 10% more expensive cleaning products and a 15% more expensive white-goods. And those who are concerned for their health and try to have a balanced and relaxed lifestyle (SALUDEV) would buy ecological products at the same price and would even pay 20% more for ecological white-goods. Therefore, in these cases H1e : “individuals who are concerned for their health and body will show a higher ecological behaviour”, would be veriﬁed. The regression analysis which studies the relationship between the willingness to buy ecological products and the ﬁve personality characteristics is shown in Table 8. As for the characteristic of extroversion (EXT), the relationship is signiﬁcant and negative in all the cases where it occurs, speciﬁcally in the disposition

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to buy at 10%, 15% and 20% more. This shows that the less extrovert or vain the individuals are, the more willing they are to buy ecological products at these price ranges. On the other hand, the characteristic of responsibility (RES) is positively related to ecological product purchase at the same price as non-ecological ones, but it shows no relationship in the other cases. That is, the more responsible the person, the more willing to buy this type of products at the same price as non-ecological ones. The characteristic of emotional stability (EMO) has proved to be related only to cleaning product purchase at the same price. It is not relevant in any other case. Finally, the characteristic of intellect and imagination (INT) shows a relationship with this behaviour for all price and product ranges except at the same price. Therefore, those individuals characterised by this type of personality would be more willing to buy ecological products 10%, 15% and 20% more expensive. We may conclude then that H2a , which stated that individuals with a less extrovert and conceited personality would show a higher ecological behaviour, and H2e , which postulated that individuals with an imaginative and intellectual personality would show a higher ecological behaviour, are veriﬁed. Finally, the characteristics of emotional stability and responsibility only increase purchase likelihood at the same price for cleaning products in the ﬁrst case and for the three products in the second one. Therefore, H2c and H2d, which referred to those people with high emotional stability and responsibility respectively, would be veriﬁed only in these cases. H2b is not veriﬁed in any case, since the characteristic of solidarity to the others does not present signiﬁcant coefﬁcients. Regarding the relationship between the three components of attitude and ecological product purchase, in Table 9 we can observe that the variable of real ecological commitment (AC) has shown a regular relationship with the purchase disposition since this association occurs for the three levels of higher price and the three products. However, the variables of verbal ecological commitment (VC) and affective commitment (AF) only appear associated to this behaviour in the disposition to buy cleaning products 10% more expensive and buy ecological food and white-goods at the same price. Consequently, H3a : “individuals with a more affective attitude (concern, interest) to the environment will show a higher ecological behaviour”, would

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be conﬁrmed only for the disposition to buy ecological food and white-goods at the same price, therefore we cannot fully conclude that people interested and concerned for the environment would be more willing to buy ecological products at different price ranges. The same could be said for H3b , which is only conﬁrmed when the consumers are willing to buy ecological cleaning products at a 10% higher price. Finally, H3c , which stated that individuals with a higher attitude of actual commitment to the environment would show a higher ecological behaviour, is clearly veriﬁed since in all the cases the individual would pay more for ecological products. Those consumers willing to buy ecological products at different price ranges are characterised by values which reﬂect the enterprising spirit of those people who feel self-fulﬁlled when facing exciting challenges and having new experiences. Furthermore, they highly appreciate the ecological attributes or beneﬁts of products, a healthy lifestyle and healthy eating habits. Among the personality characteristics which have described this behaviour best are the individuals’ scarce extroversion or vanity and the level of intellect and imagination. Finally, as for environmental attitudes, real ecological commitment is the most determining factor in the disposition to buy at different price ranges.

4.3. Discussion and managerial implications This paper contributes to improve the knowledge of the ecological consumer’s behaviour and we offer an analysis of the psychographic proﬁle of that consumer. This research has proved, ﬁrst, that psychographic variables are crucial for the environmental behaviour and, second, that some values, lifestyles, personality characteristics and attitudes increase the likelihood that consumers concerned for the environment have no objection to pay more for less polluting goods. The knowledge of these characteristics may be extremely useful for those companies whose commercial decisions involve market segmentation and those who want their products to have a pre-eminent place in the consumer’s mind. If environmental concern maintains this upward trend, the number of ecological consumers will equally grow. Therefore, the company’s continuity in the market will depend on meeting the consumers’ needs. Obviously, the consumers’ needs will determine the company’s launch of new products and its management. But the question is, how does the company address this group of consumers? And what kind of actions do they have to take?

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Before giving an answer to these questions, managers need to know the consumer’s personality and mind so as to draw their attention. This study provides companies with the knowledge of the psychographic characteristics of the consumer who is willing to pay different price range when purchasing ecological products and, indirectly, their way of thinking. First, self-fulﬁlment has a prominent place in the value structures of these individuals. They are people who enjoy challenges and new experiences which satisfy them. They also like new fashion trends. In this respect, companies may persuade them by highlighting the original and distinctive character of their products and attributing new beneﬁts to their use so that these consumers consider trying out these products as a new adventure. Second, they have an ecological lifestyle, consuming recycled products and participating in environmental activities. They also like having a balanced life and healthy eating habits. Therefore, companies should be interested in highlighting the environmental attributes of their products, mainly through labelling and packaging. On the other hand, in the case of organic farming products, their healthy aspects should be emphasised. Third, the personality characteristics which best describe the ecological consumer are two: scarcely extrovert or conceited character and imagination. Thus, these consumers, when purchasing ecological products, do not intend to prove to the others or themselves that they are contributing to the improvement of the environment. Therefore, the message that a company sends to the market, either about their environmental behaviour or to present their products, should contain no trace of vanity or leadership which may intimidate consumers. Finally, the attitude which best deﬁnes this type of consumers is an attitude of actual commitment towards the protection of the environment. This attitude is directly related to a proactive attitude from the company. In other words, the marketing managers of companies have to transmit a serious and responsible image of their activity in the market. Furthermore, that image has to be globally reﬂected by means of the company’s internal (management commitment) and external (commercial strategies) environmental organisation. Although this study has provided some knowledge of the ecological consumer’s proﬁle, these results refer to a speciﬁc ecological behaviour: the disposition to purchase ecological products at different price levels. Hence, it would be convenient to analyse these characteristics for other expressions of the ecological behaviour.

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Conclusions

This study contributes to the knowledge of the ecological consumer’s behaviour. More exactly, it presents the psychographic proﬁle of the consumers who would be willing to purchase ecological products even if they were more expensive than non-ecological ones. Consequently, it has been proved that psychographic variables (values, lifestyles, personality and attitude) are determining in the ecological behaviour in general and, more particularly, in the consumers’ disposition to pay more for ecological products. These results reveal that companies face a wide demanding market and considering the environmental principles consistently in their global and commercial strategies may give them a sustainable competitive advantage which is crucial today. In this respect, they may design suitable commercial policies to draw the ecological consumer segment’s attention. Given that consumers increasingly appreciate ecological issues and enjoy taking risks and trying out new things, it should be in the companies’ interest to reﬂect their commitment towards the environment in their products/services, thus transmitting the measures they take to maximise the impact of their products. This may be done through the product’s labelling or advertising campaigns to inform consumers about these aspects. Furthermore, advertising campaigns should be aimed at people who are highly involved in environmental protection and those who do not like to be outstanding and have a great imagination. This could justify an increase of price for their less polluting products. The results of this study may be generalised cautiously, since the sample is relatively small and the researchers propose the application of this study to a wider sample in other countries in order to compare the results and analyse if culture is a relevant moderating variable.

Acknowledgements The authors express their gratitude for the ﬁnancial help received from the Government of Aragon through the projects (PM 062/2004) and GENERES (Ref: S09/26779), and from the Ministry of Science and Technology by means of the CICYT project (Ref: SEC 2002-03949).

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Appendix 1: Values and Lifestyles Scale (VALS) Items I am often interested in theories I Iike outrageous people and things I like a lot of variety in my life I love to make things I can use everyday I follow the latest trends and fashions Just as the Bible says, the world literally was created in six days I like being in charge of a group I like to learn about art, culture, and history I often crave excitement I am really interested only in a few things I would rather make something than buy it I dress more fashionably than most people The Federal government should encourage prayers in public schools I have more ability than most people I consider myself an intellectual I must admit that I like to show off I like trying new things I am very interested in how mechanical things, such as engines, work I like to dress in the latest fashions There is too much sex on television today I like to lead others I would like to spend a year or more in a foreign country I like a lot of excitement in my life I must admit that my interests are somewhat narrow and limited I like making things of wood, metal, or other such material I want to be considered fashionable A woman’s life is fulﬁlled only if she can provide a happy home for her family I like the challenge of doing something I have never done before I like to learn about things even if they may never be of any use to me I like make things with my hands I am always looking for a thrill I like doing things that are new and different I like to look through hardware or automotive stores I would like to understand more about how the universe works I like my life to be pretty much the same from week to week Source: Based on the International Survey of Mitchell (1983). Obtained from http://future.sri.com/vals/ [14/03/03].

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Appendix 2: Lifestyles Scale (Lifestyles) Items The current civilisation is destroying the nature. I prefer consuming recycled products. I throw garbage in selective containers. The environment deterioration will be irreversible if the necessary measures are not taken. I participate in environment conservation tasks. I worry about the human activity consequences on the climatic change and act consistently. I control the salt ingestion. I practise a vegetarian diet. I regularly do exercise. I try not to eat pre-cooked food. Often eat fruits and vegetables. I eat red meat moderately. I belong to a pro-environmental association. I try to eat food without additives. Periodically, I check my health voluntarily. I try to reduce stress. Regularly, I visit the dentist. I try to take an arranged and methodical life. I try to ﬁnd the balance between work and my private life. I read the products labels. Source: Sánchez et al. (1998a).

Appendix 3: Personality Scale “The Big-Five Factor Structure” EXTROVERSION Am the life of the party. Feel comfortable around people. Start conversations. Talk to a lot of different people at parties. Don’t mind being the centre of attention. Don’t talk a lot. (+) Keep in the background. (+) Have little to say. (+) Don’t like to draw attention to myself. (+) Am quiet around strangers. (+) AGREEABLENESS Am interested in people. Sympathise with others’ feelings. Have a soft heart. (Continued)

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(Continued) Take time out for others. Feel others’ emotions. Make people feel at ease. Am not really interested in others. (+) Insult people* (+) Am not interested in other people’s problems. (+) Feel little concern for others. (+) CONSCIENTIOUSNESS Am always prepared* Pay attention to details. Get chores done right away. Like order. Follow a schedule. Am exacting in my work. Leave my belongings around. (+) Make a mess of things. (+) Often forget to put things back in their proper place. (+) Shirk my duties* (+) EMOTIONAL STABILITY Am relaxed most of the time. (+) Often feel blue* (+) Get stressed out easily. Am easily disturbed. Get upset easily. Change mood a lot. Get irritated easily. Seldom feel blue. Am not easily bothered by things. (+) Rarely get irritated. (+) INTELLECT OR IMAGINATION Have a rich vocabulary. Have a vivid imagination. Have excellent ideas. Am quick to understand things. Use difﬁcult words* Spend time reﬂecting on things. Am full of ideas. Have difﬁculty in understanding abstract ideas. (+) Am not interested in abstract ideas. (+) Do not have a good imagination. (+) Note: * = we changed the wording of these items to make them easily understood; (+) = indicates items that are inverted in their meaning. Source: http://ipip.ori.org/ipip [24/01/01].

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Appendix 4: Environmental Attitudes Scale (EAKS) Affect Commitment (AF) — It frightens me to think that much of the food I eat is contaminated with pesticides. — It genuinely infuriates me to think that the government doesn’t do more to help control pollution of the environment. — I become incensed when I think about the harm being done to plant and animal life by pollution. — I get depressed on smoggy days. — When I think of the ways industries are polluting, I get frustrated and angry. — The whole pollution issue has never upset me too much since I feel it’s somewhat overrated. (+) — I rarely ever worry about the effects of smog on myself and family. (+) Verbal Commitment (VC) or “Environmental Attitude” — I’d be willing to ride a bicycle or take the bus to work in order to reduce air pollution. — I would be willing to use a rapid transit system to help to reduce air pollution — I would donate a day’s pay to a foundation to help improve the environment. — I would be willing to stop buying products from companies guilty of polluting the environment, even though it might be inconvenient. — I’d be willing to write my congressman weekly concerning ecological problems. — I wouldn’t go house to house to distribute literature on the environment. (+) — I would not be willing to pay a pollution tax even if it would considerably decrease the smog problem. (+) Actual Commitment (AC) or “Ecological Behaviour” — I guess I’ve never actually bought a product because it had a lower polluting effect. (+) — I keep track of my congressman and senator’s voting records on environment issues. — I have contacted a community agency to ﬁnd out what I can do about pollution. — I make a special effort to buy products in recyclable containers. — I have attended a meeting of an organisation speciﬁcally concerned with bettering the environment. — I have switched products for ecological reasons. — I have never joined a cleanup drive. (+) — I have never attended a meeting related to ecology. (+) — I subscribe to ecological publications. Note: Scale used in the ﬁnal questionnaire. After passing the pre-test, we found some of these items problematic so we decided to take it off. The original scale can be obtained from Maloney et al. (1975).

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4 EXTENSIONS OF LOGISTIC GROWTH MODEL FOR THE FORECASTING OF PRODUCT LIFE CYCLE SEGMENTS Mladen Sokele∗ and Vlasta Hudek Department of Telecommunications Faculty of Electrical Engineering and Computing University of Zagreb Unska 3, HR-10000 Zagreb, Croatia ∗ [email protected] Received February 2006 Accepted February 2006 Proper forecast of product market diffusion enables optimal planning of resources, investments, revenue, marketing and sales. Quantitative forecasting methods for this purpose rely on sigmoidal growth models such as logistic growth and Bass model, which are acceptable for the ﬁrst adoption interval of product life cycle (PLC). Modelling of other PLC segments requires complex models that need large set of input data that limits their application for the forecasting purposes. This paper presents extensions of the logistic growth model that combine the principle of sigmoidal growth and the concept of interpolation splines. In addition, adaptation of the logistic model is shown to be congruent with Bass model. Applications of developed models for the forecasting of PLC segments are analysed and examined, together with possible ways of interaction between different products. Developed models and interaction types enable forecasting of entire PLC with minimum set of input data, or assessment of qualitative forecasting results.

Keywords: PLC, logistic growth model, Bass model, forecasting.

1.

Introduction

During its life cycle, every product or service passes through the following phases: growth, saturation and decline. The understanding and forecasting of 77

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each segment of product life cycle (PLC) for the business planning purposes has become more and more important in the competitive market environment and for product/services resulting from emerging technologies, such as telecommunications. Forecasting is important to entrepreneurs and governments, but usually suffers from market ﬂuctuation and uncertainty. The scope of this paper is the development of suitable models for forecasting of market adoption of products/services based on sigmoidal growth models such as logistic growth and Bass model. Focus is on products/services such as: diffusion of new technology, consumer durables, subscription services (e.g., telecom services), allocations of restricted resources, i.e., products/services that not include repeat sales. In the paper, these products/services are simply called products. There is a wide variety of existing methods that are used for the purpose of forecasting of market adoption of products. However, the typical practitioner’s problem: how to bridge the gap between known data and anticipated value in the future, is still dominant and pending due to the lack of reliable input data.

2.

Technological Forecasting — A Literature Review

Many studies have focused on market forecasting from the perspective of technological forecasting, for example, related costs of innovation and learning (e.g., Albright, 2002); competitive intelligence and the innovation process (e.g., Lemos and Porto, 1998); simulation of emerging technologies (e.g., Bers et al., 1999); technology management, technology mapping and innovation indicators (e.g., Zhu and Porter, 2002); technological progress and the technology cycle time indicator (e.g., Kayal, 1999); product/service prelaunch forecasting (e.g., Bass et al., 2001), etc. Comprehensive overviews of models appropriate for technological forecasting and their forecasting performance are made in Meade and Islam (1998) and Fildes and Kumar (2002). The pace of technological progress is a construct that has evolved from technological change theories. Measuring the pace of technological progress is believed to be important for both technology management and technology forecasting. Kayal (1999) developed a new objective measure of the pace of technological progress called the technology cycle time indicator (TCT). The TCT indicator was used in two comparison analyses: (1) assessing the pace of progress of technologies; and (2) assessing the position of various countries patenting in a particular technology ﬁeld. The ﬁndings revealed

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that the TCT provided a valid assessment in each situation. Bass et al. (2001) conducted research to plan the launch of a satellite television product, leading to a prelaunch forecast of subscriptions of satellite television over a ﬁve-year horizon. The forecast was based on the Bass model. They derived parameters of the model in part from stated-intentions data from potential consumers and in part from guessing by analogy. The forecast of the adoption and diffusion of satellite television proved to be quite good in comparison with actual subscriptions over the ﬁve-year period. Meade and Islam (1998) identiﬁed 29 models that the literature suggests are appropriate for technological forecasting. These models are divided into three classes according to the timing of the point of inﬂexion in the innovation or substitution process. Faced with a given data set and a choice of models, the issue of model selection needs to be addressed. Evidence used to aid model selection was drawn from measures of model ﬁt and model stability. An analysis of the forecasting performance of these models using simulated data sets showed that it is easier to identify a class of possible models rather than the “best” model. This leads to the combining of model forecasts. The performance of the combined forecasts appeared promising with a tendency to outperform the individual models. The observed patterns of product life cycles indicate the “stage” concerns. Such concerns include stage identiﬁcation, stage-based strategies and, a new concept of “stage modelling” introduced by Chang and Chang (2003). Stage modelling is concerned with modelling as well as aggregating individual stages in an overall inter-inﬂuence manner. Thus, stage modelling not only preserves the respective characteristics of the stages but also may be explored for the stage-related strategies. To date, this issue has not yet been explored in the product life cycle (PLC) literature. Chang and Chang proposed an approach to modelling PLCs by addressing the stage characteristicpreserving aspect. The new product diffusion was also demonstrated which was improved by this new approach. Funk (2004) applied the product life cycle theory to the issue of product line management with two goals in mind: (1) to understand how product line management evolves over the life of an industry and (2) to compare modelling approaches which emphasise economies of scale with the traditional model of the product life cycle, which emphasises dominant designs. This author found that some models of the product life cycle theory in combination with the concept of product line management provided a better explanation for the evolution of competition in the mobile phone industry than the traditional product life cycle model. In order to model the market evolution and the resulting changes, the concept

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of technological paradigms and the concept of technological regimes were integrated by Werker (2003) into a product life cycle model. The simulations performed with this model helped to understand how the dynamics of market evolution shapes market performance and competition. The results of the simulation runs showed a much more differentiated picture than economic intuition suggests and therefore give useful hints for companies’ strategies and innovation policy. The most striking result of the simulation runs for entrepreneurial strategies was that there were markets that ﬁrms would be interested to enter to realise some proﬁts and then exit again, and there were other markets that companies would want to survive in the long-run. The product life cycle theory explains how the high degree of uncertainty, as regards product designs and production methods — which is connected to the early stages of the product life cycle, requires a high level of knowledge-intensity. Since uncertainty decreases over the product life cycle, less knowledge is needed in production during later stages of the product life cycle. This implies that knowledge-intensity differs for ﬁrms that exit and enter in different stages of the product life cycle. The empirical results found by Karlsson and Nystrom (2003) showed that entrants in the early stages of the product life are more knowledge-intensive than incumbent companies. These authors have also found that ﬁrms exiting in early stages of the product life cycle are more knowledge-intensive than companies exiting in later stages. The best known model for a full description of the genesis and extensions of new-product diffusion is the Bass model. As discussed in Fildes and Kumar (2002), the basic Bass model has many apparent limitations, the most important of which is the calibration of the parameters when limited data are available as is the case with new products. Unfortunately, the parameters of a Bass diffusion model cannot be estimated, either because there are too few data points available or alternatively, unconstrained estimation leads to implausible results. Generalised Bass model incorporates marketing or economic variables, such as pricing and advertising, and expands model usage not only for early phases of the PLC, but also for the phases when product faces the change of its market potential.

3.

Product Life Cycle

A product life cycle closely resembles the proﬁle of the technology life cycle and its associated market-growth proﬁle. According to Khalil (2000),

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30 000

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Figure 1. Number of telex subscribers in Portugal 1976–2003. Source: ITU (2005).

product-market life cycle consists of six phases: Concept design prototype, Product launch, Product growth, Mature stage, Substitution products and Product obsolescence. For example, market adoption of telex service (i.e., number of telex subscribers) in Portugal presented in Figure 1 is bell-shaped. PLC passes phases of introduction (before 1976, not presented in Figure 1), growth, maturity, saturation, and decline due to the strong competition of other similar but more attractive products (fax and e-mail). Market adoption of product is not always so simple. In the case of number of payphones in Finland (Figure 2), market adoption consists of several growth and decline phases. Moreover, the number of payphones will not fade out soon, although it should be a sensible decline. The reason is the universal service regulatory framework for telecommunications. To summarise the above mentioned, a typical product during its life cycle passes through the following speciﬁc phases of market adoption, which are also described in Figure 3. T1 — Product is unique and new on the market. Its market capacity M1 is identical to the current total market capacity. T2 — New market opportunities for that product emerge (economical or technological). Its market capacity is increased to M2 .

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Figure 2. Public pay phones in Finland 1980–2003. Source: ITU (2005).

Figure 3. Typical market adoption of product during entire PLC. N(t) — number of the consumers; Mi — market capacities.

T3 — Product is confronted with competition in unchanged market capacity. T4 — Attack from competitive product(s), which leads to the number of consumers N(t) decreasing. Competitive product can be identical product but offered by other provider, or similar but technologically more advanced product.

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Only at the beginning of the PLC, logistic law of growth or the basic Bass model can successfully be applied to represent the product consumer growth. The logistic growth model (other names: Pearl growth curve, Verhulst growth curve) is congruent with the growth of the number of product consumer observed over time in a closed market, without the presence of any other product. Model is deﬁned with three parameters: M — market capacity, a — growth rate parameter, and b — time shift parameter. To emphasise the dependence of the model on its parameters, it is convenient to indicate model as L(M, a, b; t) or shortly L(t): L(M, a, b; t) =

M 1 + e−a(t−b)

(1)

The Bass diffusion model B(M, p, q, ts ; t) of new products is deﬁned with four parameters: M — market capacity, p — coefﬁcient of innovation, q — coefﬁcient of imitation, and ts — time when product is introduced. B(M, p, q, ts ; t) = M

1 − e−(p+q)(t−ts ) q 1 + e−(p+q)(t−ts ) p

(2)

During the whole PLC, market capacity changes in hops and resembles a series of stairs. In a speciﬁc time frame, adoption of product follows an S shape curve growth/decline. A particular set of conditions determines market capacity in a speciﬁc time frame: product attractiveness, product features, marketing (advertising); product availability (supply); competition (market share); technology improvements; balance between purchase power and product pricing. Due to the complexity of these conditions, the estimation of market capacity and duration of observed time frame, where these conditions are stable, is usually performed by qualitative forecasting methods. Quantitatively, it can be concluded that the adoption dynamics is the composite function compounded of the series of the smoothly joined S-curves. Analysis of a typical market adoption of product during the entire PLC gives the following conclusions: • No single regression model (logistic, Gompertz, Richards, MMF, Weibull and Bass) can describe adoption of product (penetration) in its entire range. • Penetration consists of (sub)curves, i.e., a set of sigmoidal curves. Each curve is modelling one segment.

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• Transitions between (sub)curves are smooth, i.e., (at least) 1st derivative is preserved. The modelling of the adoption of product during the entire PLC could be done by using the Norton-Bass model or multi-logistic growth function. The Norton-Bass model describes sales of multiple generations of products and it is an extension of the Bass model (1969) on the diffusion of a singlegeneration product. This model deals with the sales of successive generations of products in cases where adopters continue buying the product at a constant rate and buyers of earlier generations gravitate to later generations according to the Bass model cumulative distribution. Modelling of each product generation requires four parameters to be determined. This is similar with the multi-logistic growth (3), which is a composite function consisting of the sum of simple logistic growth models, and requires three parameter per item: ML(t) =

M2 − M1 Mn − Mn−1 M1 + + ··· + −a (t−b ) −a (t−b ) 1 1 2 2 1+e 1+e 1 + e−an (t−bn )

(3)

For illustration, adoption of product described in Figure 3 is decomposed into 4 simple logistic growth models and shown in Figure 4. Modelling with the above mentioned complex functions requires the determination of the values of numerous free parameters, which requires a large set of known data that limits their application to the forecasting purposes.

Figure 4. Multi-logistic function consisting of 4 simple logistic growth models. N(t) — number of the consumers; Mi — market capacities (in increments).

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Interaction between Products in the Market

Only at the beginning of the product life cycle would there be no interaction with other product in terms of market diffusion, therefore its growth may be approximated with simple growth models such as logistic or Bass model. In real cases, interaction between different products is evident, and can be divided into three types: • Product competition — Both products are competing in an unchanged total market capacity. • Product co-evolution — Complementary products change the total market capacity, as a result there is no decrease of existing product penetration. • Product revolution — New attractive product almost completely eliminates the existing one, total market capacity is noticeably increased. The three types of interaction between products are illustrated in Figures 5–7. Corresponding expressions (4)–(12) describe these interaction types numerically. Equations are based on the assumption that the logistic model of growth L(Mi , ai , bi ; t) satisfactorily models the components of product market diffusion.

Figure 5.

Product competition.

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Figure 6.

Figure 7.

Product co-evolution.

Product revolution.

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4.1. Product competition Ntot (t) = N1 (t) + N2 (t) = L(Mt , at , bt ; t)

(4)

N2 (t) = L(M2 , a2 , b2 ; t)

(5)

N1 (t) = Ntot (t) − N2 (t) = L(Mt , at , bt ; t) − L(M2 , a2 , b2 ; t)

(6)

4.2. Product co-evolution Ntot (t) = N1 (t) + N2 (t)

(7)

N1 (t) = L(M1 , a1 , b1 ; t)

(8)

N2 (t) = L(M2 , a2 , b2 ; t)

(9)

Ntot (t) = L(M1 , a1 , b1 ; t) + L(M2 − M1 , a2 , b2 ; t)

(10)

N2 (t) = L(M2 , a2 , b2 ; t)

(11)

4.3. Product revolution

N1 (t) = Ntot (t) − N2 (t) = L(M1 , a1 , b1 ; t) + L(M2 − M1 , a2 , b2 ; t) − L(M2 , a2 , b2 ; t)

5.

(12)

Possible Cases for Using Logistic Model of Growth for Forecasting Purposes

In the following ﬁve cases from the forecasting praxis, the use of logistic model of growth and its adaptations will be analysed and discussed.

5.1. Case 1 — Extensive set of input data Known: n points, n ≥ 4 (ti , N(ti )), i = 1, 2, . . . , n; ∃tj , tj > b (among them exist at least one point after inﬂexion). Assumed: No need for assumptions. Parameter determination: Least-squares method — ﬁnding the minimum of sum S: 2 n M N(ti ) − (13) S= 1 + e−a(ti −b) i=1

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Finding the minimum gives the system of three nonlinear equations which lead to determination of parameters M, a and b: ∂S = 0; ∂M

∂S = 0; ∂a

∂S =0 ∂b

(14)

System of equations has no exact analytical solution and for its solution an iterative numerical method should be deployed. Usability: The ﬁt of the model is usually very strong on the whole part of the product life cycle, where product is the only one on the market and can be measured with correlation coefﬁcient R. It is also possible to test (via standard errors and t-ratios) conﬁdence of the resulting parameter estimates. But, due to the fact that extensive set of data have to be already known, Case 1 has low usability for the practical forecasting purposes. However, it would be useful for an accurate determination of market capacity and product diffusion dynamics — for the forecasting by analogy of a subsequent product.

5.2. Case 2 — Sufﬁcient set of input data with assumed market capacity Known: n points, n ≥ 3 (ti , N(ti )), i = 1, 2, . . . , n. Assumed: Market capacity Ma (index a stands for assumed). Ma is usually estimated by market research and/or market segmentation techniques. Parameter determination: Least-squares method — ﬁnding the minimum of sum S: 2 n Ma N(ti ) − (15) S= 1 + e−a(ti −b) i=1 Finding the minimum gives two nonlinear equations which leads to the determination of parameters a and b: ∂S = 0; ∂a

∂S =0 ∂b

(16)

These equations have no exact analytical solution and for their solution an iterative numerical method should be deployed. Usability: Suitable for wide-ranging forecasting purposes (for new products that are similar with previous ones on the same market; or for new products, which are identical to existing ones on comparable markets). The ﬁt of the model can be measured with correlation coefﬁcient as well as the conﬁdence of the resulting parameter estimates.

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5.3. Case 3 — Minimum set of input data Known: 3 points, (ti , N(ti )), i = 1, 2, 3. Assumed: No assumptions. Parameter determination: System of three nonlinear equations which leads to determination of parameters M, a and b: M , i = 1, 2, 3 (17) 1 + e−a(ti −b) The system has no exact analytical solution and an iterative numerical method should be deployed. Usability: Values of obtained parameters are uncertain (i.e., their conﬁdence could not be tested), but it has application for the forecasting purposes, when market capacity is difﬁcult to obtain from other sources or for non-long range forecasting. N(ti ) =

5.4. Case 4 — Assumed market capacity and only two known points Known: 2 points, (ti , N(ti )), i = 1, 2. Assumed: Ma market capacity. Parameter determination: System of two nonlinear equations which has exact analytical solution for parameters a and b: Ma Ma 1 ln − 1 − ln −1 (18) a= t2 − t1 N(t1 ) N(t2 ) Ma 1 −1 (19) b = t1 + ln a N(t1 ) Usability: Similar to Case 2 — regularly used for forecasting when little data are available. Values of obtained parameters a and b are uncertain, but assumed market capacity Ma can be relatively good estimate for market research and/or market segmentation techniques, which improves accuracy.

5.5. Case 5 — Assumed market capacity and characteristic duration Known: ts — time when product has perceptible penetration, u — level of perceptible penetration (product introduction on market, start) and v (product maturity) — level of saturation. Values for levels u and v are conventional and are usually symmetric, i.e., u = 1 − v. Generally accepted values for u are 5% or 10% and for v, 95% or 90%, respectively. Condition that should be satisﬁed is 0 < u < v < 1.

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Figure 8. Logistic model of growth deﬁned via time when product observable starts ts , characteristic duration t and penetration levels u and v.

Assumed: Ma market capacity and characteristic duration t. Characteristic duration is the time interval from ts to product maturity time te = ts + t, see Figure 8. Parameter substitution: Parameters a and b in (1) should be replaced with expressions (20) and (21), which are dependant on input parameters u and v: 1 1 1 ln − 1 − ln −1 (20) a= t u v 1 −1 ln u b = ts + t (21) 1 1 − 1 − ln −1 ln u v Modiﬁed logistic model needs ﬁve parameters (M, ts , t, u and v) against three needed for ordinary logistic model, but the reason lays in dependence between t and u and v. In case of symmetrical u and v, i.e., u = 1 − v, the equations become more simple: 1 2 ln −1 (22) a= t u t b = ts + (23) 2

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t = 2 yearsa t = 5 yearsb t = 10 yearsc t = 15 yearsc

91

A framework for forecasting of new services/products prior to launch. u = 5%, u = 95% M N(t) = 1 + e−2.944(t−ts −1) M N(t) = 1 + e−1.178(t−ts −2.5) M N(t) = 1 + e−0.589(t−ts −5) M N(t) = 1 + e−0.393(t−ts −7.5)

u = 10%, v = 90% M N(t) = 1 + e−2.197(t−ts −1) M N(t) = 1 + e−0.879(t−ts −2.5) M N(t) = 1 + e−0.439(t−ts −5) M N(t) = 1 + e−0.293(t−ts −7.5)

a Adjusted

according to Modis (1998). Products consist of units sold that have typical life cycle of six to ten quarters. b Product families consist of related products that have a typical business cycle of ﬁve years. c Basic technologies consist of a set of related product families that have a typical cycle of ten to 15 years.

Therefore this model needs four parameters (M, ts , t and u) against three needed for ordinary logistic model, because of dependence between t and u: M (24) L(M, ts , t, u; t) = 1−2(t−ts )/t 1 −1 1+ u Used simpliﬁcation gives a framework for the forecasting of new product diffusion when little or no data are available. Table 1 presents resulting models for typical values of characteristic duration t for products, product families and basic technologies according to Equation (24) but uniformed on the same natural logarithm base e. Usability: Regularly used for forecasting of new product diffusion when little or no data are available. In cases of product diffusion forecasting prior to product launch, a pair characteristic duration — level of saturation for product maturity is assumed by means of analogy with existing products.

6.

Deﬁciency of Logistic Model of Growth — Linear Transformed Logistic Model

Although the logistic model is widely used for the forecasting purposes, it is not suitable for modelling product diffusion when the number of consumers grows at a fast pace immediately after product is introduced. The reason is in the shape of the logistic growth: “hardly starts to grow up”. This problem is visible from the discussion of Case 5: it is not possible to model time

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when product is introduced, and its penetration is 0 (i.e., u = 0), because Equation (20) will give an inﬁnity value for parameter a. Therefore, in Case 5, when product starts ts , it is anticipated that it has perceptible penetration u, which is higher than 0. One of the possible solutions is to perform linear transformation of the logistic model, in the way that in time ts penetration is 0. Starting from the basic logistic model (Figure 8), the idea of above mentioned linear transformation is described on Figures 9 and 10.

Figure 9. Linear transformation of logistic model — shifting on y-axis.

Figure 10. Linear transformation of logistic model — stretching to M.

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If subtraction of L(ts ) = u · M from L(t) is made, the obtained model is shifted on the y-axis, so penetration for t = ts is 0, as it was required. However, asymptotic value for t → ∞ is not M (market capacity), but (1 − u) · M, see Figure 9. Therefore, multiplication by 1/(1 − u) will stretch the model in a way that asymptotic value for t → ∞ will be M, as required, see Figure 10. Obtained model LTL(t) is linear transformed logistic model L(t): LTL(t) =

M [L(t) − L(ts )] M − L(ts )

(25)

With the following characteristics: LTL(ts ) = 0 lim LTL(t) = M

t→∞

u M M · L(ts ) =− M = − −a(t −b) M − L(ts ) 1−u e s M v−u M =w·M LTL(te ) = [L(te ) − L(ts )] = M − L(ts ) 1−u lim LTL(t) = −

t→−∞

(26)

Where w, 0 < w < 1 represents a level of saturation in time te (product maturity) in linear transformed logistic model LTL(t). As a difference with logistic model deﬁned with three parameters M, a and b, LTL(t) needs additional parameter which is the consequence of y-axis shift L(ts ) for its full deﬁnition. Since L(ts ) = u · M, 0 < u < 1 on which depends growth gradient in ts , u should be used as an additional parameter. According to this, the linear transformed logistic model LTL(M, a, b, u; t) has the following analytical form: M 1 LTL(M, a, b, u; t) = −u 1 − u 1 + e−a(t−b)

(27)

Model LTL(M, a, b, u; t) is fully deﬁned with four points (ti , N(ti )), i = 1, 2, . . . , 4 that are the basis for the system of four nonlinear equations. Their solution gives values of parameters M, a, b and u. For forecasting purposes, the modiﬁed LTL model LTL(M, ts , t, u, w; t) is more convenient where parameters are: market capacity M, product start time ts , characteristic duration t, parameter u, (see Figure 11) and w is the level of saturation in time te = ts + t. At ﬁrst sight, it seems that the modiﬁed LTL model needs one more parameter, ﬁve instead of four, but the reason lays again in the dependence between t and w.

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Figure 11. Example of linear transformed logistic model for different values for u with ﬁxed M = 50 000, ts = 2005, t = 10 years and w = 80%.

Following the deﬁnition of parameters a and b in (27) through ts , t, u and w, model LTL(M, ts , t, u, w; t) becomes fully deﬁned: 1 1 1 a= ln − 1 − ln −1 t u w + u(1 − w) 1 −1 ln u b = ts + t 1 1 − 1 − ln −1 ln u w + u(1 − w)

(28)

(29)

It is interesting that expressions (28) and (29) allows u > w (see Figure 11, u = 90%) which has no practical explanation.

7.

Forms of Linear Transformed Logistic Model of Growth — Introduction of Logistic Spline

Denoting the value for LTL(t) when t → −∞ as c, expression for L(ts ) is obtained: lim LTL(t) = −

t→−∞

M · L(ts ) =c M − L(ts )

⇒

L(ts ) = −

cM M−c

(30)

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By putting substitution for L(ts ) in expression (25) for LTL(t) model, new form for LTL(t) is obtained: cM M−c c M L(t) + = L(t) + LTL(t) = cM M−c M M−c M + M−c M−c M−c L(t) + c = +c (31) M 1 + e−a(t−b) This form of LTL(t) is called logistic spline LS(t) and it is deﬁned by four parameters M, a, b and c: =

M−c +c (32) 1 + e−a(t−b) Relation between parameters of linear transformed logistic model and logistic spline is: LS(M, a, b, c; t) =

LTL(M, a, b, u; t) ≡ LS(M, a, b, c; t) ⇔ c ; or c−M u·M c= u−1 1 M − u LTL(M, a, b, u; t) = 1 − u 1 + e−a(t−b) u=

(33)

(34)

Continuing with applying substitutions, now by extracting c from (32) utilising the fact that here are LTL(ts ) = LS(ts ) = 0: c=−

LS(t) =

M+

M

 1 + e−a(t−b)  1 + e−a(ts −b) − e−a(ts −b)   = M   1 + e−a(t−b) 

M

M e−a(ts −b) − 1 + e−a(t−b) e−a(ts −b)

(35)

e−a(ts −b) 1

e−a(t−b) 1 − e−a(t−ts ) e−a(ts −b) = M =M 1 + e−a(t−b) 1 + e−a(ts −b) · e−a(t−ts ) Progressing with substitutions: 1−

(36)

p+q = a q = e−a(ts −b) p

(37)

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We get well known Bass model: B(t) = M

1 − e−(p+q)(t−ts ) 1 + qp · e−(p+q)(t−ts )

(38)

This is the proof that linear transformed logistic model LTL(t) [or logistic spline LS(t)] is identical to Bass model B(t). Here are the set of equations that establish full link between of logistic spline LS(M, a, b, c; t) and Bass model B(M, p, q, ts ; t): LS(M, a, b, c; t) ≡ B(M, p, q, ts ; t) ⇔ aM M 1 ac p= , q=− , ts = b − ln − ; or c−M c−M a c q 1 p a = p + q, b = ts + ln , c=− M p+q p q

(39)

(40)

It is emphasised that the Bass model is obtained here by linear transformation of simple logistic model. The Bass model became famous because of introducing the coefﬁcient of innovation (p), that corrected the deﬁciency of the simple logistic growth (the “hardly starts to grow up” problem), and its form is resulted from the solution of speciﬁc (Bass) differential equations. Now, it is shown here of its congruence with and genesis from simple logistic growth! Note: The Bass model in form (38) requires that p and q have the same sign (p > 0 and q > 0, or p < 0 and q < 0) as seen from the equation for b (40). This has the consequence that c yielded from the Bass model must be c < 0 (40). Although the logistic spline model is identical to the Bass model, it has no limitation on c, so spline can be unrestrictedly shifted on y-axis depending on the case.

8.

Conditions for Using Logistic Splines Model for the Forecasting Purposes

Composite regression models that can represent the adoption of product over the whole PLC need extensive sets of observations, which makes their use for practical forecasting purposes very difﬁcult. This obstacle forces the change of our expectations — what can be obtained from PLC modelling for the forecasting purposes. The consequence could be a shift from dealing with historical data to dealing with future. On the other hand, an insufﬁcient set of input historical data cannot provide conﬁdence measure of forecasting

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results. It will be shown that the minimum set of input data consisted of: • • • •

the last known data point N(ts ); the gradient in the last known data point N (ts ); assumed market capacity M in observed time interval t ∈ [ts , te ]; assumed number of consumers at the end of the observed time interval N(te ).

And they could provide us forecasting results and certain measure of conﬁdence. By combining the principle of logistic growth (adoption curve is consisted of a set of S curves) similarity with splines gives the idea about a new interpolation method — logistic splines. Regular spline functions are used for the interpolation purposes, but originally they were strips of elastic material used to draw smooth curves through a given set of points. The most common type of spline is the cubic spline, which is formed by joining polynomials of third degree together at ﬁxed points called knots. Cubic spline curve ﬁtting ensures that each spline is equal to the data points, the 1st derivatives are continuous at the knots, and the 2nd derivatives are continuous at the knots. It is expected that logistic splines ensure forecasting of adoption dynamics during the whole-observed time interval [ts , te ] where monotone growth (logistic spline — Type-1) or monotone decline (logistic spline — Type-2) is anticipated. In continuation, it will be shown that the concept of logistic splines could be used for testing of consistency of assumptions with known data, too. Logistic spline is the function LS(t) that smoothly joins the latest (known) data about the number of consumers N(ts ) with the assumed number of consumers N(te ), and locally has a form of logistic law of growth — Figures 12 and 13. Function LS(t) has the form given in (32). Unknown parameters a, b and c can be calculated from conditions: • starting point of the logistic spline is identical to the latest known data (41); • last point of a logistic spline is identical to the (given) assumed value N(te ) (42); • logistic spline smoothly extends the existing data (43). N(ts ) = LS(ts )

(41)

N(te ) = LS(te )

(42)

N (ts ) = LS (ts )

(43)

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Figure 12. Logistic spline — growing (Type-1).

Figure 13. Logistic spline — declining (Type-2).

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Derivation N (ts ) cannot be determined analytically, only by numerical calculation and/or the data are not accurate enough, i.e., they usually contain a certain level of noise (seasonal and sales campaign ﬂuctuations), so the condition (43) should be modiﬁed to ﬁnding the minimum:

2 (44) min N (ts ) − LS (ts ) Froms (41) and (42), expressions (46) and (47) for a and b can be obtained, with parameter c as a dependant variable. Parameter c cannot be achieved analytically, however iterative minimisation of F(c) using golden section is a suitable procedure for obtaining parameter c (45): 2

2 a · (M − c) · e−a(ts −b) (45) F(c) = N (ts ) − LS (ts ) = N (ts ) − 2 1 + e−a(ts −b) The procedure is as follows: (1) Choose the interval which lays possible values for c, cmin ≤ c ≤ cmax (which will be discussed later, in detail). (2) Take c1 = cmin and c4 = cmax . (3) Calculate two inside values for c, c2 = c4 − φ(c4 − c1 ) and c3 = c1 + φ(c4 − c1 ) according to golden section minimisation procedure, where φ is golden section ratio (φ = 0.618 . . . ). (4) Calculate F(ci ), i = 1, 2, 3, 4 using the following equations for ai and bi : M − N(ts ) N(te ) − ci 1 · ai = ln (46) te − ts M − N(te ) N(ts ) − ci M − N(te ) 1 (47) bi = te + ln a N(te ) − ci (5) According to calculated values for F(ci ), i = 1, 2, 3, 4 decision is made about narrowing interval for c from [c1 , c4 ] to [c1 , c3 ] or [c2 , c4 ]. Golden section minimisation procedure is repeated from the 3rd phase to 5th phase until resulting interval for c becomes satisfactory narrow. In practical applications, number of iterations is around 40 or less. As stated before, there are two types of logistic spline: • logistic spline grows, iff N (ts ) > 0 and N(ts ) < N(te ) < M (as in Figure 12); and • logistic spline declines, iff N (ts ) < 0 and N(ts ) > N(te ) > M, (as in Figure 13).

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The model (32) can satisfy conditions (41) and (42) only if c < N(ts ) for the Type-1, and if the c > N(ts ) for the Type-2 of logistic spline. If the mentioned conditions for c are fulﬁlled, Equations (46) and (47) have solutions. These conditions on c reﬂect on the determination of the interval which should lay possible values for c, cmin ≤ c ≤ cmax in the beginning of minimising F(c): • Type-1, initial interval is c ∈ (−∞, N(ts )) since c < N(ts ) < N(te ) < M, but in practical applications (−10 · M, N(ts )) is a satisfactory large initial interval for c. • Type-2, initial interval is c ∈ (N(ts ), +∞) since M < N(te ) < N(ts ) < c, but in practical applications (N(ts ), +10 · M) is a satisfactory large initial interval for c. In an ideal set of circumstances, the result of minimisation should be parameters a, b and c, thus LS (ts ) = N (ts ). Logistic splines cannot satisfy Equation (43) if N (ts ) is too high — for Type-1, or too low — for Type-2, which will be discussed in the following section.

9.

Limits of Logistic Splines

From equation for LS (t) it is possible to ﬁnd interval where its value lays, depending on c, N(ts ), N(te ) and M. The ﬁrst step is transforming expression for LS (t) in form without a and b parameters: LS (ts ) =

a · (M − c) · e−a(ts −b)

2 1 + e−a(ts −b)

(48)

(M − c) +c 1 + e−a(ts −b)

(49)

From: LS(ts ) = follows: (M − c)2

[LS(ts ) − c]2 = [N(ts ) − c]2 =

1 + e−a(ts −b)

2

(50)

and e−a(ts −b) =

M−c −1 N(ts ) − c

(51)

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By putting Equation (46) for a, we get expression for LS (ts ), depending only on c, N(ts ), N(te ) and M, which is suitable for further analysis: 1 M − N(ts ) N(te ) − ci [N(ts ) − c] · [M − N(ts )] · · ln LS (ts ) = te − ts M − N(te ) N(ts ) − ci M−c (52) In case of logistic spline Type-1, LS (ts ) lays in range (53). It moves towards 0 when c approaches N(ts ) and move towards its upper limit for c → −∞. M − N(ts ) M − N(ts ) (53) ln 0 < LS (ts ) < te − t s M − N(te ) In case of logistic spline Type-2, LS (ts ) lays in range (54). It moves towards 0 when c approaches N(ts ) and move towards its lower limit for c → +∞. M − N(ts ) M − N(ts ) ln (54) < LS (ts ) < 0 te − t s M − N(te ) Described restricted ranges for possible values of LS (ts ) have, for the forecasting purposes, the following consequence: depending on known values for N(ts ) and N (ts ), and assumed values of M and N(te ), in case of unfulﬁlled conditions (53, 54), logistic spline cannot smoothly bridge the gap between known data and anticipated value in the future. Unsmooth joint of the logistic spline represents a warning to a forecaster that input assumptions are inadequate, such as: • Predicted values for M and/or N(te ) are wrong. Namely, values for M and N(te ) in forecasting practice are obtained usually as a result of qualitative forecasting, which can be now assessed by logistic spline concept. • Interval [ts , te ] is consisted of more than one sigmoidal curve (example in Figure 14). Examples of unsmooth joint of the logistic spline is shown in Figure 14, while a proper (smooth) joint is shown in Figure 15.

10.

Example of Forecasting by Logistic Splines

Application of logistic splines1 is shown in the example of expired analogue mobile service in Croatia (NMT-450). The service started in 1991 very slowly 1 Additional

information about usage of logistic splines and LOgistic Spline Trend (LOST) program tool can be found in http://lost-a.notlong.com.

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because of high prices of service and mobile handsets. In the period from 1994 to 1997 it had signiﬁcant growth. In 1998, the service was seriously confronted by new GSM service, and went into saturation. As a counterattack, NMT operator decreased service price (cost of call per minute) on the level of approximately 15% of GSM service price. This attempt was shortlived because GSM operators offered a pre-paid system of payment and cheap mobile handsets. As a result, the number of NMT users continued to decline. NMT service in Croatia went extinct in Q2 2005. Two different phases of the product life cycle of NMT will be examined by logistic splines for forecasting purposes: growth (Figure 16) and decline (Figure 17) phase. Given information are: number of users of the NMT-450 service from the EOY 1991 till EOY 2004. Logistic spline Type-1 (Figure 16) is used in forecast time interval from ts = 1995 to te = 1997. Values for N(ts − 1) and N(ts ) are taken as known, and assumed are values for M and N(te ). From N(1994) and N(1995), N (1995) is obtained. Forecasting results are checked with real data in period from 1995 to 1998. Standard statistical measure — MAPE (mean absolute percentage error) is used for this purpose (55). 1 LS(t) − N(t) · 100% MAPE = n t N(t)

(55)

Known: ts = 1995 N(ts-1) = 21 664 N(ts) = 32 948 Chosen end time te = 1997 Assumptions: M = 70 300 N(te) = 64 189 Resulting logistic spline: M = 70 300, a = 1.440, b = 1995.6, c = 16 629 Forecast: Time interval 1995-1998 MAPE = 0.244 %

Figure 16. Growth of analogue mobile service in Croatia (logistic spline Type-1).

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Known: ts = 2000 N(ts-1) = 85 130 N(ts) = 73 292 Chosen end time te = 2004 Assumptions: M=0 N(te) = 5 000 Resulting logistic spline: M = 0, a = 1.042, b = 2001.24, c = 93 347 Forecast: Time interval 2000-2004 MAPE = 3.78 %

Figure 17. Expiring analogue mobile service in Croatia (logistic spline Type-2).

Table 2. Forecasting results for logistic spline Type-1 (LS-1) and Type-2 (LS-2). t [year] 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

N(t) 1 669 6 320 11 239 21 664 32 948 51 857 64 189 68 987 85 130 73 292 56 600 27 000 13 400 5 000

LS-1(t) 16 704 16 940 17 914 21 664 32 948 51 428 64 189 68 714 69 916 70 208 70 278 70 295 70 299 70 300

LS-2(t) 93 346 93 342 93 330 93 299 93 208 92 954 92 240 90 274 85 130 73 292 52 570 29 181 12 905 5 000

Logistic spline Type-2 (Figure 17) is used in forecast time interval from ts = 2000 to te = 2004. Again, values for N(ts − 1) and N(ts ) are taken as known, and assumed are values for M and N(te ). From N(1999) and N(2000), N (2000) is obtained. Forecasting results are checked with real data in this period by MAPE. Results of forecasting are presented in Table 2, and values for calculated parameters are shown in Figures 16 and 17.

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Conclusion

The extensions of the logistic growth model for forecasting purposes are developed, analysed and discussed. Speciﬁc linear transformation of the logistic model is shown to be identical to the well-known Bass model. In cases with minimum set of input data, the logistic spline model is proposed for the forecasting of product life cycle segments with monotone growth or decline, or assessment of qualitative forecasting results. Whole product life cycle modelling, that includes combination of growth and decline, should be achieved combining logistic splines and sigmoidal envelopes described within interaction between products on market section.

References Albright, R. E. (2002). What can past technology forecasts tell us about the future?. Technological Forecasting and Social Change, 69(5), 443–464. Bass, F., K. Gordon, T. L. Ferguson and M. L. Githens (2001). DIRECTV: Forecasting diffusion of a new technology prior to product launch. Interfaces, 31(3), S82–S93. Bass, P. I. and F. M. Bass (2001). Diffusion of technology generations: A model of adoption and repeat sales. Working paper, Bass Economics. Bers, J. A., B. S. Lynn and C. Spurling (1999). Acomputer simulation model for emerging technology business planning and forecasting. International Journal of Technology Management, 18(1–2), 31–45. Chang, P. T. and C. H. Chang (2003). A stage characteristic — Preserving product life cycle modelling. Mathematical and Computer Modelling, 37(12–13), 1259–1269. Fildes, R. and V. Kumar (2002). Telecommunications demand forecasting — A review. International Journal of Forecasting, 18(2002), 489–522. Funk, J. L. (2004). The product life cycle theory and product line management: The case of mobile phones. IEEE Transactions on Engineering Management, 51(2), 142–152. ITU (2005). World Telecommunication Indicators Database 1960–2004. Geneva: International Telecommunication Union. Karlsson, C. and K. Nystrom (2003). Exit and entry over the product life cycle: Evidence from the Swedish manufacturing industry. Small Business Economics, 21(2), 135–144. Kayal, A. (1999). Measuring the pace of technological progress: Implications for technological forecasting. Technological Forecasting and Social Change, 60(3), 237–245. Khalil, T. (2000). Management of Technology: The Key to Competitiveness and Wealth Creation. Boston: McGraw-Hill.

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Lemos, A. D. and A. C. Porto (1998). Technological forecasting techniques and competitive intelligence: Tools for improving the innovation process. Industrial Management and Data Systems, 98(7–8), 330–337. Meade, N. and T. Islam (1998). Technological forecasting model selection, model stability, and combined models. Management Science, 44(8), 1115–1130. Modis, T. (1998). Conquering Uncertainty: Understanding Corporate Cycles and Positioning Your Company to Survive the Changing Environment. New York: McGraw-Hill. Werker, C. (2003). Innovation, market performance, and competition: Lessons from a product life cycle model. Technovation, 23(4), 281–290. Zhu, D. H. and A. L. Porter (2002). Automated extraction and visualisation of information for technological intelligence and forecasting, Technological Forecasting and Social Change, 69(5), 495–506.

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5 DEFENSIVE STRATEGIES AND CONSUMERS’ BOUNDED RATIONALITY: AN ARTIFICIAL MARKET SIMULATION Josef A. Mazanec Institute for Tourism and Leisure Studies Vienna University of Economics and Business Administration Augasse 2-6, A-1090 Vienna, Austria [email protected]

Ulrike Schuster and Jürgen Wöckl Vienna University of Economics and Business Administration Austria Received July 2004 Accepted October 2005 Twenty years after the Defender model, it is tempting to explore new ways of exposing defensive strategy recommendations to varying market conditions. This experiment analyses the consequences of changes in three factors: (1) a consumer population pursuing noncompensatory brand choice rules; (2) distinctive versus indistinctive (nonsegmented) preference structures; and (3) low versus high responsiveness to advertising. The consumers’ response is simulated on an Artiﬁcial Consumer Market (ACM). The ACM assists in constructing the surface of the incumbent’s proﬁt function under a ﬁxed-entry scenario and for experimentally varied market characteristics. The expected inﬂuences of consumers’ noncompensatory choice rules on defensive strategy is clearly demonstrated. A defensive reaction by increasing the advertising budget is recommended for most of the market scenarios. A price reduction is required for all but one immature (nonsegmented) market. A price increase pushes the incumbent’s proﬁt in all except one of the distinct-preferences scenarios; quite remarkably, this most amazing of the original game-theoretic results from the Defender model

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J. A. Mazanec, U. Schuster & J. Wöckl receives new support from ﬁndings gained with the completely different methodology of agent-based simulation.

Keywords: Defensive strategy models, micro simulation.

1.

Introduction

As demonstrated by the literature survey in the next section the strategy recommendations derived from the Defender model (Hauser and Shugan, 1983) are notably robust. Twenty years later, it is tempting to expose defensive strategy models to variations of market conditions more fundamental than those explored so far. But there is a price to pay. Such models may no longer be analytically tractable and lose their property of a game-theoretic exercise. Computer simulation methodology will have to be applied instead. Micro simulation models date back to the 1960s and 1970s (Topritzhofer, 1974). From a contemporary perspective the early attempts to mimic consumer market phenomena by computer simulation were bound to fail. The all-encompassing simulation models (Nicosia, 1966; Amstutz, 1967; Lavington, 1970; Klenger and Krautter, 1972) were over-ambitious as they did not focus on a reasonably sized and manageable sector of market reality. As a consequence the simulation model builders were forced to introduce many ad hoc parameters making them unable of unambiguously tracing back the model output. Unfortunately, there is an inverse relationship between model complexity and interpretability of the results (Mazanec, 1978, p. 32; Rangaswamy, 1993, p. 744). The situation was characterised by Ehrenberg (1968) in a JMR review of Nicosia (1966): “The book illustrates the modern model-builders syndrome of falling over himself by trying to run before he can walk.” The defensive strategy models since the Defender model have followed a different view seeking non-critical abstraction and parameter parsimony. The analyst, whether relying on game theory or computer simulation, faces the problem of deciding on where abstraction and simpliﬁcation threaten to destroy the homomorphic relation between the market reality and the model. In other words, there is a representation threshold. This experiment tries to respect this threshold while analysing the consequences of three experimentally varied factors (i.e., consumers’ decision rules, distinctness of preferences, advertising response) for a simpliﬁed mix of marketing instruments (advertising and price). The article starts with a review of defensive strategy ﬁndings, then introduces the extensions and limitations assumed for

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this experiment, adds more information about the simulation environment, proceeds with constructing smooth surfaces of the proﬁt functions, comments on the results, and draws conclusions on how to continue the series of experiments.

2.

The Defender Model and its Descendants: A Review of Findings

The Defender model developed by Hauser and Shugan (1983) triggered off a series of articles dealing with the elaboration of optimal defensive strategies for ﬁrms facing a new competitor entering the market. Over the last 20 years, the Defender model has been extended by relaxing assumptions and exploring the ensuing proﬁt-maximal strategies. The contributions to the Defender research tradition assume a mature market settled in a Nash equilibrium. After the new competitor has entered the market a new equilibrium is sought. This implies that the ﬁrms must have followed their optimal strategies not only after but also before a new entry. They change prices and their marketing expenditures for advertising and distribution to defend their competitive position. In some investigations they are allowed to change their brand position in the perceptual space too. The optimisation task is performed stepwise; ﬁrst the optimal prices are determined then the marketing expenditure is optimised given the prices. The main focus has been on those brands adjacent to the new entrant. The rest of the ﬁrms are considered to be only marginally affected and, therefore, assumed to show no competitive reaction but maintain their past strategies. The ﬁrms are proﬁt maximisers and act rationally. The entry position is assumed to be ﬁxed exogenously and is known to all brands. The customers seek to maximise utility and choose the product nearest to their ideal point, where choice usually is deterministic. Hauser and Shugan (1983) employ a utility function which is linear in the price-scaled product features. In most of the suggested models only two product features are considered. Kumar and Sudharshan (1988) used a Cobb-Douglas utility function where the product features are not price-scaled and ADBUDG functions for modelling the response to advertising and distribution. Advertising and distribution response functions are always concave, but may be coupled or decoupled. The price strategy is independent of the advertising and distribution expenditures. A ﬁrm’s marketing spending has no effect on the sales of any other brand. Since Gruca et al. (1992), only coupled response functions have been

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considered in all subsequent investigations. When coupled response functions are introduced, lower and upper bounds for price and marketing expenditure are required to guarantee the existence of a Nash equilibrium. Usually prices must be greater than or equal to the marginal costs and lower than or equal to the market reservation price. Advertising and distribution expenditures are assumed to be greater than or equal to a predetermined minimum and also an upper bound is ﬁxed. All defensive strategy articles reviewed here formulate market share models which are used in the proﬁt maximisation function. Under the coupled response functions multiplicative attraction models are applied, such as MCI models in Gruca et al. (1992), or MNL models in Basuroy and Nguyen (1998). This means that the elements of the marketing mix are allowed to interact. For the attraction models the brands are assumed to be symmetric exhibiting equal attraction coefﬁcients. Until Gruca et al. (2001), a continuous distribution of demand was assumed. Then, for the ﬁrst time, the inﬂuence of segmentation was investigated by deﬁning a discrete preference distribution. The consumers’ preferences were assumed to remain constant over time. The authors work with segment-speciﬁc ideal points representing the average ideal points of all segment members. The utility follows from the distance between the brand position and the segment ideal point and from the size of the segment’s choice set. Considering probabilistic choices made by the customers it is not only the product closest to the individual ideal combination of features that may enter the buyer’s choice set. The optimal defensive strategies of the Defender model by Hauser and Shugan (1983) proved to be remarkably robust under varied assumptions. If the market size does not change, the proﬁts of any brand in the market will always decrease in the course of a new entry. For an optimal strategy a price reduction and a decrease in advertising and/or distribution expenditure is suggested. If the market is highly segmented and the entrant attacks one of the incumbent’s segments the price should be increased. Also, if one accounts for weakly threatened market participants, the brands far away from the entrant should raise their prices (e.g., in Gruca et al., 2001). Gruca et al. (1992) considered dominant brands (with a market share exceeding 50%) and non-dominant brands separately, as in markets with coupled response functions the optimal reaction is affected by the relative market share. The Defender results were conﬁrmed for coupled response functions and non-dominant brands. Dominant brands, however, should

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raise their advertising expenditures, unless they risk losing their dominance as a consequence of the new entry. For a market growing in volume an increase in the advertising and/or distribution spending can be optimal provided that the market growth is strong enough (Kumar and Sudharshan, 1988; Basuroy and Nguyen, 1998). Under a constant market volume, both for decoupled and coupled response functions, it is advisable to cut prices, particularly for the brand nearest to the new entrant. However, if the market is highly segmented or, if the incumbent is dominant, a price increase is recommended. Similarly, brands far away from the entrant’s position should increase their prices. In general, a growing market demands an increase in marketing spending. But, depending on the market growth rate, the presence of a new competitor may call for a reduction of the advertising budget. According to the results available so far the strategy recommendations concerning the marketing effort in expanding markets are ambiguous (Kumar and Sudharshan, 1988; Basuroy and Nguyen, 1998).

3.

Simulation Models and the Agent-Based Framework

Despite the long tradition of simulation models in economics and management science their epistemological foundations are still poorly understood. While simulation models provide access to many ambitious research questions the problems of validation often lack an in-depth treatment. The issue of validation has been discussed more actively in other ﬁelds than management science. In economics, for example, there is a rich tradition of philosophical arguments and also a new thread of literature on the justiﬁcation of simulation methodology. Recent examples are provided by the researchers of the Evolutionary Economics Unit at the Max Planck Institute who use simulation methods for modelling learning processes (Brenner, 1999). Other researchers considering simulation models as miniature theories resort to views expressed by philosophers such as Popper, Kuhn or Lakatos and seek to formulate validation criteria from positivist and even hermeneutic perspectives (Kleindorfer et al., 1998; Kleijnen, 1993; Ostrom, 1988). The epistemological status of models simulating social systems has been thoroughly discussed by Troitzsch (1996, 1999). This author relates simulation modelling to the “non-statement view” of theories originally introduced into the philosophy of science by Sneed (1971) and further propagated by Stegmüller (1973; for an early appraisal in consumer behaviour theory, see

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Mazanec, 1978). In this structuralist interpretation a computer simulation programme is regarded as “a complete model of its theory” (Troitzsch, 1999). In simple words, the “non-statement view” does not consider a theory as a falsiﬁable entity (Stegmüller, 1973). However, a set of “intended applications” is part of each theory and it remains an empirical question whether one such application belongs to this set or not. To model systems with a high degree of interactions between different and partly or fully autonomous subsystems an agent-based simulation approach is preferable. This approach is particularly suited for modelling dynamic behaviours of decision making and learning in an organisation of agents (Hatakama and Terano, 1997; Beyer and Smieja, 1996; Meyer et al., 2003). The most widely known projects on simulating the behaviour of economic and social agents originate from the Santa Fe Institute (http://www.santafe.edu/). Recent agent-based approaches to studying typical management science issues have tackled problems of innovation and new product planning, segmentation and positioning strategy, or advertising budgeting (Natter et al., 2001; Bauer et al., 2003; Schuster and Wöckl, 2005). In agent-based simulation a “model” may range between the two extremes of a “reference model” mimicking the behaviours of real objects and a “virtual world” claiming no analogy to real systems (see the discussion at the Agent-based Simulation 5 Workshop 2004, http://www.scseurope.org/conf/abs2004/agent_sciences.html). The epistemological value judgments underlying the following simulation experiment are cautious and modest. The Artiﬁcial Consumer Market underlying the simulation is thought to be “realistic” in terms of consumers’ decision rules and perceptual dynamics through advertising-induced learning. These are crucial aspects of bounded rationality where the simulation environment may approximate real consumer “agents” more closely than their utility-maximising counterparts of the choice modelling tradition. Nevertheless, there is no claim of emulating a particular real market. Hence, the statements of theoretical guidance are not called “hypotheses” but “propositions”. If they get conﬁrmed by the simulation results the empirical researcher receives strong motivation for pursuing the same hypotheses about the proﬁt consequences of the defensive strategies in real product classes and markets exhibiting the perceptual and preferential characteristics similar to the experimental scenarios. The candidates that come to mind immediately are classes of technologically indistinguishable brands where the marketing strategy rests on emotions-based and advertising-driven differentiation.

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An Artiﬁcial Consumer Market to Accommodate Boundedly Rational Behaviour

4.1. Differences compared to previous defensive strategy models This section addresses the changes made in comparison with the preceding models of the Defender research tradition. One of the assumptions not yet relaxed in previous defensive strategy models relates to the consumer decision rule. This study analyses the consequences of a noncompensatory cognitive algebra. According to Gilbride and Allenby (2004) who employed Markov Chain Monte Carlo estimation methods for analysing consumers’ decision making on real markets, 92% of the consumers applied a noncompensatory screening rule at some stage of the brand decision process. Abandoning the compensatory utility function, however, renders the proﬁt optimisation analytically intractable and simulation methods are required. The micro simulation environment named the Artiﬁcial Consumer Market (ACM) will be used. It mimics the behaviours of disaggregate consumers and ﬁrms and was elaborated in a seven years’ research programme on “Adaptive Systems and Modelling in Economics and Management Science”. The relevant algorithmic features of the ACM are outlined in the Appendix. Other assumptions besides the consumers’ decision styles were relaxed for this micro simulation study. They relate to how the positions in the brand space are established and to the preferential market structure. Discrete time and periodicity. Unlike the game-theoretic analyses the simulation experiment operates in discrete time steps. They are deﬁned by the series of advertising exposures and subsequent choices. The simulation requires a decision on the duration of the pre-entry period and the post-entry phase of combat. It aims at elaborating the consequences of market entry in the short run. The number of pre-entry periods is set to two, which allows for a sufﬁcient increase in product knowledge. The time span of the entry battle is limited to two periods t = 3 and 4, i.e., two advertising exposures and two choice occasions. In this post-entry period the incumbent tries to maximise its cumulative proﬁts. Note, however, that the incumbent cannot immediately react, but continues with his strategy in t = 3 while preparing a defensive advertising budget and price for t = 4. Advertising-generated brand positions. The Defender model analysed the incumbent’s response to various predetermined positions of an attacking brand (Hauser and Shugan, 1983). Ansari et al. (1994) examined “competition in positions” where the ﬁrms react directly by changing brand

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locations in product space without incurring positioning costs. In Gruca et al. (2001) the brands’ locations in the attribute space were optimally chosen according to the PRODSRCH procedure (Sudharshan et al., 1987; Green and Krieger, 1989). In this micro simulation the brand positions are derived indirectly by letting them evolve according to the ﬁrms’ advertising efforts in periods t = 1 and 2. The more they invest the faster they travel through the perceptual space. If they consistently promote the product attributes linked to an attitudinal dimension they advance into the desired direction along this dimension. Hence, the brand positions are subject to perceptual dynamics during the pre-entry as well as the entry phases. Utility function and brand choice. The consumers are allowed to depart from rigorous rationality. In the original Defender model and the series of modiﬁcations it triggered off the consumers’ utility function is based on a measure reﬂecting a brand’s “closeness” to the consumers’ ideal brand position. This may be achieved by using Hauser and Shugan’s arctan of the attribute weights ratio (Hauser and Shugan, 1983; Ansari et al., 1994) or the Euclidean distance between the brand positions and the ideal points (Gruca et al., 2001). The consumers then aim at maximising their chosen brand’s attribute values in the proportion preferred or by minimising distance to the ideal brand proﬁle. The overall utility originates from a compensatory decision rule. Both maximisation and attribute trade-off are strong assumptions that may be debatable for many product classes and/or consumer segments. Though their relevance for real markets is unquestioned (Bettman, 1971; Wright, 1975; Bettman et al., 1998) marketing research has channelled very little effort in building models that allow for noncompensatory decision rules. West et al. (1997) and Gilbride and Allenby (2004) are notable exceptions. This study introduces two kinds of rationality bounds. First, consumers do not strictly optimise. Rather they stick to a satisﬁcing rule. They do no longer differentiate among brands once a satisfactory level (“aspiration level”) of product attributes has been reached. The second deviation from perfect rationality regards trade-offs among product attributes. A noncompensatory brand choice rule will be admitted and the share of consumers practicing a variant of noncompensatory decision making becomes one of the experimental factors. Under the modiﬁed ideal point model the total attractiveness (“utility”) of a product brand b for consumer c is the sum of the utility contributions

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of the R attitudinal dimensions: ub,c =

R

max(0, min(qc,r , δb,c,r ))

(1)

r=1

where δb,c,r is the consumer’s price adjusted attitude toward product brand b represented by its position in the R-dimensional brand space (R will be set to 4); price adjustment is done with division by the relative price pb /p, where p denotes the average selling price of all brands; qc,r is the consumer’s current ideal level on the rth attitudinal dimension; for each such dimension zero marks a threshold of relevance that must be exceeded to gain inﬂuence in the brand choice. In the “indistinct-preferences” scenarios the initial qc,r ∼ N(0, 4); in the “distinct-preferences” initialisation the qc are Gaussian with means (6 6 −6 −6), (−6 6 6 −6), (−6 −6 6 6) for three equal-sized segments with equal σ 2 = 4. Brand b is chosen by c if ub,c = max(u1,c , u2,c , . . . , uB,c ). If the choice set comprises at least one other alternative of equal attractiveness a random selection takes place. (1) allows for compensation as long as the brand positions do not over-fulﬁl the consumers’ aspirations. Besides that overfulﬁlment does no harm. This restriction is one of the elements of bounded rationality fed into the experiment. A stochastic variant of (1) is investigated too. It derives the probabilities of becoming part of the consumer’s consideration set according to Prob(b∗ |ub∗ ,c ) =

db−1 ∗ ,c b =b∗

where: db,c =

 R    qc,r − δ

b,c,r

r=1    d min b,c

−1 db,c

(2)

if qc,r > δb,c,r else

to respect the unidirectional property of the modiﬁed ideal point model (d min is set to the Matlab tolerance eps to avoid division by zero). One of the equally qualiﬁed brands in the consideration set will be selected for purchase. On aggregate level the brands’ market shares correspond to their relative ideal point distances. For the noncompensatory decision styles two sorts of thresholds are required. For the conjunctive decision rule it is save to assume that the satisfaction levels are fairly lower than the ideal levels. Remember that

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an attractive brand has to satisfy all these aspired minimum levels. Brand b enters the choice set if it exceeds the minimum bound on all relevant dimensions, i.e., R

φ(qc,r )φ(δb,c,r − β1 qc,r ) =

r=1

where:

φ(qc,r )

(3)

r=1

φ(y) =

R

1

if y > 0

0

if y ≤ 0

and 0 < β1 < 1.

For the disjunctive rule brand b enters the consideration set if it fulﬁls the minimum requirements on at least rmin dimensions, hence R

φ(qc,r )φ(δb,c,r − β2 qc,r ) ≥ rmin ,

β1 < β2 < 1.

(4)

r=1

rmin in this experiment is set to one; β1 and β2 are set to 0.5 and 0.75. The consumers on the ACM exhibit non-constant preferences as they adapt their ideal points according to qc,r,t+1 = qc,r,t + α(δc,r,max − qc,r,t ),

0≤α≤1

(5)

where α is the adaptation parameter (set to 0.2); δc,r,max is the best value of a brand along dimension r that consumer c has learned about through media advertising (or word-of-mouth; not activated in this experiment). Note that the preference adaptation is assumed symmetric and the availability of new product knowledge depends on whether consumer c is targeted by brands offering a rich and ambitious attribute proﬁle. The noncompensatory brand choice on disaggregate level is deterministic (cf. Gruca et al.’s “base scenario”, 2001, p. 57) as long as there is just one brand in the consumer’s choice set, because only one exceeds the minimum threshold of the price weighted utility. A random selection occurs for more than one buying alternatives gathered in the set and therefore considered equally attractive. Segment structure and targeting. In their “Concluding Remarks”, Ansari et al. (1994) state that the “consumer environment” in most of the positioning models “has remained simplistic”. According to Ansari et al. a major step toward a set of more realistic assumptions requires the introduction of “preference heterogeneity”. If considered consequently this requirement leads to a provision for segmented markets. Actually, this type

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of extensions to defensive strategy models was proposed by Gruca et al. (2001). These authors examined the impact of segmentation by identifying ﬁve market segments in a joint space of normally distributed individual ideal points and brand positions. The preferential overlap among the consumer segments was adjusted by determining the size of the consumers’ choice set. A different approach is adopted here. In period t = 0 the consumers lack product knowledge and assign attributes to the brands already on the market with very low probabilities (values around 0.2). As to the distribution of ideal points (representing consumer preferences) it matters whether the clusters of ideal locations are disjunct or subject to overlap. Regarding the initial preferences in t = 0 two levels were chosen: (1) three segments with distinct and non-overlapping (normally distributed) ideal points and (2) indistinct (rudimentary) ideal points with no apparent segment structure. Note that preferences are variable and subject to change in all experimental combinations. The consumers adapt their aspirations to what they believe to be realistic given the brand proﬁles learned through advertising. The ﬁrms have exact knowledge as to the number of preferential segments and the combination of brand attributes desired by these segments. As they design their advertising messages perfectly tailored to the consumers’ expectations the ﬁrms are fully aware of the consumers’ actual and ideal brand perceptions like in the original Defender model. Despite the progress achieved in market segmentation methodology (parametric, such as Wedel and Kamakura, 2001; Wedel and DeSarbo, 2002; or non-parametric, such as Mazanec and Strasser, 2000) this is not meant to be realistic. However, one cannot reliably examine the strategy consequences when at the same time the ﬁrms’ market structure measurements are error-prone to an uncertain degree. (The computer simulation environment employed in this study would be capable of simultaneously varying the ﬁrms’ strategic decisions and the quality of their market response measurements.)

4.2. Simplifying assumptions While there are extensions to Defender and its successors on one hand there are also simpliﬁcations in the competition scenarios of this study. To keep the model on a level of manageable complexity a number of simplifying assumptions regarding the marketing instruments and the scope of competitive interaction were introduced. All of these are deemed non-critical for the purpose pursued in this experiment.

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Marketing mix and market size. The artiﬁcial ﬁrms compete in one product class. Each competitor produces and sells one brand. The competing brands’ technical features are constant. So there is no investment in product design or improvement. Production costs are not considered. The only cost element relates to the ﬁrms’ setting of their advertising appropriation. The advertising budgets and the selling prices are the ﬁrms’ sole marketing instruments. There is also no concern about distribution. The number of consumers on the market is constant. As each consumer purchases not more than one brand in each period (see Gruca et al., 2001, p. 57) the market potential is limited and ﬁxed. However, the overall sales volume is variable in the market scenarios with noncompensatory choice rules. In these cases a consumer’s consideration set may remain empty as long as all brands fail to fulﬁl the tolerance threshold of minimum requirements. Competitive behaviour. The concept of a Nash equilibrium is not applicable as the condition of constant brand positions (Gruca et al., 2001, p. 56) is violated. However, there is a similar competitive pattern on the ACM that describes the situation in the pre-entry period. Prior to the entrant’s arrival the incumbent ﬁrms enjoy an approximately equal unit and dollar share of the market. Because of equal selling prices and uniform advertising budgets this results into pre-entry peace and proﬁt parity. As long as this situation is maintained no ﬁrm would seek to attack a competitor by lowering prices or increasing its advertising pressure. Proﬁt reducing retaliation measures would be most likely. The situation deviates from a genuine Nash equilibrium as the uniform and accepted market price is kept 10% below the consumers’ reservation price. All ﬁrms may increase proﬁts by uniformly raising their prices up to the acceptance limit. This, however, would destroy the purpose of the simulation experiment by eliminating the whole upward margin available for price reactions expected as a response to entry.

5.

A Note on the Technical Implementation, Software, and Parameterisation

The model of the Artiﬁcial Consumer Market (ACM) brieﬂy outlined in the Appendix has been implemented as an agent-based framework entirely in Matlab 6 (see http://www.mathwork.com/). Matlab is an interpreter-based script language for technical computing and designed in close resemblance to ordinary matrix calculus. The system of the artiﬁcial market with its “zoo”

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of consumer, incumbent and entrant agents comprises 45 functions; it runs under the Matlab Base System without needing any further toolboxes. For more complex experimentation there is another ACM version (not employed in this study) offering a simulation environment for heterogeneous agents. E.g., it may combine a market response section (the ensemble of consumer agents) written in Octave with ﬁrm agents written in Matlab (or Octave for Linux users) or R (see http://www.r-project.org); this ﬂexibility is achieved with a wrapper technique (using a XML deﬁnition format) for mapping the functionality of the agents living in an interpreter-based environment to a standardised Java interface (Meyer et al., 2003). Parameterisation is a crucial step in preparing simulation runs. In setting up the experiment the consumers’ decision rules and the preference distribution were experimental factors dictated by the Defender theory. However, other properties of the artiﬁcial market may exert unwanted and uncontrolled inﬂuence. A large number of what-if analyses, therefore, had to be conducted to spot the critical parameter and initialisation settings and to ascertain plausibility and conformity with established theory (e.g., on advertising-induced learning of brand characteristics). Most of these factors — such as the size of the market and the number of segments and ﬁrms, the perception and preference scaling in the brand space, initial settings and intervals for prices and advertising budgets, the economies of scale factor for ﬁrms spending larger communication budgets, or the speed of adaptation of the consumers aspiration levels — are noncritical and well-behaved. Only one of the two advertising effectiveness parameters [“responsiveness”, see (A1) in the Appendix] turned out to be delicate enough to demand being included as an additional experimental factor. The second critical parameter is the “attribute exuberance” factor that penalises ﬁrms trying to promote many brand characteristics all at once. In the Defender simulation scenarios it is of no relevance as the ﬁrms know exactly which attributes to promote for enforcing entry or defence. All settings are reported in the Appendix. For the reader interested in ACM design and computational details the Appendix also names consumer and market properties that might be varied (or activated), but are kept “silent” in this particular experiment.

6.

Determining the Fixed Entry Scenarios

Twelve ﬁxed entry scenarios with four companies involved will be considered. Every second scenario occurs on a mature market as assumed in

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Defender. “Mature” implies that the consumers’ brand knowledge is fairly advanced. This happens in all scenarios and means that advertising claims have been learned to an extent that the average consumer has a likelihood of 60–80% to associate an attribute actually advertised with the correct brand name. The second requirement deals with consumer preferences. In the “mature” case they are highly distinct with three sharply separated segments from period t = 0 onward. Figure 1 shows two of the four brand space dimensions in t = 2 before entry. The small dots depict the consumers’ ideal points of interest here. The plus signs denote the perceived brand positions. Note that the perceptions are not forced to stay homogeneous, avoiding an old and popular but nevertheless unrealistic assumption made in ideal point models until these days (Lee et al., 2002). In the other six “rudimentary” cases the preferences (modelled by individual ideal points) are low and indistinct with no discernible cluster structure. Figure 2 has this example. Firm 1 (3) has successfully advertised

Figure 1. Dimensions 1 and 2 of the brand space before entry in the distinct preferences scenario (1/1 compensatory, high responsiveness).

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Figure 2. Dimensions 1 and 2 of the brand space before entry in the indistinct preferences scenario (2/3 noncompensatory, low responsiveness).

dimensions 1 and 2 (3 and 4; not shown). Firm 2, the incumbent not yet aware of the imminent attack, promotes its brand along the dimensions 2 and 3 — just like the entrant (Firm 4) prepares to do in t = 3 and 4. All incumbent ﬁrms improved their target groups’ brand perceptions as they managed to shift the brand positions from about −0.2 to +0.2 into the direction of positive ideal points. Competitive threat is controlled by determining the advertising content. The entry battle is restricted to the attacking brand and the most heavily threatened incumbent. These two ﬁrms aim at improving their positions in the same two dimensions of the brand space. The other two brands are marginally hit. The entrant promotes only one of two brand space dimensions occupied by them. Thus they adhere to their pre-entry marketing strategies. These competition scenarios emulate the Defender method of placing the entrant’s brand into a position that particularly threatens one incumbent. The simulation lets the entrant operate with predetermined values for its advertising budget and price during the periods t = 3 and 4. The entrant’s

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advertising budget is set to 2.500 units, twice and a half the size of a ﬁrm’s routine budget before entry. The entry price is set to 90 units, 10% below the uniform pre-entry market price of 100. Of course, it depends on the incumbent’s reaction how far the entrant’s brand moves into the desired direction. The incumbent responds in t = 4 by resetting its price and advertising budget as to maximise the cumulative proﬁt achieved in the post-entry phase. Gruca et al. (2001) based their experiments on a single parameter setting for the advertising response function. However, it is most likely that the shape of the response function [see (A1) in the Appendix] either favours the entrant and disfavours the incumbent or vice versa. Two levels of advertising responsiveness and persistence are therefore incorporated into the market scenarios. Level one with high responsiveness comprises a low effectiveness threshold (ρ = 3.0) and high persistency (π = 0.7). Level two with low responsiveness combines a high threshold (ρ = 2.0) with low persistency (π = 0.6). Figure 3 summarises the market factors resulting from the discussion of the extensions and limitations of the micro simulation approach compared to previous defensive strategy models. Two consumer rationality levels, two preferential segment structures and two advertising response functions lead to a full factorial design with eight cells. Additionally, in each scenario with

Figure 3. Market factors in the experimental scenarios.

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compensatory consumer decision rules a second variant involving a probabilistic brand choice are run. The entrant’s advertising budget and selling price remain ﬁxed in all market factor combinations.

7.

Propositions

Summarising the propositions guiding this experiment leads to the following statements of increasing speciﬁcity: (1) The direction as well as strength of the incumbent’s optimal advertising and price response depends on (a) the consumer decision rules prevailing on the market, (b) the distinctness of consumer preferences, and (c) their responsiveness to advertising. (2) The market factors (a)–(c) produce interaction effects and, therefore, cannot be judged separately in a meaningful manner. (3) To secure short-term proﬁt the incumbent’s advertising budget exceeds its pre-entry value in all experimental factor combinations, while the change of the selling price may be negative or positive. (4) The differences of both the incumbent’s optimal price and advertising budget settings from their pre-entry values are greater for noncompensatory consumer decision rules, indistinct preferential segments, and low advertising responsiveness.

8.

Generating the Incumbent’s Proﬁt Surface from the Artiﬁcial Consumer Market Response

With only two variables in the incumbent’s defensive strategy mix it is straightforward to portray the surface of the proﬁt function for a multitude of price-advertising combinations. The Artiﬁcial Consumer Market outlined in the Appendix serves as a proxy for a closed-form objective function. It delivers the sales response each time it is provided a combination of budget and price ﬁgures. The stochastic mechanisms embedded in the ACM cause random variations and the market response slightly differs for different random seeds in the initialisation steps. To reduce the (realistic) noise in the market response an average result from 10 repeated ACM runs is obtained for each price-advertising mix. Thirty-one equidistant prices in the range between 80 and 110 are chosen. One hundred and ten is a natural upper limit as it equals the consumers’ reservation price. The lower bound of 80 lying 20% below the pre-entry market price lets the incumbent undercut the

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entrant’s promotion price by 10 units. The pricing alternatives are combined with 21 budget ﬁgures. The budgets increase from 500 (half the peaceful pre-entry value) to 2.500 (the entrant’s launching budget) in increments of 100. So the incumbent’s proﬁt surface for each market scenario rests on 651 simulated values. Reasonably smooth surfaces are derived by nonparametric regression.1 Speciﬁcally, a local linear ﬁt with a tricube weighting function and smoothing parameter 0.10 (equivalent to exploiting the 10% closest neighbours for smoothing each data point) was obtained for each market scenario. Determining the incumbent’s reaction by some optimization algorithm is less efﬁcient. It is likely that there are various local optima of very similar height of proﬁt occurring for different price-advertising mixes. Nevertheless and because of scientiﬁc curiosity such attempts were undertaken. It is worth mentioning that a crude search with the continuous function genetic algorithm developed by Houck et al. (1995) performs remarkably well in spite of the noisy market response. The GA detects “good” solutions in the majority of optimisation runs. These results, of course, do not reveal the underlying shape of the incumbent’s proﬁt function surface.

9.

Results

Table 1 exhibits the stylised results for the twelve combinations of the market factors. It translates the incumbent’s proﬁt function into recommendations to increase or to decrease price and/or budget. (Suggestions for a strong in/decrease are double-arrowed.) For the compensatory case the ﬁndings obtained for the probabilistic choice rule are shown in brackets. Ignoring the probabilistic case for a moment it is apparent that the incumbent’s proﬁtoptimal reaction allows for a price increase in conjunction with a rise of the advertising budget in all market scenarios where preferences are distinct and mature. This supports Hauser and Shugan’s (1983) Theorem 5, which is particularly remarkable given a market model entirely different from closedform game-theoretic analysis. For stochastic brand choice the price may also rise but the budget should be cut if advertising responsiveness is high. The scenarios with indistinct preferences change the picture. A tough defensive reaction — i.e., increasing budget and reducing price — is required loess function of the modreg library of the R system (http://cran.r-project.org/) was used. The value of 0.10 for the smoothing parameter is a mild setting for ironing out the random disturbances of the ACM response.

1 The

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Recommended changes of the incumbent’s price and advertising budget after entry. Low responsiveness Indistinct Preferences

High responsiveness

Distinct Preferences

Indistinct Preferences

Distinct Preferences

2/3 Noncompensatory

↑ adv.

↓ price

↑↑ adv.

↑ price

↓↓ adv.

↓ price

↑ adv.

↑ price

1/1 Compensatory [with probabilistic choice]

↑ [↑ adv.

↓ ↑] price

↑ [↑ adv.

↑ ↑] price

↑ [↓ adv.

↑ ↑] price

↑ [↓ adv.

↑ ↑] price

Figure 4. Incumbent’s proﬁt surface for the 2/3 noncompensatory, high responsiveness, and indistinct preferences scenario.

for the markets with low advertising responsiveness. But the incumbent may raise prices or decrease the advertising budget in the high responsiveness scenarios. Again, the stochastic choice condition reverses either the budget or price movement in these two cells. Figures 4 to 7 show some selected proﬁt surfaces. Figure 4 nicely demonstrates that several of the price-advertising combinations may achieve very similar results; a price increase combined with reducing the advertising

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Figure 5. Incumbent’s proﬁt surface for the 1/1 compensatory, high responsiveness, and distinct preferences scenario.

Figure 6. Incumbent’s proﬁt surface for the 1/1 compensatory, low responsiveness, and indistinct preferences scenario.

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Figure 7. Incumbent’s proﬁt surface for the 2/3 compensatory, low responsiveness, and distinct preferences scenario.

expenditure generates a marginally lower proﬁt than the low price-low advertising strategies. A surface close to unimodality results for the Figure 5 scenario. A modest increase in advertising there makes the incumbent enforce a higher price. Figures 6 and 7 pertain to the low responsiveness scenarios. In all of them except the “1/1 compensatory-distinct preferences” case the proﬁt surfaces reﬂect the effectiveness threshold. Consider Figure 6 as an example where the advertising response breaks down with budgets less than 1.000. The need for a price reduction is clearly visible in this surface chart. Price cuts are required under the indistinct preferences condition but not for the distinct preferences case. Figure 7 has an example for one of the latter scenarios. The need for raising the advertising budget to enforce a higher price becomes particularly obvious in this proﬁt function. Drawing conclusions with regard to the propositions suggested earlier it appears that (1) only holds for markets with indistinct consumer preferences. As a consequence, Proposition (2) either does not become relevant as long as the market accommodates markedly different and mature preferential segments. The expected need for increasing the advertising

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budget (Proposition 3) is supported for all (deterministic choice rule) scenarios except the one shown in Figure 4. Irrespective of the preferences being distinct or indistinct the probabilistic brand choice scenarios make a difference as they relax the “winner-takes-all” principle. They permit budget cuts for the high responsiveness cases. The strength-of-reaction assumption addressed in Proposition (4) only materialises for the two noncompensatory cases of the Figures 4 (downward) and 7 (upward) where the defensive advertising reaction suggested is particularly strong.

10.

Discussion and Emergent Issues for Continued Experimentation

Gruca et al. (2001) were right in extending the scope of defensive strategy analysis by introducing discrete concentrations of segment-speciﬁc ideal points. Hauser and Shugan (1983) analysed continuous “taste” distributions but already covered special cases of “highly segmented” markets; their Theorem 5 regarding the option of a price increase is supported here. [The defensive strategy articles published in between [Kumar and Sudharsham, 1988; Carpenter and Nakamoto, 1990; Gruca et al., 1992; Ansari et al., 1994; Basuroy and Nguyen, 1998) paid little attention to the segmentation aspect.] The feasibility of an increase in defensive pricing clearly depends on the segmentation condition. It is particularly noteworthy that the recommendations for all distinct preference scenarios in the present experiment include a price raise. This may have been the result from Defender most astonishing to market analysts and managers. Here it gets support generated with an entirely different research methodology. Following the decision by Gruca et al. (2001) of grounding the analysis on one single set of advertising response parameters would have been detrimental in the present study. It turns out that a low level of advertising responsiveness reverses the direction of optimal pricing in both indistinct preferences scenarios. Among the defensive strategy articles reviewed here Gruca et al. (2001) was the only one to compare deterministic and probabilistic choice rules. (All the rest assumed deterministic choice.) In their “supporting conditions” these authors offer largely divergent results for the two choice rules. Major differences were also obtained in this study as the probabilistic rule reverses the budgeting suggestion for both high responsiveness scenarios. This result must be evaluated considering the mainstream of consumer choice modelling where random utility and probabilistic decision rules are uncontested.

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Actually, this is an unresolved problem in marketing research and it becomes apparent in many conjoint studies. There, “winner-takes-all” and probabilistic rules are often used in parallel to predict market shares for hypothetical new product brands. Noncompensatory choice rules have not been an issue in defensive strategy models so far. It may be reassuring from the viewpoint of the earlier studies that “1/1 compensatory” versus “2/3 noncompensatory” produced opposite results only for one scenario of indistinct preferential segments and high responsiveness. But for one of the distinctive preferences settings (the one under low advertising responsiveness) the pressure for intensifying advertising is much more pronounced for the “2/3 noncompensatory” case than for the “1/1 compensatory” scenario. So, even when the recommended direction of competitive reaction is the same, a difference in strength cannot be dismissed. One may ﬁgure out numerous extensions of the type of experiment conducted here. Many characteristics of real-world markets come to mind. The present implementation of the Artiﬁcial Consumer Market would allow for adding intriguing phenomena such as fuzziness of consumers’ belief systems, adaptive reservation prices, brand loyalty, satisfaction, involvement, reactance, or word-of-mouth. The same variety of options is waiting on the strategy side of the experimental set-up. Adding more components of the marketing mix or multi-period strategies differentiating between immediate and long-term reaction are just examples. Accounting for dynamic effects such as time-to-entry or lagged-reaction issues exploits typical strengths of the micro simulation approach. By succumbing to only few of these temptations, however, the analyst may quickly lose the ability of tracing the results. Given the current ﬁndings a more reﬁned analysis of the interaction between choice rules and degree of segmentation has ﬁrst priority. Only two crude levels of segmentation were investigated here: a totally homogeneous market and three segments with non-overlapping ideal brand positions. It was found that the choice rule does not matter as long as the preferential segments are distinct “enough”. An inquisitive marketing analyst certainly would like to know more precisely where the domain of “enough” distinctiveness begins. At least two intermediate stages of partially overlapping preferences would be required to achieve greater accuracy. It seems important to reiterate that the simulation experiment has no ambition to replace ordinary empirical market analysis. But it draws the marketing scientist’s attention to consumer and market variables that are worth

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an empirical research effort. The experimental results suggest that marketing research ought to lay much more emphasis on consumers’ noncompensatory choice rules. While this issue has attracted the attention of “qualitatively” oriented consumer researchers, it appears to be rather neglected by the psychometric community within marketing science. One may hope that Gilbride and Allenby (2004) who applied highly sophisticated Bayesian methodology to analysing noncompensatory choice rules will turn out to be trend setters in this respect.

Acknowledgement This piece of research originates from a joint programme of the Vienna University of Economics and Business Administration, the Vienna University of Technology, and the University of Vienna, sponsored by the Austrian Science Foundation under grant SFB010 (“Adaptive Modelling in Economics and Management Science”; 1997–2004).

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Appendix: Outline of the Artiﬁcial Consumer Market Simulation Environment Advertising response and perceptual dynamics. Figure A1 gives an impression of the concepts involved in the Artiﬁcial Consumer Market. The consumer model of the ACM simulation environment stems from the latent brand space paradigm introduced in the most inﬂuential book on buyer behaviour ever written (Howard and Sheth, 1969) and further propagated until these days (see, e.g., Engel et al., 1973; Howard, 1977; Mazanec, 1978;

Figure A1. The ACM simulation environment.

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Kroeber-Riel, 1980; Bagozzi, 1986; Myers, 1996; see Dillon et al., 1985, for some measurement implications of the three-way data involved). The ACM distinguishes between the observable brand attributes, which are available to the ﬁrms as binary yes/no reactions (such as in the Unilever Brand Health Check administered in European countries), and the underlying latent attitude dimensions. The ACM models the brand perceptions on three levels: latent attitudinal dimensions, verbal response generating probabilities, and redundant sets of observable indicators of the latent dimensions. The advertising response function (A1) establishes the connection between the marketing agents’ allocation of their communication budgets to the target groups and the consumers’ learning of brand attributes: M = π− exp (−ρwo ) ∗ S where M =

M1 ... MB

(A1)

is a stacked matrix of dimensionality (B×C)×V with Mb

standing for brand b and mcv expressing the change factor for the probability that consumer c = 1, . . . , C attributes the product characteristic v = 1, . . . , V to brand b = 1, . . . , B; the settings are C = 300, V = 12, B = 4; exp ( · ) denotes element-wise exponentiation, the prime indicates the transpose and the ∗ operator stands for an elements-by-elements product; π is the persistency constant with a feasible range of 0.6 < π < 0.8 (set to 0.6 and 0.7 resp.); ρ is the responsiveness constant with recommended values of 2 or 3 (set to 2 and 3 resp.); w is a (B × C) × 1 vector of the relative advertising impact directed to consumer c by brand b; o = (1 1 · · · 1) is a row vector of ones with V entries; S is a (B × C) × V matrix of zeros and ones indicating the attributes the marketing agent has included as claims in its advertising message; an indirect learning effect may be added to S by increasing those zero elements not advertised but semantically associated with another advertised one. As a result of (A1) the amount of the perceptual change factor varies between a decay of −π for a non-exposure or irrelevant claim and π as the upper limit due to a relative impact of 1. If an element in M is non-positive, the relative budget impact does not excel the effectiveness threshold implicitly set by the parameters π and ρ and thus cannot prevent decay. The time index has been suppressed so far. In (A2) and (A3) it is needed for better clarity. Attribute learning and forgetting determine the absolute change M in the perception-generating probabilities G between two

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“periods” t and t + 1, i.e., advertising exposures and buying opportunities: Gt+1 = Gt + M with

m(b,c),v,t+1 =

(A2)

(1 − g(b,c),v,t )m(b,c),v

if m(b,c),v ≥ 0

g(b,c),v,t (1 + m(b,c),v )

if m(b,c),v < 0

(A3)

In accordance with basic learning theory the gain in attribute learning depends on the amount of brand knowledge already reached. It levels off for product comprehension approaching saturation, while larger gains occur when the association of an attribute with a brand is weak. The new experience conveyed via advertising leads to a change of the consumers’ attitudes toward the brands in the product class. The updated brand positions D in latent brand space result from two further steps. The ﬁrst step transforms the advertising-driven probabilities G into real-valued attribute variables Z G (A4) Z = log 1−G which are related to the brand space by the principal components reduction Z = AD

(A5)

where A is a V × R-matrix of component loadings governing the strength of association between the set of V redundant brand attributes on observational level and the small number of R directly unobservable brand attitude dimensions (R V); D is the R×(B×C)-matrix of positions in brand space. In the second step the post-advertising positions then originate from the usual derivation of components scores via D = (A A)−1 A Z

(A6)

There is also a “technology” side of the Artiﬁcial Consumer Market. The brand space does not only contain communications-driven but also technology-driven positions manipulated by the ﬁrms’ product improvement and observable through a set of technical features during actual product usage. The principal components model allows for mapping the technical features into the same space, where discrepancies may be resolved in several ways. Such a reconciled positions matrix D would entail modiﬁcations in Z via (A5). This technology-induced attitudinal change then is propagated into the redundant and fuzzy consumer language via the inverse of (A4) viz.

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the logistic squashing function (A7), which squeezes the real-valued attribute values into the interval [0, 1]. This technology/advertising aspect is not activated for the current experiment. G=

exp(Z ) 1 + exp(Z )

(A7)

The ﬁnal step in modelling the latent-space/observable-attributes system introduces a stochastic element into the hitherto deterministic relationships. When compared to uniformly distributed random data the probabilities in G produce the noisy zero-or-one items of the elongated (brands × consumers) × attributes matrix X corresponding to M in (A1). This is what the marketing agents watch and analyse on the ACM: 1 if g(b,c),v > h(b,c),v h ∼ U(0, 1) (A8) x(b,c),v = 0 if g(b,c),v ≤ h(b,c),v

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6 A USER EVALUATION OF WEB RECOMMENDER SYSTEMS Ulrike Bauernfeind Institute for Tourism and Leisure Studies Vienna University of Economics and Business Administration Augasse 2-6 1090 Wien, Austria [email protected] Received July 2004 Accepted November 2005 The World Wide Web (WWW) offers an overwhelming amount of information. Decision-aid systems like web recommenders are an appropriate means to reduce this abundance of information by ﬁltering out relevant items according to the user’s previously stated preferences. Therefore, the signiﬁcance of recommender systems increases signiﬁcantly. However, approaches measuring user satisfaction with recommender systems are rarely found. A model covering the factors impacting consumer satisfaction with recommender systems is proposed. The model is empirically tested using three recommender systems. Test persons are asked to simulate a real system/user interaction and evaluate the recommender systems afterwards. The goal is to identify factors having the most signiﬁcant impact on recommender system satisfaction.

Keywords: Recommender systems, system evaluation and satisfaction, Technology Acceptance Model (TAM).

1.

Introduction

The WWW changed from a purely information retrieval platform towards a place where customers are increasingly buying products and services. The ﬁgures estimated for the US growth in online purchases in 2004 amount to 27% when compared with 2003 (eMarketer, 2004). On the one hand, 137

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people use the Internet increasingly to purchase goods. On the other hand, there is an overwhelming amount of information about products and services, constituting the need for improved functions to help Internet users becoming more efﬁcient when using the Internet. Recommender systems offer the useful functionality in providing search results and proposals tailored to the individuals’ preferences and constraints. Recommender systems (also called advisory, counselling systems or recommenders) ﬁlter out relevant items for a customer according to his previously implicitly or explicitly stated preferences and constraints (Thompson et al., 2002). Applications of recommender systems can be found in different industries. Amazon is a very good example of a recommender system in the book sector.1 The travel and leisure industry is increasingly using recommendation technologies, e.g., Skimatcher2 or Expedia.3 Although the signiﬁcance of recommender systems is evident, evaluation approaches are rather limited. Additionally, new factors like trust or fun, whose signiﬁcance was not that high in the past, have started to emerge. Therefore, the research objective of this study is to model the factors impacting consumer satisfaction with web recommender systems. The aim is to conduct a web-based survey in which users evaluate three different recommender systems. The satisfaction is measured directly after the users have experienced the web recommender system and have done a predetermined task simulating real problem solving. Section 2 provides ﬁrst an overview of the research traditions and theories taken into consideration for this research. Second, possible inﬂuencing factors on recommender system satisfaction are discussed. In Section 3 the methodological approach is outlined. First, the research model proposed and the inﬂuencing factors of web recommender satisfaction are described. Second, the measurement development and the pilot test to be conducted are outlined. A description of the data collection procedure and study design follows. Then, the recommender systems used for the evaluation are presented. Finally, the analysis method of the user evaluations is illustrated. The paper concludes with a summary of the research goals and what implications for both researchers and web recommender system designers could be expected. 1 http://

www.amazon.com

2 http://www.skimatcher.com 3 http://www.expedia.com

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Theoretical Background

First, an overview of relevant research traditions and theories is given. Second, possible factors impacting recommender satisfaction are outlined with each inﬂuence constituting a sub-heading. Various disciplines were considered for this ﬁeld of research: psychology, business (marketing and consumer behaviour), mass communication with uses and gratiﬁcation research and adoption studies in information systems research. Psychology ﬁrst comes to mind when thinking about (user) behaviour. In particular, social psychology plays a crucial role in searching for a theoretical foundation for behaviour. The theory of planned behaviour, TPB (Ajzen, 1991) which originates from the Theory of Reasoned Action, TRA (Fishbein and Ajzen, 1975), is a well-known example often serving as a basis to develop user behaviour models, e.g., the Technology Acceptance Model (TAM). Social Cognitive Theory (SCT) stemming from Social Learning Theory (SLT) is another relevant theory coming from the ﬁeld of psychology. The domain of cognitive absorption (e.g., Agarwal and Karahanna, 2000) and the notion of Flow (originally introduced by Csikszentmihalyi, 1990 and adopted by Hoffman and Novak, 1996 to the web context) play an important role as well. The hygiene and motivation theory originally published by Herzberg et al. (1967) was adapted by Zhang and Dran (2000) for website design and evaluation. The motivational model (MM), with the core constructs of extrinsic and intrinsic motivation is well studied in different areas, e.g., human resource management and is used to explain online behaviour as well (e.g., Shang et al., 2004). Diffusion research is another relevant discipline applied in marketing or consumer research but also in sociology, education or anthropology. The focus is on the adoption and diffusion of innovations. Thus, the relevance for the Internet is obvious. While obtaining information via the WWW is quite common nowadays, buying products and services online is still not that widespread. Diffusion of innovation theories serve as a basis to explore online buyer behaviour in general (e.g., Chen et al., 2004) or concerning speciﬁc applications such as buying cars online (Molesworth and Suortti, 2001). Uses and gratiﬁcations research stemming from the area of mass communication have relevancy for the Internet as well. Models of consumer motivations for media usage are provided. Katerattanakul (2002) suggests that consumers are looking for three main gratiﬁcations when using the

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web: information search, consumer transactions and enjoyment. Eighmey and McCord (1998) concluded that in order for a computer-mediated form of communication to be chosen the ﬁrst time, it needs to be entertaining and to offer exploration. Obviously, in information systems research many contributions can be found about website adoption or satisfaction. Adoption research is concerned with all kinds of applications, e.g., automated teller machines (Dos Santos and Peffers, 1998) or computers (Venkatesh and Brown, 2001). A lot of lessons can be learned from the research about the adoption of management information systems (MIS) and the adoption of decision support systems (DSS). Reviewing the above mentioned research traditions resulted in possible inﬂuences which are outlined below.

2.1. Perceived usefulness The factor of usefulness stemming originally from the Technology Acceptance Model (Davis, 1989) is clearly one of the most important and most researched inﬂuencing factors for system usage and satisfaction. The TAM relies on two factors explaining human behaviour: perceived usefulness and perceived ease of use. Perceived usefulness describes the user’s point of view of enhancing his or her performance by using the system (Davis et al., 1989). TAM was supported by several studies and adapted to the web context (e.g., Lederer et al., 2000; Moon and Kim, 2001; Teo et al., 1999). A similar factor named information quality was proposed by DeLone and McLean (1992). Their IS Success Model included two major dimensions (system quality and information quality) to explain use and user satisfaction (those two then further inﬂuence the individual and organisational impact). Information quality focuses on the output of the system and addresses issues such as relevance, importance, content, and informativeness (DeLone and McLean, 1992). In 2003, they updated the IS Success Model for measuring e-commerce system success and added service quality as an additional inﬂuencer (DeLone and McLean, 2003).

2.2. Perceived ease of use Perceived ease of use, the second factor of the TAM, is the degree of effort the user believes he or she will need for using a particular system (Davis et al., 1989).

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DeLone and McLean employed the term system quality in their IS Success Model (1992). System quality is concerned with the information processing itself and includes availability, reliability or usability (DeLone and McLean, 1992, 2003). A term quite frequently used interchangeably with ease of use is usability. According to ISO 9241-11 (1998) usability is “the extent to which a product can be used by speciﬁed users to achieve speciﬁed goals with effectiveness, efﬁciency and satisfaction”. Lindgaard (1994) described usability as the ease of learning and using computer systems for all types of users (experienced and inexperienced users).

2.3. Perceived enjoyment An important development is that people are more and more experienced when using the Internet. Rising Internet experience leads to higher expectations and satiation effects. Not only utilitarian but also hedonic beneﬁts are sought. It is not enough any more to have a website offering necessary information which can be easily found. Satiation effects require additional appeals, e.g., fun during the purchasing process. Purchasing activities on the Internet should fulﬁl a kind of entertainment function as well. The construct of perceived enjoyment was investigated by several studies and highlighted the fact that an enjoyment or fun factor is becoming increasingly important in the environment of the Internet. Moon and Kim (2001) deﬁned enjoyment as an activity pursued mainly for pleasure rather than for performance goals. Van der Heijden (2003) added the construct of perceived enjoyment to the original TAM. According to Teo et al. (1999), the Internet is regarded useful for task fulﬁlment as the major factor and the second most important factors are surprisingly, enjoyment together with ease of use. Yi and Hwang (2003) highlighted the importance of enjoyment as antecedent of usefulness, ease of use and self-efﬁcacy. Another concept dealing with a compelling online environment is “Flow”. Originally, the term “Flow” came from the ﬁeld of psychology and was introduced by Csikszentmihalyi in 1975. Hoffman and Novak (1996) and Novak et al. (2000) adapted Flow to the web context. Flow is described as a state of mind where the user is completely devoted to the use of a system and forgets everything else around him or her, like time. Thus, the aim is to create a compelling online experience to facilitate Flow.

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2.4. Trust The inﬂuence of trust was considered in various studies, e.g., Koufaris and Hampton-Sosa (2004), Gefen and Straub (2004), Chiou (2004) and Pavlou (2001). The signiﬁcance of trust will rise because more and more people use the Internet for ﬁnancial transactions. In particular, purchase activities require websites providing the user with a feeling of security if it is required to give away personal and sensitive data like credit card information. Examples from the Internet banking area show that trust does have a tremendous impact on the attitude towards using a banking service in an online environment (Suh and Han, 2002). Even when a low risk purchase, e.g., a book is bought online, trust is a signiﬁcant inﬂuencing factor (Gefen, 2000). The need for security does not only arise when it comes to payment procedures but also when user names or passwords are required to be revealed. Therefore, websites do not only need to have high security standards but also need to give the impression that one can trust that the information is processed securely. However, there is another aspect of trustworthiness: trust is required concerning the recommendations given by the system. If a user does not trust the recommendations, it is not very likely that she or he will either buy the goods/services proposed or will come back to the recommender again.

2.5. Internet familiarity Internet familiarity or online experience serves as an antecedent or moderating effect in several studies (e.g., Wöber et al., 2002; Gefen, 2000; Igbaria and Iivari, 1995; Rodgers et al., 2005). Depending on the degree of familiarity with using the Internet, expectations might differ signiﬁcantly. In the case that the user is a very experienced one, he or she might expect not only task fulﬁlment but also some joy or fun components when visiting a website. On the other hand, an inexperienced user is likely to expect a site which is quite easy to use.

2.6. User’s attitude towards the Web Attitude is about two aspects: the general attitude about using the Internet and the attitude towards performing a certain task via the Internet. Such a task would be to search for information online, using e-services or shop online. As suggested, e.g., by Shih (2004), Suh and Han (2002) or Kucuk and

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Arslan (2000), attitude does have an inﬂuence on Internet usage, adoption or acceptance.

2.7. Involvement Involvement can be described as the degree of interest a user has in a certain product service or activity. When searching the web, there are two types of involvement possible. First, there could be situational involvement arising when using the site and when searching for a particular service or product. Second, it could also mean product involvement, the general interest for a product or service. As pointed out by Richard (2004), website involvement and involvement in purchase decisions has a signiﬁcant inﬂuence on the behaviour of users.

2.8. User satisfaction User satisfaction is crucial since it enhances loyalty and this effect is found to be stronger online than ofﬂine (Shankar et al., 2003). Satisfaction is deﬁned as a perceived pleasurable fulﬁlment of a service (Oliver, 1999). Muylle et al. (2004) described website user satisfaction as the degree of utility a website presents in the user’s decision-making process. This is of particular relevance to recommender systems because their main purpose is to offer decision support. According to Anderson and Srinivasan (2003), e-satisfaction is the contentment of the user when considering his (purchase) experience with a company’s website. Other possible outcomes found in the literature are website usage or user acceptance. Website usage could either mean current usage or future intended usage, the intention to revisit a website or loyalty (e.g., Anderson and Srinivasan, 2003; Lederer et al., 2000; Hsu and Chiu, 2003). User acceptance is actually used as a surrogate for actual behaviour and reﬂects the behavioural intention towards, e.g., the use of a certain kind of website, e-service or e-shopping (Shih, 2004; Ahn et al., 2004). Finally, electronic or web service quality was used in a number of studies as an outcome (Barnes and Vidgen, 2000; Li and Tan, 2002; Parasuraman et al., 2005; Wang and Tang, 2003). Parasuraman et al. (2005) developed a scale called E-S-QUAL (e-service quality) targeted to assess e-shopping sites. They deﬁne e-service quality (e-SQ) as the degree to which a website enables efﬁcient and effective shopping, purchasing and delivery (Parasuraman et al., 2005).

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Methodology

The research goals of this study are to contribute to the understanding of web recommender satisfaction. First, a research model is introduced and its constructs are deﬁned. A pool of underlying items was acquired by literature review. The most appropriate items are to be identiﬁed by pilot testing. Then, the main user survey is conducted to assess the impacts and relationships of the inﬂuencers on web recommender satisfaction. Structural equation modelling (SEM) is used to analyse the user evaluations.

3.1. Research model The research model outlined in Figure 1 is proposed. Literature review suggested the supposed relationships and inﬂuencing factors. Perceived ease of use and perceived usefulness are included because they are simply indispensable for website satisfaction. They are clearly one of the most researched inﬂuencing factors for system usage and satisfaction. There importance is obvious: a system can be very easy to use but if the information contained

Perceived Usefulness

Involvement

Perceived Ease of Use Satisfaction with the Recommender

Internet Familiarity

Trust

Perceived Enjoyment

Attitude towards e-service

Influencing Factors

Figure 1.

Proposed research model.

Outcome

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is not relevant or up-to-date it is useless. On the other hand, ease of use or system quality does play an important role as well. If information is not found, it is once again useless. However, they do not cover any hedonic needs and certain fun factors or security concerns. Thus, the model has to be extended. “Flow” was dropped in favour of perceived enjoyment because measurement of Flow would be more complex and would involve more than one construct to measure (Hoffman and Novak, 1996; Novak et al., 2000). Trust as the fourth major inﬂuencing factor is crucial since Internet users are getting more careful in avoiding Internet fraud or misuse of personal data. Finally, personal characteristics such as experience, attitude towards the Internet and e-business and involvement do play a role when interacting with a website. User satisfaction with the web recommender system will be used as outcome because the speciﬁc user experience formed during the interaction is the object of investigation. Therefore, neither website usage nor user acceptance would be appropriate as an outcome. Service quality would not ﬁt either, because the web recommenders involved do not primarily sell products or services, they just recommend them. There are several indirect relationships and some of the inﬂuencing factors do have an impact on each other. Applied to the context of recommenders, the impacts and relationships are hypothetical. The sum of their inﬂuences was never tested in this way. Therefore, the goal of this study is to model their impacts on recommender website satisfaction.

3.2. Measurement development The questionnaire was designed in an iterative process. First, relevant articles were used to collect items for the respective constructs. They were analysed according to their main focus and repeated appearance. Finally, for each construct about 15 items remained which are pre-tested among users. The goal is to identify the most appropriate items with the highest loadings to include them in the ﬁnal evaluation questionnaire. The items of each construct are pre-tested among 50 users. As soon as the items for each constructs are deﬁned, another pilot testing is conducted. The intention is to do a ﬁnal check of the wording of the questionnaire. The test persons are asked to do a short task to ensure that every test person did interact with the website enough to be able to evaluate its features. Therefore, another goal of pilot-testing is to assess the evaluation procedure itself, to see if the test persons understand the instructions.

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3.3. Data collection The data collection for the main survey is conducted web-based. Test users are asked to answer a questionnaire, starting with some general demographic and Internet usage questions and then proceeding to a real problem situation simulation with a concrete recommender system. The problem simulation includes a short task to do on the respective recommender to ensure certain knowledge of the recommender before evaluating it. The test task is intended to mimic real problem solving, e.g., to simulate travel planning in the case of DieToRecs, to prepare an exam with Learn@WU or to be recommended on a leisure item with Ratingzone. An example for such a task for the travel recommender DieToRecs would be: “Imagine you want to make a weekend trip to a European city with a friend. You want to stay for two nights and spend around 500 Euro per person at maximum (including the ﬂight and the hotel). Now please plan this travel with the help of the website DieToRecs.” After the test persons have done this pre-determined task, they are asked to evaluate the system according to the factors of the research model outlined in Figure 1. The questionnaire consists of a 4 point Likert scale with end points of “strongly agree” and “strongly disagree”. The sample size planned to achieve is 200 user opinions for each recommender system. The test persons are recruited via the Internet and the online questionnaire is promoted at several websites. Furthermore, a lottery is used to give test persons an incentive to participate in the survey.

3.4. Recommender systems An overview of the recommender systems used for the evaluation is given. The evaluation focuses on three recommender systems. First, DieToRecs, a travel recommender system built in the course of an EU project is used.4 The second recommender system is Learn@WU,5 the e-learning platform of the Vienna University of Economics and Business Administration (VUEBA). Finally, Ratingzone6 is a recommender system offering the user to get proposals for movies, music, books, and travels — different kind of leisure activities.

4 Project

website: http://dietorecs.itc.it/ Recommendation system: http://eu-project.hgb. tiscover.at/dialogservlet 5 http://learn.wu-wien.ac.at/ 6 http://www.ratingzone.com/

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The above-mentioned recommenders are not chosen arbitrarily but because they stem from different areas: DieToRecs from tourism, Ratingzone from the leisure area and Learn@WU is a distance learning platform. The selection does represent reality very well because the tourism and leisure industries are some of the most successful areas in e-business. European online travel sales increased by 41% from 2003 to 2004 and 7.6% of all e-sales are travel products or services in 2004 (Marcussen, 2005). The significance of e-learning has increased over the last few years and recommendation services are especially important in the e-learning sector (Chen et al., 2004; Cantoni et al., 2004). These three recommender systems are based on different recommendation techniques. DieToRecs, the travel recommender is mainly based on Case Based Reasoning (CBR) whereas Ratingzone applies a Collaborative Filtering approach. Learn@WU is a system that gives recommendations based on the user proﬁle and past user behaviour.

3.5. Analysis of evaluation results The basic goal of this study is to identify causal relationships between the variables proposed in Figure 1. Structural Equation Modelling (SEM) can handle and explain relationships between latent (unobserved) and manifest (observed) constructs. The modelling technique is a conﬁrmatory rather than an exploratory method. SEM is able to identify causal inﬂuences of the exogenous (independent) on the endogenous (dependent) variables. This is similar to regression analysis but has the additional capability to identify causal inﬂuences of endogenous variables upon one another (Anderson and Gerbing, 1988; Hair et al., 1998). This study deals with latent constructs (e.g., attitude, fun, satisfaction) and proposes hypotheses and relationships between the constructs and their respective importance. Therefore, SEM was identiﬁed to be the most appropriate analysing technique.

4.

Conclusion

A vast amount of information can be found on the Internet and it becomes increasingly important to offer convenient tools for the user to ﬁlter out relevant information. Recommender systems offer the opportunity to propose to the user targeted results. Many attempts were undertaken to evaluate websites but only a few concentrate on recommender systems. However,

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recommender systems are more complex than usual websites and therefore need thorough investigation. This study aims to accomplish an evaluation of three recommenders to test explanatory constructs for user satisfaction. Literature review suggests that a system has to fulﬁl several functions. First, the constructs of usefulness and ease of use are basic characteristics. Trust is a signiﬁcant construct because of increasing Internet fraud and misuses. Hedonic beneﬁts, like enjoyment, are becoming increasingly a factor during an interaction with a system. Finally, personal characteristics such as experience, attitude towards the Internet and e-business and involvement do play a role when interacting with a website. How does this contribution distinguish from already existing ones? First, the focus is not on the measurement of general WWW satisfaction and its inﬂuencing factors. Instead, three particular recommender systems are investigated. The satisfaction is measured directly after the users have experienced the system and have done a predetermined task simulating real problem solving and purchasing activities. When measuring such emotional constructs like enjoyment it is crucial to do the evaluation directly after the experience has taken place with a particular website because memories fade. In this study, the inﬂuencing factors of website satisfaction are combined in a novel way and factors like trust and enjoyment are added. This study aims to test a comprehensive explanatory model for system satisfaction including the above named factors. Structural Equation Modelling is used to identify important inﬂuencing factors on system satisfaction with three recommender systems. However, the scope of the ﬁndings can be much broader and of general signiﬁcance for recommenders, since the recommenders used for evaluation stem from three different areas. Results are expected to provide proposals to design recommender systems more satisfactorily for the user. Furthermore, researchers should gain insights if web recommender systems have different inﬂuencers compared to conventional websites.

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7 THE DETERMINANTS OF RELATIONSHIP MARKETING: AN APPLICATION TO THERMAL SPAS Joaquim Antunes Instituto Politécnico de Viseu Campus Repeses 3504-510 Viseu, Portugal [email protected] Received February 2006 Accepted February 2006 This study is centred on the analysis of the different roles performed by the determinants of relationship marketing and the environmental factors in satisfaction and customer loyalty. The importance of satisfaction, trust and commitment as mediating variables is analysed in the process of relationship marketing. The empirical study is carried out with 346 people who patronise Portuguese thermal spas, using a quota sampling process. In order to validate this theoretical model and to test the hypotheses, a structural equation model is used.

Keywords: Relationship marketing, satisfaction, trust, commitment, loyalty.

1.

Introduction

Relationship marketing is a new focus now at the ﬁrst line of marketing practice and academic research. Relationship marketing presents a new paradigm (Gronroos, 1994; Gummesson, 1998), centre on building stable and lasting relationships with customers. This is in contrast with the traditional approach aimed at promoting transactions.

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The business model becomes centred on the customer and is supported by technological development in terms of information management and customer service. With this investigation, we try to equate a set of constructs associated with relational marketing which responds to changes in attitudes and demands of consumers with a view to their loyalty. We intend to test the model empirically in the thermal sector as this is a promising tourism products as an alternative to traditional seaside tourism connected mainly to the sea and sun. Nevertheless, the last few years have not seen as much of an evolution in Portuguese spas as had been expected, similar to what happened in other European countries, particularly France, Germany, Italy, Switzerland and in the Central European countries. The proliferation of motivations/products brings with it the multiplication of new questions, new challenges creating a need for new research. Relationship marketing may be a strategic option for the spas so as to respond to consumers’ new demands through a more interactive and individualised approach. To this end we begin by analysing the determining factors in relationship marketing as it has been conceptualised in the literature, as well as which aspects should be equated. The theoretical model which serves as the base of the study and the respective research hypotheses are presented. Later, the methodology adopted to respond to this research is presented. Before verifying the model and hypotheses, the measurement scales are validated through their psychometric properties. Finally, the main conclusions and contributions from this investigation are presented.

2.

Theoretical Model and Research Hypotheses

Relationship marketing refers to all of the marketing activities aimed at establishing, developing and maintaining efﬁcient relationships (Morgan and Hunt, 1994). In this sense, the starting point for constructing the theoretical model is analysing the nature of relationship marketing and determining how this construct should be operationalised. Ever since the ﬁrst deﬁnition of relationship marketing was given, all of the contributions that different investigators have given point out that the ﬁnal goal of the relationship marketing strategy is to increase customer loyalty.

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Thus, loyalty will be considered the key element or result of effective relationship marketing. This premise has been analysed in various relationship marketing studies, such as Evans and Laskim (1994), Macintosh and Lockshin (1997), Lawson-Body (2000) and Chang and Ding (2001). Therefore, the construct which has been considered to measure the efﬁcacy of relationship marketing, within the scope of this study, is customer loyalty which will be considered a dependent variable. Nevertheless, there are several variables which mediate the effect of relationship marketing on customer loyalty. Since the publication of The Commitment-Trust Theory by Morgan and Hunt (1994) most studies on relationship marketing have included the relationship commitment and trust as variables which are central to the success of relationship marketing (Morgan and Hunt, 1994; Macintosh and Lockshin, 1997; Too et al., 2001). Other studies considered satisfaction as the mediating variable (Garbarino and Johnson, 1999; Rao and Perry, 2002). However, given the speciﬁcity of the sector in which we intend test the model, this study suggests an integrated model based on a double perspective: organisational/corporate and environmental. This perspective is based on the notion that customer satisfaction and loyalty is reﬂected across both dimensions, environmental factors assuming an important role in satisfaction and in tourists returning to their place of visit, as shown in the study by Haber and Lerner (1998). Thus, a theoretical construct which includes a set of environmental factors of the region where the thermal spa is situated was also considered (Figure 1).

(+)

Trust

H5

H2

(+)

H4 (+)

H1: (+)

Satisfaction

Relationship Marketing

H3

Environmental Factors of the thermal spa

(+)

Commitment

H7 (+)

Figure 1.

Loyalty

H6

(+)

H8 (+)

Conceptual model.

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Then, hypotheses are formulated. These are connected to the questions involved in this investigation and come from the revision of literature related to each construct of the model and exploratory interviews with those responsible for the main Portuguese thermal spas.

2.1. Research hypotheses Relationship marketing has been operationalised various ways. On the one hand, there is the study by Too et al. (2001) where the authors consider relationship marketing as having only one dimension. On the other hand, there are studies by Evans and Laskin (1994), Lawson-Body (2000) and Chang and Ding (2001), where they deﬁned a set of dimensions, like independent variables, to conceptualise the constructs of relationship marketing. In any of these studies, those dimensions were related to customer satisfaction and loyalty. Each dimension of relationship marketing is analysed separately as well as its effects on customer satisfaction and loyalty. For this study, we followed the methodology of these authors which considered various dimensions for the relationship marketing construct. Hence, as a result of a revision of the literature, six dimensions of relationship marketing were considered so as to operationalise the theoretical model: understanding customers’ needs; relationships with customers; internal marketing; service quality; interactive marketing and personalisation of services. These dimensions will be considered in the model as independent variables. Relationship marketing is based on the idea that working with a customer on a basis of mutual trust facilitates the development of long term relationships. In order to achieve this, organisations must know their customers and must seek direct contact with them. Understanding customers expectations and needs involves the ability of organisations to identify what customers need and to offer services at the level they expect. Understanding customer needs was one of the dimensions Evans and Laskin (1994) used in their study. Bearing these considerations in mind, we can establish the following hypothesis: H1a: Understanding bather needs is positively related to their satisfaction. Relationships with customers are deﬁned as a process of interaction where a large number of contacts between the customers and service providers/assistants/salesmen take place over time (Barroso and Martín, 1999).

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According to Bagozzi (1995), the most common and determining reason to enter into and become part of a relationship is that the customer considers this the most correct way to meet his objectives. Thus, customer relationships lead to certain beneﬁts: they reduce the uncertainty of the deal, they increase the efﬁciency of the transaction and create customer satisfaction (Dwyer et al., 1987). From these principles, the following hypothesis is proposed: H1b: Relationships with customers are positively related to their satisfaction. From the perspective of relationship marketing, workers should make an effort to know the customers’ demands so as to solve their problems. This may lead to changing a dissatisﬁed customer into a satisﬁed one. For this to occur, employees must be granted greater power to solve problems which come up thereby better satisfying customers (Evans and Laskin, 1994). The beneﬁts of making employees responsible, according to Smith (1990), are as follows: responsible employees transform superﬁcial contacts into long-lasting relational contacts; customers are more apt to perceive that organisations that empower their employees are truly committed to customer satisfaction; highly motivated employees positively inﬂuence their work environment; granting more authority and responsibility to employees means that the organisation favours less bureaucracy. Therefore, the following hypothesis is proposed: H1c: Internal marketing positively relates to bather satisfaction. Companies which try to develop a relationship marketing strategy should dedicate a large part of their efforts so that customers will see that they offer quality in their services, as this is an important input and necessary to achieve customer satisfaction (Barroso and Martín, 1999). Before a purchase or service customers will create certain expectations regarding what they think they will receive. Later these expectations are compared with the perception of the result obtained. Customers will be satisﬁed when they receive at least what they expected from their provider, and they will be dissatisﬁed when the result of the purchase or service is inferior to what they expected. Quality of service is a prerequisite to customer satisfaction (Zeithaml et al., 1996). These considerations lead us to establish the

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following hypothesis: H1d: Quality of service positively relates to bather satisfaction. With relationship marketing the customer no longer plays a passive role in the organization and is instead considered an active member (Bitner, 1995). Hence, it is not enough to consider the customer a key element for the organisation, but he must be implicated in day-to-day actions. Interactive marketing is founded on reciprocity which is a basic element of relationship marketing (Bagozzi, 1995). Thus, relationship marketing is a continuous process which requires organisations to get feedback from their customers so as to ensure that their needs are met (Evans and Laskin, 1994). Consequently, the following hypothesis is established: H1e: Interactive marketing positively relates to bather satisfaction. Any company which wants to implement a relationship marketing strategy should be able to identify its customers, differentiate them from one another, interact with them and personalise some aspect of its products or services in order to satisfy their individual needs (Peppers et al., 1999). Thus, one of the best ways to differentiate its products and services is to give them a personal dimension — personalisation — which causes a highly positive impact on the consumer (Reis, 2000). Relationship marketing allows organisations to know more about the demands and needs of their customers. Knowing their customers, along with the social relationship, built up over a series service contacts, facilitates personalisation of services in accordance with the speciﬁcations of each customer (Berry, 1995). Personalisation will, therefore, increase customer satisfaction (Mittal and Lassar, 1996; Peppers et al., 1999). Thus, the following hypothesis is proposed: H1f: Personalisation positively relates to bather satisfaction. The starting point so that organisations may develop a permanent bond with their customers through there relationship starts with their satisfaction (Storbacka et al., 1994). This can be deﬁned as a positive attitude which refers to internal beliefs or emotions which demonstrate if an individual is favourably or unfavourably predisposed towards a certain product or service. Customer satisfaction is a factor which generates trust in the consumer towards the company which offers those products/services. Trust, then, is also considered an important factor in the long run. Anderson and Narus (1990) deﬁne it as the belief that the trading partner will perform actions which will result in positive consequences for the

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company and will not carry out unexpected actions that will yield negative results. Morgan and Hunt (1994) also said that trust exists when one party is secure in the responsibility and integrity of the other party which favours continuing the relationship. The main objective for a customer and an organisation to collaborate in a relationship is that this will add value for both parts, thereby increasing the cost of changing suppliers of the product or service (Anderson, 1995). The service offered by an organisation creates certain expectations in their customers about what they expect to receive, which greatly decreases the probability of changing due to the risk they will incur. Therefore, promises made to customers must be kept allowing the expectations they create to be covered and establishing trust as a pillar of the relationship (Berry, 1995). The presence of commitment between the parts of a relationship is an important indicator of the quality of the relationship. Commitment represents a long term orientation, sustained in the desire to maintain the relationship, which achieves its height in the mature phase of the relationship (Morgan and Hunt, 1994; GeysKens et al., 1996). On the other hand, the literature also says that satisfaction holds a positive and highly inﬂuential relationship on the customer retention and loyalty (Macintosh and Lockshin, 1997; Hennig-Thurau et al., 2002). From this the following hypotheses are formulated: H2: Bather satisfaction positively relates to his trust in the organisation. H3: Bather satisfaction positively relates to his commitment to the relationship. H4: Satisfaction positively relates to bather loyalty. In many studies on relationship marketing the trust and commitment variables are mediating variables that must be taken into account in the context of lasting relationships (Anderson and Narus, 1990; Morgan and Hunt, 1994; Garbarino and Johnson, 1999; Hennig-Thurau et al., 2002). The basis for maintaining a relationship is keeping promises (Gronroos, 1990), because when a promise is not kept trust is lost and the consumer will not repeat the purchase or the consumption of the product or service. Therefore, promises made to customers must be kept, which will enable them to fulﬁll their expectations, establishing a commitment base in the relationship (Berry, 1995). That is, if the commitment is maintained, the relationship will end. However, the commitment in and of itself is not enough, both parts must maintain a mutual trust which will lessen uncertainty in the activities that are

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carried out. At no time will the veracity, honesty and clarity of the actions each part takes come into doubt. Therefore, the binomial commitment-trust is a central element in relationship marketing, positioned as a mediating variable between prior actions and the consequences of a relationship marketing strategy. Its very presence is considered basic for corporate cooperation and the desire to lengthen the relationship (Morgan and Hunt, 1994). The following hypotheses are, therefore formulated: H5: Trust in the organisation is positively related to bather loyalty. H6: Bather commitment to the relationship is positively related to his loyalty. However, environmental factors also assume an important role in tourists’ satisfaction and return as veriﬁed in the study by Haber and Lerner (1998). A tourist destination is very complex and includes a diversiﬁed set of components required to satisfy the tourists’ needs (Pearce, 1991; Cooper et al., 1999). Tourism is, for that reason, a very horizontal area which includes a large variety of services and sectors. All of them are related and inﬂuence the tourist’s whole satisfaction (Farhangmehr and Simões, 1998; Kozak and Rimmington, 2000). In the context of the tourism activity, and specially thermal spas, the tourist or bather uses a diversiﬁed set of goods and services which if one or any are incapable of responding to his expectations may lead to his dissatisfaction transcending the set of the tourist destination. The effects of the environmental factors on the perception of the tourism product inﬂuence not only the intention to return, but also the intention to recommend it to others (Murphy et al., 1999; Kozak and Rimmington, 2000). According to these perspectives, we should study the thermal spa sector considering that it lies within a wider context. Not considering its environmental surroundings would always be a partial perspective of the reality under study. Under these considerations, the following hypotheses are proposed: H7: The environmental factors of the thermal spa are positively related to bather satisfaction. H8: The environmental factors of the thermal spa are positively related to bather loyalty.

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In order to verify these hypotheses, the most appropriate method must be chosen, as described in the following section.

3.

Methodology

The methodology followed to validate the model and test the respective hypotheses is based on a study carried out on bathers at the main thermal spas in 2003. The sample includes 346 questionnaires validated for analysis, which represent a 5.26% margin of error for a conﬁdence level of 95%. The sampling process was based on interrelated quotas on the basis of proportions of how often they patronise a spa and gender. Data were collected in thermal spas using a self-administered questionnaire. Its elaboration was from studies and scales which had already been used by other authors and by exploratory interviews held with people who are responsible for the thermal spas.

3.1. Measurement scales Marketing studies preferentially use multi-item scales (Churchill, 1979) so as to allow a more comprehensive and certain assessment of the reality under study. To measure each item we will use a Likert 7-point scale (from 1-I totally disagree to 7-I totally agree). This has been the most widely used type of scale in relationship marketing studies, such as Morgan and Hunt (1994), Siguaw et al. (1998) and Foster and Cadogan (2000). These scales were validated through their psychometric properties in accordance with Churchill (1979). Thus, the acceptability of this type of scale is founded on various aspects of its construction: unidimensionality, reliability and validity. Unidimensionality is and underlying assumption and a prerequisite for constructing a scale, which means that the items are strongly associated with each other representing a single concept. The most widely used technique is factorial analysis, generating an empirical value of the dimensionality of the set of items, determining the number of factors and the weights of each variable over the factor or factors. The unidimensionality test consists of a scale in which the items have high weighting in a single factor. According to Hair et al. (1998), reliability is the degree of consistency between the multiple measures of the construct. The most widely used measure of reliability is the internal consistency between the variables of a scale.

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The motivation for internal consistency is that the individual items or indicators of the scale should measure the same construct, and in this way be highly inter-correlated. The Cronbach alpha is the most extensively used analysis to measure internal consistency. The validity of a scale is the analysis by which a scale or a set of items represents the concept under study with precision. The forms which are most widely used to measure the validity of a scale are convergent validity and discriminate validity. Convergent validity values the degree to which two measures of the same concept are correlated. For this analysis, alternative measures of a concept should be used and they should be correlated to a scale that has been created. High correlations indicate that the scale measures the intended concept. Discriminate validity is the degree by which two conceptually similarly concepts differ (Hair et al., 1998).

4.

Results

First, we analysed the properties of the scales used to measure the relationship marketing scales, mediating variables and the dependent variable of the model (see Appendix 1). These all present good internal consistency (Cronbach’s Alpha greater than 0.70) and only the construct which refers to quality present two dimensions (one designated by tangible quality and the other by intangiable quality). In all the other constructs the unidimensionality characteristic can be observed. Four factors were found to characterise the environment which explain 65.3% of the total variance. The construction of this scale was mainly based on exploratory interviews conducted with those who are responsible for the thermal spas. The convergent and discriminate validity of the scales was also veriﬁed using correlations between the various items on the scale and other different scales. The results yielded high correlations between the items and the scale itself and lower correlations with other scales. These results satisfy the convergent and discriminate validity characteristic. The following analysis refers to the validity of the model and the test of the hypotheses through the system of structural equations, supported by the Amos 4.01 software. Besides verifying and proving the hypotheses initially set forth, this analysis enables the identiﬁcation of new relationships between the variables which had not been identiﬁed before but which allow a better adjustment of the model to reality.

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On ﬁrst analysing the results some relationships are found to be insignificant, that is, whose C.R. value is less than 1.96. These relationships are removed from the model leading to a rejection of the respective hypotheses: between the relationship and satisfaction (H1b); between tangible quality and satisfaction (H1d); between personalisation and satisfaction (H1f) and between three environmental factors and satisfaction (H7) and loyalty (H8). The results of adjusting the initial model are not very satisfactory (Table 1). The Chi-Square value is high (χ2 = 258.105) and probability low (p = 0.000), which indicates a weak adjustment of the model. Some adjustment indices also present weak values, such as the AGFI (0.675) and TLI (0.826). The RMESA value is also considered unacceptable at 0.151, over 0.08 as recommended by Arbuckle and Wothke (1999). In order to improve the adjustment of the model, changes suggested by the software output (Modiﬁcation Indices) were gradually introduced. These suggested changes were new direct relationships between the independent variables and the mediating and dependent variables. These changes are consistent with relationship marketing theory and as such are considered appropriate for addition to the initial model. These changes to the model have come to change the results of the goodness of the adjustment signiﬁcantly. The results of the model now present very signiﬁcant. The value of the Chi-Square is low (χ2 = 24.581 with df = 13 and p = 0.026) which is signiﬁcant for a signiﬁcance of 0.01. The adjustment indices also present very satisfactory values with 0.997 for the CFI (Comparative Fit Index); 0.993 for the NFI (Normed Fit Index); 0.997 for the IFI (Incremental Fit Index); 0.988 for the TLI (Tucker-Lewis Index); 0.986 for the GFI (Goodness of ﬁt index) and 0.940 for the AGFI (Adjusted goodness of ﬁt index). Remember that these indices are considered satisfactory when they are close to 1 (Arbuckle and Wothke, 1999). The RMSEA (Root Mean Square Error of Approximation) presents a value Table 1.

Results of the initial model of structural equations.

Minimum Fit Function Chi-Square = 258,105 (p = 0,000) Degrees of Freedom = 29 Comparative Fit Index (CFI) = 0,944 Normed Fit Index (NFI) = 0,939 Incremental Fit Index (IFI) = 0,945 Tucker-Lewis Index (TLI)= 0,826 Goodness of ﬁt index (GFI) = 0,910 Adjusted goodness of ﬁt index (AGFI) = 0,675 Root Mean Square Error of Approximation (RMSEA) = 0,151

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J. Antunes er_2

Needs ,80

,70 -,10 ,79

Personalization

,35

Trust

,19

,53,72

er_1

,63 ,55

Internal Mark.

,35

Interactive Mark.

er_4

,82

,40 ,45

Satisfaction

Loyalty

-,08

,77

,22

,23

,14

,27 ,74

,27

,49

,61

,61

,28

,16

,23

,19

,27

,75 ,13

,41 Intangible Quality

,14

,07

Commitment

er_3

,47 Environment 2

Figure 2. Final model (standardised) of the structural equations. Table 2.

Final results of structural equations model.

Path Satisfaction ← Needs Satisfaction ← Fac2_Environ. Satisfaction ← Interactive Mark. Satisfaction ← Intangible Qual. Satisfaction ← Internal Mark. Trust ← Intangible Qual. Trust ← Personalisation Trust ← Internal Mark. Trust ← Satisfaction Commitment ← Trust Commitment ← Interactive Mark. Commitment ← Satisfaction Commitment ← Intangible Qual. Loyalty ← Trust Loyalty ← Commitment Loyalty ← Satisfaction Loyalty ← Fac2_Environ. Loyalty ← Interactive Mark.

Estimate 0.350 0.134 0.139 0.163 0.274 0.231 −0.095 0.190 0.611 0.398 0.184 0.279 0.139 0.276 0.234 0.454 0.070 −0.079

S. E. 0.046 0.032 0.034 0.045 0.056 0.039 0.035 0.050 0.042 0.059 0.031 0.058 0.041 0.050 0.044 0.051 0.026 0.028

Goodness of Fit Statistics CFI = 0.997 NFI = 0.993 IFI = 0.997 RMSEA = 0.051

GFI = 0.986 AGFI = 0.940 TLI = 0.988

C. R. 7.600 4.201 4.117 3.645 4.878 5.952 −2.692 3.819 14.586 6.776 5.904 4.820 3.360 5.520 5.278 8.965 2.644 −2.807

Standardised 0.351 0.134 0.141 0.164 0.274 0.232 −0.096 0.190 0.612 0.398 0.187 0.279 0.140 0.275 0.233 0.454 0.070 −0.080

χ2 = 24.581 DF = 13 p = 0.026

of 0.051, which is also considered satisfactory. These results in the model, presented in Figure 2, to be acceptable. Comparing this model with the initial one in Figure 1, we can see that the variables which present signiﬁcant relationships with satisfaction

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are understanding needs, internal marketing, intangible quality, interactive marketing and environment 2. Through the Amos 4.01 program, relationships and co-variances which did not present signiﬁcant values, veriﬁed by C.R. (critical ratio), were eliminated. The ﬁnal values are presented in Table 2. In this model, therefore, new relationships between the variables, which had not been initially equated, stand out. Hence, with regards to internal marketing, besides its direct relationship with bather satisfaction, the model also suggests a relationship with trust. Interactive marketing, for its turn, which had only been equated with directly inﬂuencing satisfaction, is now suggested to directly inﬂuence both commitment and loyalty. Personalisation presents signiﬁcant values, not with bather satisfaction, but with his trust in the organisation. Finally, intangible quality, which had solely been equated with directly inﬂuencing satisfaction, presents a direct inﬂuence on trust and commitment in this model. Another change to the model suggested by the results is the direct relationship between trust and commitment.

5.

Conclusions

The growing importance of relationship marketing, whether in the scientiﬁc literature or in business practice, has led many authors (such as, Gummesson, 1994; Gronroos, 1995; Gummesson et al., 1997) to admit we are in the presence of a new paradigm since it has profoundly changed how companies are organised. Relationship marketing has become a decisive approach for the new marketing context organisations face. It is deﬁned as an interactive process which allows an organisation to establish stable, long-lasting relationships with their customers. The results of this research are consistent with ﬁndings from previous studies. The variables which directly inﬂuence bather satisfaction are understanding needs, internal marketing, intangible quality and interactive marketing. Neither the relationship with bathers, nor tangible quality presented signiﬁcant values. The role of the mediating variables: satisfaction, trust and commitment in the relationship marketing process, is also unmistakable. These variables are considered fundamental to bather loyalty. Trust in the organisation plays a crucial role as it is a prerequisite to commitment. We had not equated this, but is in line with Morgan and Hunt’s (1994) Commitment-Trust theory.

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This theory provided an outstanding contribution to the study, allowing the creation of an investigative model, which was tested and validated and can be used in future research. This model has the particularity of including a simultaneous analysis of relationship marketing variables and environmental factors and their direct and indirect effects on the loyalty of spa customers. In this way this study validates the various dimensions of relationship marketing and its inﬂuence on bather satisfaction and loyalty. It contributes with the development of new measurement instruments (the scales used), validated through different statistical methods. As it is a fairly recent area of knowledge, an added difﬁculty, it has an innovating character. In our opinion, the model that was created will contribute towards developing relationship marketing in the context of thermal spas in Portugal. As for practical contributions, the study has resulted in a deep knowledge of which areas of relationship marketing most inﬂuence bather satisfaction and loyalty with regards to their respective thermal spas. This study also draws attention to the importance of environmental factors in bather loyalty. The competent authorities should thus be alerted to this key element in developing a thermal spa. The deﬁned model and the respective methodology need to be tested in other business environments in order to survey which components of relationship marketing and the environment that exert the most inﬂuence on loyalty. This study is a starting point for further research and further pursuit of answers to new questions.

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Berry, L. (1995). Relationship marketing of services — Growing interest, emerging perspectives. Journal of the Academy of Marketing Science, 23(4), 237–245. Bitner, M. (1995). Building service relationships: It’s all about promises. Journal of the Academy of Marketing Science, 23(4), 246–251. Chang, K. and C. Ding (2001). Is relationship marketing really helpful to increase repeat purchase in the Chinese market? Journal of International Marketing and Marketing Research, 26(1), 157–164. Churchill, G. (1979). A paradigm for developing better measures of marketing constructs. Journal of Marketing Research, 16(1), 64–73. Cooper, C., J. Fletcher, D. Gilbert, R. Shepherd and S. Wanhill (1999). Tourism. Principles and Practice, Second Edition. Longman. Dwyer, F., P. Schurr and S. Oh (1987). Developing buyer-seller relationships. Journal of Marketing, 51(April), 11–27. Evans, J. and R. Laskin (1994). The relationship marketing process: A conceptualization and application. Industrial Marketing Management, 23, 439–452. Farhangmehr, M. and C. Simões (1998). Estudo de factores que contribuem para o desenvolvimento do sector hoteleiro português. Revista Portuguesa de Marketing, 2(6), 31–44. Foster, B. and J. Cadogan (2000). Relationship selling and customer loyalty: an empirical investigation. Marketing Intelligence & Planning, 18(4), 185–199. Garbarino, E. and M. Johnson (1999). The different roles of satisfaction, trust, and commitment in customer relationships. Journal of Marketing, 63(2), 70–87. Geyskens, I., J. Steenkamp, L. Scheer and N. Kumar (1996). The effects of trust and interdependence on relationship commitment: A trans-Atlantic study. International Journal of Research in Marketing, 13(4), 303–317. Gronroos, C. (1990). Service Management and Marketing. Managing the Moments of Truth in Service Competition. Lexington Books and Macmillan Inc. Gronroos, C. (1994). Quo Vadis, marketing? Toward a relationship marketing paradigm. Journal of Marketing Management, 10, 347–360. Gronroos, C. (1995). Relationship marketing: The strategy continuum. Journal of the Academy of Marketing Science, 23(4), 252–254. Gummesson, E. (1994). Making relationship marketing operational. International Journal of Service Industry Management, 5(5), 5–20. Gummesson, E. (1998). Implementation requires a relationship marketing paradigm. Journal of Academy of Marketing Science, 26(3), 242–249. Gummesson, E., U. Lehtinen and C. Gronroos (1997). Comment on Nordic perspectives on relationship marketing. European Journal of Marketing, 31(1), 10–16. Haber, S. and M. Lerner (1998). Correlates of tourism satisfaction. Annals of Tourism Research, 26(1), 197–201. Hair, J., R. Anderson, R. Tathan and W. Black (1998). Multivariate Data Analysis, 5th Ed. Prentice Hall International, Inc. Hennig-Thurau, T., K. Gwinner and D. Gremler (2002). Understanding relationship marketing outcomes: An integration of relational beneﬁts and relationship quality. Journal of Service Research, 4(3), 230–247. Kozak, M. and M. Rimmington (2000). Tourist satisfaction with Mallorca, Spain, as an off-season holiday destination. Journal of Travel Research, 38, 260–269.

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Appendix 1: Final Scales Understanding needs (Cronbach’s Alpha: 0.8636) B1.1 — The spa is concerned and makes an effort to know what I need B1.2 — The spa is able to identify my needs B1.3 — The spa is able to offer the services I want B1.4 — The spa has equipment which is appropriate for my needs B1.5 — The techniques employed in the spa correspond to my needs

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Relationship with customers (Cronbach’s Alpha: 0.8726) B2.1 — The spa often communicates with its bathers B2.2 — The endeavors to deepen relations with its bathers B2.3 — The spa makes an effort to make its bathers feel at home B2.6 — My relationship with this spa is good B3.13 — There is a good employee-customer relationship Internal Marketing (Cronbach’s Alpha: 0.8801) B3.1 — The staff is considerate to me B3.3 — The staff resolves any situation or problem that comes up B3.4 — The staff know what they are doing very well B3.14 — The staff is concerned with customer satisfaction Interactive Marketing (Cronbach’s Alpha: 0.8849) B5.1 — The spa asks for our advice in order to improve its services B5.2 — The spa encourages its bathers to make suggestions B5.3 — The spa services reply quickly to questions posed by its bathers B5.4 — Those responsible for the spa consider bathers’ opinions to improve service B5.5 — I like to exchange ideas with spa staff regarding aspects of how services operate B5.6 — I suggest changes whenever the service does not meet my expectations Personalisation (Cronbach’s Alpha: 0.7564) B3.2 — The staff recognises me and knows my name B3.5 — The staff always calls me by my name B1.6 — The organisation is able to adjust its services and techniques to my needs B3.11 — The staff deals with each customer in a personalised manner Intangible Quality (Cronbach’s Alpha: 0.8907) B4.3 — Facilities are very clean and hygienic B3.7 — The staff do their job well right from the ﬁrst time B4.4 — The spa provides a fast and effective service B3.8 — The staff wear uniforms and have a good appearance B3.9 — The staff treat customers in a courteous and friendly manner B4.6 — Wearing a dressing gown and slippers in the treatment area contributes towards better service B3.12 — The staff clearly informs customers of the characteristics of the service Tangible Quality (Cronbach’s Alpha: 0.9180) B4.1 — The spa has modern equipment B4.2 — The spa facilities are visually attractive Satisfaction (Cronbach’s Alpha: 0.9015) B6.1 — I am very satisﬁed with the service at this spa B6.2 — My choice of this spa was right B6.3 — Coming to the spa has given me a great deal of satisfaction B6.4 — Coming to this spa has been a good experience B6.5 — Coming to this spa has exceeded my expectations

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Trust (Cronbach’s Alpha: 0.9316) B7.1 — I know what I am going to ﬁnd when I enter the spa B7.2 — I can trust the staff at this spa entirely B7.3 — I feel I can trust the services at this spa B7.4 — I trust that the treatments prescribed are the right ones for my situation B7.5 — I consider the money I spend at this spa well spent B7.7 — Promises made by the people at this spa (directors, doctors and staff) are trustworthy Commitment (Cronbach’s Alpha: 0.9269) B7.8 — My relationship with this spa is something I want to keep B7.9 — I believe that the organisation makes an effort for me to keep coming to this spa B7.10 — I worry about the long-term success of this spa B7.11 — I am proud to come to this spa B7.12 — Friendship with the staff makes me feel good B7.13 — I defend this spa when someone criticises it Loyalty (Cronbach’s Alpha: 0.8847) B6.6 — I intend to keep coming to this spa in coming years B6.7 — I usually speak well of this spa when I talk to other people B6.8 — I recommend this spa to my family and friends Environment 1 — Spa Activities (Cronbach’s Alpha: 0.8402) C1.3 — There are places that are suited to participating in various sports activities C1.2 — There is easy Access to cultural and recreational activities Environment 2 — Nature (Cronbach’s Alpha: 0.6264) C1.1 — This spa is situated in beautiful natural surroundings C1.11 — This location is peaceful Environment 3 — Local Services (Cronbach’s Alpha: 0.5857) C1.10 — This location is very clean C1.9 — This location has good support structures (banks, pharmacies, shops and other services) C1.7 — This spa is easy to reach (by road or other means) Environment 4 — Security (Cronbach’s Alpha: 0.5636) C1.4 — There is parking at this spa C1.8 — There is too much trafﬁc at this location (R) C1.6 — There is security at this location

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8 SUPERMARKET SITE ASSESSMENT AND THE IMPORTANCE OF SPATIAL ANALYSIS DATA Armando B. Mendes∗ CEEAplA and Mathematical Department, Azores University R. da Mãe de Deus, 9501-801 Ponta Delgada, Portugal [email protected]

Margarida G. M. S. Cardoso Department of Quantitative Methods, ISCTE, Business School Av. das Forças Armadas, 1649-026 Lisboa, Portugal [email protected]

Rui Carvalho Oliveira CESUR, Instituto Superior Técnico, Lisbon Technical University Av. Rovisco Pais, 1049-001 Lisboa, Portugal [email protected] Received February 2006 Accepted February 2006 The work presented in this paper is part of a larger project aimed at the supermarket site assessment problem, where a 3-step method for stores’ site turnover forecast is proposed. Neighbourhood delimitation techniques are used to deal with demographic and competition data related to each supermarket. Three alternative delimitation techniques and two allocation procedures are compared. Results are evaluated based on the proportion of sales turnover variance explained by the alternative predictors. ∗ Corresponding

author. 171

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A. B. Mendes, M. G. M. S. Cardoso & R. C. Oliveira Finally, Dominance Analysis is used to compare the relative importance of spatial data predictors in site assessment evaluation. As a result, the relevance of spatial analysis predictors clearly emerges being only dominated by the “sales area”.

Keywords: Supermarket site assessment, analogue discriminant site selection, multiplicative weighted Voronoi diagrams, dominance analysis.

1.

Introduction

The importance of the retail sector in Europe is well established. It is one of the biggest employers and in the 15 countries of the European Union the global value of sales turnover was 111.5 billions euros in 2000. Non specialised grocery retail such as supermarkets and hypermarkets are responsible for 85.4% of the total sales (Eurostat, 2003). In spite of the great heterogeneity observed across the different European countries, several of these countries such as Germany, Spain and Italy (see Figure 1) suffered a similar fate: after an unprecedented period of hypermarkets growth since the late 1970s, both in number and market share, it is now clear that hypermarket activity has slowed down signiﬁcantly in contrast to the small to medium supermarkets (chain outlets including discount and hard discount chains), which nowadays enjoy a better dynamism (Eurostat, 2001). Several authors (e.g., Birkin et al., 2002; Dawson, 2000; Seth and Randall, 1999) identify factors such as increasing consumer mobility, 100% 18%

11% 21%

17%

13%

24%

19% 27%

21%

10%

19% 36%

15% 11%

29%

Italy

Spain

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60%

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48%

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17%

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39%

Germany

Portugal

Austria

20%

5%

4%

5%

1998 (4.808)

2002 (4.409)

10%

6%

2002 (4.663)

11%

20% 18%

1998 (6.154)

25%

1998 (7.337)

1998 (70.400)

18%

2002 (6.249)

24%

15% 12%

1998 (74.048)

2002 (102.204)

14%

33%

19%

9%

29%

18% 34%

Hipers

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19%

20%

2002 (56.913)

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Big Supers

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2002 (60.000)

Small Supers

19%

11% 10%

17%

Free Service

18%

2002 (23.742)

23%

1998 (29.179)

Traditional

1998 (149.292)

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0%

Norway

Figure 1. Market share for 1998 and 2002 by food outlet type in several European Countries. Source: A.C. Nielsen Portugal. Total number of stores in brackets.

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increasing electronic commerce, changing household size, concentration of market power, home market saturation, and changes in planning legislation to justify the new trends in retailing. In Portugal, market share data shows that since 1996 the supermarkets are the only ones to grow simultaneously in the number of outlets and in the volume of sales. In 1997 the supermarkets obtained market leadership and consolidated its expansion strategy. Subsequently, more demanding consumers force the retail groups to invest in smaller stores, in a proximity and quality of goods and services strategy. Several authors agree that the future of the small to medium supermarket looks promising. Birkin et al. (2002) considers that in the near future, a signiﬁcant growth (or return) of this type of stores in Europe, mainly by means of franchising, can be anticipated. On the other hand, Dawson (2000) integrates this growth of smaller grocery stores in a multi-format strategy used by the largest European retail groups, a trend already very common in the United States. But, the pressures that the grocery chain supermarkets face are such that the location decisions cannot be neglectful. Investment in smaller stores has a longer run return as well as smaller economies of scale, which forces careful decision-making (McGoldrick, 2000; Salvaneschi, 1996). The stores represent locations where signiﬁcant volumes of capital are invested and, once taken, the location decisions are difﬁcult to change. In this way, companies cannot continue to make decisions with relation to marketing mix’s fourth P (of place) based on “gut feels” (Gilbert, 2002). Studies like the ones presented by Pioch and Byrom (2004) and Jones et al. (2003) conﬁrm the need for a good location, especially in standardised services with less personalised attendance, as is the case of supermarket multi-store chains. In this paper, a 3-step methodology for new supermarket site assessment is presented based on data analysis methods and using spatial data analysis. The 3-step method comprises a ﬁrst step which yields the constitution of analogue groups of existent supermarkets, using a clustering procedure. In the second step, classiﬁcation trees are used to derive rules necessary to classify new stores into speciﬁc analogue groups. Finally, at the third step, we build a linear regression model to forecast new sites’ sales, based on several predictor variables, including dummy variables referred to the analogue groups. In all these steps many variable types are used for model estimation and validation. These variables are collected using surveys, a mystery shopping

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program, competition location, and georeferenced demographic data. To include this last type of data, in a point location study, inﬂuence areas are delimited and allocation procedures deﬁned. These combination of the inﬂuence area delimitation models and allocation procedures is used for predictor calculation and evaluated based on the proportion of sales turnover variance that they are able to explain. In order to assess the relative importance of spatial analysis predictors in contrast to all other types, a dominance analysis study is presented.

2.

GIS and Inﬂuence Area Delimitation Models

The use of Geographical Information Systems (GIS) in order to support location decisions presents several advantages. The power of GIS applications resides in its capacity to integrate information related to geographical position, to manipulate many kinds of attributes, to perform space analyses, and easily produce thematic maps and other data visualisations (Church, 2002). In this way, GIS applications make possible the spatial analysis of locations integrating demographic variables, trip extent, real state data, and competition as well as customers’ locations. Other advantages are related with the easiness of modelling accessibilities and the growing readiness of road networks and geodemographic data. Although some analysts continue to delineate inﬂuence areas by simple direct observation of the customers’ distribution in the space of analogue supermarkets, the presence of GIS software in the companies has been changing this scenario. Among the simplest methods are buffers or circumferences with an appropriate radius and polygons deﬁned by shortest path algorithms (SPA) over a street network (e.g., Boots, 2002; Birkin et al., 2002; McMullin, 2000). In this article, we also suggest the use of Multiplicative Weighted Voronoi Diagrams (MWVD) ﬁrst and second order. The latter model allows, simultaneously, the integration of the supermarket attractivity and the competition in the store proximities (Boots and South, 1997). Although the Voronoi diagrams are traditionally attributed to pioneer mathematicians like Georges Voronoï (1908) and Peter Gustav Lejeune Dirichlet (1850), they have been discovered and rediscovered several times in the history of science. Actually, they can be found in part III of the Principia Philosophiae and in the treatment of cosmic fragmentation of René Descartes, both published in 1644. As examples of Voronoi diagram being rediscovered, Okabe et al. (2000) mention many cases in domains as

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crystallography, meteorology, geography, and ecology. At present, there is an impressive number of published works on algorithms and applications (see, for example, Okabe et al., 2000 or Berg et al., 2000). Concerning multiplicative Voronoi diagrams in the characterisation of proximity elements in a group of supermarket locations, Boots and South (1997) present a very complete work. Although older references can be found (see, for instance, Shieh, 1985), in the aforementioned paper a thorough vision on the theme is presented, using Voronoi diagrams for descriptive and prescriptive proposes. In this application the Voronoi diagrams are used in the characterisation of the proximity of a group of P = {p1 , p2 , . . . , pn } points in the space (with 2 ≤ n < ∞), known as the point generator group, corresponding to supermarkets. If the proximity function is the Euclidian distance, the partition will result in a series of n polygons known as Voronoi polygons (Okabe et al., 2000). Each polygon [V(pj )] generated by point pj with coordinates xj is deﬁned by: (1) V(pj ) = {x : x − xj ≤ x − xk , ∀k = j ∈ P} where k is, in turn, all other elements of the generator group. The set of all polygons V = {V(p1 ), V(p2 ), . . . , V(pj ), . . . , V(pn )} compose an Ordinary Voronoi Diagram (OVD). This diagram can be deﬁned as a space partition where each point in the space associates to the closest element of the generator group and so V(pj ) contains all the points closest to pj than to any other element of the generator group. However, this very simple model regards two stores at the same Euclidian distance as equally attractive for a potential customer. These are very simple models that can be approximately valid for similar stores in densely populated areas, without geographical barriers on walking trips and with homogeneous demographic and psychographic conditions (Berg et al., 2000). Multiplicative Weighted Voronoi Diagrams (MWVD) are deﬁned in a similar way, associating to each point of the generating group a positive weight (wj ) quantifying its attractivity, and being a function of the supermarket’s characteristics and the site. The distance function (dwj ) is given, in this case, by: (2) dwj (p, pj ) = (1/wj ) · x − xj , wj > 0 Thus, each MWVD is deﬁned by: V(pj ) = {x : dwj (p, pj ) ≤ dwk (p, pk ),

∀k = j ∈ P}

(3)

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In this paper preference is given to multiplicative Voronoi diagrams over others as the additively weighted Voronoi diagrams (see Okabe et al., 2000), since they can be related to gravitational models. Modelling the supply and demand for food, representing the supply by the point generator group, the Voronoi polygon associated to each element of the resulting partition is regarded as the inﬂuence area of the respective generating element, assigning to this area all the points in the space that maximise the utility function: (4) Uij = Aαj xi − xj and α > 0 This utility function is a particular case of the following expression for the generic utility function linking the supply points (j), in this case supermarkets, to demand points (i), in this case potential customers or points in the space: −β (5) and α, β ≥ 0, dij = xi − xj Uij = Aαj dij where Aj is the attractivity of the supply point j, dij is any kind of distance, travel time or trip cost between the supply point i and the demand j, and α, β are parameters. Gravitational models are space interaction models derived from a ratio between the utility function (5) for a supply point over the total of all utilities for the competing supply points. These models are used as an estimate of the market share of the supply point j or as an impact model. The MWVD’s use the same utility function to accomplish the space partition since the weight corresponds to the store attractivity power α, and β is ﬁxed to one. Thus, the MWVD assumes that the customers value the proximity in the choice of the store (as in the OVD) but also introduce the attractivity concept. Thus, the store choice process depends on a trade-off between the proximity and the store attractivity, as in the gravitational models. These models can still be extended if we consider that customers can frequent k > 1 supermarkets or generating points, simultaneously. The use of Order-k Multiplicative Weighted Voronoi Diagrams (OkMWVD) come from evidence found in the surveys where a large majority of customers declare to simultaneously frequent other stores, mainly hypermarkets and superstores. Consider all the subsets of k stores (generator points) among the n existent: P = {P1 (k), . . . , Pi (k), . . . , Pl (k)} with l = n Ck . Consider also one of these groups Pi (k) = {pi1 , pi2 , . . . , pik }, so the OkMWVD [V(Pi (k)] is: V(Pi (k)) = {x : maxpj {dwj (p, pj ), pj ∈ Pi (k)} ≤ minpr {dwr (p, pr ), pr ∈ P\Pi (k)}} (6) which relates any point of the space with the k nearby more attractive stores.

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Several assumptions are enumerated by Okabe and Suzuki (1997) which must be keep in mind when these models are applied to a particular location problem: • n competing stores located in the same planar and ﬁnite region; • all clients inside a Voronoi Polygon endorse only one store (in MWVD), or k stores (in OkMWVD) with probabilities proportional to the ratio of utilities; • the utility function Uij for the store j and customer i is an inverse function of the Euclidian distance between the two and a direct function of the store attractivity; • the weight function wj ( > 0) is supposed to be derived from variables related to the site and the particular store as store size, accessibilities, etc. Several of these assumptions are not considered in shortest path polygons. For instance, non planar areas can be modelled by distinct average velocities in some street fragments. But, shortest path algorithms also have disadvantages. They are adequate for car trips but unsatisfactory for walking trips, where accessibility networks are difﬁcult or impossible to deﬁne. In surveys more than 60% of the shopping trips are walking trips, and in some supermarket segments this percentage is much higher. Shortest path polygons also do not include any competition mechanism, and polygons from competitive shops frequently overlap, as seen in Figure 2. An intermediate situation between the mutual disjunctive tessellation in the MWVD and the strong overlap in shortest path polygons are the O2MWVD. These Voronoi polygons deﬁne inﬂuence areas as the spatial union among all polygons allocated to a particular supermarket, and result in the overlap with other nearby stores as is evident from Figure 2. The O2MWVD also present the advantage of frequently deﬁning larger inﬂuence areas over the MWVD that, some times, deﬁne too small polygons. As none of the mentioned models for inﬂuence area deﬁnition appear to be theoretically superior to the others, all of them are considered and compared in this paper.

3.

Supermarkets’ Site Assessment Data

3.1. Empirical framework Several attributes are relevant for the problem of supermarket site assessment. A data framework is suggested in Figure 3 where the data is classiﬁed

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Figure 2. Two and a half minutes shortest path polygons (left) and multiplicative weighted Voronoi diagrams, ﬁrst (centre) and second order (right), examples. (Stores as points and inﬂuence areas in grey. First two maps also show the road network and the third the ﬁrst order MWVD).

Data Collected

sales area retail composition

Site and Store Attributes

store configuration

chain image \ services site accessibility

geographic variables site configuration

Influence Area Characterization

Clients Characteristics

current and future expected competition current and future sales potential characterisation of the outlet \ client relation socioeconomic client characterisation

competition sales area competition quality influence area size demographic data average buy client preferences client demography

competition and geo.data

store size

Examples

census data

Variable Type

mystery shopping program

Group

in shop surveys

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Figure 3. Classiﬁcation of assessment location and site evaluation explanatory variables and data collected.

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in three groups namely: location and supermarket attributes, inﬂuence area characterisation and clients’ characteristics. This empirical framework, is intended for store and site evaluation of small to medium dimension supermarkets belonging to a retail chain, and is based in the authors’ experience and in an extensive literature review. The theoretical importance of demographic data (census data) and other spatial analysis data (competition and geographical data) is clearly marked on Figure 3. Only the store size, store conﬁguration and clients’ characteristics are not covered by this type of data. In fact, clients’ characteristics are the most relevant for chain supermarkets, as the store conﬁguration, and in some way the store size, tends to be very similar inside a chain. In spite of their relevance in store clustering and characterisation, the clients’ characteristics cannot be used in new store sales predictions, as they are collected by surveys. To cover all the relevant aspects, a large number of variables were gathered for a grocery chain with 25 supermarkets located in the Lisboa and Porto metropolitan areas. The data collection phase was very time consuming and concerned several different techniques enumerated and explained in a previous work (Mendes and Cardoso, 2006). From the fusion of all data collection procedures, a total of almost 300 variables were obtained, measured mostly in quantitative scales but some mystery shopping attributes are in nominal or ordinal scales.

3.2. Inﬂuence area characterisation In order to include inﬂuence area characterisation attributes in the present supermarket assessment study, a spatial data analysis strategy must be deﬁned. Quantitative variables from the 2001 Portuguese national geographical census are available which include high quality data ready to use in a Geographical Information System. On the other hand, inﬂuence areas polygons may be constructed using the already referred delimitation methods, speciﬁcally SPA (shortest path algorithm), MWVD and O2MWVD (1st and 2nd order Multiplicative Weighted Voronoi Diagrams). The strategy suggested in this work comprises the spatial intersection of the national geographical census data, georeferenced to polygon shapes known as statistical sections, with the delimited inﬂuence areas polygons. Taking into account that statistical sections may be divided by the inﬂuence area, an allocation procedure must be deﬁned which determines how to

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allocate statistical sections (or fractions) to inﬂuence areas. In this section, we propose and evaluate two allocation criteria combined with the mentioned inﬂuence area delimitation models. For the inﬂuence area parameters estimation in actual problems we use an empirical rule, whenever possible. The rule considers that approximately 80% of the customer’s trip origins should be inside the inﬂuence area polygon (Salvaneschi, 1996). The methodology applied maximised the number of shops obeying this rule. In order to deﬁne SPA polygons we rely on street network information and estimates of car mean velocities. The SPA parameter is the trip limit time. Using the 80% rule and experts’ opinion we deﬁne a 2 1/2 minutes threshold, which corresponds to approximately 10 minutes walking trips. For competing hypermarket identiﬁcation a 15 minutes car trip threshold were considered more appropriate as this large retail stores have considerably bigger attraction power. For inﬂuence area delimitation by Voronoi diagrams, a database with the location of more than 600 grocery outlets in Portugal is used. This data was collected in coordination with the mystery shopping program and by recording GPS coordinates outside the store door. The scale parameter α, from Equation (4), was estimated using the 80% rule leading to a square root function. It should be noted that the diagrams are very sensitive to variations in this parameter, as can be seen in Figure 4. For the store attraction function a linear regression method is used, using annual sales for the supermarket as dependent variable, and explanatory variables as “sales area”, “number of years in operation” and dummy variables for the classiﬁcation of the location as “city centre”, and the chain

Figure 4. MWVD with α = 2 (left), α = 1/2 (centre), and α = 1/10 (right) which is very alike the OVD.

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insignia. In spite of the limited number of explanatory variables available for all 600 stores, the obtained regression explains 48% of the sales variability. For the statistical sections allocation procedure, authors as Cowen et al. (2000) and McMullin (2000) use the fraction of the statistical section covered by the inﬂuence area as a weight in a weighted average, as indicated in Equation (7). This procedure implies a uniform distribution of the data variable in the statistical section. m statistical section area i covered by the inﬂuence area total statistical section area i i=1 statistical section i × related variable

(7)

Another available alternative is using the same weight in an inclusion decision rule for the statistical section. The 50% cut-off value is used to include statistical sections with higher fractions of area covered, and to exclude sections with lower fractions. This procedure has the disadvantage of distorting the original inﬂuence areas, as can be seen in the ﬁrst two diagrams in Figure 2, comparing shaded areas with inﬂuence area polygons. But the same procedure results in inﬂuence areas adjusted to the statistical sections, which is an indirect way of including geographical barriers in inﬂuence areas, as the statistical sections are deﬁned by the National Statistics Institute considering these barriers to human movement. As a result from inﬂuence area delimitation and statistical sections’ allocation method, we allow the deﬁnition of several relevant attributes as percentages of totals and densities per hectare. Competition variables such as the “sum of store areas from competitors”, “sum of competitor’s store areas weighted by the inverse of shortest path distances”, “number of hypermarkets up to 15 minutes” or “area of Voronoi polygon” are then made available. For this calculation we also deﬁne “competitor” as a store that shares borders with the supermarket (for Voronoi polygons) or, simply, all stores inside the polygon (for shortest path areas). In order to evaluate the alternative delimitation and allocation procedures, we use a linear regression based methodology. Thus, we derive R2 referred to the proportion of the supermarket annual sales (per unit of sales area) explained by attributes which are yield from each combination of inﬂuence area delimitation and allocation methods. The best results are presented in Table 1.

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Table 1. Adjusted R2 for explanatory regressions of the annual sales per sales area.a (The sign of the estimated coefﬁcients is negative for the italicised variables). DELIMITATION MODEL

ALLOCATION PROCEDURE WEIGHTED AVERAGE Adjusted R2 = 52% (“Number of non classical households”, “Number of residents less than 5 years old”, “Percentage of families with at least two children or grandchildren not married”)

DECISION RULE Adjusted R2 = 65% (“Number of classical families with children less than 5 years old”, “Percentage of non classical households”, “Percentage of women more than 65 years old”, “Density of buildings built between 1996 and 2001”)

Order 1 MWVD

Adjusted R2 = 59% (“Percentage of non classical households”, “Percentage of resident individuals employed in the ﬁrst and second economic sectors”, “Number of buildings with 1 or 2 ﬂoors”, “Density of owned classical households”)

Adjusted R2 = 66% (“Density of more than 65 years old residents”,“Percentage of individuals without any economic activity”, “Number of classical buildings”)

Order 2 MWVD

Adjusted R2 = 53% (“Percentage of non classical households”, “Percentage of women between 10 and 24 years old”, “Percentage of families with at least two children or grandchildren not married”, “Percentage of individuals working in the residential council”, “Number of buildings with more than 5 ﬂoors”)

Adjusted R2 = 67% (“Percentage of non classical households”, “Density of buildings built between 1996 and 2001”, “Percentage of individuals working in the residential council”)

Shortest Path Algorithm

a Stepwise

Linear Regressions using 5% and 10% test F in and out parameters respectively. All the models are signiﬁcant to 1% F test and all the estimated coefﬁcients are signiﬁcant by a 5% t test.

Although the adjusted R2 values are low (inﬂuence area characterisation attributes are not enough for supermarkets’ assessment), all the models are signiﬁcant (F test for 1% signiﬁcance level). Results are better when referred to the decision rule allocation method, but they do not indicate a better inﬂuence area delimitation method. As a result, we use of all alternative area delimitation procedures in the following analysis for supermarkets’ assessment.

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183

The 3-Step Method for Site Evaluation

Site assessment or site evaluation can be deﬁned as the assessment of potential locations and the selection of alternative site locations to maximise the sales of a supermarket chain (Lilien et al., 1992; Davies and Rogers, 1984). Site selection and evaluation comprises a set of different quantitative or non quantitative methodologies and techniques which include management judgment, analogue based models, multicriteria decision analysis, gravitational models, multiple regression analysis, discriminant analysis, supported with spatial data analysis, which are reviewed in Mendes and Themido (2004). In order to evaluate supermarkets’ locations, based on sales forecast for potential sites, we propose a 3-step method, based on data analysis procedures, namely cluster analysis, classiﬁcation trees and linear regression: • Step 1: Analogue groups of existent supermarkets are deﬁned using a clustering procedure (Ward method) and expert knowledge. • Step 2: Classiﬁcation tree models are used to provide the analogue groups’ characterisation as well as propositional rules which allow the classiﬁcation of new stores in one of the analogue groups. • Step 3: Linear regression models yield new site sales forecast based on several predictor variables including dummy variables for analogue groups encoding. Figure 5 depicts the 3-step method, data gathered for model estimation and data necessary for new site annual sales forecast. The data in Figure 3 is used for model estimation in the 3-step methodology. Not all data could be used in all steps. For instance, the chosen method for analogue group deﬁnition used only metric variables. In spite of that, cluster characterisation involved all the variables collected. Rule induction could use variables in any scale of measure, but because rules must include only variables that can be measured for potential new sites, all survey variables are discarded. Many of the mystery shopping attributes are also discarded as in-store characteristics. Only in-site visible characteristics are included, such as the available sales area, accessibilities, site visibility, nearby anchors, and other related with competition and inﬂuence area characterisation. For the linear regression model, another restriction applies, as the non metric variables are difﬁcult to include and hinders the process of variable

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Potential New Site Data Demographic and Geographical Data

In site visible characteristics st

nd

1 step Supermarket Analogue Groups

Ward hierarchical cluster analysis incorporating expert knowledge

In Shop Surveys Data for Model Estimation

2 step Induction of Classification Rules

Analogue outlet segments

Classification trees using several different algorithms

rd

3 step New Site Sales Forecast

Logical classification rules

Linear regression model including dummy variables for the analogue groups

Annual sales forecast

Mystery Shopping Program Annual Sales Data

Demographic and Geographical Data

Figure 5. The 3-step method for site evaluation.

selection by stepwise methods. In this way demographic and competition variables, resulting from spatial analysis procedures, are all metric and easy to measure for new potential sites, and so they acquire a particular relevance.

4.1.

Step 1 — Supermarket analogue groups

Step 1 involved the experts’ knowledge in the base clustering variables selection as well in the appreciation of the results from the successive hierarchical clustering procedures tested. The process was reinitialised several times with new base clustering variables when the clusters did not correspond to the expert’s expectations. In Figure 6 these clusters are depicted along with labels based on the characterisation presented in Mendes and Cardoso (2005). The two supermarkets in the bottom of the chart are identiﬁed as outliers. Both had been previously picked up by retailing experts as these supermarkets had poor performances and dreadful locations. In shop surveys were performed in years 2000 and 2002, but in the latter year the inquiry was only done in some of the supermarkets, so a constant value are considered for plotting proposes. Empty squares represent six new supermarkets in 2002.

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annual store sales turnover for 2000 (circle) and 2002 (square)

big transit stores big stores

transit stores

big neighbourhood

intermediate stores

small neighbourhood

percentage of exclusive trips in surveys

Figure 6. Step 1 analogue supermarket clusters by the Ward method showing two years of data. (Empty squares represent new supermarkets in the two year period).

Data used to characterise the six groups resulting from the clustering analysis are compared and the relative importance of spatial analysis data is evaluated by means of p-values associated with non-parametric Kruskal-Wallis tests. For nominal variables Chi-square tests are used. Although several types of variables are present in the rank, “inﬂuence area characterisation” related variables emerge as the largest group including nine among the 15 with the lower p-values.

4.2. Step 2 — Induction of classiﬁcation rules In Step 2, classiﬁcation rules are induced. The objective is the identiﬁcation of variables and propositional rules, in order to discriminate among the different groups of stores, for classiﬁcation of new potential sites in an analogue group. Several logical propositional rules are induced from different algorithms, and the best rules are kept. The algorithms used are CART — Classiﬁcation And Regression Trees (Breiman et al., 1984), CHAID — CHi-squared Automatic Interaction Detector (Kass, 1980; Biggs and Suen, 1991) and QUEST — Quick Unbiased Efﬁcient Statistical Tree (Loh and Shih, 1997). The three

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algorithms can be distinguished by the diversity measure used and the method to select the discriminant variable and respective partition condition. For comparing and evaluating the rules induced we propose the precision index, presented in expression (8). In this expression, the precision index for supermarket j is represented by IPj , leaveOneOut represents the estimate of the classiﬁcation error by the leave-one-out method for the model (a), the %hits the “hits percentage in the leaf” regarding the propositional rule (ar ) and %group the “percentage of stores of the group in the leaf” for the same rule. β , 0 ≤ α ≤ 1, β ≥ 1 IPj = 1 − leaveOneOuta × %hitsαar × %group1−α ar (8) The estimation of parameters α and β was carried out by maximising the number of correct classiﬁcations for estimation data. The leave-one-out method, a particular case of jackknife validation or the U-method (Crask and Perreault, 1977), is a resampling method that classiﬁes each one of the stores according to a tree built with the remaining ones. The error estimate is the number of erroneous classiﬁcations over the total number of trees built. This estimation is considered precise even with a reduced number of observations (Lattin et al., 2003; Gentle, 2002). As leafs are attributed to the modal group and the number of shops per group is low, it is desirable that only one leaf is attributed to any group, being the “percentage of stores of the group in the leaf” (i.e., the percentage of stores of a group identiﬁed by the propositional rule) a measure of the dispersion of the group for several leafs. On the other hand, the “hits percentage in the leaf” measures the degree of purity or the homogeneity of a leaf, which is intended to maximisation. Measuring rule importance by this kind of functions is common in machine learning literature (Quinlan, 1993) and in some segmentation literature (Cardoso and Moutinho, 2003). In Table 2 a ranking of variables included in classiﬁcation rules are presented based on the higher values for the precision index. Note that the same rule can be responsible for two or more leaf nodes. In this case only the best ranked leaf is presented. The importance of spatial analysis data in supermarket segmentation and classiﬁcation is very well established by the ranking in Table 2 because in any of them, variables of this type are always present.

4.3. Step 3 — New site sales forecast and dominance analysis In this section the role of variables selected by stepwise regression analysis for new site sales forecast (Figure 5) is evaluated and compared. Among

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Supermarket Site Assessment Table 2.

187

Variables from rules ranked by the precision index for α = 0.4 and β = 1.5.

VARIABLES AND ORDER IN RULE ja

MODELb

IPj

percentage of resident women between 5 to 9 years old (SPA) > number of owned classical households (SPA) > number of classical households with 3 to 4 rooms (MWVD) > public transportation centre and schools as major anchors for passage trafﬁc

CART

0.415

percentage of resident women between 5 to 9 years old (SPA) > number of owned classical households (SPA) > number of classical households with 3 to 4 rooms (MWVD) > number of non classical households (O2MWVD)

CART

0.415

density of buildings built between 1996 and 2001 (SPA)

CHAID

0.381

density of buildings built between 1996 and 2001 (SPA) > parking facilities near supermarket > number of owned classical households (SPA) > evaluation of on foot supermarket access in relation to nearby competition > number of classical buildings (MWVD)

CHAID

0.381

density of buildings built between 1996 and 2001 (SPA) > parking facilities near supermarket > number of owned classical households (SPA) > evaluation of on foot supermarket access in relation to nearby competition

CHAID

0.354

percentage of resident women between 5 to 9 years old (SPA) > number of owned classical households (SPA)

CART

0.332

percentage of resident women between 5 to 9 years old (SPA)

CART

0.322

density of buildings built between 1996 and 2001 (SPA) > parking facilities near supermarket > number of owned classical households (SPA)

CHAID

0.318

density of buildings built between 1996 and 2001 (SPA) > sum of competition store area weighted by SPA (MWVD) > percentage of families with children and grandchildren (SPA) > number of households with more than 4 persons in the family (O2MWVD)

QUEST

0.282

density of buildings built between 1996 and 2001 (SPA) > sum of competition store area weighted by SPA (MWVD) > percentage of families with children or grandchildren (SPA) > area of Voronoi polygon (MWVD)

QUEST

0.245

density of buildings built between 1996 and 2001 (SPA) > sum of competition sales area weighted by SPA (MWVD)

QUEST

0.211

a MWVD

— Multiplicative Weighted Voronoi Diagrams, O2MWVD — Order 2 Multiplicative Weighted Voronoi Diagrams, SPA — Shortest Path Algorithms. b The model stand for the algorithm as it is decided to choose one model for which algorithm.

many regression models ﬁtted to the data, the better ones are presented in Table 3. As regression analysis is a parametric method, it is recognised that the deviations or residues are adjusted in a satisfactory way to a normal distribution of null average and constant variance, and the deviations can be considered independent to each other.

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Table 3. Linear regressions for the chain supermarkets with and without analogue groups (clusters). MODELSa

WITHOUT CLUSTERb

WITH CLUSTERS ALL STORES

NO OUTLIERS

64.2%

85.1%

93.7%

Degrees of Freedom

19

15

13

F Statistic Value

14

16

37

Mean Quadratic Deviation

9,160

4,725

1,103

Regression Quality Indicators Adjusted Correlat. Coefﬁcient

Mean Absolute Deviation

376

242

117

Mean Relative Deviation

11%

13%

3.3%

10

15

19

Condition Index Estimated Coefﬁcients (Standard Constant

Deviation)c 230 (100)

49.4 (8.9)

125 (50)

0.520 (0.093)

0.265 (0.099)

0.330 (0.054)

—

0.0495 (0.0180)

0.0416 (0.0097)

Number of Classical Families with more than 4 Persons (SPA)

0.169 (0.083)

—

—

Number of Discount Stores in the Proximities

−85 (40)

—

—

Density of Buildings Built between 1996 and 2001 (SPA)

—

3.4 (1.3)

3.26 (0.87)

Area of Voronoi Polygon (MWVD)

—

0.200 (0.097)

0.188 (0.062)

Big Neighbourhoodd

n.a.

339 (60)

231 (35)

Storesd

n.a.

309 (59)

196 (95)

n.a.

269 (76)

145 (44)

n.a.

170 (65)

64 (38)

n.a.

605 (81)

465 (47)

Sales Area in Square Meters Number of Owned Classical Households (MWVD)

Intermediate Big Storesd Transit

Storesd

Big Transit Storesd a All

the models are signiﬁcant to 1% level by the F test and the estimated coefﬁcients are signiﬁcant to the 5% level by the t test. b The best model without any dummy variable. Several dependent variables and functional forms are tested. Two outliers are excluded. c MWVD — Multiplicative Weighted Voronoi Diagrams, O2MWVD — Order 2 Multiplicative Weighted Voronoi diagrams, SPA — shortest path algorithms. d See Mendes and Cardoso (2005) for the characterisation of analogue groups.

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Considering the low degrees of freedom, overﬁtting is also tested using leaving-one-out validation. In this case the method is applied determining a forecast for a supermarket after estimating the parameters of the model based in the remaining ones. The deviations of these forecasts relatively to sales values resulted in 80.3% estimate for the adjusted multiple correlation coefﬁcient to the best model. Although this value is considerably inferior to the value presented in Table 3, it is still a high value, corresponding to a very good evaluation of the regression model. The results presented in Table 3 illustrate the need for segmenting the existing supermarkets. In fact, the models including analogue groups coded as dummy variables are very well ﬁtted by more than 20% R2 difference for the best model without these dummy variables. The two identiﬁed outliers strongly inﬂuence the results as noted in the mean relative deviation for the model with all stores. In spite of that fact, the two best models show good robustness since they use exactly the same predictor variables with little deviations in the estimated coefﬁcients with the exception of the analogue group’s dummy variables. Although only a reduced number of predictors are incorporated in the model, they are very well distributed among the classes of relevant variables presented in the Figure 3. Actually, they include site and supermarket characteristic variables (“sales area”), competition (“area of Voronoi polygon”), sales potential (“number of owned classical households”) and dynamics (“density of buildings built between 1996 and 2001”). In spite of the abundance of alternative predictor variables, the presence of meaningful key variables in the models is an indicator of robustness (Themido et al., 1998). Typically, the relative importance of predictors is assessed by simply comparing their standardised regression coefﬁcients and (less often) by examining squared semipartial correlations. However, when predictors are correlated, it is recognised that regression coefﬁcients cannot be used to unambiguously explain variance shared by two or more predictors. Dominance analysis is an alternative analytic strategy that assesses the relative importance of more than one set of variables to prediction (Azen and Budescu, 2003; Budescu, 1993). This dominance analysis approach provides a general methodological framework comparable to the average squared semipartial correlations across all combinations of predictors, advocated by Johnson (2000). Azen and Budescu (2003) deﬁne three levels of dominance. Complete dominance exists between two predictors if additional contribution of one

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predictor to each of the subset models is always greater than that of the other predictor. If the average additional contribution is greater for one predictor than the other, then that predictor is said to conditionally dominate the other. Finally, if the overall average of the additional contribution is greater for one predictor than the other, that predictor is said to generally dominate the other. The three levels of dominance are related to each other in a hierarchical way: complete dominance implies conditional dominance, which in turn, implies general dominance. However, for more than three predictors the converse may not apply. For each dependent variable the dominance analysis proceeds in two steps, following Budescu’s (1993) guidelines. In Step 1 several separate regression equations based on all possible ordering of sets of variables are computed. In Step 2 the average multiple correlation coefﬁcient for each set of variables, across all possible orderings of sets, are ﬁnally computed. Through this process an overall mean is derived that represents the average usefulness of a set of predictors, and is equivalent to the percentage of variance accounted for by each variable set based on the total variance accounted for by the full model (Eby et al., 2003). In Table 4 dominance analysis results are presented for the “best” forecasting regression described in Table 3. Notice that these results are based in adjusted R2 , which is recommended for comparisons between models with different number of predictors. Adjusted R2 yields the same dominance pattern as R2 as there are monotone functions of the model’s error sum of squares (Azen, 2000). The regressions correspond to a constrained dominance analysis as the dummy variables are always included in the models for theoretical reasons. Examining the ﬁrst row of Table 4, one can see that variable “Sales Area” (SA) has a greater contribution than any other variable when enters de model right after de cluster dummy variables, providing some initial evidence that SA is dominant to the other variables. Data from the other rows conﬁrm this assertion for all other initial sets of variables. In fact, “Sales Area” (SA) completely dominates “Owned Households” (OH), which completely dominates “Buildings Built” (BB), which in turn dominates “Voronoi Area” (VA). In spite of this, VA contributes negatively in models with k = 1 and 2, indicating that the additional contribution does not compensate for the reduction of degrees of freedom. In spite of that the 3.7% explained variance increase in the k = 4 model may be relevant for forecasting accuracy.

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Supermarket Site Assessment Table 4.

Constrained dominance analysis for the “best” forecasting regression.

SUBSET MODELSa k = 1 average (clusters)•Sales Area (SA) (clusters)•Owned Households (OH) (clusters)•Buildings Built (BB) (clusters)•Voronoi Area (VA)

ADJUSTED R2 74.9% 81.5% 77.2% 75.1% 73.6%

k = 2 average (clusters)•SA•OH (clusters)•SA•BB (clusters)•SA•VA (clusters)•OH•BB (clusters)•OH•VA (clusters)•BB•VA

87.0% 83.0% 82.2% 78.2% 75.8% 74.3%

k = 3 average (clusters)•SA•OH•BB (clusters)•SA•OH•VA (clusters)•SA•BB•VA (clusters)•OH•BB•VA

90.0% 87.8% 85.9% 77.3%

k = 4 average (clusters)•SA•OH•BB•VA overall average a See

191

ADDITIONAL CONTRIBUTIONS SA 6.7%

OH 2.3% 5.4%

9.8% 7.9% 8.6%

3.1% 2.3%

8.2%

3.3% 7.0% 5.6%

BB 0.2% 1.4% 0.9%

VA –1.3% 0.7% −1.4% −0.8%

0.7% 0.8% 3.0%

–0.7% 0.9% 2.9%

3.7% −0.9%

11.9% 12.0% 11.6%

3.0%

11.8%

5.2%

1.5% 2.7%

1.0% 3.7%

5.9% 7.8% 16.4% 16.4%

7.8%

5.9%

3.7%

10.8%

4.7%

2.4%

0.7%

93.7%

Table 3 for full variable names.

For the regression without dummy variables representing the clusters, which is not constrained, it is also possible to determine complete dominance among the three predictors in the order: “Sales area” > “Number of Classical Families with more than 4 Persons” > “Number of Discount Stores” and for the regression without the identiﬁcation of outliers the results are very similar to the ones presented in Table 4 with an inversion in the ﬁrst two variables: “Owned Households” > “Sales area” > “Buildings Built” > “Voronoi Area”. Note that the difference between the regressions with and without outliers is only two outliers which are included in the ﬁrst and excluded in the last. In this way, we can conclude for the importance of outlier identiﬁcation in regressions models and the high sensibility of adjusted multiple correlation coefﬁcient and consequently dominance analysis to outliers. This is contraditory with bootstrap results presented in Azen and Budescu (2003) where the reproducibility values are very high. This contradiction is probably due to the instability of the regressions performed with very few shops, as can be evaluated from the leave-one-out adjusted multiple correlation coefﬁcient value of 80.3%.

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Discussion and Conclusions

The retailers soon realised the importance of supermarket location, but in order to understand all the aspects of supermarket performance, site locations, and the consumer’s behaviour, were forced to collect enormous amounts of data of various types, such as geographical, demographic, socioeconomic and regarding competition dynamics (Hernández and Bennison, 2000; Themido et al., 1998; Salvaneschi, 1996). In this article we focus on the role of spatial analysis data for site selection and assessment. We use a 3-step approach for site assessment. In Step 1, we obtain analogue groups of existent supermarkets, using a clustering procedure. In Step 2, we classify new supermarkets into the analogue groups. Finally, we build a linear regression model to forecast new sites’ sales, the set of predictors used including dummy variables referred to the analogue groups. The database available includes data collected by in store customer surveys to the existent stores (two different years), a program of mystery shopping intended to record visible aspects of existing stores and new sites, geographical data that endorsed the calculation of competition variables, and census demographic data. In order to derive speciﬁc spatial attributes, we test several delimitation models for inﬂuence areas (shortest path, ﬁrst and second order multiplicative weighted Voronoi diagrams are used) and two procedures to allocate statistical sections (or fractions) to inﬂuence areas. We conclude that the decision rule allocation procedure, i.e., including the entire statistical section if at least 50% of its area is inside the inﬂuence polygon, shows better performance for the present application. Regression results (Step 3) are analysed using dominance analysis in order to derive the relative importance of predictors of supermarkets performance. Dominance analysis starts with a clear deﬁnition of importance and has the advantage of complying with all four theoretical characteristics identiﬁed by LeBreton et al. (2004). These authors identify three conditions where importance measures may be particularly useful and yield different results as compared to standardised regression coefﬁcients: (a) the predictors have a high level of multicollinearity; (b) there are several predictors; and (c) the predictors collectively explain a medium to large proportion of the variance in the dependent variable. For this case, dominance analysis is particularly adequate, and conﬁrms the importance of the empirical variable classiﬁcation suggested in Figure 3.

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The dominance analysis results, and other variable importance measures used for the other two steps, underline the importance of all types of predictors (see Figure 3) and yields the importance of spatial data only surpassed for the “sales area”. This conclusion agrees with the results obtained by others (Themido et al., 1998; Salvaneschi, 1996) and supports the existence of structuring variables or key variables such as “sales area” which should always be considered (see Themido et al., 1998). Although this is not surprising in itself, the formal conﬁrmation, which we obtained, is seldom found in the literature.

References Azen, R. (2000). Inference for predictor comparasions: Dominance analysis and the distribution of R2 differences. Dissertation Abstracts International, B 61/10, 5616. Azen, R. and D. Budescu (2003). The dominance analysis approach for comparing predictors in multiple regression. Psychological Methods, 8(2), 129–148. Berg, M., M. van Kreveld, M. Overmars and O. Schwarzkopf (2000). Computational Geometry: Algorithms and Applications. Berlin: Springer-Verlag. Biggs, D. B. V. and E. Suen (1991). A method of choosing multiway partitions for classiﬁcation and decision trees. Journal of Applied Statistics, 18, 49–62. Birkin, M., G. Clarke and M. Clarke (2002). Retail Geography and Intelligent Network Planning. Chichester, UK: John Wiley & Sons. Boots, B. (2002). Using local statistics for boundary characterization. In B. Boots, A. Okabe and R. Thomas (eds.), Modelling Geographical Systems: Statistical and Computational Applications. Dordrecht, Netherlands: Kluwer Academic Publishers, 33–44. Boots, B. and R. South (1997). Modeling retail trade areas using higher-order, multiplicatively weighted Voronoi diagrams. Journal of Retailing, 73(3), 519–536. Breiman, L., J. H. Friedman, R. A. Olshen and C. J. Stone (1984). Classiﬁcation and Regression Trees. California, USA: Wadsworth International. Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114(3), 542–551. Cardoso, M. G. M. S. and L. Moutinho (2003). A logical type discriminant model for proﬁling a segment structure. Journal of Targeting, Measurement and Analysis for Marketing, 12(1), 27–41. Church, R. L. (2002). Geographical information systems and location science. Computers and Operations Research, 29, 541–562. Cowen, D. J., J. R. Jensen, W. L. Shirley, Y. Zhou and K. Remington (2000). Commercial real estate GIS site evaluation models: Interfaces to ArcView GIS.

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McMullin, S. K. (2000). Where are your customers: Raster based modeling for customer prospecting. In Proceedings of the Annual ESRI International User Conference. ESRI online Library, 795–823. Mendes, A. B. and M. G. M. S. Cardoso (2006). Clustering Supermarkets: The role of experts. Journal of Retailing and Consumer Services, 13(4), 231–247. Mendes, A. B. and I. H. Themido (2004). Multi outlet retail site location assessment: A state of the art. International Transactions in Operations Research, 11(1), 1–18. Okabe, A., B. Boots, K. Sugihara and S. N. Chiu (2000). Spatial Tessellations: Concepts and Applications of Voronoi diagrams. Chichester, UK: John Wiley & Sons. Okabe, A. and A. Suzuki (1997). Locational optimization problems solved through Voronoi diagrams. European Journal of Operational Research, 98(3), 445–456. Pioch, E. and J. Byrom (2004). Small independent retail ﬁrms and locational decisionmaking: Outdoor leisure retailing by the crags. Journal of Small Business and Enterprise Development, 11(2), 222–232. Quinlan, J. R. (1993). C4.5: Programs for Machine Learning. San Mateo, USA: Morgan Kaufmann Publishers. Salvaneschi, L. (1996). Location, Location, Location: How to Select the Best Site for Your Business. Grants Pass, USA: Psi Research — Oasis Press. Seth, A. and G. Randall (1999). The Grocers: The Rise and Rise of the Supermarket Chains. UK: Kogan Page. Shieh, Y.-N. (1985). K.H. Rau and the economic law of market areas. Journal of Regional Science, 25(2), 191–199. Themido, I., A. Quintino and J. Leitão (1998). Modelling the retail sales of gasoline in a Portuguese metropolitan area. International Transactions in Operations Research, 5(2), 89–102. Voronoï (1908). Nouvelles applications des paratrés continus à la théorie des formes quadratiques. Deuxième memoie, recherche sur les parallelloèdres primitif. Journal für die Reine und Angewandte Mathematik, 134, 198–287.

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DOCTORAL RESEARCH NOTES

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9 A FRAMEWORK FOR CORPORATE CRISIS MANAGEMENT: APPLICATION TO SMES IN AUSTRALIA∗ M. Aba-Bulgu Centre for Strategic Economic Studies, Victoria University and MSM Loss Management — Southern 18–22 Thomson Street, South Melbourne, Vic. 3205 Australia [email protected]

Sardar M. N. Islam† Centre for Strategic Economic Studies, Victoria University City Flinders Campus PO Box 14428, Melbourne, Vic. 8001 Australia [email protected] Received July 2004 Accepted March 2006 There are numerous theoretical and empirical models that have been applied in relation to corporate crisis management strategies and practice. However, the application of these models and techniques to small and medium sized business organisations (SMEs) in Australia is not well known. Qualitative and quantitative data were

∗ Revised paper presented at the 3rd International Conference on SMEs in a Global Economy in Kuala Lumpur, Malaysia, 6–7 July 2004. † Corresponding author.

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M. Aba-Bulgu & S. M. N. Islam collected from a sample of small to medium companies in Australia that experienced business interruption as a direct result of damage to their physical assets. The result of the analysis shows that these companies passed through different stages of crisis that require different levels of ﬁnancial and strategic management skills and techniques. In this research a general framework for crisis management is developed based on a multidisciplinary and systems approach. This study therefore makes some signiﬁcant contributions for a systematic study of ﬁnancial activities of business organisations in ﬁnancial crisis mode, and the development of the path that should be followed in a dynamic environment.

Keywords: Corporate crisis, ﬁnancial crisis, business interruption, crisis management model.

1.

Introduction

The small business sector plays a signiﬁcant social and economic role in the Australian economy. The latest survey by the Australian Bureau of Statistics (ABS) shows that 1,122,000 or 96% of total non-agricultural private sector businesses classiﬁed as small businesses in 2000/01. These small businesses employed 3.3 million people or 47% of the total non-agricultural private sector workforce. There is no separate statistical information regarding medium business organisations, but it is safe to assume that the majority of Australians are employed by small and medium sized enterprises (SMEs). A survey conducted by CPA Australia in August 2002 indicates that more than 40% of small businesses were adversely affected by some type of crisis event, such as ﬁre, ﬂood, etc., over the previous 12 months. This shows the vulnerability of this important economic sector to crisis events, and the need for devising strategic and ﬁnancial techniques that can be used in such situations. Whilst there is a large body of literature available in the area of disaster and crisis management at macro and large company level, there is very limited information regarding SMEs in general and, in particular, in Australia. This paper will look into the experience of such companies, and what can be done to manage a ﬁnancial crisis in the event of isolated incidents such as ﬁre, ﬂood, storm, contamination and the like. It is about corporate crisis management at small to medium business organisation level. The remainder of this note is structured as follows: Section 2. Corporate Crises — The Concept; Section 3. Research Objective and Methodology; Section 4. A Theoretical and Conceptual Framework for Crisis Management Studies; Section 5. The Financial Crisis Management Model and its Approach; Section 6. Crisis Management Phases; and Section 7. Conclusion.

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A Framework for Corporate Crisis Management

2.

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Corporate Crises — The Concept

The Macquarie Dictionary (1997) deﬁnes crisis as “a decisive or vitally important stage in the course of anything; a turning point; a critical time or occasion; a political crisis, a business crisis”. Various authors have attempted to deﬁne crisis for the purpose of understanding and managing crises before they occur, during or after the crisis period. The following three deﬁnitions provide a comprehensive picture of “crisis”, as it is understood by academia and the business world. (a) International Association of Business Communicators describes crisis as “an event, revelation, allegation or set of circumstances which threatens the integrity, reputation, or survival of an individual or organisation. It challenges the public’s sense of safety, values or appropriateness. The actual or potential damage to the organisation is considerable and the organisation cannot, on its own, put an immediate end to it”. (b) Shrivastava (1987) states that “a crisis is a low probability, high consequence event that is capable of threatening organisational legitimacy, proﬁtability and viability”. (c) Reid (2000) provides a deﬁnition of crisis as “any incident that can focus negative attention on a company and have an adverse effect on its overall ﬁnancial condition, its relationship with its audiences or its reputation in the market place”. From the above deﬁnitions, it is evident that a crisis is generally an incident that is not desirable, and an event that must be managed in order to minimise its impact on any form of organisation including its ﬁnancial, material, human and informational resources.

3.

Research Objectives and Methodology

Having described the nature of corporate crises, it is now imperative to state the objectives of this research and the methodologies adopted for ease of understanding of the remaining sections of this chapter. Accordingly, this research is designed to: (a) Develop a general framework for corporate crisis management strategies. (b) Identify and analyse the various stages of corporate crisis management following sudden incidents such as ﬁre, storm, ﬂood, accidental damage,

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machinery breakdown, etc. and risk management implications at each stage. (c) Analyse outsourcing, machine hire, etc., during various stages of business interruption. (d) Analyse the implications of various communication strategies with different stakeholders, mainly shareholders or partners, employees, customers and suppliers. (e) Identify and analyse appropriate promotional strategies during various phases of business interruption, given the level of sales, production and service provisions.

4.

A Theoretical and Conceptual Framework for Crisis Management Studies

To undertake a corporate crisis management study, it is necessary to adopt a theoretical and conceptual framework, which has the elements of successful crisis management strategies and actions. In this study this framework has been developed on the basis of two major categories of theoretical elements. The ﬁrst category is based on ﬁnancial management theories and principles including ﬁnancial distress analysis, capital structure, risk management, ﬁnancial engineering, and capital budgeting. The second category includes non-ﬁnancial management strategies such as crisis control mechanisms, corporate governance, business ethics and stakeholders analysis, and marketing management. It should be noted that these areas of discipline evolved out of well-established ﬁeld of studies and professional practices such as economics, statistics, accounting, operations research, and organisation and management theory. A diagram in the Appendix (Figure A1) provides further information.

5.

The Financial Crisis Management Model and Its Approach

From our discussion of the general concept of corporate crises and the theoretical framework, we understand that an abrupt ﬁnancial crisis would involve the loss of assets. For the purpose of this research, assets can be classiﬁed into tangible and intangible assets. Tangible assets include all physical assets of a business organisation, including stock of raw materials, ﬁnished goods, plant and machinery, ofﬁce equipment, furniture and ﬁttings, etc. Intangible assets cover goodwill and,

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more speciﬁcally, market share, reputation, etc. In this research, the main focus is an abrupt ﬁnancial crisis caused by a loss of physical assets, hence tangible assets. We also note that an abrupt ﬁnancial crisis can be caused by a loss of market share or customer withdrawal as a result of certain incidents such as sexual allegations, bad reputation or loss of customers’ conﬁdence following the destruction of assets. In any case, a business organisation in a crisis needs to restore both types of assets in order to be able to return to normal trade and generate the same level of cash ﬂows that existed prior to the crisis, and in the shortest possible time. The Financial Crisis Management Model in Figure 1 (see also Figure A1 in Appendix) depicts both scenarios, and what might be needed in order to restore normality. The model shows four different positions where a business organisation might ﬁnd itself in relation to crisis situation. From Figure 1: Position 1 represents the destruction or loss of both types of asset. Position 2 represents the loss of intangible assets only. Position 3 represents the loss of tangible assets only. Position 4 represents the normal position. The ﬁrst scenario is the worst position as the business organisation is in deep crisis due to a loss of both types of assets. From here, the organisation has three different choices to rebuild both types of its assets. These three choices

Restoration of Intangible Assets

100% 3

4

1

2

0%

100% Restoration of Tangible Assets

Figure 1. The Financial Crisis Management Model.

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3

4 NB: The variation of S Curve 1

1

2

3

4

2

Figure 2. The Financial Crisis Management Curve (The S Curve).

3

4 NB: The variation of N Curve 1

1

3

2

4

2

Figure 3. The Financial Crisis Management Curve (The N Curve).

are shown with the help of the following three Financial Crisis Management Curves: (1) The “S” Curve; (2) The “N” Curve; and (3) The “R” Curve. The “S Curve” (Figure 2) shows that the business organisation needs to rebuild its tangible assets ﬁrst, and then embark on the restoration of its intangible assets. The “N Curve” (Figure 3) is the opposite of the “S Curve” in that the viable strategy for this business is to regain its reputation and market share through the use of some third party products, etc. and then rebuild its assets. The last alternative (Figure 4), which is called the “R Curve”, is based on the gradual restoration of both types of assets at the same time. This choice is the preferred course of action provided that the business organisation is able to handle both activities effectively and simultaneously. It should be noted that this does not mean that both assets should be restored at the same rate. The second quadrant of the Financial Crisis Management Model represents the loss of physical assets while the organisation’s intangible assets are still intact. In this case, the business needs to rebuild its productive assets in

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2

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NB: The variation of R Curve

Figure 4. The Financial Crisis Management Curve (The R Curve).

3

4 NB: The variation of H Curve

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Figure 5. The Financial Crisis Management Curve (The H Curve).

the shortest possible time without damaging its intangible assets. The following diagram (Figure 5) shows the recovery path. The third position refers to a business organisation in a crisis due to the loss of customers following some sort of bad publicity, loss of reputation and the like. In this case, the battle is a move upward from position 2 to 4. Hence, it is called the “V Curve”. Figure 6 shows this scenario. The corporate crisis management models discussed here are designed to approach crisis management based on systems theory and principles in order to treat all aspects of crisis problems together in a rational manner by combining theory, empiricism and pragmatism.

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3

4 NB: The variation of V Curve

2

1

4

2

Figure 6. The Financial Crisis Management Curve (The V Curve).

6.

Crisis Management Phases

It was stated that SMEs could use different phases of a crisis as a strategy for applying different instruments identiﬁed as part of the ﬁnancial crisis management model. From the case studies, a crisis can be effectively and efﬁciently managed by dividing the corporate crisis management model and process into 6 phases: (i) assessment of incident; (ii) crisis management planning; (iii) temporary resumption of operations; (iv) replacement and reconstruction of tangible assets; (v) marketing and promotion; and (vi) permanent resumption of operations. Figure 7 shows these phases in a diagrammatic form and their discussions are provided below. Phase 1 — Assessment of Incident: Following any disaster, it is necessary to identify the nature and extent of the damage including its impact on the products and services, key processes, management and staff, customers, suppliers, ﬁnanciers, competitors and all other stakeholders. Phase 2 — Crisis Management Planning: Crisis management planning is a critical step in containing the damage because it sets out the actions to be taken from this point onward until all business assets (tangible and intangible) are restored or the system is back to normal. Phase 3 — Temporary Resumption of Operation: Depending upon the extent of the damage and the alternatives laid out in the disruption management plan, SMEs in crisis situation might decide to relocate to temporary premises,

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Phase 6

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4

Restoration of Tangible Assets

Permanent Resumption of Operation Phase 5 Marketing and Promotions Phase 4 Replacement of Tangible Assets Phase 3 1

Phase 2

Temporary Resumption of Operations 2

Crisis Management Planning

Phase 1 Assessment of Incident 0%

Restoration of Tangible Assets

100%

Figure 7. Corporate Crisis Management Phases.

hire equipment or outsource certain activities in order to resume operations temporarily. Phase 4 — Replacement and Reconstruction of Tangible Assets: It is generally assumed that the business is now operating in a temporary mode and it should undertake the reconstruction of its tangible assets in a value maximizing way. The business can apply a or the post loss investment optimisation model for this purpose. Phase 5 — Marketing and Promotion: During this phase, the business should step up its marketing effort as it is going to operate immediately or shortly in full capacity and in some cases in better and bigger conditions. This is primarily the relaying of a positive message to old, new and potential customers that the business has not only survived the damage but has also come out in better and bigger shape. Phase 6 — Permanent Resumption of Operations: The ﬁnal step in this journey is to reacquire the pre-loss physical and operational facilities and to realise the expected capabilities. It is the process of ensuring that the business will be able to serve its customers without any disruption or undue pressure on its system. In other words, all of the elements of the system are in agreement and in an optimal position (Position 4 on the ﬁnancial crisis management model).

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The various phases of the model should also have been seen as different elements of the crisis management system that interact with each other for the purpose of accomplishing the normalisation of another system that is an SME in crisis mode. This approach requires that the various phases should be seen to have an impact on each other and should be in agreement to achieve their purpose.

7.

Conclusion

In conclusion, it should be noted that SMEs can be in very difﬁcult trading and ﬁnancial problems for a very long period to come, following a crisis. The level of damage to their productive assets is not always directly related to the impact that might follow. The impact can be disastrous, sometimes due to inadequacy of insurance but in most cases due to lack of proper corporate crisis management strategies. It is essential to understand the impact of the reconstruction of both types of assets that the business organisation controls — that is, the tangible and intangible assets — and apply the necessary tools during various phases of the crisis. Depending on the type and nature of business disruption, a crisis can be better managed using the concept and techniques established in the Financial Crisis Management Model in this note. The management of ﬁnancial crisis during different phases also requires the application of the elements of the theoretical framework selectively and skillfully. This note identiﬁes these key elements and the phases involved in managing ﬁnancial crisis in relation to small and medium business organisations in Australia and probably elsewhere with minor modiﬁcations.

References Altman, E. I. (1984). The success of business failure prediction models: An international survey. Journal of Banking and Finance, 8, 171–198. Altman, E. I. (2002). Bankruptcy, Credit Risk, and High Yield Junk Bonds. Malden: Blackwell Publishers. Beaver, W. (1966). Financial ratios as predictors of failures. Journal of Accounting Research, Supplement on Empirical Research in Accounting, 11, 71–111. Block, S. (1997). Capital budgeting techniques used by small business ﬁrms in the 1990s. The Engineering Economist, 42(4), 289–302. Castagna, A. D. and A. P. Matolcsy (1981). The prediction of corporate failure: Testing the Australian experience. Australian Journal of Management, 6(1), 23–50.

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CPA Australia (2003). Small Business Survey Program: Compliance Burden. Melbourne: CPA Australia. Doherty, N. A. (2000). Integrated Risk Management: Techniques and Strategies for Reducing Risk. New York: McGraw-Hill. Finnerty, J. D. (1988). Financial engineering in corporate ﬁnance: An overview. Financial Management, 17(4), 14–33. Hickman, J. R. and W. R. Crandall (1997). Before disaster hits: A multifaceted approach to crisis management. Business Horizons, 40(2), 75–79. Hwang, P. and J. D. Lichtenthal (2000). Anatomy of organisational crises. Journal of Contingencies and Crisis Management, 8(3), 129–139. Kotler, P. (2003). Marketing Management, 11th edn. Upper Saddle River, New Jersey: Prentice Hall. Mitroff, I. I. (1988). Crisis management: Cutting through the confusion. Sloan Management Review, 29(3), 15–20. Mitroff, I. I. and G. Anagnos (2001). Managing Crises before They Happen: What Every Executive and Manager Needs to Know about Crises Management. New York: American Management Association (AMACOM). Reid, J. (2000). Crisis Management: Planning and Media Relations for the Design and Construction Industry. New York: John Wiley and Sons. Shrivastava, P. (1987). Strategic Management: Concepts and Practices. Cincinnati: South Western Publishing. Vogler, M. and C. Perkins (1991). Disaster plans must focus on more than data. Cashﬂow, 95(32), 42–43.

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Financial Distress Analysis

Statistics Capital Structure

Operations Research

Risk Management

Economics Financial Engineering

Mathematics

Capital Budgeting

Crisis Prevention & Control Corporate Governance Management Theory & Practice

Business Ethics and Stakeholders Analysis Marketing Management

Figure A1.

Financial Optimisation Models Post-loss Capex Cash Optimisation Optimal Cap Structure Insurance EOQ Project Management

. . . . . .

Strategic Crisis Management Tools BCP

. . BIA . 4 Ps of Marketing . SWOT Analysis

A Theoretical and Conceptual Framework for Corporate Crisis Management Model.

Financial Crisis Management Model

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Appendix

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10 OPTION GAMES, ASYMMETRIC INFORMATION AND MERGER ANNOUNCEMENT RETURNS Hongbo Pan∗ and Xinping Xia† School of Management, Huazhong University of Science and Technology 1037 Luoyu Road, Wuhan, Hubei Province, P.R. China, 430074 ∗ [email protected] † [email protected] Received July 2005 Accepted February 2005 This paper presents a dynamic model of mergers based on stock market valuations of merging ﬁrms with industry-wide uncertainty. The model incorporates asymmetric information and determines the terms and timing of mergers by solving cooperative option games between acquiring shareholders and target shareholders. The model predicts that (l) returns to acquiring shareholders can be negative if the managers of participants are much more optimistic over merging synergism than outside investors; (2) returns to acquiring shareholders are negatively correlated with the size of the acquirer; (3) returns to target shareholders are negatively correlated with the size of the target.

Keywords: Merger, option games, asymmetric information, size effect.

1.

Introduction

Merger announcement returns has been the subject of considerable research in ﬁnancial economics. Many empirical research ﬁnd that the returns to target are positive at cash-offer announcement,1 while the returns to the acquirer 1 Considering

the combined effects of stock-offer at announcement (Myers and Majluf, 1984), this paper put emphasis on merging announcement effects of cash-offer. 211

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are indistinguishable from zero, and are statistically insigniﬁcant (Andrade et al., 2001; Fuller et al., 2002). In addition, Moeller et al. (2004) show that the returns to acquirers are negatively correlated with the size of the acquirer. Many theories attempt to interpret the empirical evidence. The managerial hubris hypothesis (Roll, 1986) can partially explain the size effect of the acquirer at announcement, but cannot interpret the probable positive acquiring-ﬁrm abnormal returns. The market-driven acquisitions theory (Shleifer and Vishny, 2003) can only interpret the positive or negative acquiring-ﬁrm abnormal returns at announcement to some extent, but cannot explain the size effect of the acquirer. Morellec and Zhdanov (2005) show that the returns to acquiring shareholders may be negative if there is competition for the acquisition of the target, which can explain the positive or negative acquiring-ﬁrm returns partially, but cannot interpret the size effect. Therefore, acquiring-ﬁrm abnormal returns are still unclear for researches. The main aim of this paper is to provide a theoretical interpretation for the empirical evidence. A basic economic intuition tells us that returns to the acquiring ﬁrm rely on the different stock market valuations between managers and investors of merging ﬁrms which result from the asymmetric information on the merging synergism between them. By incorporating the asymmetric information over the synergy coefﬁcient between the managers and investors into option games with industry-wide uncertainty, our model shows that target obtains positive abnormal returns during merger announcement while acquirer earns positive or negative abnormal returns, which gives a rational interpretation for the above empirical evidence. Furthermore, we show that: (1) returns to acquiring shareholders are negatively correlated with the size of the acquirer which is consistent with the above empirical evidence; and (2) returns to target shareholders are negatively correlated with the size of the target which needs the proof of empirical evidence. The rest of the paper is organised as follows. Section 2 gives the timing and terms of merger. Section 3 explores announcement returns and size effect. Section 4 provides conclusions.

2.

The Timing and Terms of Merger

We assume that both ﬁrms in the same industry are price takers, and their equity values are determined by a stochastic output price with industry-wide. Similar with Dixit and Pindyck (1994), we assume the output price follows

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a geometric Brownian motion: dpt = µpt dt + σpt dBt

(1)

With B being a one-dimensional standard Brownian motion with constant parameters µ and σ. As an additional condition to ensure convergence in the value of ﬁrms, we impose r > µ and δ = r−u which is the shortfall rate. It is clear that free entry of new ﬁrms in the industry will stop the growth in the price process at any time the price reaches p∗ ; therefore the price process will have an upper reﬂecting barrier at p∗ . We assume that the target and acquirer separately produce θ and π unit products every year with inﬁnite period, and every ﬁrm in the industry can undertake a single irreversible investment, requiring an initial sunk cost I to produce one unit product. Using similar arguments as for Dixit and Pindyck (1994), the values of the target and acquirer without considering the merger option before merger are respectively given by: θ θp − pβ p∗(1−β) δ δβ π πp − pβ p∗(1−β) E2 (pt ) = δ δβ

E1 (pt ) =

(2a) (2b)

Where β is the positive root of the fundamental quadratic Q ≡ 1 2 σ β(β − 1) + (r − δ)β − r = 0 and β > 1. The upper reﬂecting barrier 2 β δI. p∗ satisﬁes p∗ = β−1 We assume that merger is irreversible, and the sunk costs are Ai (i = 1, 2), and the managers of the participants have consistent estimation over the merger synergy coefﬁcient S > 0. After merger, the rate of proﬁt ﬂow will be (S + 1)(θ + π)pt , which also has an upper reﬂecting barrier p∗ . Let λi denotes the variable terms of merger surplus share accruing to ﬁrm i. Proposition 1. The value of ﬁrm i’s option to merge is given by β pt β pi p∗(1−β) λi S(π + θ) pi − , for pt ≤ pi − Ai OMi (pt , pi , λi ) = δ β pi (3) Proof. The value of ﬁrm i’s option to merge takes the form OMi (pt , pi , λi ) = Bpβ . At the optimal exercise price of ﬁrm i, value matching must be met: β pi p∗(1−β) λi S(π + θ) β pi − (4) Bpi = − Ai δ β

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Rearranging Equation (4), we get: B = pi

(−β)

β λi S(π + θ) pi p∗(1−β) pi − − Ai δ β

(5)

Substituting Equation (5) into the form of ﬁrm i’s merger option and rearranging terms yield the result in Proposition 1. The merger mechanism follows cooperative games, and the merger process happens in two rounds. In the ﬁrst round, the managers decide on the merger timing and aim to maximise the net present value of the total merger surplus. In the second round, they decide on how to share the surplus. Proposition 2. Whether the upper reﬂecting barrier of the stochastic output price exists or not, the timing and terms of merger are given by: λ1 =

A1 = λ, A1 + A 2

p1 = p2 = p =

β(A1 + A2 )δ < p∗ (β − 1)S(π + θ)

(6)

Proof. First, we decide on the merger timing and aim to maximise the net present value of the total merger surplus. The total merger surplus of the participants is: OM(pt , p) =

β P P∗(1−β) pt β S(π + θ) p− − (A1 + A2 ) δ β p

(7)

Through ﬁrst-order condition with respect to p, we get: p=

β(A1 + A2 )δ (β − 1)S(θ + π)

(8)

2

And it satisﬁes second-order condition ∂2 OM/∂P < 0. In the second round, they decide on how to share the surplus. In order for both ﬁrms to execute the merger at p, the trigger level of price have to

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satisfy p = p1 = p2 . Therefore, we have: ∂OM1 (pt , p1 , λ1 ) =0 ∂p1 p1 =p ∂OM2 ( pt , p2 , λ1 ) =0 ∂p 2

(9a) (9b)

p2 =p

According to Equations (8), (9a) and (9b), we get: λ1 =

A1 , A1 + A 2

λ2 =

A2 = 1 − λ1 A1 + A 2

(10)

From Equations (7) and (8), in order for merger to happen, we show that the condition p < p∗ is satisﬁed. Thus, we get the conclusion of Proposition 2 which is unrelated to the upper reﬂecting barrier of the stochastic output price. Proposition 2 shows that (1) merger happens in waves with industrywide uncertainty; (2) the higher the sunk cost is, the more seriously the timing of merger will be delayed; and (3) the higher the sunk cost of ﬁrm i is, the higher the surplus share of ﬁrm i from merging is.

3.

Announcement Abnormal Returns and Size Effect

We incorporate asymmetric information into option games that outside investors have consistent beliefs that the synergy coefﬁcient is uniformly distributed on [Sd , Su ] that each outcome can occur with equal probability which is different from the managers, and we assume S > Sd because the managers of the acquirers usually have conﬁdence on the synergism of the activities. We assume the merger is not anticipated by the investors. Therefore the investors ﬁrstly have beliefs over the synergy coefﬁcient [Sd , Su ] at merger announcement, and get the synergy coefﬁcient S from the managers’ merging activity at the same time. How the investors react to the new information? And what is the relationship between the acquiring-ﬁrm abnormal returns and the size of the acquirer? We will discuss those in the following two situations.

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Case 1: S > Su . For S > Su , the managers are too optimistic on the merging synergism for the risk-averse investors to believe. Then the managerial hubris2 comes into being, and the investors will update their beliefs to Su . Just before the merger announcement, the investors cannot anticipate the forthcoming merger activity. Therefore the equity values of the participating ﬁrms are formulated respectively in Equations (2a) and (2b). After the merger announcement, the investors know that the merger surplus paid to the target is equal to the ﬁrm value of producing λS(θ + π) unit products with inﬁnite period. As the investors adjust the synergy coefﬁcient to the point Su , the merger surplus of the acquirer from the merging is equal to the ﬁrm value of producing (Su − λS)(θ + π) unit products with inﬁnite period. Therefore, just after the merger announcement, the equity values of the participating ﬁrms are respectively: β β p P∗(1−β) p P∗(1−β) θ λS(θ + π) + − A1 E1 (p, p, λ) = p− p− δ β δ β (11a) E 2 (p,

β β p p∗(1−β) p p∗(1−β) π (Su − λS)(θ + π) + − A2 p, λ) = p− p− δ β δ β (11b)

According to Equations (2a), (2b), (11a) and (11b), we get the abnormal returns of the target and the acquirer at announcement: β−1 p A1 CAR1 = 1− (12a) (β − 1)E1 p∗ β−1 p p∗(1−β) β(A1 + A2 )(Su − S) CAR2 = 1− (β − 1)SE2 β β−1 p A2 1− (12b) + (β − 1)E2 p∗ 2 At

the base of Roll (1986), we amend the managerial hubris hypothesis by excluding the condition that there is no merging synergism because many researches ﬁnd that mergers create shareholder value on average (Mulherin and Boone, 2000; Andrade et al., 2001). Therefore we call it managerial hubris when the managers are much more optimistic on merging synergism than outside investors.

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When the managers are much more optimistic on merger synergism than investors, Equation (12a) shows that the target gets positive abnormal returns because of p∗ > p. The second term of Equation (12b) is acquirer’s merger surplus if the managers execute the merger according to the investors’ belief on the merger synergism, which is usually positive. And the ﬁrst term of Equation (12b) is attributed to managerial hubris, which is negative. In general, the acquirer may get positive or negative abnormal returns which depend on managerial hubris. The more serious the managerial hubris becomes, the more probably the acquiring-ﬁrm negative abnormal returns will appear. Moreover, the managerial hubris plays more of a role in the decisions of large ﬁrms than small ﬁrms (Moeller et al., 2004), thus the acquiring-ﬁrm abnormal returns are negatively correlated with the size of the acquirer. Case 2: S ≤ Su . For S ≤ Su , the investors will update their beliefs over the synergy coefﬁcient to the point S. Similarly, before the merger announcement, the equity values of the participating ﬁrms will be expressed in Equations (2a) and (2b). After merger announcement, the investors update synergy coefﬁcient to S. Using similar arguments as in Case 1, we can get the equity values of the participating ﬁrms after merger announcement: β β p P∗(1−β) p P∗(1−β) θ λS(θ + π) p− p− + − A1 E1 (p, p, λ) = δ β δ β (13a) E 2 (p,

β β p p∗(1−β) p p∗(1−β) π (1 − λ)S(θ + π) p, λ) = p− p− + − A2 δ β δ β (13b)

From Equations (2a), (2b), (13a) and (13b), we get the abnormal returns of the target and the acquirer at announcement: β−1 p A1 1− (14a) CAR1 = (β − 1)E1 p∗ A2 CAR2 = (β − 1)E2

1−

p p∗

β−1 (14b)

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When the synergy coefﬁcient from the managers falls into the beliefs over the synergy coefﬁcient of the investors, we show that both participants will get positive abnormal returns at announcement. Further more, as the size of the acquirer (E2 ) increases, the sunk cost of the acquirer (A2 ) generally increases less than the size of the acquirer (E2 ). According to Equations (6) and (14b), we show that the acquiring-ﬁrm abnormal returns are negatively correlated with the size of the acquirer. Similarly, the returns to target are negatively correlated with the size of the target, which is constant in Equation (12a). The analysis of Cases 1 and 2 leads to the following proposition. Proposition 3. Target obtains positive abnormal returns during merger announcement, while acquirer earns positive or negative abnormal returns which depending on the managerial hubris, that is whether the managers of participants are much more optimistic over merging synergism than outside investors or not. The returns to acquiring shareholders are negatively correlated with the size of the acquirer, and the rule is constant to the target. The major conclusions in Proposition 3 are consistent with the empirical evidence, and the conclusions give a basic economic intuition interpretation for empirical evidence, that is returns to acquiring shareholders rely on the different stock market valuations between managers and investors of merging ﬁrms which result from the asymmetric information on the merging synergism between them. When the managers of participants are much more optimistic over merging synergism than investors, the acquiring-ﬁrm returns may be negative. At the base of stock market valuations and asymmetric information, the proofs of Proposition 3 verify the size effect of both acquirer and target. The conclusion on the target’s size effect needs the proof of empirical evidence.

4.

Conclusions

Under the circumstance of industry-wide uncertainty, this paper models the intuition that returns to the acquiring ﬁrm rely on the different stock market valuations between managers and investors of merging ﬁrms which result from the asymmetric information on the merging synergism between them. The model shows that (l) target obtains positive abnormal returns during merger announcements, while acquirer earns positive or negative abnormal returns which depending on whether the managers of participants are much

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more optimistic over merging synergism than outside investors or not; (2) the returns to acquiring shareholders are negatively correlated with the size of the acquirer; (3) returns to target shareholders are negatively correlated with the size of the target. The major conclusions of the model are consistent with the empirical evidence, and the target’s size effect needs the proof of empirical evidence.

Acknowledgements We are grateful to Jie Yang, Minggui Yu, Yixia Wang for helpful discussions. All errors are solely ours.

References Andrade, G., M. Mitchell and E. Stafford (2001). New evidence and perspectives on mergers. Journal of Economic Perspectives, 15, 103–120. Dixit, A. and R. Pindyck (1994). Investment under Uncertainty. Princeton, New Jersey: Princeton University Press. Fuller, K., J. Netter and M. Stegemoller (2002). What do returns to acquiring ﬁrms tell us? Evidence from ﬁrms that make many acquisitions. Journal of Finance, 57, 1763–1793. Moeller, S., F. Schlingemann and R. Stulz (2004). Firm size and the gains from acquisition. Journal of Financial Economics, 73, 201–228. Morellec, E. and A. Zhdanov (2005). The dynamics of mergers and acquisitions. Journal of Financial Economics, 77, 649–672. Mulherin, H. and A. Boone (2000). Comparing acquisitions and divestitures. Journal of Corporate Finance, 6, 117–139. Myers, S. and N. Majluf (1984). Corporate ﬁnancing and investment decisions when ﬁrms have information investors do not have. Journal of Financial Economics, 87, 355–374. Roll, R. (1986). The hubris hypothesis of corporate takeovers. Journal of Business, 59, 197–216. Shleifer, A. and R. Vishny (2003). Stock market driven acquisitions. Journal of Financial Economics, 70, 295–311.

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RESEARCH METHODOLOGY PAPERS

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11 ANALYSING DATA USING GLM MODELS G. D. Hutcheson School of Education Manchester University Manchester, M13 9PL, UK [email protected] Received February 2006 Accepted February 2006 Generalised linear models may be applied to the analysis of data in the social sciences and provides a basis for postgraduate training in data analysis. The three techniques of Ordinary least-squares (OLS) regression, proportional odds models and multinomial logistic regression enable a huge range of hypotheses to be evaluated for univariate models of continuous, ordered categorical and unordered categorical data. As these techniques are part of the same theoretical model, the interpretation of model parameters, model ﬁt statistics, diagnostics and model-selection techniques are very similar and may, therefore, be learned within a typical postgraduate research course. This paper provides a basic introduction to the use of these models and demonstrates similarities between the models using a range of data.

Keywords: Generalised linear models, OLS regression, proportional odds, multi-nomial logistic regression, continuous ordered categorical data.

1.

Introduction

Generalised Linear Models (GLMs) were proposed by Nelder and Wedderburn (1972) and represent a family of statistical tests that can be used to analyse a wide variety of data. They are sufﬁciently general to be applicable to much social science data and provide a comprehensive set of analytical tools. Of particular importance is the uniﬁed theoretical framework that enables certain “economies of scale” to be realised (for example, the interpretation of the parameter estimates and model-ﬁt statistics are similar, as are model-building techniques and model diagnostics) and a full 223

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set of analyses taught within the conﬁnes of a typical postgraduate statistics course. Whilst this paper can only provide an overview of the techniques that comprise the generalised linear model, full details can be found in Dobson (2001), Fahrmeir and Tutz (2001), Gill (2000), Hoffman (2003), Hutcheson and Sofroniou (1999), Lindsey (1997), and McCullagh and Nelder (1989). The aim of many analyses is to predict (or model) the behaviour of a particular variable. At a very basic level it is possible to predict one variable, to a greater or lesser degree, given information about other variables. For example, Variable Y can be predicted by Variable X1 and Variable X2 Variable Y might be wage, educational attainment, test score, share price, success-failure, university chosen or religious afﬁliation. Variables X1 and X2 could be age, average school grade, gender, nationality, race, attractiveness, weight or attitude to innovation. Using the concrete example of a particular company’s share price, the relationship above could be written as: Share Price may be predicted by Output and Market Conﬁdence. From the relationship above one can deduce that share price may be determined by the company’s output and the conﬁdence shown in the market the company operates in. This is not likely to be a perfect relationship as a number of other variables not represented in the model are also likely to inﬂuence share price (such as government policy and exchange rates). The model can be said to consist of three components, the response variable, Y (share price), the explanatory variables, X1 and X2 (output and market conﬁdence) and a function that links the two. These three components form the basis of the Generalised Linear Model where they are commonly referred to as the random component, the systematic component and the link function. The GLM can be summarised as: Random Component → Link Function → Systematic Component with a concrete example being: Share Price → Link Function → Output and Market Conﬁdence The appropriate link function and analysis technique is dependent upon the level of measurement of the response variable. For example, if the response variable is continuous, the link between the random and systematic components of the model is direct and an OLS regression can be used. If, on the other hand, the response variable is categorical, the link between the

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Generalised linear modelling techniques.

Response Variable Continuous Ordered categorical Unordered categorical (binary) Unordered categorical (polytomous) a The

225

Link Function Identity Logit Logit Logit

Techniquea Ordinary least squares regression Proportional odds model Logistic regression Multinomial logistic regression

analysis techniques shown here only provides a minimal set of possible analyses.

random and systematic components of the model is not direct requiring an analysis technique to be used that does not assume a direct link. A minimal list of analysis techniques for different types of response variable are shown in Table 1.

2.

Modelling Continuous Data

The data that are to be used here to illustrate the technique are from Koteswara (1970), reported in Hand et al. (1994), who presents data collected over 30 four-week periods from March 18th 1951 to July 11th 1953. The data show ice cream consumption (pints per capita), the price of ice cream (dollars per pint), the weekly family income (dollars) and the mean outdoor temperature (degrees Fahrenheit). These data are shown in Table 2.

2.1. Simple OLS regression The research problem here is to model consumption. For simplicity, here we will only take into account a single explanatory variable, outdoor temperature. The basic relationship we are trying to model is of the form: Ice cream consumption may be predicted by outdoor temperature. As consumption and temperature are both continuous variables, this relationship can be depicted directly using a scatter-plot (see Figure 1). On the graph, a line is also depicted that has been derived using an algorithm that minimises the sum of the squares of the distances from each data point to the line (hence it is known as the least-squares technique) producing a line of best-ﬁt. This line describes the relationship between consumption and temperature, and in this case we can see that the relationship is roughly

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G. D. Hutcheson Table 2. Ice Cream Consumption 0.386 0.374 0.393 0.425 0.406 0.344 0.327 0.288 0.269 0.286 0.298 0.329 0.318 0.381 0.381 0.470 0.443 0.386 0.342 0.319 0.307 0.284 0.326 0.309 0.359 0.376 0.416 0.437 0.548

Ice cream consumption. Price 0.270 0.282 0.277 0.280 0.272 0.262 0.275 0.267 0.265 0.282 0.270 0.272 0.287 0.277 0.287 0.280 0.277 0.277 0.277 0.292 0.287 0.277 0.285 0.282 0.265 0.265 0.265 0.268 0.260

Family Income 78 79 81 80 76 78 82 79 76 82 85 86 83 84 82 80 78 84 86 85 87 94 92 95 96 94 96 91 90

Temperature 41 56 63 68 69 65 61 47 32 28 26 32 40 55 63 72 72 67 60 44 40 32 27 28 33 41 52 64 71

linear and represented quite well by the line.1 The relationship between consumption and temperature is represented by the slope of the graph. For each unit increase in temperature, consumption is expected to change by a certain amount. This amount is known as the regression coefﬁcient, β. The line of best-ﬁt can be described exactly from the regression coefﬁcient and the point where the line crosses the Y axis; readily available statistical software can compute these parameters and these are shown in Table 3. From the estimates provided in Table 3, one can obtain the intercept (α) and the regression

1 Although there is a suggestion that the relationship is curvi-linear, further analyses (not included

in this chapter) reveal that this is not signiﬁcant. A linear relationship would appear to be adequate for these data.

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Figure 1. The relationship between ice cream consumption and outdoor temperature. Table 3. Regression parameters for a simple regression model of ice cream consumption. (Intercept) Temperature

Estimate 0.2069 0.0031

Standard Error 0.0247 0.0005

Model: consumption = α + β temperature.

coefﬁcient for temperature (β) to get the equation of the line of best-ﬁt. Consumption = α + β temperature Consumption = 0.2069 + 0.0031 temperature Given a certain temperature (provided that it is within the range of observations recorded during the study), one can predict the amount of ice cream that will be consumed. For example, when the temperature is 50 degrees Fahrenheit, Ice cream consumption = 0.2069 + (0.0031 ∗ 50) = 0.3619

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For each unit increase in temperature, per capita consumption of ice cream is expected to increase by 0.0031 pints. This increase in ice cream consumption is the average increase one would expect. In addition to identifying the regression parameters α and β, it is also useful to determine how well the model ﬁts the data. Model-ﬁt can be determined by comparing the observed scores (the data) with those predicted from the model (the line of best-ﬁt). The difference between these two values (also known as the deviation or residual) provides an indication of how well the model predicts each data point. The sum of all the squared residuals is known as the residual sum of squares (RSS) and is essentially a measure of how much the model deviates from the data. A poorly ﬁtting model will deviate markedly from the data and will have a relatively large RSS, whereas a good-ﬁtting model will not deviate markedly from the data and will have a relatively small RSS (a perfectly ﬁtting model will have an RSS equal to zero). The RSS statistic therefore provides a way determining how well the model ﬁts the data. This statistic is also known as the deviance and is discussed in depth by Agresti (1996, pp. 96–97). The deviance is a very useful statistic as it allows the signiﬁcance of individual and groups of variables within a model to be computed. The signiﬁcances can be readily obtained by comparing the deviance statistics for nested models. For example, the signiﬁcance of the relationship between temperature and ice cream consumption can be ascertained by comparing the deviance in the models “ice cream consumption = α” and “ice cream consumption = α + β temperature”. The only difference between these two models is that one includes temperature and the other does not. Any change in deviance can therefore be attributed to the effect of temperature. Commonly available statistical software provides these statistics for simple OLS regression models and these are shown in Table 4. For our example of ice cream consumption, the addition of the explanatory variable “temperature” into the model results in a change in deviance of 0.0755 (RSSdiff ) which can be assessed for signiﬁcance using the

Table 4.

Measures of deviance for a simple regression model of ice cream consumption.

Model Consumption = α

RSS 0.1255

df 29

Consumption = α + β temperature

0.0500

28

RSS represents the deviance in the model. RSSdiff is the difference in deviance between the two model.

RSSdiff

F-value

P-value

0.0755

42.28

4.79e-07

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Table 5. t-statistics for a simple regression model of ice cream consumption. (Intercept) Temperature

Estimate 0.2069 0.0031

Standard Error 0.0247 0.0005

t-value 8.375 6.502

P-value 4.13e-09 4.79e-07

F-distribution (for a full discussion of this, see Hutcheson and Sofroniou, 1999). It should be noted that this procedure is exactly the same as is used to calculate the t-statistics that are usually provided for each explanatory variable as part of the analysis output. For the model above, the t-statistic for temperature is 6.502, which is directly comparable to the F-statistic.2 In this case, the square of t equals F (6.5022 = 42.28). From our simple regression model above we can state the relationship between consumption and temperature and the signiﬁcance of this relationship. Unsurprisingly, it appears that the greater the temperature, the more ice cream is consumed. This relationship is signiﬁcant.

2.2. Multiple OLS regression The model presented above was quite simple in that it only included a single explanatory variable. It is relatively straightforward, however, to extend the OLS regression model to cases where there is more than one explanatory variable. For example, if one was to predict ice cream consumption given outdoor temperature, family income and price, the equation for the regression model would be: Ice cream consumption = α + β1 temperature + β2 income + β3 price The parameters for this model shown in Table 6 are interpreted in much the same way as for the simple regression model. For example, for a unit Table 6. Regression parameters for a multiple regression model of ice cream consumption. (Intercept) Price Family income Temperature

Estimate 0.1973 −1.0444 0.0033 0.0035

Standard Error 0.2702 0.8344 0.0012 0.0004

2 The F-statistic is tested at k − 1 and n − k degrees of freedom whilst the t-statistic is tested at n − k − 1 degrees of freedom; where k = the number of terms in the model (excluding the intercept) and n = the sample size.

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increase in price, the amount of ice cream consumed is predicted to go down by 1.0444 pints per capita, while taking account of family income and temperature. Similarly, for a unit increase in temperature, consumption is predicted to increase by 0.0035 pints per capita while taking account of price and family income. The signiﬁcance of each parameter and group of parameters for predicting ice cream consumption can be calculated by comparing the deviances of nested models. For example, the signiﬁcance of price may be obtained by comparing the RSS values for two nested models, one that contains price and one that does not. The change in the RSS value between these two models indicates the effect that price has on the prediction of consumption. A similar procedure is used to ascertain the signiﬁcance of all parameters in the model. In this case, the deviance statistic of the full model (containing all parameters) is compared to the null model (containing no parameters). The difference between them indicates the effects that all the parameters have on the prediction of consumption. The calculation of these statistics is shown in Table 7 below. For the models below, the F-value for price is 1.5669 and this is tested on 1 and 26 degrees of freedom giving a signiﬁcance value of 0.2218. Price does not appear to be signiﬁcantly related to consumption (at least within the range of the data collected). The value of F for this one parameter is analogous to the t-statistic commonly provided by analysis software. The t-statistic computed for price is −1.2518, which corresponds to an F-value of 1.5669 (−1.25182 ). The value of F for all three parameters in the model is Table 7. The signiﬁcance of groups and individual parameters in a multiple regression model of ice cream consumption. Model RSS df Determining the effect of all three variables consumption = 0.0353 26 α+β1 temperature + β2 income + β3 price consumption = α

0.1255

Determining the effect of price consumption = α + 0.0353 β1 temperature + β2 income + β3 price consumption = α + β1 temperature + β2 income

0.0374

RSSdiff

F-value

P-value

0.0902

22.1749

2.45 e-7

0.0021

1.5669

0.2218

29 26

27

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22.1749 which is tested on 3 and 26 degrees of freedom giving a signiﬁcance of P < 0.0001 (see Hutcheson and Sofroniou, 1999 for a discussion of computing F-values). Taken together, all three parameters do enable a better prediction to be made of ice-cream consumption. The OLS regression model for continuous response variables is very versatile and can be adapted in a number of ways to model non-linear relationships, categorical explanatory variables, interactions and hierarchically structured data. These topics are beyond the scope of this article and interested readers should consult the numerous books and articles that deal with these speciﬁc topics; see, for example, Aitken and West (1991), Fox (2002), Hardy (1993), Jaccard et al. (1990), Raudenbush and Bryk (2001), Ryan (1997) and Pinheiro and Bates (2000).

3.

Modelling Categorical Data

The OLS regression model may be applied to continuous response variables, but is not appropriate to use when modelling categorical data. This can be demonstrated using the hypothetical example of whether or not a sale is made given the years of experience of a sales team. In this case, the response variable is a binary classiﬁcation of success and the explanatory variable is continuous and represents years of service. A model of “success” can be represented as: Success may be predicted by the experience of the sales team In general, we may expect that the more experience a sales team has, the greater the chance there is that a sale will be made. The scatterplot in Figure 2 shows the raw data plotted as empty circles and suggests that this may be the case as the successful sales tend to be clustered more to the right hand side of the graph. The relationship between success and experience can, however, be more clearly seen using the probability of success data which is shown as ﬁlled circles.3 These data clearly shows that the probability of success increases with the experience of the sales team. From Figure 2, it can be seen that the relationship between the probability of success and experience is not linear. As a consequence, the linear OLS regression model shown in the graph does not provide a particularly close ﬁt to the data. Most importantly, the data are constrained between 3 To

obtain this graph, experience was catergorised and the probability of success calculated for each experience category.

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Figure 2. The probability of success and the experience of the sales team.

0 and 1 (the raw data and the probability measure) but the model is not. At values of experience below 13 years, the model underestimates probability (as the value of probability cannot go below zero, the model actually provides illegal values of probability) whilst it overestimates probability for values of experience above 40 years (again, the model provides illegal values, as probabilities cannot assume values greater than 1). The relationship between the probability of success and years of experience would appear to be S-shaped (sigmoid) rather than linear. Clearly, the linear OLS regression model “success = α + β experience” does not provide an accurate representation of the relationship between the response and explanatory variables and is not, therefore, appropriate for these data. It would be possible, however, to appropriately apply a linear model to these data if the relationship between the probability of success and experience were represented as a straight line. This is what is achieved when the response variable is transformed using a logit (log odds). The logit link transforms the non-linear relationship Probability of success = α + β experience into the linear relationship logit (Probability of success) = α + β experience

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Figure 3. The log odds of the probability of success plotted against experience.

Figure 3 shows the log odds (the logit) of the probability of success plotted against experience. Of particular interest here is the fact that the data are not now constrained to values between 0 and 1, and a linear model more closely represents the relationship. In essence, the logit has transformed the S-shaped relationship suggested by Figure 2 into a linear relationship between the random and systematic component of the model. It is easy to demonstrate that the logit model provides a better representation of the relationship between success and experience by transforming the predicted values (the model) to show probability rather than the log odds of probability.4 Figure 4 plots the model according to a straight forward measure of probability and clearly shows that the resultant S-shaped model more accurately reﬂects the relationship between the probability of success and experience than does the OLS regression model shown in Figure 2.

4 For example, a value of −3 on the logit scale can be transformed to a probability by using the inverse of the logit, which equals 0.33. Similarly, a value of 2.5 on the logit scale equals a probability of 0.924.

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Figure 4. The probability of success plotted against experience.

4.

Modelling Binary Data

Logistic regression can be used to model a dichotomous response variable. As the response variable is dichotomous, a logit link is used to link the random and systematic components of the model. The relationship we are to model here is the one between union membership (a member or not) and wage.5 Using the logit model, this relationship is represented as: logit (probability of being a union member) = α + β wage This is a very simpliﬁed model and merely states that the probability someone is a union member may be related to the amount they earn. There are clearly many more variables that are likely to play a role in union membership, but these are not included in this example. The scatterplot in Figure 5 shows the raw data and the categorised probabilities and suggests that the probability of someone being a union member increases as their wage increases. This is not, however, a particularly strong relationship and it is unclear from the graph whether or not it is signiﬁcant. In order to more accurately quantify the relationship between wage and union membership, we will compute a logistic regression. Table 8 shows the 5 These

data were obtained from the Current Population Survey (CPS), see Berndt (1991).

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Figure 5.

235

Union membership and wage.

Table 8. Regression parameters for a simple logistic regression model of union membership. (Intercept) Wage

Estimate −2.207 0.072

Standard Error 0.233 0.020

Odds Ratio 1.075

Model: logit(p) = α + β wage.

parameters for this model which can be formulated as: logit (probability of being a union member) = −2.207 + (0.072 ∗ wage) and is interpreted in the following way. As wage increases by 1 dollar per hour, logit(p) increases by 0.0726 . This is almost identical to the way in which the parameters for an OLS regression model are interpreted. The only difference here is that the parameters relate to the log odds of the response variable rather than the actual value of the response variable. Log odds are, however, difﬁcult to interpret as we do not commonly think in these terms. A more useful statistic to work with is the odds, which in this case are 1.075 6 Techniques

to obtain the conﬁdence intervals associated with these parameters can be found in Sofroniou and Hutcheson (2002).

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(e0.072 ). For each unit increase in wage, the odds of being a member of the union increase from 1 to 1.075 (a 7.5% increase). The log-likelihood statistic provides a measure of deviance for a logistic regression model (that is, a measure of the difference between the observed values and those predicted from the model) and can be used as a goodness-ofﬁt statistic. This measure of deviance for a logistic regression model broadly corresponds to the RSS statistic, which is a measure of deviance for an OLS regression model (see Ryan (1997, p. 267). The log-likelihood statistic is usually quoted as −2 times the log-likelihood (−2LL) as this has approximately a chi-square distribution, thus enabling signiﬁcance to be evaluated. The interpretation of −2LL is quite straightforward — the smaller its value, the better the model ﬁt (a −2LL score equal to 0 indicates a perfect model where there is no deviance). Similar to OLS regression, the effect of a particular explanatory variable may be computed by comparing the deviance between nested models (one model including the explanatory variable and the other not) and evaluating signiﬁcance using the chi-square distribution with the number of degreesof-freedom equal to the difference in the number of terms between the two models. For a simple logistic regression model, the effect of the explanatory variable can be assessed by comparing the −2LL statistic for the regression model with that for the null model [see Equation (1)]. These statistics are shown in Table 9. −2LLdiff = ( − 2LL0 ) − ( − 2LL1 )

(1)

Where −2LL0 is the measure of deviance in the null model and −2LL1 is the measure of deviance in the full model. We have only provided a brief introduction to logistic regression and logit models. More detailed information may be found in Collett (1991), Hosmer and Lemeshow (2000), Kleinbaum et al. (2002) and Menard (1995). Table 9. Measures of deviance for a simple logistic regression model of union membership. Model Logit(p) = α Logit(p) = α + βx

Deviance (−2LL) 503.084

df 533

490.500

532

−2LLdiff

P-value

12.584

0.0004

Model: logit(p) = α + β wage. p is the probability of union membership. −2LLdiff is the difference in deviance between the two models.

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The logistic regression model shown above can be generalised to model polytomous ordered and unordered categorical variables. Two techniques that deal with these analytical problems are shown below, the proportional odds model for ordered categorical data and multi-nomial logistic regression for unordered categorical data.

5.

Modelling Ordered Categorical Data

There are a number of methods available to model ordered categorical data — linear-by-linear models, continuation ratio logits and proportional odds are some of the more widely used. The use of linear-by-linear techniques and continuation-ratio logits is covered by Hutcheson and Sofroniou (1999) and will not, therefore, be covered in any detail here. The technique we will be dealing with here is the proportional odds model which can be understood as an extension of logistic regression. A binary logistic regression models one dichotomy whereas the proportional odds model uses a number of dichotomies and combines these into a single model. Recoding the consumption variable from Table 2 into three categories (“low”, where consumption is below 0.33, “medium”, where consumption is between 0.33 and 0.38, and “high”, where consumption is above 0.38) produces an ordered variable representing the amount of ice cream consumed. As this new coding scheme representing consumption is not continuous, an OLS regression is not an appropriate technique to use. The data can, however, be analysed as a series of dichotomies, comparing lower with higher groups. In this case, low consumption is compared to medium and high and then low and medium is compared to high. Using this method of categorising the data enables the order to the accounted for as comparisons are being made between lower and higher levels of the variable (Y ≤ j and Y > j) and is unaffected by the actual codes chosen to represent the categories. The model assumes that the effect of the explanatory variables is the same for each cumulative probability and provides a single parameter for the variable. If the errors are independently distributed according to the standard logistic distribution, we get the ordered logit model shown in Equation (2): Logit[p(Y > j)] = α + β temperature

(2)

The parameters for the model “logit[p(Y > j)]= α + β temperature” where p is the probability of being in a higher consumption category is shown in Table 10 below. As two comparisons have been made in this model, there are

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G. D. Hutcheson Table 10. Parameters for a proportional odds model of ice cream consumption. Intercept(1) Intercept(2) Temperature

Table 11.

Estimate 4.993 7.727 0.128

Standard Error 1.539 2.068 0.035

Odds Ratio

1.137

Measures of deviance for a proportional odds model of ice cream consumption.

Model Logit[p(Y > j)] = α Logit[p(Y > j)] = α + β temperature

Deviance (−2LL) 60.947 39.052

−2LLdiff 21.895

df 1

P-value 0.000003

two parameters for the intercepts. Of more interest, however, is the parameters associated with the explanatory variable “temperature”. For each unit increase in temperature, logit[p(Y > j)] increases by 0.128. The log odds of being in a higher consumption category compared to a lower one increases by 0.128. The odds of being in a higher consumption category compared to a lower one increases by 1.137 for each unit increase in temperature. Within the limits of the observations made in this study, each time the temperature increases by 1 degree, the odd of you consuming more ice cream increase by 13.7%. The hotter it gets, the more ice cream is consumed. The signiﬁcance of the overall model and the explanatory variable can be computed in much the same way as for a binary logit model. That is, the deviances are compared between nested models. Table 11 shows the deviance statistics for the model and shows that the addition of the variable “temperature” leads to a signiﬁcant reduction in the deviance. Temperature is therefore a signiﬁcant predictor of the category Y. The proportional odds model shown above included just three categories of the response variable. The model is, however, easy to generalise to greater numbers of categories and also to the additional of multiple categorical and continuous explanatory variables. For more information on the proportional odds model see Agresti (1996), Agresti and Finley (1997), Clogg and Shihadeh (1994), Fox (2002) and Powers and Xie (2000).

6.

Modelling Unordered Categorical Data

A logit modelling technique that can be used to analyse unordered categorical data is multinomial logistic regression. It is important, however, to distinguish this model and the log-linear model, a technique that can also

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be used on categorical data. The basic difference is that a multinomial logistic regression distinguishes between a single response variable and a set of explanatory variables, whereas a log-linear model treats every variable as a response. Multinomial logistic regression is a univariate model that explicitly models a single response variable. The two techniques are, however, similar as evidenced by the fact that when all explanatory variables are categorical the multinomial logistic regression models correspond to log-linear models. As most applications are concerned with a predicting a single response variable,7 we will concentrate on the multinomial technique it applies to a single response variable and can be understood as a simple generalisation of the logistic regression model. Whilst a full description of log-linear models is beyond the scope of this chapter, detailed information may be found in Agresti (1990), Anderson (1997), Christensen (1997), Simonoff (2003) and Zelterman (1999). Multinomial logistic regression allows each category of an unordered response variable to be compared to an arbitrary reference category providing a number of logistic regression models. For example, if one were to model which of three supermarkets is likely to be chosen by a customer, two models could be computed, one comparing supermarket A with the reference category (supermarket C) and one comparing supermarket B with the reference category. The multinomial logistic regression procedure therefore outputs a number of logistic regression models that make speciﬁc comparisons. When there are j categories, the model consists of j-1 logit equations which are ﬁt simultaneously. Multi-nomial logistic regression is basically multiple logistic regressions conducted on a multi-category unordered response variable that has been dummy coded. To demonstrate this technique we will use an example of supermarket choice behaviour (see Hutcheson and Moutinho, 1998 and Moutinho and Hutcheson, 2000). The aim of this analysis is to model which supermarket someone is likely to choose given their salary and whether they use a car or not.8 The model is of the form shown in Equation (3): log

P(Y = j) = α + β1 salary + β2 car P(Y = j )

(3)

7 And, it must be said, to maintain consistency with the other techniques presented in this chapter. 8 The

original data contains many more variables; these have just been chosen for the purpose of illustration.

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G. D. Hutcheson Table 12. Parameters for a multinomial logistic regression model of supermarket choice. Supermarket Kwik Save

Tesco

Parameter (intercept) salary car (1)

Estimate 3.126 −0.005 −1.662

Standard Error 0.773 0.001 0.780

(intercept) salary car (1)

3.022 0.000 −1.976

0.741 0.001 0.752

Odds Ratio 0.995 0.190 0.774 0.139

Reference category = Sainsburys.

This equation simply represents a comparison between one supermarket (Y = j) and the reference supermarket (Y = j ). This is the odds of being in one category compared to the other and is computed as a log, hence this is a logit model (log odds). The parameters for the model are shown in Table 12. As the multinomial logistic regression is essentially multiple logistic regressions, the interpretation of the parameters is very similar. The parameters are provided as logits and refer to a comparison between the identiﬁed supermarket and the reference category (Sainsburys). For a unit increase in salary, the log odds on someone shopping in Kwik Saves compared to Sainsburys goes down by 0.005. For a unit increase in salary, the odds of someone shopping in Kwik Save compared to Sainsburys is 0.995:1. Put another way, Sainsburys attracts wealthier shoppers. For a unit increase in car,9 the log odds of shopping in Tesco as opposed to Sainsburys is 1.976 lower. For car users compared to non car users the odds of shopping in Tesco as opposed to Sainsburys is 0.139:1. Sainsburys attracts more car users. The signiﬁcance of the overall model and the explanatory variables can be computed in much the same way as for a binary logit model. That is, the deviances are compared between nested models. Table 13 shows the deviance statistics for a model including salary and car use and for models where individual and groups of variables have been removed. The signiﬁcance of the changes in deviance (−2LL) are also shown. You will note that there are 4 degrees of freedom associated with the ﬁrst comparison, as two parameters have been removed from two models (two

9 The

variable car has been dummy coded here to indicate no car (0) and car (1), which is the reference category. A unit increase in car therefore provides a comparison between those with a car and those without.

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Analysing Data Using GLM Models Table 13. choice.

Measures of deviance for a multinomial logistic regression model of supermarket

Model Deviance (−2LL) Determining the effect of all explanatory variables log log

P(Y=j) P(Y=j ) P(Y=j) P(Y=j )

241

=α

= α + β)1 salary + β2 car

Determining the effect of salary P(Y=j) log P(Y=j ) = α + β car P(Y=j) log P(Y=j ) = α + β1 salary + β2 car Determining the effect of price P(Y=j) log P(Y=j ) = α + β salary P(Y=j) log P(Y=j ) = α + β1 salary + β2 car

124.804

−2LLdiff

df

P-value

45.584

4

< 0.0005

31.986

2

< 0.0005

11.298

2

0.004

79.220

111.206 79.220

90.518 79.220

separate logistic regressions have been computed, one comparing Kwik Save and Sainsburys and one comparing Tesco and Sainsburys), whilst there are two degrees of freedom associated with the other models as there is a single parameter removed from the two models. These are combined statistics for the overall model — it should be noted that individual comparisons are also typically provided by analysis packages. That is, there is an overall signiﬁcance assigned to car, but also an indication of how signiﬁcant this variable is when distinguishing between individual supermarkets. If, for example, Tesco and Sainsburys are both out-of-town stores which require patrons to use a car, whereas Kwik Save is an in-town store without a car park, the variable car might be signiﬁcant in the model, but may only show a signifanct effect when predicting attendance between Tesco and Kwik Save or Sainsburys and Kwik Save, but not Sainsburys and Tesco. We have only managed to provide a very general and brief introduction to the multi-nomial logistic regression model here. Further information about this model and other related techniques for analysing unordered categorical data can be found in Agresti (1990, 1996), Fox (2002) and Venables and Ripley (2002). This paper has examined the use of GLM models, speciﬁcally the techniques of OLS regression, proportional odds models and multi-nomial logistic regression. These three techniques enable continuous, ordered and unordered data to be modelled and provide the basis of a uniﬁed system for data analysis.

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References Agresti, A. (1990). Categorical Data Analysis. John Wiley & Sons, Inc. Agresti, A. (1996). An Introduction to Categorical Data Analysis. John Wiley & Sons, Inc. Agresti, A. and B. Finlay (1997). Statistical Methods for the Social Sciences, Third edition. Prentice-Hall. Aitken, L. S. and S. G. West (1991). Testing and Interpreting Interactions, 2nd Edition. Sage Publications. Anderson, E. B. (1997). Introduction to the Statistical Analysis of Categorical Data. Springer-Verlag. Christensen, R. (1997). Log-Linear Models and Logistic Regression. Springer Texts in Statistics. Springer-Verlag. Clogg, C. C. and E. S. Shihadeh (1994). Statistical Models for Ordered Variables. Sage Publications. Collett, D. (1991). Modelling Binary Data. Chapman & Hall. Dobson, A. J. (2001). An Introduction to Generalized Linear Models, 2nd Edition. Chapman & Hall. Fahrmeir, L. and G. Tutz (2001). Multivariate Statistical Modelling Based on Generalized Linear Models. Springer Series in Statistics. Springer-Verlag. Fox, J. (2002). An R and S-PLUS Companion to Applied Regression. Sage Publications. Gill, J. (2000). Generalized Linear Models: A Uniﬁed Approach. Quantitative Applications in the Social Sciences. Sage Publications. Hand, D. J., F. Daly, A. D. Lunn, K. J. McConway and E. Ostrowski (1994). A Handbook of Small Data Sets. Chapman & Hall. Hardy, M. A. (1993). Regression with dummy variables. In M. S. Lewis-Beck (ed.), Regression Analysis. International Handbooks of Quantitative Applications in the Social Sciences, Volume 2. Sage Publications. Hoffman, J. P. (2003). Generalized Linear Models. Allyn & Bacon. Hosmer, D. W. and S. Lemeshow (2000). Applied Logistic Regression. Wiley Series in Probability and Statistics. Wiley-Interscience. Hutcheson, G. D. and L. Moutinho (1998). Measuring preferred store satisfaction using consumer choice criteria as a mediating factor. Journal of Marketing Management, 14, 705–720. Hutcheson, G. D. and N. Sofroniou (1999). The Multivariate Social Scientist: Introductory Statistics Using Generalized Linear Models. Sage Publications. Jaccard, J., R. Turrisi and C. K. Wan (1990). Interaction Effects in Multiple Regression. Sage University Paper Series on Quantitative Applications in the Social Sciences. Sage Publications. Kleinbaum, D. G., M. Klein and E. R. Pryor (2002). Logistic Regression, 2nd Edition. Springer-Verlag. Koteswara, R. K. (1970). Testing for the independence of regression disturbances. Econometrica, 38, 97–117.

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Lindsey, J. K. (1995). Introductory Statistics: A Modelling Approach. Oxford University Press. Lindsey, J. K. (1997). Applying Generalized Linear Models. Springer Texts in Statistics. Springer-Verlag. Menard, S. (1995). Applied Logistic Regression Analysis. Quantitative Applications in the Social Sciences, Volume 106. Sage Publications. McCullagh, P. and J. A. Nelder (1989). Generalized Linear Models, 2nd edition. Chapman and Hall. Moutinho, L. and G. D. Hutcheson (2000). Modelling store patronage using comparative structural equation models. Journal of Targetting, Measurement and Analysis for Marketing, 8(3), 259–275. Nelder, J. and R. W. M. Wedderburn (1972). Generalized linear models. Journal of the Royal Statistical Society, A, 135, 370–384. Pinheiro, J. C. and D. M. Bates (2000). Mixed-Effects Models in S and S-PLUS. Statistics and Computing. Springer. Powers, D. A. and Y. Xie (2000). Statistical Methods for Categorical Data Analysis. Academic Press. Raudenbush, S. W. and A. S. Bryk (2001). Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd Edition. Advanced Quantitative Techniques in the Social Sciences. Sage Publications. Ryan, T. P. (1997). Modern Regression Methods. John Wiley & Sons. Simonoff, J. S. (2003). Analyzing Categorical Data. Springer Texts in Statistics. Springer-Verlag. Sofroniou, N. and G. D. Hutcheson (2002). Conﬁdence intervals for the predictions of logistic regression in the presence and absence of a variance-covariance matrix. Understanding Statistics: Statistical Issues in Psychology, Education and the Social Sciences, 1(1), 3–18. Venables, W. N. and B. D. Ripley (2002). Modern Applied Statistics with S, Fourth Edition. Springer. Zelterman, D. (1999). Models for Discrete Data. Oxford University Press.

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12 THE ISSUE OF MISSING VALUES, THEIR PRESENCE AND MANAGEMENT: A RELEVANT DEMONSTRATION OF DATA ANALYSIS IN MARKETING USING CaRBS Malcolm J. Beynon Cardiff Business School, Cardiff University Aberconway Building, Colum Drive, Cardiff CF10 3EU, Wales, UK [email protected] Received February 2005 Accepted July 2005 Missing values are an often-alleged incumbency to the effectiveness of successful data analysis. Their presence able to be explained or not may be the issue, the very least acknowledged. This study discusses the extant issues of the presence of the missing values in data analysis, with particular attention to their management, including imputation. Following this discussion, the nascent Classiﬁcation and Ranking Belief Simplex (CaRBS) system for data analysis (object classiﬁcation) is presented which has the distinction of not requiring the a priori consideration (management) of any missing values present. Moreover, they are treated as ignorant values and retained in the analysis, a facet of CaRBS being associated with the notion of uncertain reasoning. A problem on the classiﬁcation of standard and economy food products is considered, with knowledge on their inherent nutrient levels used in their discernment. The visualisation of the intermediate and ﬁnal results offered by the CaRBS system allows a clear demonstration of the effects of the presence of missing values, within an object classiﬁcation context.

Keywords: CaRBS, Dempster-Shafer theory, ignorance, imputation, missing values, product categorisation.

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Introduction

The problem environment that presents itself to a researcher manifests their future approach, including the analysis technique to be adopted and perceived achievable results. The quality of this environment may be in the hands of the researcher when collecting their data, including the number and completeness of responses to a questionnaire survey, or the level of access to (and quality of) related databases. Of course, the best avoidance of having to analyse incomplete data sets (with missing values present) is through planning and conscientious data collection (De Sarbo et al., 1986). Even so, it is not uncommon for a researcher to be confronted with the presence of missing values in the data set they may have constructed. Concern on the presence of missing values in data analysis can be found over nearly forty years ago in Aﬁﬁ and Elashoff (1966). Since then it is continually the focus of study, covering general issues such as the nature of their presence (Allison, 2000; Schafer and Graham, 2002) and subsequent management (Huisman et al., 1998). Also more speciﬁc techniques to replace (impute) a missing value with a surrogate (West, 2001; Olinsky et al., 2003). The focus identiﬁed is that the emphasis is still on the management of the missing values, so traditional analysis techniques can be used on complete (ﬁlled in) data sets. This study describes a series of object classiﬁcation based analyses on a data set with induced different levels of missing values present in each case. The Classiﬁcation and Ranking Belief Simplex (CaRBS) system is primarily used here, introduced in Beynon (2005), it is a novel object classiﬁcation technique for data analysis. Developed further in Beynon and Buchanan (2004), its rudiments are based on the Dempster-Shafer theory of evidence (Dempster, 1968; Shafer, 1976), hence operates in the presence of ignorance. Its introduction (CaRBS) contributes further to the nascent research area of uncertain reasoning within data analysis. Further methodology that are closely associated with this research area are fuzzy set theory (Zadeh, 1965) and rough set theory (Pawlak, 1982). Their similarity lies with the acknowledgement that data is often imprecise and incomplete, Smets (1991, p. 142) groups these (and others aspects) using the term ignorance and state; “. . . the various forms of ignorance can be encountered simultaneously and it is necessary that we are able to integrate them.” The utilisation of CaRBS in this study is an exposition of this integration. One further aspect of its utilisation is the graphical based exposition of the

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ﬁndings (using simplex plots), including the evidential support offered by each criterion describing an object. In the context of this study it allows direct comparisons to be made in the results from the analyses when different levels of missing values are present and if they are managed or not. The data set investigated here is typical of any considered in a classiﬁcation problem. Its general structure is that of a number of objects, described by criteria (also called characteristics and attributes), each categorised to one of a number of decisions. The speciﬁc problem concerns product categories, and in particular whether product formulations are a rational starting place to discern between such categories (Ehrenberg, 1972; Foxall, 1999). With food products particularly considered, the concomitant marketing orientated issues of nutrient content, branding and consumer choice are related research topics (see Roe et al., 1999; Caswell et al., 2003). With the speciﬁc data set described later, emphasis here is on a study that balances the exposition of the problem (product categorisation), analysis technique (CaRBS) and analysis environment (presence of missing values). The structure of the rest of the paper is as follows. In Section 2, the issue of the presence and management of missing values in data analysis is discussed. In Section 3, a small food product data set and its preparation prior to analysis is described. In Sections 4 and 5, a series of CaRBS analyses of this data set is presented with emphasis on the graphical results. In Section 6, conclusions are given together with directions for future research.

2.

Missing Values in Data Analysis

For the last 30-plus years, the investigation into the presence and management of missing values in data sets has kept pace with the actual ability to analyse the data sets appropriately (starting with Aﬁﬁ and Elashoff, 1966; Rubin, 1976; Little, 1976). Indeed, a reason for this need to concern oneself with this issue is that most data analysis techniques were not designed for their presence (Schafer and Graham, 2002). The increase in the amount of data present in the world confers the issue of the ever presence of missing values, especially true when the size of individual data sets analysed similarly continue to increase. Recent research papers support this continued interest in their presence, including Lakshminarayan (1999), Allison (2000), West (2001) and Olinsky et al. (2003). Whether the data was accrued from responses to a questionnaire survey or through accessing related databases, the reasons for the presence of missing values may dictate how they should be future described. That is,

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the possibility that missing observations (values) differ in important ways from the complete observations (Brame, 2000). A typical solution is to make simplifying assumptions about the mechanism that causes the missing data (Ramoni and Sebastiani, 2001). The mechanisms (causes) of missing data were classiﬁed into three categories, based around the distributions of their presence (Rubin, 1976): Missing Completely at Random (MCAR): The fact that an entry is missing is independent of both observed and unobserved values in the data set (e.g., equipment failure). Missing at Random (MAR): The fact that an entry is missing is a function of the observed values in the data set (e.g., respondents are excused ﬁlling in part of a questionnaire due to answers given previously). Missing Not at Random (MNAR): An entry will be missing depends on both observed and unobserved values in the data set (e.g., personal demographics of a respondent contribute to the incompleteness of a questionnaire). It is noted in the literature that confusion has surrounded the use of these terms (Regoeczi and Riedel, 2003). For MCAR, this assumption can be tested statistically and is highly unlikely to hold, whereas there are no statistical tests of the MAR assumption (ibid.), MNAR may require the identiﬁcation of variables explaining why the values are missing (Acock, 1997). In the majority of studies, looking at the missing value issue, these general assumptions are stated and discussed, see the references presented here already. In the case of the utilisation of questionnaire survey data, Huisman et al. (1998) reviewed the notion of re-approaching respondents (follow-up), who had previously skipped questions, they further discerned the causes of nonresponses (missing values), presenting six non-exhaustive grouped reasons (see also De Leeuw, 2001): Missing by design: Although branching prevents a respondent from having to answer questions that do not apply to him/her, there still are some questions inapplicable for respondents. Inapplicable item: The non-respondent wrongfully thinks that a question does not apply to him/herself. Cognitive task too difﬁcult: The non-respondent has problems remembering situations that occurred earlier or understanding the question(s). Refuse to respond: The non-respondent refused to answer a question without giving a (clear) reason for it. Don’t know: Non-respondent gave a non-substantive answer: don’t know.

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Inadequate score: The response did not ﬁt in the given response categories. Graham and Donaldson (1993) outline three relevant points have to be considered: (1) the sample of non-respondents; (2) the method of reapproaching; and (3) the moment of re-approachment. A balanced sample of respondents should be re-approached. The method of re-approachment is largely dependent on the amount of missing data, and the nature of the missingness (Huisman et al., 1998), whereas the moment of re-approachment is the time between the returning of the questionnaire and the follow-up. When utilising the information available in external databases, the lack of knowledge on why a missing value is present may mitigate the ability of the researcher to identify the speciﬁc mechanism for its presence and subsequently how to manage its existence (Lakshminarayan et al., 1999). The range of choice on how to manage the missing values can seem as confusing as the issues for their presence. An overriding concern is that some thought should be made; the effect of a lack of thought is well expressed by Huang and Zhu (2002, p. 1613): “Inappropriate treatment of missing data may cause large errors or false results.” One way of viewing the different approaches to their management is in terms of those which are more older non-technical methods, such as case (listwise) deletion and single imputation against the more modern methods such as maximum likelihood and multiple imputation (Schafer and Graham, 2002). Case deletion, is a popular (relatively easy) approach whereby individual surveys or cases in a database are discarded if their required information is incomplete. This by its nature incurs the loss of information from discarding partially informative case (Shen and Lai, 2001). Further, serious biases may be introduced when missing values are not randomly distributed (Huang and Zhu, 2002). De Leeuw (2001) describes the resultant loss of information, less efﬁcient estimates and statistical tests, Gupta and Lam (1998) partition the concerns as: (1) In small samples, the deletion of too many cases may reduce the statistical signiﬁcance of conclusions. (2) Cases with missing values may carry critical information for the ﬁtting and prediction process.

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(3) Ignoring cases with missing values may hinder the application of statistical conclusions to future cases with missing values. Also associated with this approach is re-weighting, whereby the remaining complete cases are weighted so that their distribution more closely resembles that of the full sample (Schafer and Graham, 2002; Huang and Zhu, 2002). Imputation is another popular approach to the management of missing values, whereby an incomplete data set becomes ﬁlled-in by the replacement of missing values with a surrogate value (Sande, 1982; Huisman, 2000; Olinsky et al., 2003). It is potentially more efﬁcient than case deletion, because no cases are sacriﬁced, retaining the full sample helps to prevent loss of power resulting from a diminished sample size (Schafer and Graham, 2002). While a relatively simple solution, concomitant dangers have been highlighted, including from Dempster and Rubin (1983, p. 8): “The idea of imputation is both seductive and dangerous. It is seductive because it can lull the user into the plausible state of believing that the data are complete after all, and it is dangerous because it lumps together situations where the problem is sufﬁciently minor that it can be legitimately handled in this way and situations where standard estimators applied to the real and imputed data have substantial biases.” Little (1988) support this danger, suggesting naïve imputations may be worse than doing nothing. De Leeuw (2001) identiﬁes the availability of modern and user-friendly software encourages the use of imputation, with approaches that include: Mean Imputation: The missing value for a given attribute in a record is ﬁlled in with the mean of all the reported values for that attribute. One factor often highlighted is that the distribution characteristics (including variance) of the completed data set may be underestimated. Hot Deck Imputation: The missing value for a record is ﬁlled in with a value from an estimated distribution for the missing value from the current data sample. In a simple univariate hot deck imputation, missing values are replaced by a random draw from the observed values. This approach may still distort concomitant distributions. Cold Deck Imputation: The missing value for a record is ﬁlled in with a value from an estimated distribution for the missing value from a source other than the current data sample.

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West (2001) in an overview of missing data philosophy, as a prelude to a special issue on this topic, suggest these traditional methods have lower statistical power, making it more difﬁcult to detect true effects. They go on to suggest that modern methods offer the promise of improving both the accuracy and often the statistical accuracy power of results. Multiple Imputation: Each missing value is replaced with more than one surrogate value within a simulation analysis (see Sinharay et al., 2001). Regression and Stochastic Regression Imputation: Missing values are predicted by a regression of the unobserved variable values against observed ones for that record (or case), with a noise term added to the imputed value in the stochastic case. Maxmimum-Likelihood Based Approaches: Missing categorical values are predicted by conditional and expectation likelihood functions. There is often an assumption that data have a multivariate normal distribution, a condition that is often not met in practise (Enders, 2001). Selections of recent speciﬁc techniques that purport to affect information from incomplete data sets include: Gupta and Lam (1996, 1998), Ragel (2000), Ramoni and Sebastiani (2001), Ibrahim et al. (2001) and Vasechkina and Yarin (2002). Many of these techniques include their own utilisation of methodologies such as neural networks, genetic algorithms and decision trees, hence the future development of the management of missing values will continue as these methodologies themselves develop. A further consideration for a researcher is that since the management of missing values is a pre-processing step it may take a considerable amount of pre-processing time to allow for its completion (Pyle, 1999; Huang and Zhu, 2002). There is also an inherent issue on the effect of the size of the sample experiment and the management of missing values (Carrierie, 1999). The researcher should conﬁrm to themselves the appropriateness of the management procedure utilised and the sample size they are working with.

3.

Description of Small Food Product Data Set and Its Preparation Prior to Analysis

The data set considered here relates to a series of surveys undertaken by the UK’s Food Standards Agency (2004). Moreover, they surveyed baked bean and tinned pasta products in February 2004, to discern their nutrient levels

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(including sugar, etc.). Within the objective of the programme it is stressed (ibid.): “The data obtained will be used to raise consumer awareness of related food and diet issues to inform discussions with the food industry, and other bodies, aimed at encouraging reductions in the salt content of processed foods. This will in turn, help consumers to be better able to choose a healthy diet and achieve nutrient intake guidelines.” As a research area the connection between nutrient levels and consumers perception of health is often investigated, including through product labelling (Caswell et al., 2003). The relationship between the product marketing of the manufacturer and their customer’s choice process is central to this analysis. Foxall et al. (2004) found consumer choice patterns when buying supermarket food products can be related to their tendencies to maximise utilitarian and informational reinforcement. Further literature has considered the relationship between promotional activity, brand speciﬁc factors and consumer choice characteristics (Bolton, 1989; Fader and Lodish, 1990; Narasimhan et al., 1996; Gupta, 1988). In this study only two product categories from those surveyed are considered, namely, Standard baked beans in a tomato sauce (Std) and Economy baked beans in a tomato sauce (Ecy). These two product categories offer an interesting classiﬁcation problem, since their consumer orientated discernment is based almost solely on price. The question considered here is whether there is a level of discernment of these product categories based on nutrient levels (including sugar, etc.), deﬁned here as criteria. Moreover, the criteria considered are (their abbreviation and unit of scale given); Sugars (SG - g), Fibre (FB - g), Salt (ST - g), Fat (FT - g), Protein (PN - g) and Energy (EG kcal). In summary, could a consumer discern between these products based on their criteria values and not use the acknowledged price differential that should exist (which we understand is important here due to the standard and economy nature of the categories). In the non-exhaustive survey of these two product categories, 25 individual products were considered, 15 Std (standard) and 10 Ecy (economy), see Appendix A for their details. In its original form the data set was complete (none of the 6 × 25 = 150 criterion values are missing), hence could be analysed accordingly. This is undertaken here (primarily using CaRBS), also when missing values are created in this data set. Shen and Lai (2001)

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Description of data set with different numbers of missing values inherent.

D0% 5.728, 0.892 (0) 3.452, 0.248 (0) 1.264, 0.147 (0) 0.332, 0.143 (0) 4.336, 0.591 (0) 80.120, 8.463 (0)

D10% 5.704, 0.903 (1) 3.505, 0.228 (4) 1.274, 0.133 (6) 0.335, 0.146 (2) 4.336, 0.591 (0) 79.957, 8.800 (2)

D25% 5.729, 0.946 (4) 3.511, 0.231 (7) 1.275, 0.115 (9) 0.329, 0.152 (8) 4.336, 0.626 (3) 79.895, 9.118 (6)

D50% 5.713, 0.652 (9) 3.517, 0.254 (13) 1.322, 0.063 (16) 0.308, 0.144 (13) 4.425, 0.555 (13) 77.786, 8.090 (11)

considered such a problem with eight levels of missing values imposed on a survey based data set (ranging from 0% upto 20%). Here, three levels of missing value presence are considered, namely when 10% (15), 25% (37) and 50% (75) of the data are missing, see Appendix A (these data sets are labelled D10%, D25% and D50%, respectively). The process for creating missing values here is within the MCAR environment (see Section 2), whereby their presence is independent of the observed and unobserved values. Based on this environment, randomly a row and column of the data set are drawn and the corresponding entry is deleted until a speciﬁed percentage of all entries are missing (see Huisman, 2000). To gauge the effect of the creation of missing values the descriptive statistics of the remaining data values of the criteria are reported for each of the analyses undertaken here, see Table 1. The values in Table 1 are the respective mean, standard deviation and number of missing values (in brackets) for each criterion in D0%, D10%, D25% and D50%. The mean values reported are those used to take the place of the missing values in the created incomplete data sets. The D0% column describes the original complete data set (no missing values), the mean values presented here are not used for imputation in this case, but as with the others presented, to standardise the criterion values (along with the standard deviation value, see later). The difference between the mean and standard deviation values for a single criterion (nutrient) highlight the effect they have due to the creation of the missing values. When using the mean imputation method for the management of missing values this with undoubtedly produce distorted ﬁlled-in data sets, replacing D10%, D25% and D50%.

4.

CaRBS Analysis of Baked Bean Data Set (D0%)

This section undertakes a CaRBS analysis of the “original” complete baked bean data set (D0%), the rudiments of the techniques are presented in Appendix B. One reason for this detailed presentation is the novel analysis

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approach of uncertain reasoning central to CaRBS. Here, the Std (standard) product category is deﬁned the hypothesis (x), with Ecy (economy) its compliment (¬x), due to only two product categories considered. From Appendix B, the ﬁrst stage of the CaRBS system is the evaluation of the incumbent control variables, which optimise the deﬁned objective function that attempts to minimise ambiguity in the classiﬁcation of products but not the concomitant ignorance. That is, ambiguity relates to levels of belief (mass) apportioned to both the Std and Ecy categories separately, whereas ignorance is the level of belief unable to be apportioned to them individually (see later). Deﬁned as a constrained optimisation problem, the trigonometric differential evolution (TDE) technique was utilised (Storn and Price, 1997; Fan and Lampinen, 2003),1 on the standardised version of the baked bean data set D0% (each criterion value subtracted by the mean and divided by the concomitant standard deviation value). This allows standard bounds to be placed on the control variables, given as ki ∈ [−2, 2], θi ∈ [−1, 1] and Ai ∈ (0, 1], i = SG, . . . , EG. Each Bi control variable is set to 0.4, since even when given a domain to exist in, it is found to take the constrained maximum value (in this case the 0.4), see Beynon and Buchanan (2004). The TDE was then run and the subsequent control variables associated with each criterion found, reported in Table 2. The discussion on these control variable values is restricted to ki , which are all at the upper bound of 2.000. This implies as each criteria (nutrient) value increases more mass value supports that the product is in the standard category (Std). These values allow the construction of the criterion and category BOEs associated with each product, demonstrated on the products P12 and P24, see Table 3. Table 2. Control variables for CaRBS system on the complete “standardised” baked bean data set. Criteria ki θi Ai

SG 2.000 −0.424 0.811

FB 2.000 −0.008 0.401

ST 2.000 0.998 0.923

FT 2.000 −0.999 0.825

PN 2.000 0.108 0.337

EG 2.000 0.163 0.304

TDE related parameters are; ampliﬁcation control F = 0.99, crossover constant CR = 0.85, trigonometric mutation probability Mt = 0.05 and number of parameter vectors NP = 100. 1 The

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255

Criterion and category BOEs for the two products P12 and P24.

Criterion BOE P12∗ mP12,i ({Std}) mP12,i ({Ecy}) mP12,i ({Std,Ecy})

SG 0.641 0.175 0.000 0.825

FB 0.998 0.321 0.000 0.679

ST 0.245 0.000 0.000 1.000

FT −0.223 0.000 0.000 1.000

PN 0.447 0.197 0.000 0.803

EG −0.014 0.062 0.163 0.775

Category BOE 0.537 0.081 0.383

P24∗ mP24,i ({Std}) mP24,i ({Ecy}) mP24,i ({Std, Ecy})

−1.376 0.000 0.126 0.874

−0.209 0.000 0.133 0.867

−1.800 0.000 0.000 1.000

−0.223 0.000 0.000 1.000

0.108 0.098 0.098 0.804

−0.250 0.000 0.225 0.775

BOE 0.060 0.448 0.492

In Table 3, the standardised criteria values of the two products are given (P12∗ and P24∗ ). The construction of these BOEs is demonstrated for the evidence from the SG criterion for the P12 product, deﬁned mP12,SG (·), which starts with the associated conﬁdence value cfSG (v), with criteria value 6.3g, so when standardised, using Table 1, v = (6.3 − 5.728)/0.892 = 0.641, it follows: 1 1 = = 0.894 cfSG (0.641) = 1 + e−2.000(0.641+0.424) 1 + e−2.000(0.641+0.424) Using this value the three mass values which deﬁne mP12,SG (·) are given by: mP12,SG ({Std}) =

0.811 × 0.400 0.400 0.894 − 1 − 0.811 1 − 0.811

= 1.892 − 1.717 = 0.175 −0.400 0.894 + 0.400 = −1.892 + 0.4 mP12,SG ({Ecy}) = 1 − 0.811 = −1.492(negative) so assign 0.000 and mP12,SG ({Std, Ecy}) = 1.000 − mP12,SG ({Std}) − mP12,SG ({Ecy}) = 1.000 − 0.175 − 0.000 = 0.825 These three mass values mP12,SG ({Std}) = 0.175, mP12,SG ({Ecy}) = 0.000 and mP12,SG ({Std, Ecy}) = 0.825 describe the evidence from the SG criterion to the classiﬁcation of the P12 product. They suggest the SG criterion is not ambiguous in the evidence it offers, with only evidence supporting its speciﬁc classiﬁcation to Std (no speciﬁc evidence supporting Ecy) the rest is ignorance. Considering the other criterion BOEs associated with P12 in Table 3, the ST and FT criteria each have total ignorance associated with their evidence

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(a)

(b)

{Std, Ecy} ST

FT

EG

{Std, Ecy} ST FT SG FB PN EG

SG PN FB

P24

cy} {E

td} {S

d} {St

cy}

P12

{E

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Figure 1. Simplex coordinate representation of criterion and category BOEs for P12 and P24.

(mP12,ST ({Std, Ecy}) = 1.000 and mP12,FT ({Std, Ecy}) = 1.000). This is not because they are missing values (see later) but that the optimisation process has not constrained them to offer any evidence in this case (the large Ai values associated with ST and FT restrict the domain of their values where speciﬁc evidence will be offered, see Figure B1 in Appendix B). The criterion BOEs from all the criteria can then be combined to produce the concomitant category BOE for P12 (see Appendix B), deﬁned mP12 (·), also given in Table 3. With mP12 ({Std}) = 0.537 > 0.081 = mP12 ({Ecy}), then its classiﬁcation is to being Std, which is correct (see Table A1). Each of the BOEs (triplet of mass values) can be represented as a point (simplex coordinate) in a simplex plot (standard domain of representation of evidence and ﬁnal classiﬁcation using CaRBS), see Figure 1. The shaded regions in each simplex plot in Figure 1 denote the subdomains where the criterion BOEs are represented (constrained by the Bi control variables, here equal to 0.4 in each case). The vertical dashed lines partition where in the simplex plot there is a majority of evidence to Ecy (left) or Std (right). The other simplex coordinate reported in each simplex plot is the category BOE for that product, for P12 and P24 they are to the right and left of the vertical lines, signifying classiﬁcation to Std and Ecy, respectively (correct classiﬁcation in both cases). The majority of the criterion BOEs are represented on the top two edges of the simplex plots, a direct consequence of the objective function utilised, which attempted to mitigate ambiguity (away from vertical dashed line, see Appendix B). Their varying heights in the simplex plot a consequence of not enforcing the reduction of ignorance in the evidence from each criterion. The ﬁnal classiﬁcation of all the 25 baked bean products, to Std and Ecy, are based on their category BOEs, reported in Figure 2.

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{Std, Ecy}

(a)

24

(b)

{Std, Ecy}

3 10

16

1

25 21 20

5

8

23

12

cy}

13

{E

18

15

4 9 6 14 11

td} {S

{E

7 2

d} {St

cy}

19 17 22

257

Figure 2. Simplex coordinate representation of category BOEs for all products.

The results in Figure 2 confer the classiﬁcation of products known to be Ecy (Figure 2a) and Std (Figure 2b), with correct classiﬁcation for those to the left and right of the vertical dashed lines, respectively. It follows, there is a 92.0% (23 of the 25) correct classiﬁcation of products, split into 14 Std (out of 15) and 9 Ecy (out of 10) products. The varying heights of the category BOEs’ simplex coordinates in the simplex plots exposit the different levels of ignorance associated with their classiﬁcation. A benchmark multivariate discriminant analysis (MDA) produced 88% correct classiﬁcation of the products (split into 13 Std (out of 15) and 9 Ecy (out of 10) products).2 These analyses each identify high levels of discernment of the Std and Ecy products, based on their related nutrient levels. It follows, as a model of a customer’s choice it suggests their ability to discern between these products without the need for attention to price differentials. Further research would be required to identify the major criteria (nutrients) that make this discernment possible.

5.

CaRBS Analyses with Created Missing Values

This section undertakes similar CaRBS analyses (to that in Section 4) on the baked bean data set with different levels of missing values present (data sets D10%, D25% and D50%, see Section 3). One feature of a CaRBS analysis is 2 For

the MDA, a check was made on the normality of the group distributions of the individual criteria (Lin and Piesse, 2004), the Shapiro-Wilk test was utilised (Shapiro and Wilk, 1965). It was found the normality of the criteria SG, FT and PN could be rejected. Hence these criteria should not be incorporated in the MDA (they are kept for completeness). This check is needed with MDA, but not a pre-requisite when using CaRBS.

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that it can operate on an incomplete data set, hence here two series of analyses are presented, ﬁrst on the incomplete data sets and then on the “imputed” ﬁlled-in data sets (using the mean values of the remaining data values, see Table 1). In each series of analyses only the simplex plot representation of results are reported (and discussed).

5.1. CaRBS analyses of original incomplete data sets The analyses of the incomplete data sets D10%, D25% and D50% using CaRBS requires one further formulisation due to the presence of missing values. That is, where a criterion value is missing its associated criterion BOE is made up of only ignorance, namely mi,j ({Std, Ecy}) = 1 (with mi,j ({Std}) = 0 and mi,j ({Ecy}) = 0). Moreover, a missing value is considered an ignorant value and so offers no evidence in the subsequent classiﬁcation of the product. To illustrate, in Appendix A, for the P12 product in D10%, its SG criterion now has a missing value (a 3 in brackets in Table A1 identiﬁes it is missing in D10%, D25% and D50%). It follows, its criterion BOE mP12,SG (·) will now be made up of the three mass values mP12,SG ({Std}) = 0, mP12,SG ({Ecy}) = 0 and mP12,SG ({Std, Ecy}) = 1. This is in contrast to its values exposited in the previous section (see Table 3), which were found when optimising the concomitant objective function. The optimisation process is affected by the non-missing values, with their respective criterion BOEs found from the control variable values evaluated, throughout this process a missing value has their concomitant criterion BOEs ﬁxed as given above. The optimisation process was undertaken, using TDE, on D10%, D25% and D50%, the resultant details of the P12 product are reported in Figure 3 (only labels for non-total ignorant evidential criterion are given). {Std, Ecy}

(b) D25%

(c) D50%

FT EG PN FB

PN EG

{Std, Ecy}

FB P12

{Std, Ecy}

EG P12

d} {St

td} {S

td} {S

{E cy}

P12

{E cy}

(a) D10%

{E cy}

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Figure 3. Simplex coordinates of criterion and category BOEs for P12 (D10%, D25% and D50%).

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Brieﬂy discussing the reported simplex plot in Figure 3a, the classiﬁcation evidence of P12 in the D10% data set closely resembles that given in Figure 1a. The only major difference is on the SG criterion BOE, which due to it now being missing has its simplex coordinate at the {Std, Ecy} vertex (not labelled here). The result on the category BOE m12 (·) (labelled P12) is that slightly more ignorance is associated with the classiﬁcation it confers (simplex coordinate further up the simplex plot than in Figure 1a). The results in Figure 3c are different, with four missing values now present amongst the criteria describing P12 (see Table A1), it shows only the EG criterion offers non-ignorant evidence. It follows, the category BOE (for P12) is at the same position of the EG criterion BOE, the results still confer its correct classiﬁcation. The results pertaining to each of the products are presented in Figure 4 (simplex coordinates of category BOEs, a cross and circle labelling Ecy and Std product categories, respectively). The results in Figures 4a and 4b, show a relatively similar spread of simplex coordinates as in Figure 2. When looked from left to right there is a general movement upwards across the simplex plots of identiﬁed simplex coordinates. In Figure 4b, the P8’s simplex coordinate has moved considerably towards the {Std, Ecy} vertex (for D25%), due to ST, FT, PN and EG being missing for this product (each now offers ignorant evidence see Table A1). The simplex coordinates in Figure 4c elucidate the effect of the relative high number of missing values (induced) in the data set, with their positions nearer the {Std, Ecy} vertex. Indeed, product P21’s simplex coordinate is at this vertex, indicating their category BOE is associated with total ignorance. This a consequence of ﬁve out of six of its criterion (nutrient levels) are missing (see Table A1), the remaining criterion offers only ignorant evidence also.

(a) D10%

(b) D25%

{Std, Ecy}

(c) D50%

{Std, Ecy}

{Std, Ecy} 21

8 8

18

24

17 20 22 19

18

22 23

24 1 12 14 13 18 9 10 11 16 3 5 4 6 2 15 7

20 17

19

d} {St

5 16 10 3 7 14 12 23 1 4 2 6 9 13 15 11

d} {St

7 12 3 10 5 2 6 23 13 11 4 9 15 14

{E cy}

8 1

d} {St

{E cy}

19

24

16

{E cy}

21 25

25 21 20 22 17

25

Figure 4. Simplex coordinates of category BOEs of products (on D10%, D25% and D50%).

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A summary of the classiﬁcation results in these simplex plots indicate a 92% level of correct classiﬁcation with each of the D10%, D25% and D50% data sets (as with D0%). Keeping the missing values as missing in this section means that a MDA study is not possible. The important consequence of these analyses is that the fullest interpretation can be given on the results since there is no transformation of the data sets in anyway.

5.2. CaRBS analyses of “imputed” ﬁlled-in data sets The analyses here are on the ﬁlled-in versions of the baked bean data sets, D10%, D25% and D50%, described earlier (see Section 3). One inhibiting factor is the small sample size present in these data sets (25 products), this would argue against the use of case deletion, or even the more recent model based approaches due to the limited data present (see Section 2). To illustrate, Shen and Lai (2001) in a simulation study imposed a maximum of 20% missing values in a data set because any higher may mean no complete cases would exist, which would mitigate the ability to use case deletion. Here, itself somewhat inappropriate, the mean imputation process is utilised, whereby the concomitant mean values given in Table 1 in Section 3 replaces the respective missing values in each case. These ﬁlled-in data sets thus have no missing values and the optimisation process inherent with CaRBS is undertaken accordingly (as previously prescribed). Considering again the P12 product, the criterion and category BOEs over the ﬁlled-in D10%, D25% and D50% data sets are presented using the simplex plot representation, see Figure 5. The results in Figure 5 are directly comparable with those in Figure 3, with levels of similarity existing in the D10% and D25% data sets. With

{Std, Ecy}

EG

(b) D25%

PN FB

{Std, Ecy} EG

(c) D50%

PN FB

{Std, Ecy} PN

FT

P12

P12 d} {St

d} {St

td} {S

{E cy}

P12

{E cy}

(a) D10%

{E cy}

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Figure 5. Simplex coordinates of criterion and category BOEs for P12 (ﬁlled-in D10%, D25% and D50%).

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16 1

8

7 12

5 2

23 15 13

20 22 17

6 4 14

11

19

25 16 10 3 5 21 12 7 24 14 2 1 8 4 18 23 15

23 17 9 6

10 18

13 3 14 5

9 2

4

6

19

11

11 15

d} {St

13

{Std, Ecy} 24 21 8 25 7 20 12 1 22 16

d} {St

9

d} {St

{E cy}

20 24 22 21 17 18

3 10

(c) D50%

{Std, Ecy}

{E cy}

25

19

(b) D25%

{Std, Ecy}

{E cy}

(a) D10%

261

Figure 6. Simplex coordinates of category BOEs of products (ﬁlled-in D10%, D25% and D50%).

respect to the D50% data set (Figures 3c and 5c) a noticeable difference is shown, here in Figure 5c there is evidence from the criteria FT and PN to classify the P12 product (its correct classiﬁcation is to Std, so incorrect in this case). This is in contrast to that in Figure 3c, where there was evidence from only EG (which subsequently offered the correct classiﬁcation of P12). This example shows the CaRBS technique when operating on a ﬁlled-in D50% data set has found an incorrect classiﬁcation, whereas it is correctly classiﬁed when using only the data that was present in D50%. The results on the classiﬁcation of the 25 products in the ﬁlled-in data sets D10%, D25% and D50% are reported in Figure 6. The results in Figure 6 are comparable with those in Figure 4. For D10% and D25%, the results are similar. For D50% there is a similar movement upwards of the simplex plots, but there is also a movement of some product classiﬁcations to the left of their positions found previously when the missing values were not ﬁlled-in. This is a consequence of the surrogate values taken by the missing values. It is found 88%, 88% and 80% levels of correct classiﬁcation were found for the ﬁlled-in D10%, D25% and D50% data sets. Comparison of these results with when the incomplete data sets were considered (using CaRBS) can be made, but by ﬁlling in the missing values the analyses are on different data sets (for example on incomplete D10% and ﬁlled-in D10%). One noticeable difference in classiﬁcation results associated with D50%, where there were 92% and 80% levels of correct classiﬁcation on the incomplete D50% and ﬁlled-in D50% data sets, respectively. A concomitant MDA investigation can be undertaken here since there are no missing values in any of the ﬁlled-in data sets. It was found 88%, 84% and 88% levels of correct classiﬁcation exist for the ﬁlled-in D10%, D25% and D50% data sets.

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Conclusions

This paper has presented a discussion on the presence and management of missing values, traditionally considered an inherent feature of data analysis. The plethora of approaches to manage them (including imputation) is a consequence of the varying reasons for the causes (mechanisms) to their presence. This discussion is informative to research that is based on data sets constructed from questionnaires and/or external databases. To offer a mitigation of the need for this management issue, the Classiﬁcation and Ranking Belief Simplex (CaRBS) system is employed on a small object classiﬁcation problem. One aspect of the utilisation of CaRBS is that it can operate on an incomplete data set with missing values inherent. It further highlights the nascent notion of uncertain reasoning to the reader, in this case with the rudiments of CaRBS based on the Dempster-Shafer theory of evidence. Indeed the detail in the evaluation of the incumbent “bodies of evidence” of criteria support to the classiﬁcation of objects in the CaRBS system offers the fullest opportunity for a reader’s understanding. The food product category problem considered is representative of a classiﬁcation problem in marketing and consumer choice. The particular issue being the discernment of standard and economy baked beans products based on their individual nutrient levels (salt, fat, etc.). The small size of the data set would be problematic for traditional analysis techniques as well as not perpetuating the achieving of an appropriate management of any missing values. The graphical results, using simplex plots, from the CaRBS analyses show the effects of imputing or not imputing the missing values. With their solution a constrained optimisation problem, the results further exposit the separate issues of ambiguity and ignorance in their classiﬁcation. The presentation of the considered data set allows the reader to undertake his or her own analyses. These could include the application of other classiﬁcation techniques, as well as alternative approaches to the management of missing values. The continued comparisons of the results will allow a reader to obtain an understanding on the effects of using different surrogates for the missing values (when present).

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Appendix A: Description of Baked Bean Data Set This Appendix reports the nutrient values associated with each of the 25 “baked bean in tomato sauce” products considered, see Table A1. Within the table the classiﬁcation of each product to either being Std (Standard) or Ecy (Economy) is noted. Also included in Table A1 is the labelling of which elements of the data set were deﬁned as missing. This is a progressive creation of missing values, whereby a value deﬁned missing in the D10% case would automatically be missing in the D25% and D50% data sets. It follows, labels 1, 2 or 3 (in brackets) acknowledge these values were considered missing for only the D50% case (1), D50% and D25% cases (2) and D50%, D25% and D10%

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P1 Heinz P2 Heinz Organic P3 Crosse & Blackwell P4 HP P5 Tesco P6 Sainsbury’s P7 Asda P8 Waitrose P9 Safeway P10 Marks & Spencer P11 Somerﬁeld P12 Spar P13 Co-op P14 Budgens P15 Morrisons P16 Tesco Value P17 Sainsbury’s Low Price P18 Asda Smart Price P19 Safeway Savers P20 Somerﬁeld Makes Sense P21 Nisa Today’s Value P22 Co-op Everyday P23 Corale Premium Quality P24 Iceland Great Value P25 Morrisons Bettabuy

Description of 25 baked bean products. SG (g) FB (g) ST (g) FT (g) PN (g) EG (kcal) Category 5.0 (1) 5.3 (0) 4.7 (1) 6.1 (0) 6.2 (2) 6.3 (0) 5.0 (0) 5.1 (0) 5.8 (0) 5.2 (0) 7.1 (0) 6.3 (3) 5.0 (0) 7.1 (0) 8.7 (1) 5.5 (0) 5.4 (0) 6.0 (1) 5.4 (0) 5.2 (2) 5.2 (2) 6.0 (0) 5.9 (0) 4.5 (1) 5.2 (0)

3.6 (0) 3.9 (0) 3.5 (0) 3.7 (2) 3.5 (2) 3.7 (0) 3.7 (1) 3.3 (0) 3.7 (0) 3.5 (0) 3.5 (1) 3.7 (1) 3.0 (0) 3.5 (1) 3.7 (0) 3.5 (0) 3.1 (3) 3.7 (0) 3.1 (0) 3.2 (1) 3.2 (2) 3.0 (3) 3.4 (1) 3.4 (3) 3.2 (3)

1.0 (1) 1.3 (3) 1.3 (1) 1.3 (0) 1.3 (0) 1.3 (1) 1.3 (3) 1.0 (3) 1.3 (0) 1.3 (0) 1.5 (3) 1.3 (1) 1.0 (1) 1.5 (2) 1.5 (0) 1.3 (0) 1.3 (0) 1.3 (1) 1.3 (0) 1.3 (1) 1.3 (2) 1.3 (0) 1.0 (2) 1.0 (3) 1.3 (3)

0.2 (0) 0.2 (0) 0.3 (2) 0.7 (1) 0.3 (0) 0.4 (3) 0.3 (0) 0.6 (2) 0.5 (0) 0.3 (1) 0.3 (1) 0.3 (0) 0.4 (2) 0.3 (2) 0.2 (2) 0.3 (2) 0.2 (3) 0.2 (0) 0.2 (0) 0.3 (1) 0.3 (0) 0.2 (0) 0.7 (0) 0.3 (0) 0.3 (1)

4.6 (1) 4.9 (0) 4.6 (0) 4.7 (0) 4.6 (0) 4.9 (0) 4.6 (1) 4.2 (2) 4.7 (0) 4.6 (2) 4.7 (1) 4.6 (1) 5.0 (0) 4.7 (1) 2.9 (0) 4.5 (0) 3.9 (1) 2.9 (1) 3.9 (0) 4.2 (0) 4.2 (2) 3.0 (1) 4.9 (1) 4.4 (1) 4.2 (0)

73 (2) 76 (0) 84 (0) 85 (0) 85 (0) 85 (1) 77 (0) 81 (3) 101 (1) 85 (0) 93 (0) 80 (0) 90 (1) 92 (2) 69 (0) 78 (2) 65 (0) 69 (0) 65 (0) 78 (0) 78 (1) 75 (1) 83 (3) 78 (0) 78 (2)

Std Std Std Std Std Std Std Std Std Std Std Std Std Std Std Ecy Ecy Ecy Ecy Ecy Ecy Ecy Ecy Ecy Ecy

cases (3). To illustrate the notation used in Table A1, for the product P1, its EG criterion value is labelled 2 indicating it was considered missing in the D50% and D25% data sets only, and not the D10% case. A brief inspection of these data sets identiﬁes product P19 has no missing values throughout each created data set. In contrast, P8 and P21 have only one or two nonmissing values in the D25% and D50% cases.

Appendix B: Description of CaRBS System This Appendix brieﬂy described the rudiments of the CaRBS system for object classiﬁcation (for a detailed discussion see Beynon, 2004 and Beynon and Buchanan, 2004). Its aim is to construct a body of evidence (BOE) for each criteria value that includes levels of exact belief (mass values) in the support

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1 1 1 e − k (v−θ i

i

0

1

Bi mj,i({x})

Ai

)

267

cfj,i( v) mj,i({x, ¬x})

0.5

mj,i({¬ x}) 0

0

θi v

(a)

vj,i, 1

0 vj,i, 2

vj,i, 3

1 (b)

{x , ¬x } (c) ej,i, 1 pj,i,v

{¬x}

ej,i, 3

ej,i,2

{x}

Figure B1. Progression through the stages of the CaRBS system for a characteristic value v.

for the classiﬁcation of an alternative to a given hypothesis ({x}), its compliment ({¬x}) and concomitant ignorance ({x, ¬x}). These mass values can then elucidate evidence on the level of preference for an alternative, with x and ¬x depicting the extremes of preferred and not preferred respectively. To brieﬂy describe the CaRBS system, Figure B1 reports the transformation of an individual criteria value into a criterion BOE. In Figure B1, stage (a) shows the transformation of a value vj,i (jth alternative, ith criteria) into a conﬁdence value cfi (vj,i ), using a sigmoid function, with control variables ki and θi . Stage (b) transforms a criterion’s conﬁdence value cfi (vj,i ) into an criterion BOE, made up of the three mass values mj,i ({x}), mj,i ({¬x}) and mj,i ({x, ¬x}), which represent the exact beliefs in {x}, {¬x} and

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{x, ¬x}, respectively ({x, ¬x} representing ignorance). From Safranek et al. (1990) these mass values are deﬁned by: mj,i ({x}) = and

Bi Ai Bi −Bi cfi (vj,i ) − , mj,i ({¬x}) = cfi (vj,i ) + Bi 1 − Ai 1 − Ai 1 − Ai mj,i ({x, ¬x}) = 1 − mj,i ({x}) − mj,i ({¬x})

where Ai and Bi are two further control variables. When either mj,i ({x}) or mj,i ({¬x}) are negative they are set to zero (before the calculation of mj,i ({x, ¬x})). The control variable Ai depicts the dependence of mj,i ({x}) on cfi (vj,i ) and Bi is the maximum value able to be assigned to mj,i ({x}) or mj,i ({¬x}). Stage (c) shows the mass values in a BOE mj,i (·); mj,i ({x}) = vj,i,1 , mj,i ({¬x}) = vj,i,2 and mj,i ({x, ¬x}) = vj,i,3 , can be represented as a simplex coordinate (single point) in a simplex plot (equilateral triangle). That is, the ratios of the distances of the simplex coordinate pj,i,v to the edges of the simplex plot (pj,i,v ej,i,k , k = 1, . . . , 3) are the same as the ratios of the mass values vj,i,k , k = 1, . . . , 3. When nA criteria describe each alternative oj , j = 1, . . . , nO , a number of criterion BOEs are constructed. Within DST, Dempster’s rule of combination is used to combine two (or more) independent BOEs. With respect to the CaRBS system, this will allow the combination of the criterion BOEs to produce a ﬁnal BOE associated with an alternative and its level of preference (and subsequently used to rank the alternatives). With x and ¬x exhaustive classiﬁcation outcomes, the combination of two BOEs mj,i (·) and mj,k (·), deﬁned (mj,i ⊕ mj,k )(·), results in a combined BOE whose mass values are given by: (mj,i ⊕ mj,k )({x}) mj,i ({x})mj,k ({x}) + mj,k ({x})mj,i ({x, ¬x}) + mj,i ({x})mj,k ({x, ¬x}) = 1 − (mj,i ({¬x})mj,k ({x}) + mj,i ({x})mj,k ({¬x})) (mj,i ⊕ mj,k )({¬x}) mj,i ({¬x})mj,k ({¬x}) + mj,k ({x, ¬x})mj,i ({¬x}) + mj,k ({¬x})mj,i ({x, ¬x}) = 1 − (mj,i ({¬x})mj,k ({x}) + mj,i ({x})mj,k ({¬x})) (mj,i ⊕ mj,k )({x, ¬x}) = 1 − (mj,i ⊕ mj,k )({x}) − (mj,i ⊕ mj,k )({¬x}) This combination rule can be iteratively employed to augment the evidence in the criterion BOEs into the respective ﬁnal BOE.

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