Neighborhood Structures and Crime: A Spatial Analysis (Criminal Justice: Recent Scholarship)

Criminal Justice Recent Scholarship

Edited by Marilyn McShane and Frank P. Williams III

A Series from LFB Scholarly

Neighborhood Structures and Crime A Spatial Analysis

George Kikuchi

LFB Scholarly Publishing LLC El Paso 2010

Copyright © 2010 by LFB Scholarly Publishing LLC All rights reserved. Library of Congress Cataloging-in-Publication Data Kikuchi, George, 1980Neighborhood structures and crime : a spatial analysis / George Kikuchi. p. cm. -- (Criminal justice: recent scholarship) Includes bibliographical references and index. ISBN 978-1-59332-396-7 (hardcover : alk. paper) 1. Criminal statistics. 2. Neighborhoods. 3. Crime analysis. 4. Spatial analysis (Statistics) I. Title. HV6208.K55 2010 364.2'2--dc22 2010001568

ISBN 978-1-59332-396-7 Printed on acid-free 250-year-life paper. Manufactured in the United States of America.

Table of Contents

Tables ..................................................................................................vii Figures .................................................................................................. ix Acknowledgement ..............................................................................xiii Chapter 1. Introduction .......................................................................... 1 Introduction.................................................................................... 1 Statement of Problem..................................................................... 2 Theoretical Orientation .................................................................. 5 Summary...................................................................................... 12 Chapter 2. Longitudinal Analysis of Crime Rates at the Neighborhood Level .......................................................................... 15 Introduction.................................................................................. 15 Explaining Crime Waves ............................................................. 17 Analysis of Change ...................................................................... 19 Research Questions...................................................................... 22 Data.............................................................................................. 24 Exploratory Spatial Data Analysis ............................................... 26 Method I: Growth Curve Models................................................. 27 Results: Growth Curve Model ..................................................... 31 Method II: Spatial Panel Model ................................................... 49 Results: Spatial Panel Model ....................................................... 59 Summary...................................................................................... 64 Chapter 3. An Analysis of Spatially Varying Associations between Neighborhood Characteristics and Crime ............................................ 69 Introduction................................................................................. 69 Research Question ...................................................................... 72 Spatial Dependency and Spatial Heterogeneity .......................... 72 Theoretical Expectations regarding Spatial Variability .............. 77 Methods ...................................................................................... 79 Data............................................................................................. 84 Results for Spatial Regression Models ....................................... 87 Results for Geographically Weighted Regression Models.......... 94 v

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Neighborhood Structures and Crime: A Spatial Analysis

Summary................................................................................... 107 Chapter 4. A Spatial Analysis of Criminal Offenders’ Target Selection ............................................................................................ 113 Introduction............................................................................... 113 Neighborhood Characteristics and Crime ................................. 115 Journeys to Crime ..................................................................... 117 Target Selection as Rational Choice ......................................... 119 A Summary of Literature Review ............................................. 120 Hypotheses................................................................................ 121 Data........................................................................................... 125 Method ...................................................................................... 129 Results....................................................................................... 131 Summary................................................................................... 138 Chapter 5. Conclusion........................................................................ 145 What is Special about Space in Criminology? .......................... 145 Theoretical Implications of the Longitudinal Analysis of Crime ........................................................................................ 148 Theoretical Implications of the Analysis of Spatial Dependency and Spatial Heterogeneity .................................... 150 Theoretical Implications for Criminal Offenders’ Target Selection.................................................................................... 155 Policy Implications ................................................................... 157 Limitations of the Current Research and Directions for Future Research.................................................................................... 161 Appendices A. Maps of Seattle Data ............................................................ 165 B. Maps of Philadelphia Data ................................................... 175 C. Maps of Glendale Data ........................................................ 179 References ......................................................................................... 181 Index ................................................................................................. 197

Tables

2.1 Moran’ I Spatial Autocorrelation Coefficients of Crime Rates and OLS Residuals...................................................................... 27 2.2 Baseline Growth Curve Models of Homicide, Robbery, Burglary, and Auto Theft Rates per 1,000 People ....................................... 32 2.3 Comparisons of Observed Means and Predicted Levels of Crime Based on the Baseline Growth Curve Models ............................. 34 2.4 Variance-Covariance Matrix of Random Effects of Growth Curve Models ......................................................................................... 36 2.5 Growth Curve Models of Crimes between 1960 and 2005 with Neighborhood Characteristics as Time Invariant Predictors........ 40 2.6 Changes in Neighborhood Characteristics as Time Variant Predictors. .................................................................................... 46 2.7 Spatial Panel Models of Changes in Crime Rates Predicted by Changes in Neighborhood Characteristics ................................... 60 3.1 Descriptive Statistics for Neighborhood Characteristics................ 87 3.2 OLS Regression of Crime Rates on Neighborhood Characteristics.............................................................................. 88 3.3 Spatial Regression of Crime Rates on Neighborhood Characteristics.............................................................................. 92 3.4 Spatially Varying Coefficient Estimates from Geographically Weighted Regression of Violent Crimes...................................... 96 3.5 Spatially Varying Coefficient Estimates from Geographically Weighted Regression of Property Crimes.................................... 98 4.1 Descriptive Statistics for Neighborhood Characteristics.............. 127 4.2 Data Structures of a Conditional Logit Model (Hypothetical Data) .......................................................................................... 128 4.3 Conditional Logit Models of Offenders’ Target Selection Predicted by Neighborhood Characteristics............................... 131 4.4 Conditional Logit Models of Offenders’ Target Selection using Racial Characteristics of Neighborhoods and Offenders ........... 134 vii

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Neighborhood Structures and Crime: A Spatial Analysis

4.5 Conditional Logit Models of Offender Target Selection by Youth and Adult Offenders........................................................ 137 4.6 Conditional Logit Models of Target Selection by Single and Multi-Offenders ......................................................................... 139

Figures

2.1 Five Trajectories of Neighborhood Crime Rates (Hypothetical Data) ............................................................................................ 29 2.2 An Averaged Trajectory of Burglary Rates across Five Neighborhoods............................................................................. 29 2.3 Predicted Trajectories of Homicide for Average Neighborhoods and Increasingly Socially Disorganized Neighborhoods ............ 45 3.1 Global Statistics ............................................................................. 83 3.2 Local Statistic ................................................................................ 83 3.3 Spatially Varying Regression Coefficients of the Percentage Male Youth on Aggravated Assault.......................................... 101 3.4 Spatially Varying Regression Coefficients of Racial Heterogeneity on Aggravated Assault ....................................... 101 3.5 Spatially Varying Regression Coefficients of Residential Language Ability on Aggravated Assault ................................. 101 3.6 Spatially Varying Regression Coefficients of Population Density on Aggravated Assault.............................................................. 102 3.7 Spatially Varying R-square of Geographically Weighted Regression of Aggravated Assault............................................ 102 3.8 Spatially Varying Regression Coefficients of Racial Heterogeneity on Robbery ......................................................... 102 3.9 Spatially Varying Regression Coefficients of the Percentage Public Transportation on Robbery ............................................ 103 3.10 Spatially Varying Regression Coefficients of Language Ability on Robbery ................................................................... 103 3.11 Spatially Varying R-square of Geographically Weighted Regression of Robbery............................................................... 103 3.12 Spatially Varying Regression Coefficients of Racial Heterogeneity on Residential Burglary...................................... 104 3.13 Spatially Varying Regression Coefficients of Language Ability on Residential Burglary ............................................................ 104 ix

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Neighborhood Structures and Crime: A Spatial Analysis

3.14 Spatially Varying Regression Coefficients of Socio-economic Disadvantage on Residential Burglary....................................... 104 3.15 Spatially Varying Regression Coefficients of Residential Mobility on Residential Burglary............................ 105 3.16 Spatially Varying Regression R-square of Geographically Weighted Regression of Residential Burglary . 105 3.17 Spatially Varying Regression Coefficients of Language Ability on Auto Theft................................................................. 105 3.18 Spatially Varying Regression Coefficients of Socio-economic Disadvantage on Auto Theft ...................................................... 106 3.19 Spatially Varying R-squares of Geographically Weighted Regression of Auto Theft........................................................... 106 4.1 Spatial Distribution of Burglary Rates per 1,000 Households in Glendale, Arizona ...................................................................... 127 4.2 A Criminal Offender’s Choice and Alternatives.......................... 128 A.1 Homicide Rate per 1,000 People................................................. 165 A.2 Robbery Rate per 1,000 People................................................... 166 A.3 Burglary Rate per 1,000 Households .......................................... 166 A.4 Auto Theft Rate per 1,000 People............................................... 167 A.5 The Proportion of the Foreign Born Population.......................... 167 A.6 The Proportion of Children Living with Both Parents ................ 168 A.7 The Proportion of Public Transportation Users .......................... 168 A.8 The Proportion of Employed Females ........................................ 169 A.9 The Proportion of Male Youth (Ages 15-24).............................. 169 A.10 Residential Mobility.................................................................. 170 A.11 Racial Heterogeneity................................................................. 170 A.12 Socio-economic Disadvantage .................................................. 171 A.13 The Parameter Estimates of Homicide Trajectory .................... 171 A.14 The Parameter Estimates of Robbery Trajectory ...................... 172 A.15 The Parameter Estimates of Burglary Trajectory...................... 172 A.16 The Parameter Estimates of Auto Theft Trajectory .................. 173 B.1 The Spatial Distribution of Crime in Philadelphia ...................... 175 B.2 The Spatial Distribution of Demographic Variables in Philadelphia (1)......................................................................... 176 B.3 The Spatial Distribution of Demographic Variables in Philadelphia (2)......................................................................... 177 C.1 The Spatial Distribution of Socio-Demographic Characteristics in Glendale, AZ (1) ................................................................... 179

Figures

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C.2 The Spatial Distribution of Socio-Demographic Characteristics in Glendale, AZ (2) ................................................................... 180

Acknowledgements

First of all, I would like to thank Dr. Scott Feld, Dr. Raymond Florax, Dr. Jack Spencer, and Dr. Scott Desmond for helping me as I prepared this book. Thanks also go to Purdue University for providing me with financial support. I would also like to thank the Seattle Police Department, the Philadelphia Police Department, the Inter-university Consortium for Political and Social Research (ICPSR), and Mr. Bryan Hill for providing me with data and Dr. Wim Bernasco and Dr. Paul Elhorst for providing me with statistical program codes for conditional logit modeling and spatial panel modeling. Many thanks also go to Mr. Leo Balk for making this book possible. Finally, but not the least, my deepest gratitude to my parents who have given me moral support for pursuing an academic career.

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CHAPTER 1

Introduction

INTRODUCTION Spatial and temporal analyses of crime have been classic topics in criminology. For example, several of the first empirical studies in criminology by European scholars, such as Guerry, Quetelet, and Durkheim, involved analyses of the spatial distribution of crime in France (Beirne 1993). Furthermore, in the United States, Shaw and McKay (1942) conducted a seminal study of juvenile delinquency in Chicago that illustrated the spatial concentration of juvenile delinquency in the inner city over time. Spatial concentrations of crime in cities were also vividly illustrated by a study in Minneapolis (Sherman et al. 1989). Sherman and his colleagues found that 3% of the city’s addresses generated more than 50% of the calls to police and five of the top ten crime hot spots included bars and taverns. An analysis of crime based upon neighborhood characteristics is important for criminological inquiries for several reasons. First, crimes are not randomly distributed over space. In fact, crimes are so highly concentrated over space that the addresses of past crimes were six times more predictive for future crime than known offenders’ identities (Sherman 1995). Second, certain neighborhood conditions, such as income inequality and job unavailability, give rise to criminal motivation. Regardless of demographic characteristics, individuals living in disadvantaged neighborhoods are more likely to develop criminal inclinations than those living in affluent neighborhoods. Third, certain neighborhood and place characteristics are crime conducive, offering suitable opportunities with low levels of guardianship. For example, neighborhoods with high residential turnover provide anonymity for potential offenders who live outside the neighborhood. Existing studies also indicate the risk of store clerks being murdered 1

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Neighborhood Structures and Crime: A Spatial Analysis

varies considerably by types of business establishments because of the routine activities of both motivated criminals and legitimate citizens that occur there (Davis 1987). Any individual behavior is a product of interaction between the person and the setting (Felson and Clarke 1998). Crime, in particular, requires offenders and victims and social contexts that unite them (Miethe and McDowall 1993; Miethe and Meier 1990; Miethe and Meier 1994; Rountree et al. 1994; Wilcox et al. 2003). Crime occurs in micro-environments that have unique configurations of social and physical characteristics that provide varying levels of crime opportunity and guardianship. Even highly motivated offenders may give up committing a crime if the perceived chances of getting caught are high. A crime-conducive environment translates individuals’ criminal inclinations into action. Therefore, criminological inquiries need to explicitly incorporate spatial and temporal contexts of crime. STATEMENT OF PROBLEM While space and neighborhood characteristics are important in criminological research, empirical studies have been hindered because space is difficult to statistically analyze. Reviews of existing research on neighborhoods and crime have noted several limitations (Anselin et al. 2000; Kubrin and Weitzer 2003a). These limitations can be summarized as a failure to incorporate spatial and temporal dynamics of crime at the neighborhood level. First, although there are many studies that have examined the relationship between neighborhood characteristics and crime using cross-sectional data (e.g., Messner and Tardiff 1985; Miethe and Meier 1990; Miethe et al. 1987; Sampson and Groves 1989), the temporal aspects of crime at the neighborhood level have received limited attention (Bursik and Grasmick 1992; Kubrin and Herting 2003). Existing studies have relied mainly on cross-sectional data and failed to examine changes in neighborhood characteristics and crime rates over time. Official crime statistics (e.g., Uniform Crime Reports) indicate the United States experienced a rapid increase in violent crime between 1960 and the late 1980s, followed by a decrease. Many cities followed similar patterns of crime rate increases and decreases. What is less known, however, is whether neighborhoods

Introduction

3

within cities followed a similar rapid increase and decrease in crime over time. Despite city-level statistics showing crime rate increases, many neighborhoods might have remained safe. Several authors argue that neighborhood changes in crime over time, or the criminal careers of communities, have not been fully investigated (Maltz 1995; Schuerman and Kobrin 1986; Sherman 1995). Although there are studies that have conducted longitudinal analyses of crime at the macro level (e.g., states, counties, and cities), it is important to recognize that neighborhood characteristics are likely to vary considerably within cities. The process of social disorganization and criminal opportunities generating crimes is likely to operate at the neighborhood level. Second, despite the widely recognized importance of space in criminology, it has been difficult to fully incorporate spatial effects of crime and neighborhood characteristics in regression models. As crimes are likely to be spatially concentrated, researchers need to explicitly incorporate this spatial effect in their regression models (i.e., spatial dependency). As the level of crime in surrounding neighborhoods is often a strong predictor of the level of crime in a neighborhood, the omission of a spatially lagged crime variable is a model misspecification. Additionally, as a result of the spatial concentration of crime, the residuals (i.e., the difference between the ) predicted and actual values: Yi − Yi ) of ordinary least squares (OLS) regression are likely to be correlated, which violates an assumption of OLS regression. In plain English, the non-independence of observations in spatial data can be explained as observations close to each other are more similar than those far apart. Violating the assumption of independence results in the inefficient estimation of regression coefficients and biased estimation of standard errors (which means flawed statistical significance tests). Thus, without an explicit consideration of spatial effects, statistical inferences are no-longer trustworthy. In addition to spatial dependency, there are several reasons to suspect that structural relationships between neighborhood characteristics and crime vary across space (i.e., spatial heterogeneity) (Anselin et al. 2000; Fotheringham 1997; Fotheringham et al. 2002a; Wilson 2005). Although a theory may predict a simple linear relationship between a neighborhood characteristic and crime, there may exist unobserved contextual effects that are specific to certain parts of the study area. For example, social disorganization theory

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Neighborhood Structures and Crime: A Spatial Analysis

hypothesizes that economic deprivation gives rise to criminal motivation and there is a positive association between the percentage of households in poverty and the level of crime. If a disadvantage neighborhood is surrounded by affluent neighborhoods, the effect of economic deprivation on criminal motivation may be stronger, as residents’ relative deprivation will be stronger than in other areas. As OLS regression is topologically invariant (meaning the spatial arrangement of data does not matter in OLS) and cannot address these spatial processes, existing studies have not fully investigated the spatial dynamics of crime at the neighborhood level. For both spatial dependency and spatial heterogeneity, one needs regression models specifically designed to incorporate these spatial processes. As such spatial regression models, and especially statistical packages to conduct estimation, have been developed only relatively recently, many criminological studies do not fully examine the spatial dynamics of neighborhood characteristics and crime. Third, the spatial analysis of crime has often relied on crime incident location data and failed to account for where offenders are coming from. Some neighborhoods may be vulnerable to outsiders, while other neighborhoods experience high crime rates due to offenders living within the area. Different types of crime prevention strategies may be necessary depending on where offenders are coming from. Crimes committed by insiders may be more suitably prevented through a developmental model of crime prevention (e.g., youth counseling, community centers for youth activities, and improved schools). However, crimes committed by outsiders may be more suitably prevented by changing the opportunity structure of neighborhoods (e.g., strengthening the ability to identify potential outsiders). These three limitations of existing research can be summarized as a failure to account for spatial and temporal dynamics of crime and neighborhood characteristics. This research proposes to complete a series of studies to better understand how neighborhoods influence criminal opportunity and behavior by taking advantage of recent methodological developments in psychology and spatial econometrics. In particular, based on social disorganization theory and routine activities theory, this book examines: 1) longitudinal changes in neighborhood characteristics and crime; 2) spatially heterogeneous associations between neighborhood characteristics and crime; and 3)

Introduction

5

criminal offenders’ target selection. These studies are attempts to further understand how neighborhood spatial and temporal dynamics influence crime rates. THEORETICAL ORIENTATION Using social disorganization theory and routine activities theory as a theoretical framework, this study develops research questions about the temporal and spatial distribution of neighborhood characteristics conducive to crime. Social Disorganization Theory Shaw and McKay (1942) conducted a study of the spatial distribution of juvenile delinquency in Chicago in the 1920s, which led them to propose social disorganization theory. Based on their spatial analysis, Shaw and McKay recognized that high crime areas were spatially concentrated in the inner city. Also, crime rates were high in the inner city and gradually decreased with distance from the city center. After mapping the “delinquency areas” of Chicago for many years, Shaw and McKay also discovered the spatial configuration of high crime areas remained the same over time. That is, juvenile delinquency was heavily concentrated in inner city neighborhoods over time, despite an almost total change in the racial and ethnic composition of residents. In addition to their findings on the distribution of juvenile delinquency, Shaw and McKay also found that neighborhoods in the inner city were characterized by various social problems. First, these inner city neighborhoods were economically disadvantaged, as indicated by a high proportion of people on public assistance, low median rent, low rate of housing ownership, and high unemployment. Housing conditions were deteriorated and the jobs that were available to residents were typically industrial jobs, while clerical and professional jobs were typically available to suburban residents. Second, these high-crime neighborhoods were residentially unstable and characterized by a high residential turnover rate. Third, various health problems were noted in the inner city, such as infant mortality, tuberculosis, and mental disorder. Fourth, the high-crime

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Neighborhood Structures and Crime: A Spatial Analysis

neighborhoods were characterized by racial heterogeneity. According to Shaw and McKay, the mixture of various ethnic groups hindered the realization of common values and goals among neighborhood residents. Based on these empirical findings, Shaw and McKay argued the spatial distribution of juvenile delinquency was a function of ecological characteristics, not the personal characteristics of individuals living in neighborhoods. That is, their theoretical model suggested that structural characteristics, such as poverty and residential mobility, led to the social disorganization of neighborhoods, which in turn resulted in an increase in crime. While Shaw and McKay’s empirical study and theoretical framework were influential in developing subsequent studies of crime, several limitations of their work have been noted (Bursik 1988; Kornhauser 1978; Kubrin and Weitzer 2003a; Sampson and Groves 1989). Most notably, Shaw and McKay’s theoretical model did not articulate the causal mechanism that linked neighborhood social disorganization to high crime rates. In fact, based upon their theoretical model, two versions of social disorganization theory can be conceived (Kornhauser 1978). First, a strain variant of social disorganization theory links structural characteristics and crime through the frustrated wants of residents living in disadvantaged neighborhoods. Frustrated wants (strain) are the result of discrepancies between aspirations and expectations. While money and social status are assumed to be universal aspirations, legitimate means to achieve them are not available to everyone. For residents living in economically disadvantaged neighborhoods, illicit activities often provide easier means to meet their aspirations. That is, the strain variant of social disorganization theory hypothesizes that the criminal motivation and frustrated wants resulting from the structural characteristics of neighborhoods is the intervening variable leading to an increase in crime. Second, a control variant of social disorganization theory links structural characteristics and crime through diminished informal social control. Informal social control in socially disorganized neighborhoods is weakened in several ways. Due to high residential mobility and racial heterogeneity, residents of disorganized neighborhoods cannot establish or maintain consensus about norms and values. A sense of belonging, attachment to community, social solidarity, and social

Introduction

7

cohesion are weakened. Residents who intend to leave their neighborhoods as soon as they can afford to do so have little vested interests in addressing neighborhood problems. Without common goals among neighborhood residents, effective social control cannot be implemented and criminal opportunities flourish. Trash on streets, abandoned buildings, graffiti, and drunken people become signs that neighborhood residents care little about social problems in their neighborhoods. Such physical and social incivility also lower the moral costs for potential offenders who target these neighborhoods. Furthermore, Shaw and McKay (1942) observed that individuals living in disorganized neighborhoods have fewer stakes in conformity, which lowers controls or restraints against committing crimes. As conflicting value systems existed (e.g., conventional norms vs. delinquent subcultures), juveniles living in disorganized neighborhoods often did not develop attachments to conformity. Having been exposed to delinquent subcultures, these juveniles become low in internal control and develop beliefs that are inconsistent with conventional values and norms. Moreover, as traditional social institutions, such as family and school, deteriorate, individuals with limited education, no jobs, and no attachment to significant others have fewer moral costs and stakes in conformity to prevent them from getting involved in illegal activities. In essence, the control model of social disorganization theory argues that social control, created internally and externally, influence the costs of crime. High levels of social control in organized neighborhoods make it difficult for residents to commit crimes, while diminished informal social control lowers stakes in conformity and weakens restraints from committing crimes. Comparing the two variants of social disorganization theory, Kornhauser (1978) argues that the control version is more consistent with empirical research than the strain version. Further extending the control variant of social disorganization theory, several studies used survey data to identify the role of social ties and social networks among neighborhood residents in establishing informal social control (Bursik and Grasmick 1993b; Elliott et al. 1996; Lowenkamp et al. 2003; Sampson 1991; Sampson and Groves 1989; Veysey and Messner 1999). For example, Sampson and Groves (1989) showed that the effects of structural characteristics on the level of crime were mediated by the extent of participation in community activities,

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Neighborhood Structures and Crime: A Spatial Analysis

the breadth of local friendship networks, and the presence of unsupervised youths. Their argument is that the structural characteristics of a neighborhood, such as poverty, residential mobility, and racial composition, decrease social ties among neighbors, participation in community organizations, and informal monitoring of neighborhood youth, which in turn results in an increase in the level of crime. Additionally, Bursik and Grasmick (1993b) argue that social control in neighborhoods is anchored at various social and physical institutions (e.g., family, school, religious institutions, political groups). In particular, they argue the level of social organization and social control vary across neighborhoods, depending on the extent of internal social cohesion among community members, as well as the extent of community leaders’ ties to external resources (e.g., policy makers). Bursik and Grasmick’s model of social disorganization theory is often called a systemic model that emphasizes the importance of relational networks among community residents. Their systemic model suggests that structural characteristics, such as socio-economic status, heterogeneity, and residential instability, affect the formation of relational networks, which in turn affects varying types of social control (e.g., private control, parochial control, public control, and socialization). In contrast to Bursik and Grasmick’s theoretical model, Sampson (2004) argues that social ties do not necessarily lead to effective social control. Instead, he argues that collective efficacy, defined as mutual trust among residents and a willingness to intervene when problems arise, is the key variable that links social ties and the level of social control (Morenoff et al. 2001; Sampson 2004; Sampson et al. 1997). Using a multilevel framework, Sampson and his colleagues show that collective efficacy can be reliably measured at the neighborhood level. Together with concentrated disadvantage, immigrant concentration, residential instability, and collective efficacy, their empirical analysis explained a substantial amount (70%) of the variability in violence. More importantly, although the level of violence is high in disadvantaged neighborhoods, collective efficacy mediated a substantial amount of the effects of socio-economic disadvantage and residential instability on the level of violence in neighborhoods.

Introduction

9

In sum, social disorganization theory provides a theoretical framework to understand relationships between neighborhood characteristics and crime. The strain variant of social disorganization theory argues that increased criminal motivation produced by neighborhood disadvantage is an intervening variable that connects neighborhood characteristics and crime rates. Thus, the distribution of crime over space is a result of variation in the distribution of motivated offenders. The control variant of social disorganization theory, on the other hand, links the structural characteristics of neighborhoods to the level of crime through informal social control. Social ties among community members, vested interests in community problems, and shared value systems help to strengthen informal social control. The control variant of social disorganization theory explains the spatial distribution of crime by varying levels of social control that neighborhoods exert. Routine Activities Theory In addition to social disorganization theory, routine activities theory has been used to explain the distribution of crime over space, especially at the micro level. Routine activities theory views criminal incidents as the intersection of offenders and victims under specific circumstances. In particular, routine activities theory argues that a crime occurs when a motivated offender and a suitable target converge in time and space in the absence of capable guardians (Cohen and Felson 1979). Interestingly, the theory argues that the amount of crime can change even without an increase/decrease in the number of offenders. The number of crimes can increase as the availability of suitable targets increases. Decreasing the level of guardianship changes criminal opportunity, which leads to an increase in criminal behaviors. Even holding the quantity of all three elements constant, the crime rate can still increase as the frequency of convergence of the three elements increases in time and space. It is important to note that routine activities theory is not a theory that explains the emergence of criminal motivation. Instead, the theory treats criminal motivation as given and focuses on the contexts and situations in which crime is most likely to occur. In order to explain criminal events, routine activities theory assumes that human behaviors

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Neighborhood Structures and Crime: A Spatial Analysis

are products of rational choice. Thus, criminal behavior can be predicted based on the costs and benefits involved in the commission of a crime. The costs and benefits involved in crime vary depending on situations and targets. For example, while targets in close proximity to motivated offenders’ houses are convenient (benefits), the likelihood of being detected (costs) becomes high. Targets with high monetary values (benefits) are also likely to have strong guardianship (costs). In essence, routine activities theory considers opportunity a necessary condition, if not sufficient, for a crime to occur. Thus, the routine activities theory contends that crimes are non-randomly distributed over space and time because opportunity is not uniformly distributed over space and time. Under the routine activities framework, places and social contexts can facilitate (or inhibit) crime in several ways. First, particular physical features of a place can affect the level of social control and criminal opportunities (Clarke 2002; McNulty and Holloway 2000; Sampson 2002; Weisel 2002). For example, high rise buildings reduce natural surveillance because residents are living vertically and are removed from monitoring activities at the street level. Furthermore, residents may not know each other because of high residential turnover, which provides anonymity for potential offenders. Apartment complexes also have the same structure, doors, and locks across units, which increases the number of potential targets for crime with the same methods. Second, regardless of physical features, the crime level at places is also affected by routine activities that occur there (Block and Block 1995; Davis 1987; Duffala 1976; Eck 1995; Roncek and Maier 1991; Sherman et al. 1989). For example, bars and taverns may attract people with low self control. Alcohol consumption at these places may further promote potential violent encounters. Abandoned buildings and rundown housing may provide an attractive market for illicit drug dealers without fear of complaints from dwelling owners. In addition to micro-level variation in crime at the place level, routine activities theory also provides a theoretical framework for understanding crime at the macro level. In fact, Cohen and Felson (1979) first applied routine activities theory to explain crime rates at the aggregate level. Their point of departure was an apparent contradiction between improving social conditions and increasing crime rates in the

Introduction

11

1960s. While the socio-economic conditions of American citizens, especially African Americans, improved substantially (e.g., increased level of education, increased median household income, drop in unemployment, decrease in the number of persons living below the poverty line), crime rates sharply increased. As conventional criminological theories at the time would have predicted a decrease in crime under these circumstances, such crime trends provided a challenge. Cohen and Felson (1979) argued that the increase in crime rates was attributable to changes in the routine activity patterns of American citizens. An increase in non-household activities caused by the increased labor force participation of married women left many houses unguarded. An increase in non-household activities shifted the domain of routine activities from private to public. The wider availability of small, high-value products, such as TVs and radios, meant an increase in suitable targets for crime. Using the Uniform Crime Reports data measured between 1947 and 1974, Cohen and Felson (1979) found that increased non-household activities, defined as the proportion of married women with jobs and non-husband-wife households, were significantly associated with increased crime rates, after controlling for unemployment rates and the proportion of male youths in the population. In sum, routine activities theory argues that the routine activities of both legitimate citizens and motivated offenders lead to variation in criminal opportunities. Places and neighborhoods may become crime hot spots because large numbers of people are attracted for reasons not related to criminal motivations (e.g., shopping malls and transportation hubs). Crime hot spots may also emerge as motivated offenders are attracted to particular places and neighborhoods due to suitable opportunities for crime. Furthermore, an increase in the level of crime can occur if the level of guardianship changes (e.g., removing attendants at parking lots). By framing crime incidents as the temporal and spatial intersection of motivated offenders and unguarded targets, routine activities theory provides a theoretical framework to better understand temporal and spatial specific opportunity structures for crime.

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Neighborhood Structures and Crime: A Spatial Analysis

SUMMARY Space is a substantively important topic in criminology. Many theoretical and empirical criminologists have incorporated space in their studies. In fact, one of the first quantitative studies of crime in America was a spatial analysis of juvenile delinquency in Chicago by Shaw and McKay (1942; 1969). In addition to social disorganization theory, other theoretical perspectives, such as routine activities theory and environmental criminology, also recognize the role of space in shaping criminal behavior (Brantingham and Brantingham 1981b; Cohen and Felson 1979). Aside from theoretical works, space has obvious and practical importance in criminology. For example, most police departments conduct patrol activities based on beats. Law enforcement agencies often conduct crackdowns on particular offenses in select areas. In fact, the locations of past crimes can be more predictive of future crime than the identities of known offenders (Sherman 1995). It has also been found that drug activity in one neighborhood contributes to the level of other crimes in surrounding neighborhoods (Felson 2006; McCord and Ratcliffe 2007; Renegert et al. 2005; Rengert et al. 2000). Despite the importance of space to criminology, space is methodologically difficult to analyze. Two types of spatial effects, spatial dependency and spatial heterogeneity, provide challenges to conventional statistical methods. While many statistical models, including ordinary least squares (OLS) regression models, assume independently distributed observations, spatial units are hardly independent observations (i.e., spatial dependency). The characteristics of a neighborhood are likely to be similar to those of surrounding neighborhoods. Furthermore, what happens in one neighborhood is likely to affect surrounding neighborhoods. For example, focused crime prevention activities have been shown to lower the level of crime not only in a target neighborhood, but also surrounding neighborhoods, an effect known as the diffusion of benefits (Bowers and Johnson 2003; Clarke and Eck 2005; Weisburd et al. 2006). Researchers in spatial econometrics also argue that traditional regression models often fail to capture something special about space. That is, relationships between neighborhood characteristics and crimes can vary in strength and direction over space (i.e., spatial

Introduction

13

heterogeneity) (Fotheringham et al. 2002a; Fotheringham et al. 2002b; LeSage 2004). For example, as human behaviors in downtown areas can be quite different from other areas, social processes of neighborhood characteristics affecting the level of crime can be different in downtown areas. As space is a continuous surface, however, a simple dichotomy of downtown vs. periphery may neglect important spatial processes. In addition to methodological problems, data availability has also hindered research on neighborhoods and crime. For example, many neighborhood level studies of crime have been cross-sectional, ignoring temporal dynamics of change. Although Shaw and McKay’s analysis provided insights on the longitudinal aspects of neighborhoods and crime, their conclusions emphasized the temporal stability of neighborhood characteristics and the level of crime. Although such findings led Shaw and McKay to argue for the importance of contextual effects, rather than compositional effects, more recently researchers have argued that changes in neighborhood characteristics are important for explaining changes in crime over time (Bursik and Grasmick 1992; Chamlin 1989; Griffiths and Chavez 2004; Kubrin and Herting 2003; Sampson et al. 1997; Sherman 1995; Weisburd et al. 2004). As longitudinal data of crime are often available for large scale macrolevel units of analysis, such as county and state, however, empirical studies on longitudinal changes in crime at the neighborhood level have been limited. Furthermore, aggregate analyses of neighborhood characteristics and crime sometimes neglect that crime incidents are ultimately individual behaviors. For example, many neighborhood level studies establish a statistical association between the socio-economic disadvantage of neighborhoods and the level of crime. Such analysis, however, does not explain if offenders are committing crimes in their own neighborhoods, due to an increase in frustrated wants, or if they are coming from outside neighborhoods, due to reduced guardianship. An analysis of offenders’ behavior can benefit from information about known criminals. Data that include the addresses of known offenders have not been as widely available as crime rate data. This book addresses these limitations of previous research in three analytical chapters, followed by a summary chapter. Based on theoretical discussions provided in Chapter 1, each subsequent chapter provides a detailed discussion of a particular problem, as well as

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Neighborhood Structures and Crime: A Spatial Analysis

statistical analyses. As previous studies have neglected longitudinal changes in crime, Chapter 2 presents a longitudinal analysis of crime at the neighborhood level using data from 1960 to 2005. In order to examine spatially heterogeneous associations between neighborhood characteristics and crime, Chapter 3 explicitly examines two types of spatial effects, spatial dependency and spatial heterogeneity. As crimes are ultimately individual behaviors, aggregate studies of crime often miss the role of offenders in generating crimes. Chapter 4 overcomes this problem by combining data on neighborhood characteristics and criminal offenders’ travel patterns. Based upon empirical analyses from Chapters 2 to 4, Chapter 5 synthesizes the results and discusses both the theoretical importance of the findings and policy implications.

CHAPTER 2

Longitudinal Analysis of Crime Rates at the Neighborhood Level

INTRODUCTION Historically, the crime rate in the United States experienced a rapid increase between 1960 and the early 1990’s, followed by a gradual decrease. According to the Uniform Crime Reports, produced by the Federal Bureau of Investigation, violent crime in the United States dropped sharply from 758.2 crimes per 100,000 people in 1991 to 473.5 crimes per 100,000 people in 2006 (Federal Bureau of Investigation 2006). Given that violent crime had been increasing in a relatively linear fashion since 1960, the decline in violent crime after 1991 is particularly striking. In contrast to the dramatic increase and decrease in violent crime, property crime increased and decreased more regularly over time. Although the level of property crime also increased rapidly after 1961, it stayed around 5,000 crimes per 100,000 people, with random fluctuations, between 1975 and 1991. Property crime gradually decreased after 1991 and reached a low point (3,334.5 crimes per 100,000 people) in 2006. The dramatic decline in the level of crime after 1990 not only caught the attention of criminologists, but policy makers and the media as well (Conklin 2003; Sacco 2005; Zimring 2007). A variety of factors contribute to the creation of “crime waves” (Sacco 2005), or longitudinal changes in the level of crime. Some criminologists argue that changes in the demographic composition of the population lead to changes in crime (Phillip and Laub 1998; Steffensmeier and Harer 1999), while others argue that demographic composition has a limited affect on crime (Levitt 1999). While the media and scholarly research often attributes changes in the crime rate to economic conditions (Allen 1996; Bursik and Grasmick 1993a), the mechanisms by which 15

16

Neighborhood Structures and Crime: A Spatial Analysis

economic conditions affect the level of crime are more complicated than some might think (Conklin 2003; Freeman 1995; Young 1993). Furthermore, changes in social institutions, such as family, political, and economic institutions, may affect the enforcement of conformity, which subsequently affects the level of crime (Lafree 1998a; Lafree 1998b). Additionally, the level of crime is associated with the availability of guns and drugs (Blumstein 1995). The rapid increase in crime in the 1970s has also been attributed to changes in the routine activities of individuals (Cohen and Felson 1979). Increased exposure to motivated offenders is likely to increase violent crimes, while a reduction in household guardianship may contribute to an increase in residential burglary. Finally, technological innovations also affect the level of crime. For example, the increased production of portable, high value items, such as car stereos, laptop computers, and portable music players, creates attractive targets for thieves (Cohen and Felson 1979; Roman and Chalfin 2007; Sacco 2005). What is less understood, however, is whether neighborhoods within a city have followed the same trends in crime rate changes, as most neighborhood level studies have utilized a cross-sectional design (Bursik 1988; Kubrin and Weitzer 2003a; Sherman 1995). Some neighborhoods may have experienced a faster increase in crime rates than others. Dramatic increases and decreases in city-wide crime statistics may be caused by crime rate changes in a few neighborhoods. In fact, despite the increases and decreases of city-wide crime rates, some neighborhoods may have remained safe neighborhoods throughout the entire period. Sherman (1995) and Maltz (1995) argued that a longitudinal analysis of neighborhood changes and crime rates could borrow several concepts identified in developmental criminology. That is, just as individuals go through several stages in escalating their anti-social behavior, criminal places (and neighborhoods) may also go through such stages as onset, growth, escalation in crime seriousness, persistence, decline, and termination. Furthermore, as Moffitt (1993) provides a taxonomy to categorize adolescents in terms of their involvement in criminal activities (i.e., adolescence-limited offenders and life course persistent offenders), there may be different types of neighborhoods that have unique pathways of changes in the level of crime over time.

Longitudinal Analysis of Crime Rates at the Neighborhood Level

17

As most neighborhood studies have used cross-sectional data, it is possible that neighborhood characteristics based on social disorganization theory and routine activities theory do not explain and predict crime rate trends over time. Some structural characteristics may explain the initial level of crime rates, but may fail to predict changes (either increase or decrease) over time. That is, a life course perspective on neighborhoods has been lacking in previous research. In order to overcome the limitation in previous neighborhood research that have been based on cross-sectional data, this chapter sets up a series of research question to analyze crime trends at the neighborhood level over time. First, how can neighborhood crime rate trajectories between 1960 and 2005 be described? Is there evidence of a systematic trend in crime rate changes over time? How do individual neighborhoods deviate from the overall crime rate trajectory? Are crime rate trajectories best captured by linear or non-linear trends? Second, is there any association between the initial level of crime and rate of change over time? For example, do high crime neighborhoods get worse by further increasing their levels of crime over time? Do safe neighborhoods with relatively low levels of crime experience slower increases in the levels of crime than other neighborhoods? Third, what are the neighborhood characteristics that are associated with the initial level of crime and rates of change over time? Drawing on social disorganization theory and routine activities theory, various neighborhood characteristics, such as socio-economic disadvantage, residential instability, and demographic composition, are included in statistical models in order to explain individual variability in crime rate trajectory forms. EXPLAINING CRIME WAVES Research that examines national crime trends indicates that various factors affect the level of crime over time (Conklin 2003; Sacco 2005; Zimring 2007). First, the demographic composition of the population is likely to affect the level of crime (Blumstein 1995; Blumstein et al. 1989; Steffensmeier and Harer 1999). In particular, an increased proportion of male youths increases crimes because young males are the most crime prone segment of the population (Gottfredson and Hirschi 1990; Moffitt 1993; Piquero et al. 2007). Second, socio-

18

Neighborhood Structures and Crime: A Spatial Analysis

economic conditions are associated with the level of crime (Allen 1996; Bursik and Grasmick 1993a; Kubrin and Herting 2003). A decrease in the proportion of households in poverty is likely to contribute to better parenting practices and improved school performance, which in turn results in lower rates of crime and delinquency (Agnew 2005). A decrease in unemployment also reduces the level of crime, as jobs provide increased stakes in conformity, direct supervision, and means to obtain money through legal channels. Third, various aspects of the criminal justice system affect the level of crime. Among others, improved policing strategies, more police, increased incarceration, and tougher gun and drug control laws may reduce the level of crime (Blumstein 1995; Bowling 1999; Braga 2001; Kelling and Coles 1996). Fourth, changes in the pattern of routine activities among citizens affect opportunities for crime, which in turn affect the level of crime (Cohen and Felson 1979). For example, an increased participation of married women in the workforce leaves houses unguarded during the day. Technological innovations also create criminal opportunity by producing portable items with high monetary values. For example, the development of laptop computers and portable music players increases the number of attractive targets due to light weight and high monetary value (Roman and Chalfin 2007; Sacco 2005). It is unlikely that any of the above factors affect the level of crime independently. Rather, several factors are probably interrelated in their effect on crime trends. For example, a stronger economy, represented by higher median incomes and fewer people in poverty, is associated with parenting practices and the school performance of juveniles. Increased employment in legitimate businesses is also likely to affect drug markets and juveniles’ involvement in gangs. Furthermore, these factors are not likely to affect trends for different crime types equally. For example, changes in drug markets may affect the level of burglary, robbery, and homicide, but not rape. Increases in the number of employed women may also represent increases in non-household activities (decreases in guardianship at houses) and in exposure to motivated offenders. Such changes in opportunities for crime are not likely to be associated with crimes occurring in domestic situations, such as domestic violence. Finally, these factors are likely to affect the level of crime in neighborhoods differently. For example, an increased availability of guns and drugs in a city may increase the level of

Longitudinal Analysis of Crime Rates at the Neighborhood Level

19

violence in economically disadvantaged neighborhoods, while they may not affect the level of crime in affluent suburbs. ANALYSIS OF CHANGE Social disorganization theory argues that crime rates increase when neighborhoods lack effective informal social control and/or neighborhoods increase frustrated wants of neighborhood residents (Bursik 1988; Bursik and Grasmick 1993b; Kornhauser 1978; Kubrin and Weitzer 2003a; Sampson and Groves 1989). Structural characteristics, such as residential mobility, racial heterogeneity, and socio-economic disadvantage, often hinder the development of social ties among residents and identification of common goals, which in turn decreases the informal social control that is needed to regulate crime and disorder in neighborhoods. Economic deprivation is also likely to fuel criminal motivation, which increases the number of motivated offenders. Routine activities theory, on the other hand, explains the source of crime incidents through a crime triangle of the motivated offender, attractive targets, and capable guardians (Cohen and Felson 1979; Felson 2006). In particular, the theory argues that a crime occurs when a motivated offender and attractive target intersect in time and space in the absence of a capable guardian. While empirical research has largely supported the predictions of social disorganization theory and routine activities theory (e.g., Miethe and Meier 1994; Sampson and Groves 1989), many of these studies have used cross-sectional data (Bursik 1988; Byrne and Sampson 1986; Kubrin and Weitzer 2003a). Thus, it has not been fully examined if the results based on crosssectional data apply equally to longitudinal relationships between neighborhood characteristics and the level of crime. Nonetheless, there are several studies that have examined longitudinal data on crime at the macro level (Bursik and Webb 1982; Chamlin 1989; Heitgerd and Bursik 1987; Morenoff and Sampson 1997; Taylor and Covington 1988). Using residual change scores and crime data from 1940 to 1970, Bursik and Webb (1982) found that some variables were associated with changes in specific time periods, while the same variables did not predict changes in other time periods. Bursik and Webb’s study illustrates that different neighborhood characteristics causally affect crime rate changes in a specific historical

20

Neighborhood Structures and Crime: A Spatial Analysis

time period. Chamlin (1989) also examined models of social disorganization theory and crime by including both temporally static and dynamic predictors and found that changes in ecological characteristics affected changes in the level of crime. In particular, using residual change scores, Chamlin found that changes in residential mobility and poverty affected changes in robbery, while changes in population size and the Gini index of economic concentration affected changes in homicide. Based on the findings from his temporally dynamic models, Chamlin argued that unexpected changes in the ecological structure of cities would disrupt mechanisms of informal social control, which in turn would result in an increase in crime. Until recently, longitudinal analysis of crime at the neighborhood level has been limited to using difference scores and/or residual change scores to examine changes between two time points. The use of residual change scores is attractive in ecological studies of crime for at least two reasons (Bursik and Grasmick 1992; Kubrin and Herting 2003). First, the predicted values calculated in the process of producing residual change scores automatically adjust for changes that other neighborhoods are experiencing. Thus, residual change scores remove the effects of ongoing changes that are common to other areas in a specific time period. Second, residual change scores are statistically independent of the initial level of a variable. A residual change score of zero represents the expected level of a variable at time t, given the level of a variable at time t-1. Thus, residual change scores represent unexpected changes that are not accounted for by the prior state of a variable (e.g., crime rates). Despite such attractiveness, residual change scores (or an analysis of two time points to examine changes, in general) suffer from several limitations. First, residual change scores only examine betweenneighborhood effects and fail to account for within-neighborhood variations over time (Bursik and Grasmick 1992; Kubrin and Herting 2003; Rogosa 1995). That is, with data measured at two time points, the variability of neighborhood trajectories cannot be examined and the parameters of the growth function are assumed to be the same across individual neighborhoods. Such an assumption, however, is not realistic, as it is likely that neighborhoods differ in their trajectories of crime (e.g., functional forms and rates of change). Second, as it is rather cumbersome to create residual change scores, typical applications of the method have examined only changes between two

Longitudinal Analysis of Crime Rates at the Neighborhood Level

21

time points. Pair-wise comparisons, such as Time 1 against Time 2 and Time 2 against Time 3, however, assume that changes in earlier time points are independent of changes in later time points. That is, changes between Time 1 and Time 2 do not affect changes between Time 2 and Time 3. Such an analytical approach only provides a snapshot of the overall crime trends that neighborhoods experience. Third, an analysis of two time points does not allow researchers to assess the functional form of changes over time, as a straight line is the most complex functional form that can be fitted through two points (Rogosa 1995). As illustrated by crime rates between 1960 and 2005 in the United States, cities experienced a rapid increase in crime followed by a decrease (or deceleration) of crime rates (Federal Bureau of Investigation 2006). Such non-linear trends cannot be captured with an analysis of two time points. Although an analysis of two time points provides more information than an analysis of one time point (i.e., cross-sectional analysis), the dynamic nature of changes in the level of crime and neighborhood trajectories cannot be fully examined by such a method. In order to overcome these limitations, a few recent studies have advocated for using growth curve modeling in order to analyze longitudinal crime data (Bursik and Grasmick 1992; Griffiths and Chavez 2004; Harada 2007; Kubrin and Herting 2003; Weisburd et al. 2004). For example, Kubrin and Weitzer (2003b) found that, after disaggregating homicides into three subtypes (altercations, felonies, and domestic killings), each homicide type had a different trajectory pattern over time. Furthermore, including neighborhood characteristics in their growth curve models as predictors indicated the trajectory for each homicide type was predicted by different neighborhood characteristics. Moreover, using a group-based, semi-parametric method for analyzing trajectories (Nagin 1999; Nagin 2005), an analysis of homicide rates in Chicago between 1980 and 1995 found that only 6% of the neighborhoods were classified as high-crime neighborhoods (Griffiths and Chavez 2004). While these neighborhoods experienced dramatic increases and decreases, they also maintained higher crime rates than other neighborhoods throughout the period. All other neighborhoods experienced slight changes, if any, in crime rates and remained relatively safe. The development of these studies that utilize growth curve models reflects a growing interest among criminologists in search of the

22

Neighborhood Structures and Crime: A Spatial Analysis

sources of change and stability in the level of crime at the neighborhood level. Despite a theoretical interest in the longitudinal nature of crime and neighborhood characteristics, empirical analyses have been largely hindered due to the absence of appropriate statistical models. Furthermore, many longitudinal studies of crime are based on city-level and county-level data, while social disorganization and routine activities are more likely to operate at the neighborhood level. Thus, as a more appropriate test of social disorganization theory and routine activities theory in the longitudinal context, this study examines the relationships between neighborhood characteristics and the level of crime between 1960 and 2005 at the neighborhood level. RESEARCH QUESTIONS Based upon social disorganization theory and routine activities theory, this research examines the sources of stability and change in the level of crime across neighborhoods. In particular, the following research questions guide an analysis of neighborhood characteristics and the level of crime. Research Question 1: Is there evidence of a systematic trend and individual variability in trajectories of crime over time? In order to answer this question, unconditional growth curve models with only crime variables are examined. That is, changes in crime rates are examined by analyzing linear and non-linear rates of change, without considering neighborhood characteristics. Research Question 2: Is there any association between the initial level of crime and rates of change over time? Do neighborhoods with higher initial levels of crime experience a faster increase in crime than neighborhoods with lower initial levels of crime? Do neighborhoods with a faster increase in crime experience slower non-linear change (deceleration) in subsequent time periods? In order to answer this research question, covariances among the random effects of unconditional growth curve models will be analyzed.

Longitudinal Analysis of Crime Rates at the Neighborhood Level

23

Research Question 3: What neighborhood characteristics predict the initial level and rate of change in crime rates? In order to answer this question, conditional growth curve models will be specified where neighborhood characteristics are introduced as timevariant predictors. That is, neighborhood characteristics are allowed to change over time and such time-variant characteristics are used to predict the trajectory of crime across neighborhoods. Hypotheses The following hypotheses are tested to analyze changes in neighborhood characteristics and the level of crime. In general, changes in neighborhood characteristics are hypothesized to be related to changes in crime rates. H1: Lower socio-economic disadvantage in a neighborhood is associated with lower levels of crime (decreased criminal motivation and increased stakes in conformity). H2: Lower residential mobility in a neighborhood is associated with lower levels of crime (increased informal social control and vested interests in community). H3: Lower racial/ethnic heterogeneity in a neighborhood is associated with lower levels of crime (the presence of value/norm consensus and increased informal social control). H4: A higher proportion of children living with both parents in a neighborhood is associated with lower levels of crime (increased direct control) H5: A higher proportion of immigrants in a neighborhood is associated with higher levels of crime (lack of value/norm consensus and decreased informal social control) Additionally, several hypotheses based on routine activities theory are: H6: A lower proportion of women with jobs in a neighborhood is associated with lower levels of crime (decreased guardianship and increased exposure to motivated offenders). H7: A lower proportion of workers taking public transportation in a neighborhood is associated with lower levels of crime (decreased exposure to motivated offenders).

24

Neighborhood Structures and Crime: A Spatial Analysis

H8: A lower proportion of male youths in a neighborhood is associated with lower levels of crime (the decreased number of motivated offenders) DATA Crime and census data measured at the census tract level (N=113) in Seattle in 1960, ‘70, ‘80, ‘90, 2000, and 2005 were used. The crime data in 1960, ‘70, and ‘80 were originally collected by Miethe and Meier (1994) and obtained through the Inter-university Consortium for Political and Social Research (study number 9741). The crime data in 1990, 2000, and 2005 were directly obtained by contacting the Seattle Police Department. Crime variables followed the definitions in the Uniform Crime Reports, collected by the Federal Bureau of Investigation, and included homicide, robbery, burglary, and auto theft. The crime variables were calculated as rates per 1,000 people per census tract. Neighborhood characteristics that are theoretically important for explaining the level of crime were selected based on social disorganization theory and routine activities theory. Three key theoretical concepts of social disorganization theory are socioeconomic disadvantage, residential instability, and racial heterogeneity. First, as indicators of socio-economic disadvantage, four variables included in this study were the percentage unemployed, percentage of households below the official poverty line, percentage of population over 25 years of age who do not have a high school or equivalency diploma, and percentage of households whose occupancy exceeds 1.0 person per room. These four variables were combined through principal component analysis to create a factor representing the socioeconomic disadvantage of neighborhoods. The factor loadings for these variables across time exceeded at least 0.6 for each time period and most of the factor loadings were above 0.8. The extracted factor explained 60% to 78% of the variance in the observed data for each year. Chronbach’s alpha for these variables was 0.7 to 0.85 for each year. Second, a factor representing neighborhood instability was extracted from five variables using principal component analysis. The original variables for this factor included percentage of the population

Longitudinal Analysis of Crime Rates at the Neighborhood Level

25

ages 5 and over who changed their address in the past five years, percentage vacant houses, percentage renter occupied housing units, percentage multiple-housing units (i.e., more than one housing unit per building, like an apartment building), and the percentage divorced. Factor loadings of these variables for each time period were above 0.70 and, on average, 70% of the variance of the observed data was explained by this factor for each time period. Third, using the demographic composition of neighborhoods, a measure of racial heterogeneity was created. In particular, percentage White, percentage African American, and percentage other race were extracted from the census data. While recent census data provide detailed racial categories, the 1960 and 1970 census only provided these three racial categories. An indicator of racial heterogeneity was calculated using these three racial variables. In particular, the formula used for calculating the racial heterogeneity index is 3

1−

∑p

2 i

,

i =1

where pi is the proportion of each racial category (Sampson and Groves 1989). A higher value for the index represents a greater degree of racial heterogeneity in neighborhoods. The maximum value of the index is 0.667 when a neighborhood is 33% White, 33% African American, and 33% other race, while the minimum value is zero when one racial group dominates a census tract. In addition to these three factors and variables representing key concepts of social disorganization, other demographic characteristics were also included. First, following Shaw and McKay’s study (1942; 1969), the percentage of the population that is foreign born was included in the analysis. Second, the percentage of children living with both parents was included in order to assess direct control of youths by parents. Finally, a series of variables were identified from routine activities theory that indicate the opportunity structure of neighborhoods. As a measure of exposure to motivated offenders, the percentage of workers who use public transportation was included. Furthermore, the percentage of employed females was included as a measure of exposure to motivated offenders and level of household guardianship. Third, the percentage of males who are between 15 and 24 years old was used to

26

Neighborhood Structures and Crime: A Spatial Analysis

control for the proportion of criminally prone individuals (i.e. motivated offenders). EXPLORATORY SPATIAL DATA ANAYSIS Prior to the analysis of longitudinal changes in neighborhood characteristics and the level of crime, the data were explored in order to uncover spatial effects underlying the data. Table 2.1 shows the Moran’s I spatial autocorrelation coefficients for crime at each time point. In order to analyze spatial autocorrelation, the queen specification was used to create a spatial weights matrix. Thus, spatial units were defined as neighbors when they either shared boundaries or vertices (i.e., the specification is called the queen specification based on the movement of the queen piece in the game of chess). A positive value of Moran’s I indicates that similar values of a variable are spatially clustered, while a negative value of Moran’s I indicates that dissimilar values of a variable are spatially clustered. For example, in 1960, the Moran’s I was positive and significant (0.352), indicating that neighborhoods with high levels of homicide were spatially clustered and that neighborhoods with low levels of homicide were spatially clustered. Overall, the results indicated that all crime measures were spatially clustered, which is typical for neighborhood crime rate data. What is more important for the subsequent analysis of associations between neighborhood characteristics and the level of crime is whether the spatial autocorrelation remains after taking into account neighborhood characteristics. While many regression models, including ordinary least squares (OLS), assume independently distributed error terms, statistical analysis on spatial data often results in spatially correlated residuals. Violating the assumption of independently distributed residuals in OLS regression affects coefficient estimates, standard error estimates, and statistical tests depending on underlying spatial processes (i.e., spatially autocorrelated dependent variable or spatially autocorrelated errors). Thus, Table 2.1 also presents the results of Moran’s I spatial autocorrelation coefficient of OLS residuals after neighborhood characteristics were included in the OLS regression models. The results indicated that the residuals of the OLS regression of crime on neighborhood characteristics were significant for only six of the twenty regression models (five years *

Longitudinal Analysis of Crime Rates at the Neighborhood Level

27

four crime types). Furthermore, of the six significant Moran’s I, four were weak in strength (approximately 0.1 and below). That is, although all crime measures were spatially clustered, the results indicated the spatial concentration was explained to a large extent by neighborhood characteristics. Thus, it was concluded that statistical problems caused by spatial data were not considerable for the Seattle data that this research examined and that aspatial statistical models were likely to be valid (although a supplemental analysis was also conducted using spatial panel models). Table 2.1 Moran’ I Spatial Autocorrelation Coefficients of Crime Rates and OLS Residuals Homicide Robbery Homicide

Residuals

Robbery

1960

0.352

0.016

0.339

0.027

1970

0.529

0.218**

0.460

0.271**

1980

0.522

0.122**

0.434

0.054

1990

0.301

-0.055

0.406

-0.042

2000

0.081

-0.110

0.443

-0.068

Burglary

Residuals

Auto Theft

Burglary

Residuals

Auto Theft

Residuals

1960

0.554

0.035

0.599

1970

0.462

0.020

0.461

0.098*

1980

0.424

0.034

0.498

0.061

1990

0.463

0.028

0.498

0.114**

2000

0.331

0.038

0.431

0.067*

-0.016

METHOD I: GROWTH CURVE MODELS This study focuses on the sources of stability and change in the level of crime at the neighborhood level over time. Are there any systematic

28

Neighborhood Structures and Crime: A Spatial Analysis

patterns in crime rate changes? Is there individual variability in pathways of neighborhoods in their criminal careers? What structural characteristics predict the initial level of crime and rates of change over time? A growth curve model is suitable for answering these research questions because the method analyzes a trajectory at the group level along with individual variability in growth patterns (Bollen and Curran 2006; Bursik and Grasmick 1992; Kubrin and Herting 2003; RabeHesketh and Skrondal 2002; Singer and Willett 2003). The basic idea behind the growth curve model is to estimate regression lines (or curves) for each individual observation (Figure 2.1). It is quite possible that such regression lines vary considerably in their functional forms across individuals. Some may show an increase, while others show a static pattern over time. The varying regression lines at the individual level are then smoothed to produce summary measures (e.g., mean and variance) that characterize the average trend for individuals as a whole (Figure 2.2). It is this unobserved curve that is believed to underlie and to have given rise to the observed data. While various regression lines based on observed data reflect individual level patterns, the unobserved curve represents the group level trend. Formally, a growth curve model can be considered as a multilevel model where there are two levels (Bollen and Curran 2006; Bursik 2001; Rabe-Hesketh and Skrondal 2002; Singer and Willett 2003). The first level equation that assesses within neighborhood changes is

yit = α i + β i (Time ) it + ε it

where yit is a crime rate for neighborhood i at time t, and α i and β i are an intercept and slope that characterizes the trajectory pattern for each neighborhood. The subscript i of α and β indicates possible variation across individual neighborhoods in trajectory patterns. In order to capture this variation across individual neighborhoods, the second level equations that express the intercept and slope are formed as α i = µα + ξ and β i = µ β + ξ . αi

βi

The ξ indicates the extent of deviation from the mean intercept and slope for each neighborhood in the trajectory patterns. Substituting α i

30

Trajectories of Burglary Rates for Five Neighborhoods

Block Group

20

3532 002 3536 005

10

3550 002 3564 001

0

3564 004

2000

2001

2002

2003

2004

2005

Figure 2.1 Five Trajectories of Neighborhood Crime Rates (Hypothetical Data)

0

10

20

30

The Averaged Trajectory and Means of Burglary Rates

2000

2001

2002

2003

2004

2005

Figure 2.2 An Averaged Trajectory of Burglary Rates across Five Neighborhoods

30

Neighborhood Structures and Crime: A Spatial Analysis

and β i in the level-1 equation gives the combined model:

yit = {µα + (Time ) it µ β } + [ξ + ξ (Time ) it + ε it ] . αi

βi

The terms in the first bracket reflect a fixed component, while the terms in the second bracket reflect a random component. That is, while the fixed component captures the overall trajectory pattern across neighborhoods, the random component reflects individual variability in trajectory patterns. Using the same notations, a quadratic trajectory can be expressed as: Level 1: yit = α i + β 1i (Time ) it + β 2 i (Time ) it + ε it 2

α i = µα + ξ

αi

Level 2: β1i = µ β 1 + ξ

β 2i = µβ 2 + ξ

β 1i

β 2i

Using a growth curve for the analysis of change is advantageous for several reasons (Bollen and Curran 2006; Bursik and Grasmick 1992; Duncan et al. 1999; Kubrin and Herting 2003; Singer and Willett 2003). First, a growth curve model provides summary measures (e.g., mean and variance) to characterize an underlying trajectory that has given rise to a large set of observations. For example, the initial level of crime rates and the shape and rates of change over time can be analyzed with a growth curve. Second, various functional forms of change over time can be analyzed. For example, changes can be linear (increase or decrease) or quadratic (acceleration or deceleration). Third, both time-invariant and time-variant covariates can be incorporated in analytic models to explain variability in the initial level of crime and rates of change over time at the individual level. For example, economically disadvantaged neighborhoods may have higher levels of crime at the start, as well as a faster increase in crime over time. Finally, covariation between the initial level and rates of change can also be examined. For example, those neighborhoods that start with a high crime rate may experience a faster increase in crime rates over time. In short, a growth curve model allows researchers to simultaneously assess the overall trends (the group level trajectory), along with individual variability in such trends. This is especially attractive for a temporally dynamic model of social disorganization

Longitudinal Analysis of Crime Rates at the Neighborhood Level

31

theory, as the growth curve model allows for variation in neighborhood trajectories of crime rate changes, as well as variations in structural characteristics over time. Furthermore, the growth curve model allows researchers to fully assess continuous changes over time, as opposed to temporal autoregressive structures in which snap shots of each time point are examined. RESULTS: GROWTH CURVE MODELS As a modeling strategy, a series of growth curve models were examined. First, two sets of models were compared where the first was a linear trajectory model, while the second model was a non-linear trajectory model with a quadratic term. The purpose of the analysis was to identify trajectory forms for each crime type and to analyze the goodness of fit of the trajectory in explaining varying levels of crime over time. An appropriate model specification could be evaluated in two ways: 1) by comparing Bayesian Information Criterion (BIC) across two models; and 2) by comparing predicted values with observed values. Table 2.2 presents the estimates of growth curve parameters for trajectories of each crime time, as well as fit statistics to assess model fit. Before interpreting growth curve parameters, model fit statistics can be looked at to compare linear and non-linear models. Unlike Rsquared in ordinary least square (OLS) regression, which shows the amount of explained variance, BIC in and of itself is not interpretable. BIC, instead, can be used to make comparisons across models. In general, the model with the lower BIC value is the preferred model. Furthermore, Raftery (1996) suggests that absolute differences in BIC of 0-2 are weak evidence, 2-6 are positive evidence, 6-10 are strong evidence, and 10 and above are very strong evidence. Using these rules, quadratic models were found to be better models for all crime types. BIC values for quadratic models were smaller than for linear models and absolute differences in BIC indicated strong evidence for such conclusions (i.e. absolute differences in BIC exceeded 10). Given crime rates increased sharply in the 1960’s and 1970’s and gradually decreased subsequently, quadratic trajectories of crime trends in these time periods were in accord with initial expectations.

BIC

Time squared

Time

Intercept

-756.9

-834.7

3915.5

3343.3

(0.142)

(0.652)

(0.003)

(0.091)

3.853

(0.201)

1.089

5185.9

(0.264)

-0.907

4559.9

(0.223)

-3.4842

(0.936)

15.139

(0.701)

10.831

Quadratic

Burglary

(1.890)

20.35

Quadratic Linear

-0.789

(0.011)

(0.003)

0.284

(0.479)

3.184

Linear

Robbery

-0.013

0.048

(0.010)

(0.013) -0.009

0.069

Quadratic

0.102

Linear

Homicide

3964.4

(0.169)

2.775

(0.444)

4.405

Linear

3836.2

(0.084)

0.203

(0.381)

1.815

(0.330)

5.015

Quadratic

Auto Theft

Table 2.2 Baseline Growth Curve Models of Homicide, Robbery, Burglary, and Auto Theft Rates per 1,000 People

Longitudinal Analysis of Crime Rates at the Neighborhood Level

33

Estimates of growth curve parameters can be interpreted to further examine the nature of change over time for each crime type. The results of quadratic growth curve for homicide indicated that an average homicide trajectory was characterized by: 2

Homicidet = 0.069 + 0.048Timet − 0.013Timet

The first term, intercept, indicated the predicted level of homicide for time = 0. That is, the model indicated the predicted level of homicide in 1960 was 0.069 per 1,000 population. As the linear term was positive and the non-linear term was negative, this indicated the homicide trajectory had an initial increase followed by a decrease over time. By substituting time = 1 for 1970, time = 2 for 1980, time = 3 for 1990, time = 4 for 2000, and time = 4.5 for 2005, predicted levels of homicide based on the modeled trajectory could be computed. In particular, the predicted levels of homicide were 0.069 (1960), 0.104 (1970), 0.113 (1980), 0.096 (1990), 0.053 (2000), and 0.022 (2005). As observed means for homicide in these time periods were 0.058 (1960), 0.122 (1970), 0.104 (1980), 0.089 (1990), 0.051 (2000), and 0.037 (2005), it was concluded that the modeled trajectory closely represented the observed changes in homicide. Trajectory forms of other crime types can also be represented using the same notation. 2

Robberyt = 1.089 + 3.853 * Timet − 0.789 * Timet

2

Burglaryt = 10.831 + 15.139 * Timet − 3.484 * Timet 2

AutoTheftt = 5.015 + 1.815 * Timet + 0.203 * Timet

Similar to homicide, trajectories for robbery and burglary were characterized by an initial linear increase and subsequent non-linear decrease over time. As comparisons between predicted values and observed means in Table 2.3 indicate, the modeled trajectories closely followed observed trends for both of these crimes between 1960 and 2005. Unlike homicide, robbery, and burglary, the trajectory form for auto theft was characterized by an initial linear increase followed by a non-linear increase (i.e., acceleration). Comparing the observed means to the predicted level of auto theft indicated that the model closely followed observed trends in auto theft during these time periods. Thus, the answer to research question one was that all crime trajectories between 1960 and 2005 were best captured by non-linear

0.058 0.123 0.104 0.089 0.051 0.038

1960

1970

1980

1990

2000

2005

Observed

0.022

0.053

0.096

0.113

0.104

0.069

Predicted

Homicide

2.743

2.854

6.142

4.679

4.340

0.832

Observed

2.450

3.877

5.547

5.639

4.153

1.089

Predicted

Robbery

12.442

10.499

22.955

27.200

26.141

8.249

Observed

8.406

15.643

24.892

27.173

22.486

10.831

Predicted

Burglary

17.013

14.368

12.125

7.051

8.437

3.834

Observed

17.293

15.523

12.287

9.457

7.033

5.015

Predicted

Auto Theft

Table 2.3 Comparisons of Observed Means and Predicted Levels of Crime Based on the Baseline Growth Curve Models

Longitudinal Analysis of Crime Rates at the Neighborhood Level

35

trajectories. For homicide, robbery, and burglary, the trajectories were best represented by an initial linear increase, followed by non-linear decrease (i.e., deceleration). For auto theft, the trajectory was best represented by initial linear increase, followed by non-linear increase (i.e., acceleration). Such descriptions of trajectories are group-level trends, however. It is reasonable to assume that crime rate trajectories for each neighborhood will vary. In order to examine how individual neighborhoods vary in their trajectory forms, random components of the growth curve were analyzed. Table 2.4 presents the variancecovariance matrix of growth curve parameters (intercept, linear term, and non-linear term) that showed variability in initial level and rate of change at the individual neighborhood level. The diagonal elements of the matrix represent the individual variability (variance) in the estimates of the intercept, linear, and quadratic terms. As all of these variance estimates were statistically significant, the results indicated that the initial level of crime, as well as rate of linear and non-linear change, varied considerably for each neighborhood. For example, although the estimated mean level of homicide in 1960 was 0.069, the levels of homicide varied significantly for each neighborhood (variance = 0.015, p<.01). More interestingly, the rate of change varied for each neighborhood. For example, the estimated mean rate of linear increase in homicide was 0.048, although the statistically significant variance of the linear term indicated the rate of linear change varied considerably for each neighborhood (variance = 0.017, p<.01). Variability also existed for the rate of non-linear change (variance = 0.001, p<.01). Covariance estimates among growth curve parameters were used to further investigate the nature of variability in trajectory forms at the individual neighborhood level. The covariance estimate of the intercept (i.e., initial level) and linear term was positive for the homicide trajectory, indicating that a larger value of the intercept was associated with a larger value of the linear term (bigger slope = faster increase). That is, neighborhoods with higher initial levels of homicide in 1960 were predicted to experience a faster linear increase in homicide than neighborhoods with lower initial levels of homicide. The covariance estimate of the intercept and quadratic term can also be interpreted in a similar manner. A negative covariance for the intercept and quadratic term for the homicide trajectory indicated that a larger value of the intercept was associated with a smaller value of the quadratic term. As the average rate of non-linear change for homicide

Auto Theft

Burglary

Robbery

Homicide 0 017 -0 004 0 334 1 432 -0 315 1 163 1 522 -0 364 0 513 0 534 -0 101

Linear Quadratic Intercept Linear Quadratic Intercept Linear Quadratic Intercept Linear Quadratic

-0 123

0 668

0 467

-0 431

1 833

1 12

-0 331

1 502

0 326

-0 006

0 017

Linear

Homicide

0 03

-0 164

-0 119

0 107

-0 453

-0 284

0 083

-0 377

-0 083

0 001

Quadratic

-2 497

11 747

9 764

-6 623

27 021

24 946

-6 671

30 638

6 589

Intercept

-9 947

51 326

43 095

-30 738

127 694

103 563

-28 754

128 76

Linear

Robbery

2 166

-11 313

-9 564

6 83

-28 422

-22 789

6 111

Quadratic

-6 043

32 92

48 524

-25 751

104 221

69 437

Intercept

Note: All variance and covariance estimates are significant at p<.05

0 015

Intercept

Intercept

-13 303

79 979

48 181

-50 313

172 6

Linear

Burglary

3 091

-18 34

-11 812

10 106

Quadratic

0 748

-2 999

8 38

Intercept

Table 2.4 Variance-Covariance Matrix of Random Effects of Growth Curve Models

-10 112

20 884

Linear

Auto Theft

1 127

Quadratic

Longitudinal Analysis of Crime Rates at the Neighborhood Level

37

was negative to begin with (-0.013 in Table 2.2), a smaller value of the quadratic term also meant a bigger negative value (i.e., bigger downward change). Thus, the negative covariance between the intercept and the quadratic term for homicide indicated that neighborhoods with a higher initial level of homicide in 1960 experienced a steeper downward change at later time periods. Finally, the covariance between the linear and non-linear term can be examined to investigate the nature of change over time. A negative covariance between the linear and quadratic terms indicated that a larger value of the linear term was associated with a smaller value of the quadratic term. As a smaller value of the quadratic term could also be described as a bigger negative value, the negative covariance between the linear and quadratic terms indicated that neighborhoods that had experienced a faster linear increase in an early time series experienced a larger nonlinear downward change in subsequent time series. The covariance of growth curve parameters for other crime series can be interpreted in a similar manner. The patterns of association were the same for robbery and burglary trajectories that had the same functional form (i.e., initial linear increase, followed by non-linear decrease). As for auto theft, the nature of change was different. The trajectory form for auto theft was different from other crime types as it was characterized by a linear increase followed by accelerated increase (non-linear upward change). A negative covariance between the intercept and linear term for auto theft indicated that neighborhoods with a lower initial level of auto theft in 1960 experienced a faster linear increase. A positive covariance between the intercept and quadratic term indicated that neighborhoods with a higher initial level of auto theft subsequently experienced a faster non-linear increase. Finally, a negative covariance between the linear and quadratic terms indicated that neighborhoods that initially experienced a slower linear increase subsequently experienced a faster non-linear increase. Thus far, the analysis has examined the nature of trajectory forms by looking at crimes only. As individual neighborhoods experienced varying initial levels of crime and rate of change over time, the next set of analyses examined relationships between the trajectory forms and neighborhood characteristics. When predictors are included in a growth curve model, the model could be mathematically expressed as follows.

38

Neighborhood Structures and Crime: A Spatial Analysis Level 1: 2

Crimeit = β 0i + β1i * Time − β 2 i * Time + ε it

Level 2:

β 0 i = µ 0 + γ 0 ( NeighborhoodCharacteristic ) i + ζ 1i β1i = µ1 + γ 1 ( NeighborhoodCharacteristic )i + ζ 2i β 2 i = µ 2 + γ 2 ( NeighborhoodCharacteristic )i + ζ 3i As predictors were treated as time-invariant in this model, neighborhood characteristics appear as level 2 variables that change their values across neighborhoods, but stay constant across time. The β 0 i in the first level-2 equation indicates the predicted level of crime for neighborhood i in 1960. The µ 0 is the grand mean level of crime in 1960, while γ 0 represents the effect of neighborhood characteristics on the level of crime in 1960. Thus, when γ 0 is positive, it is concluded that a higher level of a neighborhood characteristic is associated with higher levels of crime. Similarly, when γ 0 is negative, it is concluded that a higher level of a neighborhood characteristic is associated with lower levels of crime. While the first level-2 equation is essentially a cross-sectional association, as both the level of crime and neighborhood characteristics are measured in 1960, the second level-2 equation represents the association between the rate of linear change in crime and neighborhood characteristics. For example, β1i in the second level-2 equation indicates the predicted rate of liner change in crime for neighborhood i. The µ1 is the grand mean rate of linear change in the level of crime, while γ 1 represents the effect of neighborhood characteristics on variability in the rate of linear change across neighborhoods. For instance, when γ 1 is positive, it is concluded that a higher level of this neighborhood characteristic is associated with a steeper (faster) rate of linear increase in the level of crime over time. Similarly, when γ 1 is negative, it is concluded that a higher level of this neighborhood characteristic is associated with a less steep (slower) rate of linear change in the level of crime over time. Similar to the second level-2 equation, the third level-2 equation also represents relationships between neighborhood characteristics and change in crime rates over time. While the former is concerned with the rate of linear change over time, the latter is concerned with the rate of non-linear change in the level of crime over time. For example, β 2 i

Longitudinal Analysis of Crime Rates at the Neighborhood Level

39

in the third level-2 equation indicates the predicted rate of non-liner change in crime for neighborhood i. A positive value of β 2 i indicates that neighborhood i experiences upward non-linear change (acceleration), while a negative value of β 2 i indicates that neighborhood i experiences downward non-linear change (deceleration). The µ 2 is the grand mean rate of non-linear change in the level of crime, while γ 2 represents the effect of neighborhood characteristics on variability in the rate of non-linear change across neighborhoods. For instance, when γ 2 is positive, it is concluded that a higher level of this neighborhood characteristic is associated with a larger positive rate of non-linear change in the levels of crime over time. Similarly, when γ 2 is negative, it is concluded that a higher level of this neighborhood characteristic is associated with a larger negative rate of non-linear change in the level of crime over time. Table 2.5 presents the results of the conditional growth curve model of homicide, robbery, burglary, and auto theft with neighborhood characteristics as predictors. The table is divided into three panels, where the first panel presents the association between neighborhood characteristics and the intercept (the initial level of crime in 1960). As all independent variables included in the model are meancentered, the estimate of the intercept indicates the predicted level of crime in neighborhoods with mean characteristics in 1960. For example, the estimated intercept for the homicide model, 0.073, indicated homicide rate in neighborhoods with mean characteristics of independent variables included in the model were 0.073 per 1,000 population in 1960. The coefficient estimates of independent variables in the same first panel indicated how certain neighborhood characteristics increased or lowered the levels of crime. For example, a statistically significant positive effect of residential mobility (0.034, p<.01) indicated neighborhoods characterized by higher levels of residential mobility experienced higher levels of homicide than neighborhoods with lower levels of residential mobility in 1960. Mathematically, the interpretation could also be made by using the terminology presented above. In particular, the predicted level of homicide for neighborhood i could be calculated as follows. β1i = µ1 + γ 1 ( NeighborhoodCharacteristic ) i = 0.073 + 0.034 * ResidentialMobility

0.073** 0.001 0.001 -0.000 -0.004 -0.001 0.034* 0.182* 0.015 0.052** 0.006* 0.001 -0.004+ -0.002 -0.004 0.028 0.023 0.220**

Intercept

% Foreign

% Both Parent

% Public Transport.

% Female Employed

% Young Male

Residential Mobility

Heterogeneity

Disadvantage

Linear

% Foreign

% Both Parent

% Public Transport.

% Female Employed

% Young Male

Residential Mobility

Heterogeneity

Disadvantage

(0.019)

(0.111)

(0.019)

(0.003)

(0.005)

(0.002)

(0.001)

(0.003)

(0.011)

(0.016)

(0.094)

(0.016)

(0.002)

(0.004)

(0.002)

(0.001)

(0.003)

(0.009)

Homicide Estimate s.e.

1.873**

6.772*

3.383*

-0.319**

-0.032

-0.096

0.027

0.209*

3.987**

-0.062

6.203**

0.554+

-0.042

0.009

-0.015

-0.004

0.096+

1.141**

s.e.

(0.622)

(3.628)

(0.609)

(0.095)

(0.148)

(0.065)

(0.034)

(0.103)

(0.358)

(0.328)

(1.917)

(0.321)

(0.050)

(0.078)

(0.034)

(0.018)

(0.054)

(0.189)

Robbery Estimate

4.731**

7.236

4.179**

-0.208

0.049

0.093

0.069

-0.469*

15.351**

0.681

10.145+

4.796**

-0.263+

-0.185

0.031

0.085

-0.052

11.022**

(1.346)

(7.816)

(1 312)

(0.205)

(0.323)

(0.141)

(0.074)

(0.223)

(0.774)

(0.984)

(5.725)

(0.96)

(0.151)

(0.238)

(0.010)

(0.055)

(0.163)

(0.567)

Burglary Estimate s.e.

1.674**

0.940

0.922+

-0.184*

-0.159

-0.055

0.039

-0.007

1.815**

0.256

-0.842

2.445**

-0.052

-0.067

-0.013

0.030

0.120

5.111**

(0.512)

(3.023)

(0.517)

(0.077)

(0.122)

(0.053)

(0.029)

(0.084)

(0.294)

(0.482)

(2.846)

(0.483)

(0.074)

(0.114)

(0.050)

(0.028)

(0.079)

(0.278)

Auto Theft Estimate s.e.

Table 2.5 Growth Curve Models of Crimes with Neighborhood Characteristics as Time Invariant Predictors.

-0.002* -0.000 0.001+ 0.001 0.001 -0.007+ -0.018 -0.004

% Foreign

% Both Parent

% Public Transport.

% Female Employed

% Young Male

Residential Mobility

Heterogeneity

Disadvantage

Note: +p<.10, *p<.05, **p<.01

-0.014**

Quadratic

s.e.

(0.004)

(0.024)

(0.004)

(0.001)

(0.001)

(0.000)

(0.001)

(0.001)

(0.002)

Homicide Estimate

-0.135

-1.793*

-0.708**

0.068**

0.008

0.018

-0.006

-0.049*

-0.817**

s.e.

(0.137)

(0.801)

(0.134)

(0.021)

(0.032)

(0.014)

(0.008)

(0.023)

(0.079)

Robbery Estimate

-1.050**

-2.414

-1.001**

0.059

0.004

-0.017

-0.017

0.107*

-3.538**

(0.316)

(1.838)

(0.309)

(0.048)

(0.076)

(0.033)

(0.017)

(0.052)

(0.182)

Burglary Estimate s.e.

-0.237*

-0.823

-0.103

0.052**

0.050+

0.016

-0.007

0.006

0.201**

(0.121)

(0.710)

(0.122)

(0.018)

(0.029)

(0.013)

(0.007)

(0.019)

(0.069)

Auto Theft Estimate s.e.

Table 2.5 Growth Curve Models of Crimes with Neighborhood Characteristics as Time Invariant Predictors (cont.).

42

Neighborhood Structures and Crime: A Spatial Analysis

As residential mobility is a standardized factor, the above equation means a one standard deviation increase in residential mobility in a neighborhood increased the level of homicide in 1960 by 0.034, controlling for the effects of other neighborhood characteristics (all independent variables were mean centered). The coefficient estimates of other independent variables can be interpreted in a similar fashion. In accord with social disorganization theory, the results indicated that neighborhoods with high heterogeneity experienced high initial levels of homicide in 1960. The linear term of the growth curve (second panel in Table 2.5) can be interpreted in a similar fashion, although interpretations are made with respect to rate of linear change over time. The coefficient estimate of the linear term, 0.052, indicated that neighborhoods with mean characteristics of the independent variables included in the model experienced a linear increase in the homicide rate by 0.052 per decade. Statistically significant coefficient estimates of several independent variables indicated how neighborhood characteristics were associated with variation in the rate of linear change in homicide. For example, a positive effect of the percentage foreign born (0.006) indicated high proportions of foreign born residents in neighborhoods were associated with a steeper linear increase in homicide. Mathematically, the interpretation could also be made by using the terminology presented above. In particular, the predicted rate of linear increase in homicide for neighborhood i could be calculated as follows. β 2 i = µ 2 + γ 2 ( NeighborhoodCharacteristic )i = 0.052 + 0.006 * %ForeignBorn This means that a one unit increase in the percent foreign born population resulted in a 0.006 larger linear slope (steeper/faster linear increase), controlling for the effects of other neighborhood characteristics. Similarly, neighborhoods characterized by a low percentage of public transportation users and high levels of socioeconomic disadvantage were associated with a steeper linear increase in the level of homicide over time. Finally, the quadratic term (third panel) was interpreted with respect to the effects of neighborhood characteristics on non-linear change in the level of crimes over time. For example, neighborhoods with mean characteristics experienced a downward non-linear change (0.014), as indicated by the coefficient estimate of the quadratic term.

Longitudinal Analysis of Crime Rates at the Neighborhood Level

43

The rate of non-linear change, however, varied by neighborhood characteristics. In particular, neighborhoods characterized by a high percentage of foreign born residents (-0.002), low percentage of public transportation users (0.001), and high residential mobility (-0.007) experienced faster downward non-linear change than other neighborhoods. The predicted rate of non-linear decrease could be calculated as follows. β 3i = µ3 + γ 3 ( NeighborhoodCharacteristic )i = −0.014 − 0.002 * %ForeignBorn This means that a one unit increase in the percentage foreign born residents resulted in a larger negative estimate for β 3i (steeper downward curvature) by 0.002. The results for other crime types can be interpreted in a similar fashion. As for robbery, a high percentage of foreign born residents (0.096), high residential mobility (0.554), and high level of racial heterogeneity (6.204) were associated with high levels of robbery in 1960. As for the rate of change, neighborhoods that experienced faster linear increases in robbery were characterized by a high percentage of foreign born residents (0.209), high residential mobility (3.383), and high racial heterogeneity (6.772), and high socio-economic disadvantage (1.873). The percentage young males (-0.319) was negatively associated with the linear increase, indicating that neighborhoods characterized by a high percentage of young males experienced a slower linear increase over time. Finally, subsequent non-linear decrease was predicted by percentage foreign born (-0.049), percentage young males (0.068), residential mobility (-0.708), and racial heterogeneity (-1.793). The level of burglary in 1960 was higher in neighborhoods characterized by high residential mobility (4.796) and racial heterogeneity (10.145), while it was lower in neighborhoods characterized by a low percentage of young males (-0.263). Different neighborhood characteristics predicted variation in rate of change over time, however. Neighborhoods that experienced a faster linear increase were characterized by high residential mobility (4.179) and high socioeconomic disadvantage (4.731). The percentage foreign born was negatively associated with the linear increase (-0.469), indicating that neighborhoods with a high percentage of foreign born residents experienced a slower linear increase in burglary. In terms of

44

Neighborhood Structures and Crime: A Spatial Analysis

subsequent non-linear decrease, neighborhood characteristics, such as high residential mobility (-1.001) and high socio-economic disadvantage (-1.050), were associated with a faster non-linear decrease. The percentage foreign born was positively associated with the nonlinear decrease (0.107), indicating neighborhoods with a high percentage of foreign born residents were not likely to experience dramatic change in the level of burglary over time. Finally, different patterns also emerged for auto theft. As for the level of auto theft in 1960, neighborhoods characterized by high residential mobility (2.445) experienced higher levels of auto theft than other neighborhoods. Rates of linear change in auto theft, however, were predicted by the percentage young males, residential mobility, and socio-economic disadvantage. In particular, neighborhoods with high residential mobility (0.922) and high socio-economic disadvantage (1.674) experienced a faster linear increase in auto theft, while neighborhoods with a high percentage of young males (-0.184) experienced a slower linear increase in auto theft. Subsequent nonlinear increase, on the other hand, was predicted by the percentage of females employed (0.050), percentage young males (0.052), and socioeconomic disadvantage (-0.237). In particular, a steeper non-linear increase in auto theft was predicted in neighborhoods characterized by a high percentage of females employed, high percentage of young males, and non-disadvantaged neighborhoods. In addition to neighborhood characteristics measured in 1960 as time invariant predictors, the next set of models included changes in neighborhood characteristics as time variant predictors. Within the multilevel framework of growth curve models, time variant predictors appear as level-1 predictors. Thus, using the same notation, the growth curve models could be expressed as follows. 2

Level 1:

Crimeit = β 0 i + β1i * Timet + β 2 i * Timet +

β 3 ( ∆NeighborhoodCharacteristic )it + ε it

β 0 i = µ 0 + γ 0 ( NeighborhoodCharacteristic ) i + ζ 1i Level 2: β1i = µ1 + γ 1 ( NeighborhoodCharacteristic )i + ζ 2 i

β 2 i = µ 2 + γ 2 ( NeighborhoodCharacteristic )i + ζ 3i Thus, the models included neighborhood characteristics measured in 1960 that explain variability in the initial level of crime ( β1i : intercept)

Longitudinal Analysis of Crime Rates at the Neighborhood Level

45

and rate of change ( β 2i : linear change and β 3i : non-linear change) as level-2 predictors. Based on degrees of social disorganization and criminal opportunity, neighborhoods’ trajectories of crimes can vary in their initial levels of crime and rate of change. Changes in neighborhood characteristics that vary over time and appear as level-1 predictors affect the predicted levels of crime, controlling for the overall trajectory. For example, a positive value of β 3i shifts the predicted level of crime upward, while a negative value of β 3i shifts the predicted level of crime downward. The results of the growth curve models with changes in neighborhood characteristics as time-variant predictors are presented in Table 2.6. The table is divided into four panels, where the first panel indicates coefficient estimates of changes in neighborhood characteristics over time as level-1 predictors, which is the focus of this analysis. Interpretation of the coefficient estimates from the second to fourth panels are the same as the previous models where coefficient estimates showed associations between neighborhood characteristics and variability in growth curve parameters (i.e., initial level and rate of change in crime trajectories). As for homicide, consistent with social disorganization theory, increases in racial heterogeneity and socioeconomic disadvantage of neighborhoods were associated with increases in the level of homicide (the coefficient estimates were 0.277 and 0.045, respectively). 0 45 04 0 35 03 0 25 02 0 15 01 0 05 0 1970

1980 Average Neighborhoods

1990

2000

Disorganized Neighborhoods

Figure 2.3 Predicted Trajectories of Homicide for Average Neighborhoods and Increasingly Socially Disorganized Neighborhoods

-0.001 0.000 -0.001 0.003 0.026 0.277** 0.045* 0.031** 0.017 0.002 -0.005 -0.006 0.011 0.081 0.295* -0.013

∆ %Both Parents

∆ %Public Transport.

∆ %Female Employed

∆ %Young Male

∆ Residential Mobility

∆ Heterogeneity

∆ Disadvantage

Intercept

% Foreign

% Both Parent

% Public Transport.

% Female Employed

% Young Male

Residential Mobility

Heterogeneity

Disadvantage

Note: +p<.10, *p<.05, **p<.01

0.001

s.e.

(0.057)

(0.181)

(0.057)

(0.009)

(0.014)

(0.006)

(0.003)

(0.010)

(0.011)

(0.021)

(0.089)

(0.02)

(0.003)

(0.001)

(0.001)

(0.001)

(0.002)

Homicide

∆ %Foreign

Coef

-1.576

8.540**

-3.011

0.029

0.221

0.146

-0.080*

0.046

1.103**

-0.149

3.219+

0.457

0.240**

0.003

0.023+

0.006

-0.07*

Coef.

s.e.

(1.125)

(3.588)

(1.133)

(0.186)

(0.267)

(0.119)

(0.068)

(0.187)

(0.405)

(0.390)

(1.880)

(0.388)

(0.058)

(0.018)

(0.013)

(0.009)

(0.036)

Robbery

-2.261

15.164**

-1.41

-0.350

-0.715

0.138

-0.119

-0.305

15.306**

1.055

1.652

1.768*

-0.004

0.024+

-0.027

-0.003+

-0.025

Coef.

s.e.

(2.699)

(7.681)

(2.685)

(0.437)

(0.649)

(0.287)

(0.156)

(0.451)

(4.484)

(0.351)

(4.078)

(0.811)

(0.013)

(0.013)

(0.048)

(0.002)

(0.072)

Burglary

-0.461

2.185

4.169**

0.062

-0.060

-0.167

-0.045

0.346

4.448*

-1.503+

7.022**

1.248**

0.067

s.e.

(1.392)

(8.314)

(1.474)

(0.241)

(0.335)

(0.149)

(0.087)

(0.233)

(0.875)

(0.910)

(2.305)

(0.494)

(0.091)

(0.025)

(0.031)

(0.013)

(0.050)

Auto Theft

0.063**

-0.082

0.005

0.020

Coef.

Table 2.6 Changes in Neighborhood Characteristics as Time Variant Predictors.

-0.000

% Female Employed

Note: +p<.10, *p<.05, **p<.01

-0.010

0.000

% Public Transport.

Disadvantage

-0.000

% Both Parent

0.032

0.001

% Foreign

Heterogeneity

-0.028*

Quadratic

0.003

0.149**

Disadvantage

-0.004

-0.216

Heterogeneity

Residential Mobility

-0.001

Residential Mobility

% Young Male

0.002

0.005

% Public Transport. -0.013

0.000

% Both Parent

% Young Male

-0.007

% Foreign

s.e.

(0.011)

(0.065)

(0.011)

(0.002)

(0.003)

(0.001)

(0.001)

(0.002)

(0.015)

(0.056)

(0.336)

(0.057)

(0.009)

(0.013)

(0.006)

(0.003)

(0.010)

(0.022)

Homicide

% Female Employed

0.078

Linear

Coef

-0.347

2.530*

-1.456**

0.098*

0.034

0.048*

-0.029

-0.040

-1.053**

2.172*

7.977**

7.043**

-0.444*

-0.188

0.257*

0.074

0.189

s.e.

(0.235)

(1.384)

(0.234)

(0.037)

(0.056)

(0.025)

(0.018)

(0.039)

(0.289)

(1.238)

(3.323)

(1.239)

(0.195)

(0.295)

(0.130)

(0.071)

(0.207)

(1.678)

Robbery 5.1069**

Coef.

-1.417**

3.273

-2.276**

0.055

-0.150

-0.004

-0.067

0.127

-3.743**

6.821*

10.319*

10.297**

-0.159

0.780

0.001

0.299

-0.418

13.914**

Coef.

s.e.

(0.551)

(3.226)

(0.544)

(0.085)

(0.133)

(0.058)

(0.031)

(0.092)

(0.623)

(2.758)

(5.186)

(2.736)

(0.432)

(0.665)

(0.291)

(0.156)

(0.463)

(3.565)

Burglary

-0.219

-0.689

0.015

0.047

0.019

0.005

-0.025

0.031

-0.152

2.321*

-0.895

s.e.

(0.28)

(1.669)

(0.29)

(0.044)

(0.067)

(0.029)

(0.016)

(0.046)

(0.386)

(1.067)

(7.71)

(1.273)

(0.206)

(0.306)

(0.135)

(0.077)

(0.213)

(2.22)

Auto Theft

2.112+

-0.214

-0.075

0.035

0.122

-0.188

3.973

Coef.

Table 2.6 Changes in Neighborhood Characteristics as Time Variant Predictors (cont.).

48

Neighborhood Structures and Crime: A Spatial Analysis

The interpretation of the model can be facilitated by plotting predicted levels of crime based on the growth curve models with hypothetical neighborhood characteristics. Figure 2.3 presents hypothetical growth curves of homicide for neighborhoods that experienced increasing disadvantage and racial heterogeneity over time (for example, ∆Disadvantage = 0.5 and ∆Heterogeneity = 0.1 for each time point) and for neighborhoods that did not experience changes in these characteristics. The neighborhoods with increasing social disorganization experienced higher levels of homicide than neighborhoods without changes in social disorganization over time. As for robbery, increases in the percentage of public transportation users (0.023), percentage of young males (0.240), and racial heterogeneity (3.219) increased the level of robbery at each time point. Furthermore, increases in the percentage of the foreign born population (-0.070) decreased the level of robbery at each time point. These results provided somewhat limited support for social disorganization theory, as only one of the key predictors of the theory was significantly associated with the level of robbery, controlling for neighborhood characteristics measured in 1960. The results provided support for routine activities theory, as increased public transportation users could be interpreted as having increased exposure to motivated offenders. Increases in young males could also be interpreted as increases in exposure to criminally prone individuals. The third model in Table 2.6 was concerned with a trajectory of burglary over time. The results indicated that the level of burglary was higher in neighborhoods that experienced increases in the percentage of females employed (0.024) and residential mobility (1.768). Furthermore, increases in the percentage of children living with both parents were associated with a lower level of burglary (-0.003). These results might suggest that the level of burglary was susceptive to changes in the opportunity structure of neighborhoods. From the perspective of social disorganization theory, increases in residential mobility might indicate decreased informal social control, which subsequently resulted in increased level of crime. From the routine activities perspective, increases in residential mobility could be interpreted as increased anonymity, which created suitable opportunities for intruders. An increase in non-household activities, reflected by female employment, could also signify decreased guardianship, which contributed to increases in burglary.

Longitudinal Analysis of Crime Rates at the Neighborhood Level

49

Finally, the level of auto theft was positively associated with changes in the percentage of females employed (0.063), racial heterogeneity (7.022), and residential mobility (1.248). Thus, increases in the percentage of females employed, racial heterogeneity, and residential mobility increased the level of auto theft in neighborhoods. These results were in accord with predictions based on routine activities theory and social disorganization theory. Somewhat surprisingly, socio-economic disadvantage was negatively associated with the level of auto theft, which is contrary to social disorganization theory. The finding could be explained by routine activities theory, however. Although the number of cars increased rapidly since 1960, the increase in cars was likely to be faster in affluent neighborhoods. Thus, the number of targets for auto theft, which is one of the three elements of routine activities theory, was likely to be higher in neighborhoods with higher socio-economic status. METHOD II: SPATIAL PANEL MODELS Growth curve models are used to characterize the shape of trajectories of crime and to examine the extent of variability in the initial level and the rate of change explained by neighborhood characteristics. Growth curve models are attractive models for the analysis of change and have been used in several studies that examined changes in crime rates over time at the neighborhood level (Bollen and Curran 2006; Bursik and Grasmick 1992; Griffiths and Chavez 2004; Hipp et al. 2004; Kubrin and Herting 2003; Weisburd et al. 2004). Similar to the reason that ordinary least squared (OLS) regression models are not suitable models for the analysis of spatial data, however, growth curve models on spatial data may produce biased results because an analysis of spatial data requires a specialized estimation technique (Anselin 1988; Florax and Nijkamp 2005). As spatial effects are not simply an additional variable in regression models, including spatially lagged crimes in growth curve models is not enough to properly capture spatial effects. The argument was made in this chapter that problems caused by the spatial dependency of dependent variables was not considerable, as the auto-correlation of residuals was not significant for 14 out of 20 models after controlling for neighborhood characteristics (Table 2.1).

50

Neighborhood Structures and Crime: A Spatial Analysis

Nonetheless, in order to examine a possibility of invalid conclusions in the previous analysis based on growth curve models, spatial panel models are employed to supplement the longitudinal analysis of crime rates at the neighborhood level. Similar to the criticism against residual change scores, spatial panel models suffer from some limitations, such as comparisons of two time points and modeling of only linear change. However, spatial panel models can take into account the spatial dynamics of data through a spatial weights matrix. Furthermore, the panel model is more advantageous than crosssectional analysis of crimes. The advantages of using a panel model includes the ability to control for unobserved heterogeneity, the limited effects of omitted variables bias, the ability to examine temporally dynamic relationships, increased degrees of freedom, increased efficiency, more information, more variability, and less colliniarity among predictors (Baltagi 2001; Elhorst 2003; Frees 2004; Hsiao 2002). Although the main disadvantage of panel data analysis is often attrition and selectivity bias, it does not apply to the data examined in this chapter because the census and crime data have no missing observations. Model Specifications of Panel Regression There are two main model specifications in the analysis of panel data. These two model specifications differ in their treatment of unobserved heterogeneity that is specific to cross-sectional unit and time in data. The first model specification is a fixed effect model that control unobserved heterogeneity by including unique intercepts for individual and/or time. The two-way fixed effects model that has unique intercepts for both cross-sectional units and time can be expressed as follows, using the notation and framework presented by Frees (2004) and Park (2005): yit = (α + µi + λt ) + xit′ β + ε it . The µi and λt represent the effects of unobserved variables unique to individual i and time t, which are invariant over individual or time. As can be seen in the above equation, the fixed effect model includes unobserved heterogeneity across individuals and time via a part of the intercept. When there is only one intercept term varying across

Longitudinal Analysis of Crime Rates at the Neighborhood Level

51

individuals or time, the above fixed effect model can be reduced to the one-way effect model with either µi = 0 or λt = 0 . While the fixed effect model can be estimated simply by including dummy variables for individuals and/or time (least squares dummy variable regression, or LSDV), the coefficient estimates of the dummy variables are not consistent, as the number of these parameters increases as the number of cross-sectional units and/or time points increases (i.e., incidental parameter problems). Furthermore, this estimation method uses many degrees of freedom. An alternative method of estimating the fixed effect model is by eliminating the intercept terms (i.e., demeaning operation). Although statistical software automatically conducts the demeaning operation (e.g., the xtreg command with fe option in Stata and the proc tscsreg command with fixone option in SAS), the operation can be considered as a three step procedure for the one-way fixed effect model (the two-way fixed effect model can also be estimated by extending the steps presented here): 1) calculate the group means of the dependent and independent variables; 2) calculate the deviations from the means for both the dependent and independent variables; 3) run OLS regression on the transformed variables without intercept (Park 2005). Thus, in effect, the one-way fixed effect model is to run OLS on the following model: yit − yi. = xit − xi. + ε it − ε i. . In contrast to the LSDV regression, this estimation of the fixed effect model can be called a within effect estimation. Although the within effect estimation does not directly produce the group effects, these effects can be calculated by using the following formula (Park 2005): d i = yi. − β ′ xi. . The d i is the group effect for individual i, yi. is the group mean of the dependent variable for individual i, β ′ is the coefficient estimate from the within effect regression model, and x is the group mean of an i independent variable for individual i. The same computation can also be done for the one-way fixed effect model with the time effect by substituting subscript i. with .t. Furthermore, the more involved formulae for the two-way fixed effect model with both individual and time specific effects are as follows: d i = ( yi. − y.. ) − β ′( xi. − x.. ) and d t = ( y.t − y.. ) − β ′( x.t − x.. ) .

52

Neighborhood Structures and Crime: A Spatial Analysis

Finally, although the present discussion focused on the treatment of unobserved heterogeneity through intercepts, it is possible to consider individual and/or time specific coefficient estimates, although such model specification is beyond the scope of this book. The second model specification of panel data analysis is the random effect model. While the fixed effect model incorporates the effects of unobserved heterogeneity that is specific to individual and/or time through unique intercepts, the random effect model incorporates the unobserved heterogeneity through an additional term that is a part of errors. In particular, the two-way random effect model can be expressed as follows, using the notation and framework presented by Frees (2004) and Park (2005): yit = α + xit′ β + ( µi + vt + ε it ) . 2

The µi is a random variable with zero mean and variance σ µ that captures a cross-sectional specific effect and vt is a random variable 2 with zero mean and variance σ v that captures a time specific effect. Similar to the fixed effect model, the two-way random effect model can be reduced to the one-way model when there is no cross-sectional or time specific effect. Thus, the one-way random effect model has the random effect that varies across individual or time, while the two-way random effect model has the random effects that vary across individual and time. The random effect models assume that xit′ , µi , vt , and ε it are independent of each other. The random effect model is estimated by generalized least squares (GLS) when the variance structure of the model is known/given, while it is estimated by feasible generalized least squares (FGLS) when the variance structure of the model is unknown. The estimation of the random effect model tends to be more difficult and computationally intensive than the fixed effect model. Furthermore, the two-way random effect model is more difficult to estimate than the one-way random effect model. Finally, similar to the fixed effect model, it is possible to consider random coefficient estimates that vary across individual and/or time, although such model specification is beyond the scope of this book.

Longitudinal Analysis of Crime Rates at the Neighborhood Level

53

Model Specifications for Spatial Panel Regression There are several model specifications of spatial panel models (Anselin et al. 2008; Elhorst 2003). Similar to regular panel models, spatial panel models can employ either fixed effects or random effects. The former controls for unobserved heterogeneity among subjects and/or time periods through a variable intercept for each subject and/or time period, while the latter controls for heterogeneity through a random variable that is a part of the error terms. For fixed effects and random effects models, spatial effects can be incorporated via the spatial lag of the dependent variable or spatial lag of error terms. Using the notation and framework presented by Elhorst (2003), the one-way fixed effect spatial lag model that incorporates subject specific effects can be mathematically expressed as follows: Yt = δ WYt + X t β + µ + ε t . The δ is called a spatial autoregressive parameter that represents the strength and direction of spatial interaction of the dependent variable, while W is an N * N spatial weights matrix that describes the spatial arrangement of the data. The matrix is coded as wij = 1 when neighborhoods i and j are adjacent, and it is coded as wij = 0 when they are not adjacent (the spatial weight matrix is row standardized during the estimation of a model in order to ease computational burdens and to facilitate the interpretation of the spatially lagged term (Anselin 1988; 2000; Florax and Nijkamp 2005). There are various specifications of what constitute neighbors. For example, spatial units are considered to be neighbors if they share a boundary in the rook specification, while they are defined as neighbors if they share either a boundary or vertex in the queen specification (the name of rook and queen comes from the movement of pieces in the game of chess). Furthermore, neighbors can also be defined based on distance (e.g., distance from centroids). These definitions of neighbors need to be specified exogenously and a priori by researchers before running regression models. Regardless of the definition of neighbors, however, it is important to note that the spatial effect extends beyond immediate neighbors because of the so-called spatial multiplier. That is, due to the presence of spatial multiplier in spatial lag regression models, a shock in a location has effects on the entire spatial system, although the effects diminish in their strength with distance. Finally, similar to the

54

Neighborhood Structures and Crime: A Spatial Analysis

one-way fixed effect model of the aspatial panel data, µ captures the effect of unobserved heterogeneity that is specific to each crosssectional unit. By substitution subscript i with t, the model can be extended to capture the panel model with time specific effects. Furthermore, the model can also be extended to the two-way fixed effects by including both subject and time specific effects. The second way of capturing spatial effects of the data in the panel model is the fixed effect spatial error model which can be expressed as follows: Yt = X t β + µ + φt , φt = δ W φt + ε t . Similar to the fixed effect spatial lag model, δ is a spatial error autocorrelation and W is a spatial weights matrix. Furthermore, µ captures the unobserved subject specific effect, although the model can be changed to the one-way fixed effect with a time specific effect. Furthermore, the model can be extended to the two-way fixed effect with both subject and time specific effects by incorporating an additional variable intercept capturing a time specific effect. The third and fourth model specifications of spatial panel model are a variant of the random effect model. A crucial difference between the fixed effect and random effect models is their treatment of unobserved heterogeneity. The fixed effect model incorporates the cross-sectional unit specific effect via the variable intercept, while the random effect model captures the heterogeneity through a random variable, which is a part of the errors. Similar to aspatial panel models, the random effect model uses fewer degrees of freedom and is more efficient. The one-way random effect spatial lag model can be expressed as follows, using the notation and framework presented by Elhorst (2003): Yt = δ WYt + X t β + v, with v = (ιT ⊗ I N ) µ + ( I T ⊗ I N )ε . where ιT is a T*1 vector of ones, and I N and I T are identity matrices of sizes N and T, respectively. Similar to the aspatial random effect model, the above model treats the spatial unit variable intercept as a random variable, µi , that is assumed to have a normal distribution with zero 2 mean and variance σ µ . Furthermore, µ , ε , and X are assumed to be independent of each other. The δ is a spatial autoregressive coefficient of the dependent variable and W is a spatial weights matrix that describes the spatial arrangement of data.

Longitudinal Analysis of Crime Rates at the Neighborhood Level

55

The random effect spatial error model that captures spatial effects through the structure of errors can be mathematically expressed as follows using the same framework: −1

Yt = X t β + v, with v = (ιT ⊗ I N ) µ + {I T ⊗ ( I N − δ W ) }ε .

The δ is a spatial autocorrelation coefficient that represents the strength and direction of spatial clustering of unobserved variables. Similar to the other random effect model specification, the random variable, µi , is assumed to have a normal distribution with zero mean 2 and variance σ µ . Furthermore, µ , ε , and X are assumed to be independent of each other. In addition to these four model specifications (i.e., the fixed effect spatial lag, fixed effect spatial error, random effect spatial lag, and random effect spatial error models), several model specifications have also been theoretically developed. For example, Elhorst (2003) presents the fixed coefficient and random coefficient models for both spatial error and spatial lag effects. These panel models may be employed when spatial heterogeneity cannot be fully accounted for by the variable intercept in the fixed effect models and by the random variable in the random effect models discussed above. Additionally, Anselin and his colleagues (2008) have developed taxonomies for spatio-temporal models, such as pure space recursive models, timespace recursive models, time-space simultaneous models, and timespace dynamic models. As computer programs to estimate these additional model specifications have not been developed yet, these model specifications are beyond the scope of this book. Estimation of Spatial Panel Models Similar to the analysis of aspatial panel data, the fixed effect spatial panel model estimates regression coefficients by demeaning the dependent and independent variables, which eliminates the variable intercept (Elhorst 2003). Then, maximum likelihood (ML) estimation can be conducted on the transformed variables. Due to the problem known as the incidental parameter problem, the coefficient of the spatial unit cannot be consistently estimated when T is short and N is large. That is, the number of parameters to be estimated increases as the number of spatial units increases. This may not be a serious

56

Neighborhood Structures and Crime: A Spatial Analysis

problem as long as researchers’ interests lie on estimating slope coefficients, as the problem of estimating the spatial unit effects is not transmitted to the estimation of slope coefficients (Elhorst 2003). It is important to note, however, that Anselin and his colleagues argue the framework of the fixed effect model presented by Elhorst (2003) ignores the demeaning operation of the error terms. When the error term is appropriately demeaned, however, the variance–covariance matrix of the demeaned error term becomes singular, which makes the estimation of the model infeasible. As for the random effect model, several methods of estimation have been proposed, including the maximum likelihood (ML), the instrumental variable (IV), and the generalized methods of moment (GMM) (Anselin et al. 2008; Baltagi et al. 2007; Baltagi et al. 2003; Elhorst 2003; Elhorst 2005; Kelejian and Robinson 1993). The result of Monte Carlo simulation indicated the maximum likelihood estimation is preferred over other estimation methods, as the maximum likelihood estimation tends to be more efficient (Elhorst 2005). Furthermore, from a practical standpoint, researchers may need to choose the maximum likelihood estimation because the publicly available computer program for spatial panel models developed by Elhorst (2003) uses the maximum likelihood estimation. Model Selection of Spatial Panel Models Model specifications can be done based on three criteria. The first is based on statistical tests, while the second is based on theoretical consideration of which models are more appropriate for one’s research question and data. The third is the availability of computer programs to estimate statistical models. First, a series of statistical tests are available to compare the fixed effect model, the random effect model, and the pooled OLS model (Baltagi 2001; Frees 2004; Hsiao 2002; Park 2005; Verbeek 2004). The fixed effect model can be tested against the pooled OLS model via an F-test that compares residual sums of squares between the two models. The variance of the cross-sectional specific effect can also be tested for the random effect model by a variant of Lagrange Multiplier test (sometimes called Breusch-Pagan test due to the developers of the test). As the random effect model use fewer degrees of freedom, the

Longitudinal Analysis of Crime Rates at the Neighborhood Level

57

models are considered to be more efficient and desirable than the fixed effect model. When random effects are correlated with independent variables, however, the coefficient estimates of the independent variables are no longer unbiased. In such a case, the fixed effect model is said to be preferred. A proper model specification can be evaluated based on a statistical test, known as the Hausman test. The Hausman test compares the coefficient estimates of the fixed effect model (unbiased but inefficient) with those of the random effect model (maybe biased but efficient). The interpretation of the Hausman test in spatial data require caution, however, as the assumption of independently distributed error terms is often violated in spatial data. Finally, for both fixed and random effect models, spatial effects can be incorporated via a spatially lagged dependent variable or spatially lagged error term. A choice of spatial lag or spatial error models can be determined by the Lagrange Multiplier test (Anselin 1988; Anselin 2003; Florax and Nijkamp 2005). Second, the appropriateness of the fixed effect and random effect panel model also needs to be evaluated from a substantive viewpoint (Hsiao 2002; Verbeek 2004). In particular, it should be examined if one’s research question and available data are suitable for which model specification. Hsiao (2002: 43) argues that “the fixed-effects model is viewed as one in which investigators make inferences conditional on the effects that are in the sample. The random-effects model is viewed as one in which investigators make unconditional or marginal inferences with respect to the population of all effects”. That is, inferences from the fixed effect model are conditional on the values of fixed effect intercepts and the particular sample observed at particular locations/areas. Thus, the fixed effects model is appropriate if observations in the sample are “‘one of a kind,’ and cannot be viewed as a random draw from some underlying population” (Verbeek 2004: 351). The inferences from the random effect model, on the other hand, are unconditional on the values of individual intercepts and are made with respect to the population characteristics. In particular, the crime rate and census data of Seattle that this chapter examines can be considered as a realization of a stochastic (random) process (Anselin 1988; Haining 2003). What appears to be an exhaustive list of areal (census tract) observations is considered to have been drawn from the super-population that has given rise to observable crime and sociodemographic data. Official crime statistics do not represent all crime

58

Neighborhood Structures and Crime: A Spatial Analysis

incidents that have occurred in Seattle. Many offenses remain unreported (i.e., so-called dark figures) (Mosher et al. 2002). The reporting practices of criminal justice agencies also affect the number of crimes included in the police reports. Thus, what is observed as Uniform Crime Reports can be considered to have been stochastically drawn from some underlying distribution of crime phenomenon. Furthermore, although the census also appears to be the population, the census data only represent socio-demographic characteristics of neighborhood residents under a particular condition at a particular time. Similar to the crime data, the census does not necessarily cover the 100% of the population living in the United States. Under such a framework, the random effect model that makes unconditional inferences with respect to the population characteristics seems to be more appropriate for the current research than the fixed effect that treats the sample as a one of a kind and not a random draw from an underlying population distribution. Furthermore, in the context of regression analysis, the error term represents the effects of variables that are not included in the model (or, not observed variables.). As panel analysis models control for unobserved heterogeneity through either the variable intercept (fixed) or a random variable (random), it may be more reasonable to treat both of the unobserved effects (i.e., heterogeneity and errors) as random, instead of treating one effect as fixed and the other as random (Hsiao 2002). Thus, the choice of the random effect model is consistent with the implication of the statistical model. In addition to statistical and theoretical concerns, the third criterion in selecting an appropriate model is the availability of statistical programs. Ideally, the model specification of spatial panel analysis should be evaluated based on statistical properties of coefficient estimates (e.g., unbiased, consistency, and efficiency), as well as substantive consideration of data and research questions, as discussed above. Because of the complexities involved in calculating spatial effects, however, a practical concern regarding the availability of computer programs is also crucial in the analysis of spatial panel models. Griffiths and Chavez (2004: 938) recognized the difficulty of longitudinal analysis of spatial data in their analysis of homicide trajectories in Chicago over time by saying “current quantitative methodologies equipped to capture temporal changes, such as pooled cross-sectional time series or hierarchical linear modeling, are unable to

Longitudinal Analysis of Crime Rates at the Neighborhood Level

59

accommodate spatial terms because the parameters of these models cannot be properly identified.” Although the development of computer programs for the analysis of spatial panel data is an active research topic in spatial econometrics (Anselin et al. 2008; Baltagi et al. 2007; Baltagi et al. 2003; Elhorst 2003), computer programs for estimation are not widely available. The only program for the analysis of spatial panel data that is publicly available is a series of commands in a Matlab library developed by Elhorst (2003). The library contains the fixed effect spatial error and spatial lag models, the random effect spatial error model, and the dynamic panel model with serially lagged dependent variable and spatial error. Thus, from a practical viewpoint, the choice of spatial panel models is constrained among these model specifications, unless researchers develop their own syntaxes and programs. RESULTS: SPATIAL PANEL MODELS Using spatial panel models, it was examined how changes in neighborhood characteristics were related to changes in the level of crime (Table 2.7). Prior to running spatial panel models, the model specification was determined by examining the Breusch Pagan test and Hausman test for appropriateness of random effects models. The Breusch Pagan tests on the presence of variability in the random effect were significant for all crime types, indicating the need to control for the random effect. Furthermore, the Hausman tests were insignificant for all crime types at the alpha 0.05 level except for auto theft, indicating that coefficient estimates of the random effect models for these three crime types were not biased and that the random effect models were the preferred models over the fixed effect models because of the efficiency of the random effect model. Even for auto theft, it is important to note that the conclusion of the Hausman test might not be valid as the assumption of the independence of errors was likely to be violated in spatial data. It was also argued in the previous section that the random effect model was substantively suitable for the data and research questions that this chapter pursued. Finally, as Anselin and his colleagues (2008) noted, the fixed effect model developed by Elhorst

∆ %Young Male

∆ %Female Employed

∆ %Public Transport.

∆ %Both Parents

∆ %Foreign

Time Dummy (2000)

Time Dummy (1990)

Time Dummy (1980)

Time Dummy (1970)

0.284* (0.136)

0.004 (0.003)

-0.005 (0.030)

(0.000)

(0.071)

(0.002) -0.002**

0.155*

(0.025)

(0.000) 0.001

0.039

-0.001*

-0.327** (0.101)

(0.002)

(0.024) -0.007**

-3.919* (1.545)

-0.048*

(1.686)

(0.028)

(1.681) -0.293

(0.029) 0.010

-2.346

-0.052+

4.059* (1.405)

0.058

∆ Robbery

(0.083)

∆ Homicide

(0.194)

0.173

(0.045)

0.194**

(0.102)

0.282**

(0.031)

-0.054+

(0.144)

-0.099

(2.045)

-5.071**

(2.247)

-1.687

(2.246)

-1.868

(2.724)

6.661**

∆ Burglary

(0.111)

0.375**

(0.026)

0.039

(0.058)

0.173**

(0.018)

-0.001

(0.083)

-0.022

(1.285)

-0.209

(1.398)

4.248**

(1.392)

-3 915*

(2.779)

5.443**

∆ Auto Theft

Table 2.7 Spatial Panel Models of Changes in Crime Rates Predicted by Changes in Neighborhood Characteristics

2.22

40.22**

11.23

52.41**

0.687** (0.044)

0.182** (0.077)

-0.000 (0.048)

0.002

(0.984)

(0.026) (0.056)

3.609**

(0.995)

(0.027) -0.055*

-0.390

(5.74)

0.078**

21.304**

0.220+ (0.132)

∆ Robbery

Note: +p<.10, *p<.05, **p<.01. Standard errors are in parentheses.

Hausman Test

Breusch Pagan Test

Spatial Error

Random Effect

∆ Residential Mobility

∆ Disadvantage

∆ Heterogeneity

∆ Homicide

5.52

51.37**

(0.034)

0.643**

(0.050)

0.001

(1.394)

2.765*

(1.409)

3.236*

(5.248)

12.743**

∆ Burglary

20.64**

11.40**

(0.049)

0.703**

(0.068)

0.001

(0.796)

2.123**

(0.805)

-2.289**

(2.719)

5.417*

∆ Auto Theft

Table 2.7 Spatial Panel Models of Changes in Crime Rates Predicted by Changes in Neighborhood Characteristics (cont.)

62

Neighborhood Structures and Crime: A Spatial Analysis

(2003) was problematic. Thus, based on these evaluations of the model specification, the analysis in this chapter was conducted using the random effect model with the spatial error component. Changes in the level of homicide were associated with changes in the percentage foreign born residents, percentage of children living with both parents, percentage of females employed, racial heterogeneity, socio-economic disadvantage, and residential mobility. In particular, increases in racial heterogeneity and socio-economic disadvantage were associated with increases in homicide, supporting theoretical expectations of social disorganization theory. Increased heterogeneity was expected to further hinder the realization of common goals among neighborhood residents. Furthermore, increased socioeconomic disadvantage was likely to increase frustrated wants among neighborhood residents. Moreover, increases in the percentage of foreign born residents and percentage of children living with both parents were associated with decreases in the level of homicide. As an increase in the number of immigrants was likely to lead to forming ethnic neighborhoods with unified value systems over time, the negative association between percentage foreign born and the level of crime was in accord with a theoretical expectation. Furthermore, the negative association between the percentage of children living with both parents and the level of homicide could also be attributed to increased direct control by the family as an institution. Finally, the spatial error term that subsumed the effect of spatially correlated unobserved variables was significant, indicating the importance of considering spatial effects in this analysis. In contrast to these findings in accord with theoretical expectations, the negative associations of percentage females employed, residential mobility, and the level of homicide were unexpected. From the perspective of routine activities theory, increases in employed females indicated increased exposure to motivated offenders and increase nonhousehold activities, resulting in lowered guardianship. As women were much less likely to be victims of homicide than men, however, percentages of females employed might not be the best measure of opportunity structures for homicide. Instead, the negative association between the level of homicide and percentage females employed could be explained by increased female employment in neighborhoods with higher socio-economic status that had lower levels of homicide to begin with.

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As for robbery, changes in the percentage of foreign born residents, percentage of public transportation users, percentage of young males, racial heterogeneity, and residential mobility were associated with changes in the level of robbery. In particular, increases in robbery were predicted by increases in the percentage of public transportation users, percentage of young males, racial heterogeneity, and residential mobility. These positive effects of racial heterogeneity and residential instability supported the expectations of social disorganization theory, while the positive effects of public transportation users and young males supported the expectations of routine activities theory. Increases in both racial heterogeneity and residential mobility were likely to diminish informal social control at the neighborhood levels. Increases in public transportations users meant an increased frequency of encountering motivated offenders. An increased number of male youth also represented an increased frequency of encountering criminally-prone individuals. Furthermore, similar to the homicide model, an increased percentage of the foreign born population was related to a lower level of robbery. As for burglary, predictions from social disorganization theory and routine activities theory were supported. In particular, increases in burglary were predicted in neighborhoods that experienced increases in public transportation users, employed females, racial heterogeneity, socio-economic disadvantage, and residential mobility. That is, increased criminal opportunity was created through increased nonhousehold activities, which resulted in increasing the level of burglary in neighborhoods. Furthermore, increases in residential mobility and racial heterogeneity were likely to reduce informal social control in neighborhoods. Changes in socio-economic disadvantage structures of neighborhoods also affected strain among motivated offenders. Finally, increases in the percentage of children living with both parents were associated with a decrease in burglary. Living with both parents was likely to increase direct control of adolescents, which decreased the number of motivated offenders under no supervision. Furthermore, increases in the number of intact families might also strengthen the household guardianship against potential intruders by increasing the number of individuals residing in them. Finally, changes in auto theft were associated with changes in the percentage of public transportation users, percentage of young males, racial heterogeneity, socio-economic disadvantage, and residential

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mobility. As for variables based upon routine activities theory, increased numbers of public transportation users and young males were associated with increases in the level of auto theft. The number of public transportation users has often used as a proxy of exposures to motivated offenders (e.g., Miethe and Meier 1994). In order to explain the relationship between the variable and the level of auto theft, public transport users might be interpreted as an indication of frustrated wants. That is, those who did not have access to cars and were forced to use public transportation might be motivated to steal cars. In fact, as evidence partially supporting such claims, changes in the percentage of young males, who were most likely to be involved in auto theft, were associated with increases in auto theft. As for variables based on social disorganization theory, increases in racial heterogeneity and residential mobility were associated with increases in auto theft. Contrary to the hypothesized relationship, changes in socio-economic disadvantage were negatively associated with changes in auto theft. This might be due to the number of available crime targets in neighborhoods. That is, motorization had rapidly expanded since 1960, although the process was likely to be faster in neighborhoods composed of affluent households that had financial resources. Thus, the number of auto thefts was likely to be higher in neighborhoods with higher socio-economic status than disadvantaged neighborhoods. Thus, such a finding was in accord with routine activities theory that considered crime occurred when motivated offenders and attractive targets converged in time and space. For all crime types, time dummy variables captured something peculiar to each time point that was not explained by the neighborhood characteristics included in the panel regression models. As these variables captured unobserved heterogeneity at each time point, their coefficient estimates were not in and of themselves interesting from the substantive viewpoints. Controlling for the unobserved heterogeneity through time dummy variables, however, increased the ability of the panel regression models to predict the levels of crime at each point. SUMMARY Ecological analysis of crime has been a popular topic since the inception of quantitative criminology in the United States by the

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Chicago school sociologists. The analyses to date have been largely based on cross-sectional data. Attention has not been paid to how longitudinal changes in the level of crime are associated with neighborhood characteristics. It has not been fully examined if the results based on cross-sectional analysis are also true for longitudinal analysis at the neighborhood level. Although there are several studies that have examined changes in the level of crime and neighborhood characteristics, this chapter has argued that these studies have suffered from methodological problems. While residual change scores have been used in several studies (Bursik and Webb 1982; Chamlin 1989; Taylor and Covington 1993), the method only provides a comparison between two time points, providing snapshots of relationships between neighborhoods and crime. Additionally, the analysis of two time points only captures linear changes and neglects non-linear changes across time. To overcome these problems, growth curve models were suggested in this chapter as an analytical strategy to examine changes in crime and neighborhood characteristics (Bursik and Grasmick 1992; Kubrin and Herting 2003; Rogosa et al. 1982; Rogosa 1995). Using growth curve models, average trajectories of homicide, robbery, and burglary rates in Seattle between 1960 and 2005 were characterized by non-linear shapes, with initial increases followed by subsequent non-linear decreases. As for auto theft, the average trajectory was also characterized by a non-linear shape, although the non-linear change was in an upward trend (acceleration). That is, the auto theft trajectory was characterized by an initial linear increase followed by non-linear increases (i.e., acceleration). The different shape of the trajectory for auto theft could be explained by an increase in the number of cars over time, which increased the number of targets for auto theft. The analysis of growth curve models indicated, however, that there was considerable individual variability in trajectory forms. That is, the initial level of crime and rate of linear and non-linear changes varied considerably across individual neighborhoods. In general, neighborhoods characterized by higher initial levels of crime were likely to experience faster linear increases in crime over time than neighborhoods characterized by lower initial levels of crime. These high crime neighborhoods, however, were likely to experience subsequent non-linear decreases at a faster rate than low crime neighborhoods.

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Neighborhood characteristics were introduced to explain the individual variability in the initial levels of crime and rate of change over time. While the results somewhat varied by crime types, key predictors of social disorganization theory, such as racial heterogeneity, residential mobility, and socio-economic disadvantage, seemed to be strong predictors of both the initial level of crime and rate of change over time. In particular, racial heterogeneity and residential mobility were good predictors of the initial level of crime, while socio-economic disadvantage was a good predictor of the rate of change over time. As for variables from routine activities theory, only a few variables were statistically significant when they were treated as fixed neighborhood characteristics over time. When these variables were treated as timevariant predictors, many of them were significantly associated with the level of crime. That is, the opportunity structure of crime in neighborhoods was likely to change at each time point, which affected the level of crime at each time point. Social disorganization variables measured in 1960 and treated as time-invariant predictors, on the other hand, were strong predictors of the shape of trajectories in subsequent time periods. As the analysis of spatial data requires a specially designed estimation technique, the results of growth curve models can be biased. Thus, spatial panel data models were also employed to supplement the longitudinal analysis of crime. These results were also largely in accord with the theoretical expectations of social disorganization theory and routine activities theory. Key predictors of social disorganization theory, such as socio-economic disadvantage, racial heterogeneity, and residential mobility were associated with the level of crime for the most part. For example, increases in racial heterogeneity were associated with increases in all crime types. Although variables from routine activities theory were also associated with changes in crime in the expected direction, the effects seemed to be more sensitive to types of crime. That is, as routine activities theory focuses on suitable opportunities for crime, different neighborhood characteristics were likely to produce varying criminal opportunities for specific crimes. For example, increases in public transportation users were associated with financially motivated crimes, such as robbery, burglary, and auto theft. As changes in the number of employed females also affected the prevalence of non-household activities, which were likely to leave

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houses unattended, changes in female employment were associated with changes in burglary. Overall, the results of the longitudinal analysis presented in this chapter were in accord with the predictions of social disorganization theory and routine activities theory. Individual variability in neighborhood trajectories of crime was explained by key predictors of social disorganization theory, such as racial heterogeneity, residential mobility, and socio-economic disadvantage. When the analysis included both time-variant and time-invariant neighborhood characteristics, variables from routine activities theory seemed to be more predictive when they were treated as time variant predictors. That is, changes in the level of crime seemed to be susceptible to changes in criminal opportunities at each time point. Variables from social disorganization theory, on the other hand, seemed to be a robust predictor of crime trajectories that characterized changes in the level of crime at the neighborhood level for decades later. Previous studies on longitudinal changes in neighborhood characteristics and the level of crime were predominantly conducted at the large macro level (e.g., state, county, and city). Thus, it was less known how neighborhoods within cities experienced changes in the level of crime over a long period of time. The longitudinal analysis on crime at the neighborhood level presented in this chapter indicated that the shape of crime trajectories varied considerably across neighborhoods. Variation in crime trajectories, however, was largely explained away by social disorganization theory and routine activities theory. Additionally, it was also indicated that the pattern of association was crime specific, where property offenses were more strongly characterized by changes in opportunities for crime.

CHAPTER 3

An Analysis of Spatially Varying Associations between Neighborhood Characteristics and Crime

INTRODUCTION Spatial aspects of crimes have been a classic research topic in criminology. In fact, one of the first quantitative studies of crime in America was a spatial analysis of juvenile delinquency in Chicago conducted by Shaw and McKay (1942; 1969). The importance of considering space in quantitative criminological research can be easily illustrated. First, crimes are spatially concentrated in select neighborhoods in cities, as many studies have illustrated (Andresen 2006; Block and Block 1995; Bowers et al. 2004; Brantingham and Brantingham 1994; Chainey and Ratcliffe 2005; Johnson and Bowers 2004). Second, crimes may diffuse over space, where high levels of crime affect the level of crime in surrounding neighborhoods (Cohen and Tita 1999; Cork 1999; Cornish and Clarke 1987; Tita et al. 2005). Third, attention to space also has practical implications, as law enforcement activities are often based on geographic areas, such as police beats. Fourth, space can also be a pertinent research subject, as sociological criminology is often interested in the interactions of individuals and environmental factors. For example, although the lifestyle perspective of victimization focuses on individuals’ characteristics to explain victimization risks (Hindelang et al. 1978), several studies have found that one’s victimization risks also vary by neighborhood characteristics (Miethe and McDowall 1993; Miethe et al. 1987; Rountree et al. 1994). 69

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Despite the importance of space in criminology, spatial analysis often provides challenges to researchers for several reasons. First, although widely-used ordinary least squares (OLS) regression is a powerful statistical model for examining the relationship between an independent variable and a dependent variable, controlling for many other variables, spatial data violate the assumption of independently distributed residuals. Violation of this assumption occurs because spatial units, such as neighborhoods, are not independent observations. Rather, the spatial dependency of variables, defined as the spatial clustering of similar values of a variable, occurs almost everywhere. In order to take the spatial dependency of data into account, and to obtain unbiased estimates of measures of association between independent and dependent variables, researchers need to utilize specialized regression models, such as spatial regression models (Anselin 1988; Anselin et al. 2000; Florax and Nijkamp 2005). The second challenge of spatial data is caused by another spatial effect, spatial heterogeneity. Spatial heterogeneity indicates that structural associations between two variables change by location, such as downtown and suburbs. For example, the effect of leisure activities on one’s victimization risk may be stronger in the downtown area than suburbs, because of a greater exposure to motivated offenders. Similar to spatial dependency, a failure to take into account spatial heterogeneity in regression analysis results in biased regression coefficient estimates and standard errors (Anselin 1988; Anselin et al. 2000; Florax and Nijkamp 2005). Although spatial heterogeneity is often addressed by including dummy variables to capture spatial locations (e.g., downtown), it is important to note that space is not a discrete ecological unit. Rather, spatial processes occur in a continuous fashion. Thus, the discrete distinction of downtown vs. other areas neglects the continuity of spatial areas. Third, criminological research using neighborhoods as a unit of analysis sometimes suffers from the ecological fallacy, as crimes are ultimately individual behaviors. That is, conclusions based upon statistical analyses of aggregate data do not always accurately represent the behavior of individuals, such as criminal offenders and victims. Although it may be most appropriate to test social disorganization theory at the neighborhood level, too much attention on neighborhoods may mask criminal activities occurring at the place level (Block and Block 1995; Sherman 1995; Sherman et al. 1989; Stark 1987).

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In order to overcome the challenges of spatial data, this research employs geographically weighted regression models in order to examine social disorganization theory and routine activities theory. By estimating location specific measures of association between neighborhood characteristics and the level of crime over continuous space, the model address two types of spatial effects, spatial dependency and spatial heterogeneity (Fotheringham et al. 2002a; Fotheringham et al. 2002b; Fotheringham et al. 1998; LeSage 2004). Furthermore, by estimating location specific measures of association, geographically weighted regression models can be used as a bridge between macro and micro data where social processes of crime can occur both at neighborhood and place levels. For example, while social disorganization theory makes predictions at the neighborhood level, routine activities theory emphasizes the importance of places in generating criminal events (Davis 1987; Sherman 1995; Sherman et al. 1989; Stark 1987; Tita et al. 2005). The estimation of locally specific associations between neighborhood characteristics and the level of crime implies the results have multiple regression coefficient estimates (i.e., coefficient estimate for each location). Although estimating multiple coefficient estimates and proposing hypotheses that depend on locations may not be standard practices in sociological research, the results of geographically weighted regression can also be used as evidence to support an existing theory. For example, if measures of association between a neighborhood characteristic and the level of crime do not vary over space, the results provide further support for the theory as the predictions are robust and do not vary by location. Furthermore, it is also important to note that geographically weighted regression models are not the only, unique statistical model to produce location specific coefficient estimates. For example, multilevel modeling, which is increasingly used in sociological research, produces aggregate unit specific coefficient estimates through random effects (Rabe-Hesketh and Skrondal 2002; Singer and Willett 2003). Multilevel modeling, however, ignores spatial dependency among observations and the continuity of spatial processes (Fotheringham et al. 2002a; Fotheringham et al. 2002b). Similarly, the random coefficient model neglects the spatial structure of data, although the model can estimate location specific coefficient estimates (Brunsdon et al. 1999).

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RESARCH QUESTION Based on social disorganization theory and routine activities theory, this chapter addresses the following research question: Are the associations between neighborhood characteristics and the level of crime stationary? Traditional regression models, such as OLS regression and spatial regression models, are very strong analytical tools for testing hypotheses. Because of their focus on discovering general patterns, these models may sometimes fail to capture variations in multivariate relationships across space. Spatial regression models that capture spatial non-stationarity (i.e., spatially varying associations), such as geographically weighted regression, can be used to assess if the relationships between neighborhood characteristics and the level of crime vary across space. If the results of the analysis show evidence of spatial stationarity (i.e., stable associations across space), it will provide further support for social disorganization theory and routine activities theory, as theoretical explanations are shown to be universal and do not depend on location. If the association is spatially non-stationary, on the other hand, the results of geographically weighted regression models uncover interesting local patterns. Various locations are expected to exhibit spatially varying associations (e.g., downtown, the edge of spatial data, and a disadvantaged neighborhood surrounded by affluent neighborhoods). SPATIAL DEPENDENCY AND SPATIAL HETEROGENEITY Analysis of spatial data needs to distinguish two types of spatial effects, namely spatial dependency and spatial heterogeneity. Failure to take into account these spatial processes causes both substantive and methodological problems. For example, although the spatial clustering of crimes has been noted since the inception of American criminology, recent studies also indicate the spatial interaction of neighborhood characteristics, including the level of crime, among adjacent neighborhoods (Anselin et al. 2000; Kubrin and Weitzer 2003a; Morenoff and Sampson 1997; Morenoff et al. 2001). This spatial interaction process, often called spatial externalities, indicates that neighborhoods are susceptible to what happens in adjacent neighborhoods. For example, neighborhoods surrounded by socially

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cohesive neighborhoods with high levels of informal social control are likely to experience lower levels of crime. It has also been shown that focused crime prevention strategies aimed at the crackdown of select offenses often results in reducing crimes not only in the target neighborhoods but also surrounding neighborhoods (i.e., the diffusion of benefit effects) (Weisburd et al. 2006). On the other hand, the presence of a drug market in a neighborhood is likely to outwardly increase the level of crime in surrounding neighborhoods if law enforcement agencies fail to suppress the market (Felson 2006; Rengert et al. 2000; Rengert et al. 2005). Furthermore, from a methodological viewpoint, failing to properly deal with spatial effects results in biased regression coefficient estimates and standard errors, which subsequently affects hypothesis tests. Thus, analytical strategies to properly deal with spatial effects require specialized statistical models. Statistically speaking, spatial dependence means the value of a variable in one location depends on the value of the variable in a nearby location (Anselin 1988; Anselin 1990) or, as Tobler’s first law of geography states, “everything is related to everything else, but near things are more related than distant things (1970: 236).” This means that similar values of a variable are spatially clustered. For example, high levels of crime are often concentrated in a few neighborhoods adjacent to each other (Anselin 1988; Cohen and Tita 1999; Sherman 1995; Sherman et al. 1989). In such cases, crimes exhibit spatial dependency, as high crime neighborhoods are spatially clustered. Thus, spatial dependency is also called spatial auto-correlation and/or spatial clustering. Spatial dependency of crimes can occur, for example, when a criminal offender commits multiple offenses in neighborhoods adjacent to each other. Additionally, spatial dependency of crimes can also occur if an illicit drug market and/or gang covers multiple neighborhoods as their territory. As reported crimes that are committed by these drug dealers and gang members are likely to be concentrated in adjacent neighborhoods, the level of crime in these neighborhoods is likely to be similar. This can also be a problem with macro-level studies that use administrative boundaries as units of analysis. The underlying, true social process generating crimes may occur beyond administrative boundaries, although researchers employ these boundaries and data due to convenience. That is, spatial dependency can also occur due to discrepancies between the true social process and data.

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Failure to incorporate spatial dependency results in biased coefficient estimates and biased standard errors, depending on underlying spatial processes (i.e., spatial lag and spatial error) (Anselin 1988; Anselin et al. 2000; Florax and Nijkamp 2005). As these biased estimations subsequently result in invalid statistical inference, the problem is a very serious one in analyzing multivariate relationships between neighborhood characteristics and the level of crime. Researchers, mainly in spatial econometrics, have developed a series of spatial regression models to deal with spatial dependency (Anselin 1988; Anselin et al. 2000; Florax and Nijkamp 2005). Among spatial regression models, widely employed models are spatial lag models and spatial error models. Appropriate model specifications can be determined from theory and statistical tests on data. The second type of spatial effect, spatial heterogeneity, implies spatially varying structural relationships (Anselin 1988; Anselin 1990). In plain English, spatial heterogeneity means that associations between variables vary over space. For example, if spatial heterogeneity exists, associations between the same two variables can be positive in one area and negative in another area. There are many reasons to suspect that structural relationships between neighborhood characteristics and crime vary across space. For example, several studies suggest that the effect of economic deprivation on crime is stronger in an economically disadvantaged neighborhood if the surrounding neighborhoods are also economically disadvantaged (Bursik and Grasmick 1993a; Evans 1989; Malczewski and Poetz 2005). Furthermore, although residential mobility may weaken social ties among residents and diminish informal social control, the effect may be stronger in disadvantaged neighborhoods, where the presence of criminally-prone individuals is greater, than in affluent suburbs, where criminally motivated individuals are scarce. Because of the presence of business establishments and differences in the routine activities of both legitimate citizens and motivated offenders, the mechanisms by which neighborhood characteristics affect the level of crime may differ in the downtown area, compared to other parts of a city. Associations between neighborhood characteristics and the level of crime can also vary around the edge of administrative boundaries. For example, using crime data for all counties in Indiana, a spatial regression model will fail to capture crime-spillovers from Chicago. Therefore, associations between neighborhood characteristics and the level of crime may be

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different in the northwest corner of Indiana and elsewhere where information on the level of crime in surrounding neighborhoods is available. Although spatial heterogeneity is often a methodological issue, it can also be of theoretical interest. Several attempts have been made to integrate social disorganization theory and routine activities theory (Miethe et al. 1991; Miethe and Meier 1990; Miethe and Meier 1994). Social disorganization theory and routine activities theory, however, could lead to contradictory hypotheses about the same variable. For example, if median income is positively associated with crime rates, the association supports routine activities theory (i.e., higher income indicates more attractive targets), while if the association is negative, it supports social disorganization theory (i.e., lower income indicates more strain and fewer resources to address neighborhood problems). Furthermore, several studies suggest the association between median income and crime rates is parabolic, where households with the highest and lowest income levels experience the largest victimization risk (Cohen and Canter 1981; Miethe et al. 1987). Although several studies have tested such contradicting hypotheses with a single regression equation to assess which theoretical explanation is supported (but not both), it is possible that both explanations are true, depending on specific neighborhoods and social contexts. That is, associations between the median income level and crime rates may vary across space, where the association may be positive in one area (e.g., high attractiveness due to affluence) and it may be negative in another area (e.g., city center with characteristics of social disorganization). A failure to take into account spatial heterogeneity in regression analysis results in heteroskedasticity and biased regression estimates (Anselin 1988; Anselin 1990; Florax and Nijkamp 2005). A typical way to deal with spatial heterogeneity is to include a variable that distinguishes locations (e.g., downtown vs. the suburbs). Several studies have included a dummy variable indicating city center for a neighborhood level study and/or a dummy variable indicating the southern region for a county level study (Baller et al. 2001; Miethe et al. 1991). However, a distinction between suburb vs. city center, or south vs. other regions, may not be enough to address spatially varying population distributions that underlie the observed data. It is important to realize that spatial processes occur continuously.

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Several authors have argued that geographically weighted regression is a suitable analytical method to address such continuous spatial processes and to disaggregate associations between variables (Fotheringham et al. 2002a; Fotheringham et al. 2002b; Fotheringham et al. 1998; LeSage 2004). Geographically weighted regression, originally developed in spatial econometrics, has been applied in various fields of social science, including criminology (Cahill and Mulligan 2007; Malczewski and Poetz 2005; Wilson 2005), demography (Nakaya 2001), political science (Calvo and Escolar 2003), education (Fotheringham et al. 2001), epidemiology (Fotheringham et al. 1998), and economics (Fotheringham et al. 2002a; Zhao et al. 2005). Of particular relevance to the current research, Wilson (2005) has applied geographically weighted regression in order to assess the spatially varying relationship between the presence of churches and the level of homicide in a neighborhood. Controlling for various neighborhood characteristics, he found that the association between churches and the level of crime varied across space in terms of strength and direction. There are several reasons why the relationship between the presence of churches and the level of crime in neighborhoods differs by location. First, religions institutions are not uniform in their ability to reduce the level of crime. Religious institutions may be expected to foster social ties and cohesion among church goers, which subsequently affects the level of crime in neighborhoods. However, some churches are more civically engaged than others in addressing problems and disorder in neighborhoods. Second, it is important to recognize that criminal offenders are mobile agents going from one neighborhood to another. Churches’ ability to address problems and disorder may be limited to those caused by criminal offenders residing in their neighborhoods. Given the importance of spatial dependency and spatial heterogeneity, this research conducts the analysis by using spatial regression models and geographically weighted regression models. The next section describes theoretical expectations regarding spatially varying associations of neighborhood characteristics and the level of crime, based on social disorganization theory and routine activities theory. After describing Philadelphia crime data that are used to test spatial dependency and spatial heterogeneity, the results of both spatial regression models and geographically weighted regression models are presented.

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THEORETICAL EXPECTATIONS REGARDING SPATIAL VARIABILITY Social disorganization theory explains the level of crime via neighborhood characteristics that affect the level of social control and create frustrated wants among neighborhood residents (Bursik 1988; Kornhauser 1978; Kubrin and Weitzer 2003a; Sampson and Groves 1989). Key predictors from this theoretical perspective are socioeconomic disadvantage, residential mobility, and racial heterogeneity. Additionally, predictors that are often included in tests of social disorganization theory include the divorce rate, intact families, and crowded housing. Hypotheses developed based on social disorganization theory are as follows: H1: Lower socio-economic disadvantage in neighborhoods is associated with lower levels of crime (reduced criminal motivation and increased stakes in conformity). H2: Lower residential mobility in neighborhoods is associated with lower levels of crime (increased informal social control and vested interests in community). H3: Lower racial/ethnic heterogeneity in neighborhoods is associated with lower levels of crime (value/norm consensus and increased informal social control). H4: A lower divorce rate is associated with lower levels of crime (increased stakes in conformity and attachment to significant others). H5: A lower percentage of children living with both parents is associated with higher levels of crime (reduced direct control and attachment to significant others). H6: A lower percentage of crowded housing is associated with lower levels of crime (reduced frustration). These hypotheses, based upon social disorganization theory, are not likely to change based on location, as these neighborhood characteristics are likely to affect the level of social control and creation of frustrated wants, regardless of location. Thus, it is expected that the results of geographically weighted regression models will suggest spatial stationarity (i.e., stable relationships between variables across space) for these neighborhood characteristics. For example, from a social disorganization perspective, socio-economic disadvantage

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should not have a positive effect crime in one neighborhood and a negative effect in another. Other variables from social disorganization theory, however, may point to spatial non-stationarity (i.e., spatially varying relationships). One such neighborhood characteristic is the immigrant population and language ability. Shaw and McKay’s early findings indicated that one characteristic of high crime neighborhoods in the inner city was a high percentage of immigrants and residents with limited ability to speak English (Shaw and McKay 1942; Shaw and McKay 1969). Shaw and McKay argued that discrepancies between mainstream and sub-cultural value systems in the inner city, and the inability to realize common goals, resulted in higher levels of crime in these neighborhoods. It is important to note, however, that the number of immigrants is an index of homogeneity, as opposed to an index of heterogeneity. Thus, although an immigrant population may pose a threat to the realization of common goals to some extent, high concentrations of immigrants in selected neighborhoods result in creating homogeneous neighborhoods with a unified value system. That is, the effect of immigrant population and language isolation may change at some point (tipping point). Geographically weighted regression models can be used to capture such an effect. Routine activities theory predicts the level of crime through the interaction of a motivated offender, an attractive target, and the absence of capable guardians. Changes in the volume of any of these three elements can result in changes in the volume of crime. For example, assuming criminal offenders are rational actors, an increase in crime can occur if the number of attractive targets increases. Crime can also increase if the number of capable guardians decreases. Additionally, routine activities theory also argues that changes in the interaction of these three elements in time and space affect the volume of crime. For example, even without increases in the number of motivated offenders and attractive targets, increases in the frequency of these two elements converging in time and space affect the number of crimes. Thus, several hypotheses based on routine activities theory are: H8: A lower proportion of women with jobs is associated with lower levels of crime (increased guardianship and decreased exposure to motivated criminals).

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H9: A lower proportion of workers taking public transportation is associated with lower levels of crime (decreased exposure to motivated criminals). H10: A higher average number of persons per occupied housing unit is associated with lower levels of crime (increased guardianship). H11: Neighborhoods in the downtown have higher levels of crime (increased frequency of motivated offenders and potential victims converging in time and space). H12: A lower proportion of male youths is associated with lower levels of crime (fewer motivated offenders) H13: A smaller population size in neighborhoods is associated with lower levels of crime (fewer motivated offenders and suitable targets) It is important to note that theoretical explanations based upon routine activities theory can be contradictory. For example, an increase in the median income and median housing prices may indicate an increase in attractive targets. Thus, the theory may predict an increase in the number of residential burglaries in these neighborhoods. An increased median income, however, may also represent an increase in guardianship, as these houses are more likely to be equipped with advanced security devices. Geographically weighted regression models that capture spatially varying associations can be used to identify neighborhoods which represent attractive targets because of higher levels of income (i.e., positive association between income and the level of crime) and which represent strong guardianships because of higher levels of income (i.e., negative association between income and the level of crime). METHODS In order to assess stability in the associations between neighborhood characteristics and the level of crime across space, two types of regression models are examined. The first type consists of OLS regression models and spatial regression models, both of which provide stationary results (i.e., one regression coefficient estimate for each predictor). The second type consists of geographically weighted regression models which fully examine spatially varying associations

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by estimating measures of association at each location (e.g., census block groups). Analytical Strategy I: Spatial Regression Models OLS regression is a powerful statistical tool for examining multivariate relationships between an independent variable and a dependent variable, controlling for the effects of other independent variables. In the analysis of neighborhood characteristics and the level of crime, using multiple regression models is necessary, as many factors affect the level of crime in neighborhoods. It has been shown, however, that using OLS regression on spatial data violates the assumption of independently distributed residuals. This violation leads to biased regression estimates and invalid hypothesis tests. Furthermore, as OLS models are said to be topologically invariant (i.e., the results will be the same regardless of the spatial arrangement of data), the models are inadequate for examining the spatial dynamics of crime and neighborhood relationships. Thus, in order to investigate spatial processes of neighborhood characteristics and crime, spatial regression models are utilized. In particular, a series of exploratory data analysis techniques (e.g., Moran’s I on OLS residuals and Lagrange Multiplier tests) will be utilized to search for the proper specification of spatial regression models. There are two common categories of spatial regression models: spatial lag model and spatial error model. The spatial lag model is specified as y = ρWy + β X + ε where W is a spatial weights matrix that determines the extent of the spatial process in the data. A specification of the spatial weights matrix is provided a priori by researchers who may use various definitions of neighbors (e.g., neighbors share a common border or are within a certain distance). The regression coefficient of the lagged variable in and of itself does not provide theoretically meaningful interpretations (Anselin et al. 2000). The importance of including the spatially lagged term is to filter out the confounding effects of spatial autocorrelation. Thus, “the main motivation for this is to obtain the proper inference on the coefficients of the other covariates in the model (the β )” (Anselin et al. 2000: 239). The second category of spatial regression model, the spatial error model, is specified as y = β X + ε , where ε = λW ε + µ . Here, the

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spatial autocorrelation is modeled through the structure of error terms. Researchers may want to model the spatial error, for example, in a situation where an unmeasured independent variable, such as social networks among neighborhood residents, is spatially correlated across multiple areas. Because of an omitted variable that is spatially correlated, the regression model results in residuals that are spatially correlated. Just like in the spatial lag model, the coefficient of lagged error terms in the spatial error model may not be in and of itself substantively interesting to researchers. Rather, the inclusion of lagged terms will be done in order to improve the precision of estimates for other theoretically important predictors. The search for model specifications is largely empirical and data driven. In particular, Lagrange Multiplier tests will be conducted based upon residuals from the OLS. Although some may criticize the data driven approach, this is not problematic since the lagged coefficients of either the spatial lag model or spatial error model are not the primary focus. Both model specifications are done in order to improve the precision of the estimates of other predictors that researchers are theoretically interested in (i.e., neighborhood characteristics based upon social disorganization theory). Analytical Strategy II: Geographically Weighted Regression Although spatial heterogeneity can be dealt with in traditional regression models by including dummy variables representing spatial locations (e.g., downtown vs. peripheral), such an approach fails to capture continuous spatial processes. Furthermore, traditional regression models are not useful for identifying locally specific patterns, as the models focus on finding generalizable relationships. In order to fully examine spatial heterogeneity, geographically weighted regression models are analyzed in this research. Geographically weighted regression (GWR) produces local parameter estimates by running multivariate regressions for each location (Fotheringham et al. 2002a). When regression the dependent variable on a set of independent variable at each location, observations are weighted based on distance. Formally, the GWR equation is shown below (Fotheringham et al. 2002a): yi = β0(u ,v ) + βk (u ,v ) xik + εi . i i i i

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Terms with u and v subscripts indicate the x and y coordinates of observations. Thus, this regression model produces regression coefficient estimates at every location where samples are obtained. As GWR weights the values of all observations based upon distance, observations in close proximity are weighted more heavily than ones far away. The idea behind such distance weighted subsamples is that what happens across the street has a stronger effect than what happens further away. Thus, spatial dependency is also taken into account in GWR through the distance based weighting of observations. By running regression models at every location, GWR assesses location specific multivariate associations between the level of crime and neighborhood characteristics. The results of GWR can be analyzed in two ways. First, the measures of dispersion for regression coefficients, such as range and interquartile range, are examined. The extent of variability in coefficient estimates can also be statistically tested using the Monte Carlo simulation. Second, coefficient estimates from GWR are mapped to visually examine spatially varying associations. Such maps of coefficient estimates may point out something peculiar to select regions and neighborhoods that existing theories may not expect. Local vs. Global Statistics Differences between traditional regression models that produce stationary (constant) coefficient estimates across space and GWR models that produce spatially varying coefficient estimates can be illustrated by local and global univariate statistics. Figure 3.1 shows the mean residential burglary rate in Philadelphia is 13.8 burglaries per 1,000 housing units. This descriptive statistic is a global statistic. A global statistic can be viewed as an average statistic for an entire study area. On the other hand, Figure 3.2 illustrates spatial variation in local residential burglary rates (i.e., a local statistic). Local statistics can show some interesting spatial variations that global statistics cannot detect. For example, that the residential burglary rate in Philadelphia is 13.8 per 1,000 housing units may not be useful information for those who intend to purchase a house in Philadelphia, because such information neglects considerable spatial variation of burglary rates within the city. In fact, there are many neighborhoods that are free

Figure 3.1 Global Statistics

Figure 3.2 Local Statistic

84

Neighborhood Structures and Crime: A Spatial Analysis

from victimization risks. Thus, it is more likely that the purchasers would like to know where high crime areas are within a city. Although these are univariate statistics, the same comparison of global and local applies to bivariate and multivariate statistics. That is, relationships between variables may change over space. Spatially varying relationships between variables have rarely been examined in criminological research, except for a few (Cahill and Mulligan 2007; Malczewski and Poetz 2005; Wilson 2005). This research explores such spatial dynamics by using geographically weighted regression (Fotheringham et al. 2002a; Fotheringham et al. 2002b). DATA In order to examine the spatially varying relationships between neighborhood characteristics and the level of crime, based on social disorganization theory and routine activities theory, data were obtained from the Philadelphia Police Department and the Census. The crime data from the Philadelphia Police Department contained different types of offences (1998-2006), allowing crime specific analysis. In particular, this research treats aggravated assault, robbery, residential burglary, and auto theft as key dependent variables. In order to deal with random fluctuations in crime, these dependent variables were converted to average crime rates per year. First, crime count averages per year were calculated for each crime type (e.g., the total aggravated assault count between 1998 and 2006 divided by nine). Then, the averages were converted to rates per 1,000 population, using population counts in the 2000 census. As houses are the target of residential burglary, the number of houses in a neighborhood was used as the denominator for the residential burglary rate. When creating rates based upon population and housing, the level of crime gets artificially inflated in scarcely populated areas. Furthermore, if these scarcely populated areas are kept in the analysis, neighborhood characteristics of these areas become represented by only the few people residing in them. Oftentimes, these scarcely populated areas have unique geographical characteristics, such as river beds, that cannot be captured by socio-demographic characteristics of census data. Thus, in order to deal with these problems, block groups with less than 150 people were excluded from the analysis (for residential burglary,

An Analysis of Spatially Varying Associations

85

block groups with less than 100 households were excluded). As several outliers still remained, even after exclusion of the scarcely populated areas, all observations that fell beyond three standard deviations from the mean were eliminated from the analysis. As three standard deviations from the mean varied by crime type, exclusion of outliers was done by creating crime specific data. Out of the initial sample of 1816 block groups, approximately 5% of the block groups were excluded from the analysis for each crime. Independent variables were included that measure various aspects of neighborhood characteristics from social disorganization theory and routine activities theory. As a measure of economic disadvantage, the percentage of households below the official poverty line and the percentage of households receiving public assistance were included. Additionally, measures of disadvantage in terms of employment and education were included. In particular, the percentage of people over 15 years of age who are unemployed and the percentage of people over 25 years of age who do not have a high school diploma or an equivalency diploma were included in the analysis. Furthermore, as a measure of disadvantaged housing conditions, the percentage of households whose occupancy per room exceeds 1.0 was included. These five variables were combined as a principal component that represented socio-economic disadvantage of neighborhoods. The factor loadings for each variable were: the percent poverty (0.85), the percent public assistance (0.83), the percent unemployed (0.70), the percent no high school education (0.80), and the percent crowded houses (0.69). The extracted factor explained 60.2% of the variance in the observed variables, indicating the factor adequately represented the underlying construct. Furthermore, Chronbach’s alpha for these variables was 0.82. As measures of residential instability, four variables from the census were used. The percentage of the population over five years of age who changed their address in the past year was included as a key measure of residential mobility. Furthermore, the percentage of renter occupied housing units and the percentage of single households were included. Finally, the percentage of housing units with more than one unit in the building (e.g., apartment complexes) were included. Based on principal component analysis, these four variables were combined to create a factor that represented the residential instability of neighborhoods. Factor loadings for these variables were: the percent

86

Neighborhood Structures and Crime: A Spatial Analysis

different address (0.73); the percent renter-occupied housing units (0.88); the percent single households (0.73); and the percent multiple housing units (0.89). The extracted principal component explained 66% of the variance in the observed variables. Furthermore, Chronbach’s alpha for these variables was 0.82. In addition to these social characteristics of neighborhoods, a series of variables that measure demographic characteristics of neighborhoods were included in the analysis. First, as a key predictor of social disorganization theory, an index of racial heterogeneity was created based on the racial composition of neighborhoods. In particular, the 2 index of racial heterogeneity was calculated as 1 − ∑ pi , where pi is the proportion of each of the following racial groups: non-Hispanic Caucasian, African American, Hispanic, Asian, and Other (Kubrin 2000; Sampson and Groves 1989). This index of racial heterogeneity ranges from 0 to 0.8 where 0 indicates complete homogeneity (one racial group dominates 100%) and 0.8 indicates complete heterogeneity (each racial group comprises 20% of the population). As a second measure of the demographic composition of neighborhoods, a principal component of language ability was created from the following three variables: the percentage of individuals who do not speak English well or do not speak it at all, the percentage of linguistically isolated households, and the percentage of the population that is foreign born. Factor loadings for these variables were: the percent with limited English speaking ability (0.91); the percent linguistically isolated (0.91); and the percent foreign born (0.78). The extracted principal component explained 75.8% of the variance in the observed variables. Chronbach’s alpha for these variables was 0.802. Finally, there were several neighborhood characteristics that were derived from social disorganization theory and routine activities theory, but that did not load with any of the created indexes. In order to control for the size of the criminally prone population, the percentage of males between 15 and 24 years of age was included. Additionally, as an indicator of family disruption, the percentage of children living with both parents and the percentage of males ages 15 and over who were divorced was included. As measures of guardianship and criminal opportunity, the percentage of workers over 15 years of age who use public transportation, the percentage of females over 15 years of age who were employed, and the average household size were included. Finally, as a control variable, population density was calculated using

An Analysis of Spatially Varying Associations

87

population counts and the land size of block groups. Descriptive statistics for both crime and neighborhood characteristics are presented in Table 3.1. Table 3.1 Descriptive Statistics for Neighborhood Characteristics Std. Mean Min. Max. Dev. % Male Youth % Both Parents % Divorced Male Racial Heterogeneity % Public Transportation % Female Employed Average Household Size Language Ability Socio-economic Disadvantage Residential Mobility Population Density (1000 / km2) Aggravated Assault Rate Robbery Rate Residential Burglary Rate Auto Theft Rate

14.7 45.3 14.1 0.28 29.9 88.6 2.58 -0.01 -0.03 0.01 8.85 6.39 6.30 13.81 9.17

8.97 27.97 10.70 0.22 17.28 10.90 0.49 0.94 0.90 0.92 4.63 4.64 4.58 6.28 4.12

0.0 0.0 0.0 0.0 0.0 25.9 1.08 -0.77 -1.58 -1.65 0.11 0.00 0.00 1.01 1.03

97.23 100.00 80.43 0.79 100.00 100.00 4.46 8.94 3.61 4.06 32.23 23.90 28.74 35.05 32.33

RESULTS FOR SPATIAL REGRESSION MODELS Table 3.2 shows the results of OLS regression models, where four types of crime were regressed on neighborhood characteristics separately. Examining the statistical significance and direction of coefficient estimates showed most of the variables were in accord with theoretical expectations of social disorganization theory and routine activities theory. Before interpreting each coefficient estimate, however, the adequacy of the regression models needs to be examined. In particular, the residuals from the OLS regression models exhibited statistically significant auto-correlation, indicating that residuals were not

(0.585)

(0.469)

-1.362**

(0.011)

(0.009) -0.780**

0.008

(0.008)

(0.006) 0.004

0.051**

0.058**

(0.256) (0.323) Notes: **p<.01, *p<.01. Standard errors are reported in parentheses.

Average Household Size

% Female Employed

% Public Transportation

2.302**

-0.601

Racial Heterogeneity

0.028** (0.010)

0.023** (0.008)

% Divorced Male

-0.022** (0.005)

-0.036** (0.004)

-0.024 (0.015)

Robbery

% Both Parents

% Male Youth

Aggravated Assault -0.022* (0.009)

(0.429)

4.095**

(0.010)

0.025**

(0.009)

0.031**

(0.713)

8.135**

0.025* (0.012)

-0.013 (0.009)

Residential Burglary 0.015 (0.015)

Table 3.2 OLS Regression of Crime Rates on Neighborhood Characteristics

(0.300)

-1.261**

(0.010)

0.028**

(0.007)

0.012

(0.566)

6.365**

0.027** (0.010)

-0.021** (0.005)

-0.010 (0.010)

Auto Theft

0.12** 65.34** 233.82**

Moran's I of Residuals

LM-Error

LM-Lag

2.15

275.05**

235.06**

0.22**

2.091** (0.197) 0.434** (0.162) -0.246** (0.024) 10.672** (1.249)

0.318 (0.191)

Robbery

Robust LM-Lag 198.31** 42.15** Notes: **p<.01, *p<.01. Standard errors are reported in parentheses.

Robust LM-Lag

Intercept

Population Density

29.83**

2.938** (0.159) -0.312* (0.129) -0.207** (0.019) 10.410** (0.950)

Socio-economic Disadvantage

Residential Mobility

-0.124 (0.113)

Language Ability

Aggravated Assault

63.77**

8.24**

407.75**

352.22**

0.28**

2.071** (0.234) 1.152** (0.210) -0.285** (0.028) 0.693 (1.564)

-0.884** (0.171)

Residential Burglary

0.35

92.98**

360.36**

452.99**

0.31**

0.959** (0.186) 0.062 (0.153) -0.347** (0.023) 11.911** (1.107)

0.302* (0.137)

Auto Theft

Table 3.2 OLS Regression of Crime Rates on Neighborhood Characteristics (cont.)

90

Neighborhood Structures and Crime: A Spatial Analysis

independently distributed, as the OLS regression models assumed. Thus, in order to take into account the spatial structure of crime, spatial regression models need to be examined. Proper model specifications of the spatial regression model can be statistically examined by conducting Lagrange Multiplier (LM) tests. Following decision rules outlined by Anselin (2003), LM-lag and LMerror tests were first examined. As both of these were statistically significant for all crime types, robust forms of these tests were also examined. Robust forms of LM-lag tests examine if the spatial autocorrelation of error remains after controlling for the spatial lag of the dependent variable, while robust LM-error tests determine if the spatial auto-correlation of the dependent variable needs to be controlled for after taking into account the spatial auto-correlation of error. When robust LM-lag is significant (or large) and robust LM-error is not significant (or small), this indicates a spatial lag regression model is the proper model specification (i.e., spatial auto-correlation of the dependent variable can be fully taken into account by including spatial lag of the dependent variable). When robust LM-lag is not significant (or small) and robust LM-error is significant (or large), this indicates a spatial error regression model is the proper model specification. Based upon these decision rules, it was found that the spatial lag model was the proper model specification for aggravated assault, robbery, and residential burglary, while the spatial error model was the appropriate model specification for auto theft. The results of spatial regression models are shown in Table 3.3. As with OLS regression models, the direction of most of the coefficient estimates was in accord with theoretical expectations of social disorganization theory and routine activities theory. However, some variables became insignificant after controlling for the spatial structure of the data via spatial lag of the dependent variables or of the residuals, while the effects of other variables on the dependent variable became smaller. All spatial lag terms were statistically significant and moderately strong in their magnitude, indicating the importance of taking into account the spatial structure of the data. Statistically significant spatial lags of crimes indicated these crimes were spatially clustered. A statistically significant spatial lag of residuals indicated that some unknown variables not included in the model were spatially clustered. These spatial lag effects might point to diffusion of crimes and other variables over space. Furthermore, from a methodological

An Analysis of Spatially Varying Associations

91

standpoint, it was also beneficial to take into account these spatial effects, as the precision of regression coefficient estimates for other independent variables increased. The level of aggravated assault was higher in neighborhoods characterized by a low percentage of male youths, a low percentage of intact families, a high percentage of divorced males, a high percentage of public transportation users, a small household size, high socioeconomic disadvantage, low residential mobility, and low population density. The negative association of percent male youths and residential instability was somewhat unexpected from the perspective of social disorganization theory. For another violent crime, robbery, the pattern of associations was similar to aggravated assault. The level of robbery was high in neighborhoods characterized by a low percentage of intact families, high percentage of divorced males, high racial heterogeneity, high percentage of public transportation users, small household size, low language ability, high socio-economic disadvantage, and low population density. The level of residential burglary was strongly predicted by neighborhood characteristics included in the model, as eight out of eleven predictors were statistically significant. The level of residential burglary was high in neighborhoods characterized by high racial heterogeneity, a high percentage of public transportation usage, a high percentage of employed females, large household size, high language ability, high socio-economic disadvantage, high residential mobility, and low population density. A pattern unique to residential burglary was that high residential mobility predicted a high level of residential burglary, while the effect of socio-economic disadvantage was somewhat smaller than its effect on other crimes. Finally, for auto theft, a low percentage of intact families, high racial heterogeneity, high percentage of employed females, low language ability, and low population density were associated with the low level of auto theft in neighborhoods. Contrary to other crime types, socio-economic disadvantage did not predict the level of auto theft. These regression analyses, however, are so-called global regression models because one parameter is estimated for each independent variable that characterizes the pattern of association for the whole study area. Due to their focus of seeking the general pattern of association, however, global regression models may neglect important

-1.258**

(0.011)

(0.008) -0.660**

0.006

(0.008)

(0.006) 0.002

0.049**

(0.579)

(0.462) 0.055**

2.189**

(0.008)

(0.008) -0.757

0.016**

(0.005)

(0.004) 0.023**

-0.021**

(0.015)

(0.008) -0.034**

-0.023

-0.022**

Robbery

(0.251) (0.320) Notes: **p<.01, *p<.01. Standard errors are reported in parentheses.

Average Household Size

% Female Employed

% Public Transportation

Racial Heterogeneity

% Divorced Male

% Both Parents

% Male Youth

Aggravated Assault

(0.415)

3.916**

(0.013)

0.025*

(0.009)

0.031**

(0.702)

7.343**

(0.015)

0.024

(0.008)

-0.012

(0.014)

0.013

Residential Burglary

Table 3.3 Spatial Regression of Crime Rates on Neighborhood Characteristics

(0.591)

-1.049

(0.009)

0.028**

(0.007)

0.011

(0.547)

5.393**

(0.014)

0.022

(0.005)

-0.014**

(0.01)

-0.011

Auto Theft

0.150** (0.033)

(0.027)

(1.253)

(0.949) 0.175**

9.692**

(0.023)

(0.019) 9.178**

-0.263**

(0.261)

(0.127) -0.218**

0.437

(0.196)

(0.161) -0.251*

1.900**

(0.14)

(0.111) 2.649**

0.345*

-0.084

Robbery

Notes: **p<.01, *p<.01. Standard errors are reported in parentheses.

Spatial Lag of Error

Spatial Lag of Crime

Intercept

Population Density

Residential Mobility

Socio-economic Disadvantage

Language Ability

Aggravated Assault

(0.030)

0.262**

(1.546)

-2.552

(0.027)

-0.277**

(0.204)

1.214**

(0.228)

1.766**

(0.171)

-0.828**

Residential Burglary

(0.032)

0.421**

(1.05)

12.011**

(0.023)

-0.411**

(0.149)

0.126

(0.287)

0.361

(0.131)

0.315*

Auto Theft

Table 3.3 Spatial Regression of Crime Rates on Neighborhood Characteristics (cont.)

94

Neighborhood Structures and Crime: A Spatial Analysis

local patterns of association (Fotheringham et al. 2002a; Fotheringham et al. 2002b). As the comparison of local and global univariate statistics indicated previously, global statistics represent average statistics for the whole study area, while local statistics capture the spatial variation of a variable. Thus, in order to analyze the spatial stationarity of associations between neighborhood characteristics and the level of crime, the next set of analysis was conducted in order to investigate the spatially varying strength of associations and/or their direction. RESULTS FOR GEOGRAPHICALLY WEIGHTED REGRESSION MODELS Geographically weighted regression (GWR) produces local parameter estimates for multivariate regression; that is, GWR produces location specific measures of association between neighborhood characteristics and the level of crime. Observations are weighted based upon distance in order to calculate estimations. That is, observations in close proximity are weighted heavier than observations far away. The results of GWR models can be examined in two ways. First, summary measures, such as range and interquartile range, can be examined for each independent variable. This indicates variability in both the strength and direction of association for each neighborhood characteristic. Furthermore, variability in coefficient estimates can be statistically examined to determine if such variability can occur by chance alone. The statistical test for the variability of coefficient estimates is based upon Monte Carlo simulation (Fotheringham et al. 2002a; Fotheringham et al. 1998). Finally, coefficient estimates (i.e., measures of association) can also be plotted on a map to examine where the association is strong and/or positive/negative. The GWR results for violent offences (aggravated assault and robbery) are presented in Table 3.4. For aggravated assault, the percentage of male youths, racial heterogeneity, language ability, and population density varied significantly. For robbery, racial heterogeneity, the percentage of public transportation users, language ability, and population density varied significantly over space. It should be noted that the effects of racial heterogeneity, a key predictor of social disorganization theory, varied across space for both

An Analysis of Spatially Varying Associations

95

aggravated assault and robbery. When interquartile ranges and the medians were examined, slightly different patterns emerged across crime types. For example, more than 50% of the coefficient estimates for racial heterogeneity were negative values for aggravated assault, while more than 50% of the coefficient estimates for racial heterogeneity were positive values for robbery, as indicated by the median of the coefficient estimates. Furthermore, language ability and population density also varied in their effects on both violent offences, although the range of the effects for population density was small and constrained to negative values. The results of geographically weighted regressions for property offences (residential burglary and auto theft) are presented in Table 3.5. For residential burglary, the effects of racial heterogeneity, language ability, socio-economic disadvantage, residential instability, and population density varied significantly across space. Compared to violent offences, unique patterns for residential burglary were that the effects of socio-economic disadvantage and residential instability varied across space, which was unexpected from the perspective of social disorganization theory. The spatially varying effect of socioeconomic disadvantage was interesting from the perspective of routine activities theory, as this might indicate some affluent neighborhoods represent attractive targets. As for auto theft, the effects of language ability, socio-economic disadvantage, and population density varied significantly across space. Similar to residential burglary, of particular interest for routine activities theory was the spatially varying effects of socio-economic disadvantage. In addition to the numeric analysis of coefficient estimates from GWR, another way to examine spatially varying associations between neighborhood characteristics and the level of crime is through the visual inspection of coefficient estimates produced in each neighborhood (Figures 3.3 through 3.19). Darker shades represent stronger relationships. Furthermore, the direction of association can be examined through maps (a) and (b) for each Figure. In essence, these maps decompose the relationship between neighborhood characteristics and the levels of crime across space. For aggravated assault, the percentage of male youths, racial heterogeneity, and language ability varied significantly over space. It should be noted that the global regression model indicated a negative

-0.081 -0.056 -0.090 -6.788 -0.015 -0.053 -1.800 -1.124 0.403 -1.033

% Male Youth

% Both Parents

% Divorced Male

Racial Heterogeneity

% Public Transportation

% Female Employed

Average Household Size

Language Ability

Socio-economic Disadvantage

Residential Mobility

-0.442

1.864

-0.487

-0.505

-0.022

0.025

-3.624

0.003

-0.037

-0.042

5.912

Q1

-0.184

2.438

0.135

0.035

0.007

0.050

-2.282

0.013

-0.025

-0.019

9.552

Median

0.266

2.782

0.569

0.481

0.035

0.065

0.424

0.024

-0.020

0.017

13.235

Q3

2.025

3.726

2.820

2.271

0.111

0.099

3.820

0.079

0.006

0.078

17.592

Max

0.200

0.210

0.000

0.440

0.530

0.130

0.000

0.990

0.560

0.010

0.060

p-value

**

**

**

Population Density -0.479 -0.335 -0.286 -0.217 -0.122 0.000 ** Notes: The significance test is based on the Monte Carlo procedure (Fotheringham et al. 2002a; Hope 1968). **p<.01, *p<.0

-0.109

Min

Intercept

Aggravated Assault

Table 3.4 Spatially Varying Coefficient Estimates from Geographically Weighted Regression of Violent Crimes

-0.057 -0.044 -0.025 -4.704 -0.004 -0.038 -1.754 -0.655 0.844 -0.941

% Male Youth

% Both Parents

% Divorced Male

Racial Heterogeneity

% Public Transportation

% Female Employed

Average Household Size

Language Ability

Socio-economic Disadvantage

Residential Mobility

0.101

1.027

0.382

-1.393

-0.017

0.027

-0.458

-0.009

-0.028

-0.041

8.301

Q1

0.419

1.357

0.661

-0.942

-0.001

0.048

1.162

0.008

-0.017

-0.028

11.217

Median

0.754

1.850

1.021

0.426

0.024

0.073

2.275

0.016

-0.008

0.006

14.915

Q3

1.318

2.754

2.425

1.141

0.051

0.093

4.022

0.041

-0.002

0.023

18.967

Max

0.090

0.170

0.000

0.090

0.750

0.010

0.010

0.990

0.610

0.220

0.000

p-value

**

**

**

**

Population Density -0.515 -0.463 -0.409 -0.313 -0.132 0.000 ** Notes: The significance test is based on the Monte Carlo procedure (Fotheringham et al. 2002a; Hope 1968). **p<.01, *p<.05

2.005

Min

Intercept

Robbery

Table 3.4 Spatially Varying Coefficient Estimates from Geographically Weighted Regression of Violent Crimes (cont.)

-0.062 -0.072 -8.074 -0.077 -0.108 -0.158 -6.747 -1.956 -1.454

% Both Parents

% Divorced Male

Racial Heterogeneity

% Public Transportation

% Female Employed

Average Household Size

Language Ability

Socio-economic Disadvantage

Residential Mobility

0.828

0.570

-1.287

2.581

-0.015

-0.008

2.426

-0.022

-0.026

-0.014

-0.344

Q1

1.658

1.605

-0.624

4.089

0.009

0.025

5.286

-0.002

-0.014

0.017

4.034

Median

2.287

2.747

-0.070

5.180

0.041

0.042

8.793

0.036

0.003

0.050

7.508

Q3

3.767

5.065

1.426

10.154

0.206

0.175

14.883

0.134

0.051

0.247

16.849

Max

0.030 *

0.000 **

0.000 **

0.310

0.260

0.300

0.000 **

0.600

0.720

0.300

0.590

p-value

Population Density -0.983 -0.474 -0.335 -0.246 0.029 0.000 ** Notes: The significance test is based on the Monte Carlo procedure (Fotheringham et al. 2002a; Hope 1968). **p<.01, *p<.05

-0.092

-12.505

Min

% Male Youth

Intercept

Residential Burglary

Table 3.5 Spatially Varying Coefficient Estimates from Geographically Weighted Regression of Property Crimes

-0.122 -0.095 -0.036 -6.136 -0.052 -0.050 -3.222 -0.822 -2.524 -1.379

% Male Youth

% Both Parents

% Divorced Male

Racial Heterogeneity

% Public Transportation

% Female Employed

Average Household Size

Language Ability

Socio-economic Disadvantage

Residential Mobility

-0.058

-0.640

0.298

-1.123

-0.002

-0.015

3.094

-0.007

-0.021

-0.037

9.222

Q1

0.226

-0.254

0.528

-0.650

0.014

0.010

4.363

0.015

-0.008

-0.007

14.073

Median

0.558

1.186

0.911

0.063

0.047

0.026

4.920

0.033

0.003

0.017

17.082

Q3

2.282

3.992

3.036

1.745

0.121

0.079

8.678

0.088

0.039

0.118

21.920

Max

0.720

0.000 **

0.000 **

0.850

0.710

0.170

0.100

0.790

0.260

0.380

0.140

p-value

Population Density -0.889 -0.567 -0.473 -0.335 0.008 0.000 ** Notes: The significance test is based on the Monte Carlo procedure (Fotheringham et al. 2002a; Hope 1968). **p<.01, *p<.05

-2.994

Min

Intercept

Auto Theft

Table 3.5 Spatially Varying Coefficient Estimates from Geographically Weighted Regression of Property Crimes (cont.)

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association between the percentage of male youths and the level of aggravated assault, which was unexpected from the perspective of social disorganization theory. However, the results of GWR indicated the direction of association between the percentage of male youths and the level of aggravated assault varied significantly across space (Figure 3.3). In particular, the association was strongly positive (indicated as dark gray in Figure 3.3 (a)) in downtown areas. This may be capturing the association between criminally prone individuals (male youths) and the type of physical confrontations that occur in city centers, as opposed to physical violence in domestic situations. In fact, several studies have shown that downtown areas produce higher levels of physical violence due to the concentration of bars (Roncek and Bell 1981; Roncek and Maier 1991; Roncek and Pravatiner 1989; Sherman et al. 1989). It was also interesting to note that the effects of racial heterogeneity and language ability counteracted each other (Figures 3.4 and 3.5, respectively). The effects of racial heterogeneity on crime were negative in western regions, while they were positive in eastern regions (Figure 3.4). The effects of language ability on crime were positive in western regions, while they were negative in eastern regions (Figure 3.5). This could be attributed to language ability being an index of homogeneity, while racial heterogeneity is an index of heterogeneity. That is, although limited ability to speak English may hinder the realization of common goals among neighborhood residents, concentration of immigrant populations may actually foster creation of common (sub-cultural) value systems. Finally, although population density varied in its strength across space, the directions of association were all negative across space (Figure 3.6). As for robbery, similar to aggravated assault, the effects of racial heterogeneity were opposite those of language ability (Figures 3.8 and 3.10, respectively). Interestingly, the effect of the percentage of public transportation users on robbery was positive, except for downtown areas (Figure 3.9). This was interesting as the key reason to include the use of public transportation in this research was to investigate its effects on robbery (i.e., increased exposure to motivated offenders). Although the results of global regression (Table 3.2 and 3.3) indicated significant positive effects, geographically weighted regression captured different local patterns of association occurring in downtown areas.

Figure 3.3 Spatially Varying Regression Coefficients of the Percentage Male Youth on Aggravated Assault

Figure 3.4 Spatially Varying Regression Coefficients of Racial Heterogeneity on Aggravated Assault

Figure 3.5 Spatially Varying Regression Coefficients of Language Ability on Aggravated Assault

Figure 3.6 Spatially Varying Regression Coefficients of Population Density on Aggravated Assault

Figure 3.7 Spatially Varying R-square of Geographically Weighted Regression of Aggravated Assault

Figure 3.8 Spatially Varying Regression Coefficients of Racial Heterogeneity on Robbery

Figure 3.9 Spatially Varying Regression Coefficients of the Percentage Public Transportation on Robbery

Figure 3.10 Spatially Varying Regression Coefficients of the Language Ability on Robbery

Figure 3.11 Spatially Varying R-square of Geographically Weighted Regression of Robbery

Figure 3.12 Spatially Varying Regression Coefficients of Racial Heterogeneity on Residential Burglary

Figure 3.13 Spatially Varying Regression Coefficients of Language Ability on Residential Burglary

Figure 3.14 Spatially Varying Regression Coefficients of Socioeconomic Disadvantage on Residential Burglary

Figure 3.15 Spatially Varying Regression Coefficients of Residential Mobility on Residential Burglary

Figure 3.16 Spatially Varying R-square of Geographically Weighted Regression of Residential Burglary

Figure 3.17 Spatially Varying Regression Coefficients of Language Ability on Residential Burglary

Figure 3.18 Spatially Varying Regression Coefficients of Socioeconomic Disadvantage on Auto Theft

Figure 3.19 Spatially Varying R-square of Geographically Weighted Regression of Auto Theft

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Looking at spatially varying associations for property offences, similar patterns of associations for language ability and racial heterogeneity were observed (Figures 3.12 and 3.13, respectively). Of particular interest were spatially varying associations of socioeconomic disadvantage on the level of residential burglary (Figure 3.14). While social disorganization theory predicts that socioeconomic disadvantage increases the level of crime, the geographically weighted regression results indicated the opposite was true for a few selected neighborhoods. For these selected neighborhoods, explanations based upon routine activities theory may be more applicable, as these neighborhoods may represent attractive targets with higher perceived payoffs by criminal offenders. SUMMARY By realizing the importance of considering two types of spatial effects, spatial dependency and spatial heterogeneity, this research investigated whether theoretical predictions of social disorganization theory and routine activities theory are constant across space. In particular, GWR models were employed in order to examine neighborhoods within the city of Philadelphia as a continuous space. In order to provide comparisons with GWR, traditional regression models were first analyzed. Not surprisingly, the results of OLS egression models were found invalid, as the assumption of independently distributed residuals was violated (i.e., spatial autocorrelation of residuals) (Table 3.2). Thus, in order to address problems caused by spatial data, spatial regression models were examined. It is important to note, however, that OLS regression models were still used in order to determine proper model specification of the spatial regression models. When the results of spatial regression models were examined, many key predictors from both social disorganization theory and routine activities theory were significantly related to crime. In particular, racial heterogeneity, socio-economic disadvantage, and the percentage of divorced males were strongly and consistently associated with higher levels of both violent and property crimes. Somewhat unexpectedly, however, the effect of residential mobility was minimal and limited to robbery and residential burglary. Predictors based on

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routine activities theory were also relatively consistent with theoretical expectations. For example, the percentage of public transportation users predicted three of four crimes examined. Furthermore, as an indicator of lower guardianship, the percentage of employed females predicted both property offenses. In addition to the spatial dependency that was taken into account in spatial regression models, spatial heterogeneity occurring in a continuous space was fully examined by using GWR models. Several observations could be made based on numeric and visual inspection of the results. First, it was found that the effects of language ability and racial heterogeneity varied considerably across space. As expected, however, the effects of these two variables counteracted each other. In particular, language ability was negatively associated with the level of crime in eastern regions and positively associated with crime in western regions of Philadelphia. The opposite pattern was observed for racial heterogeneity. From the perspective of social disorganization theory, both of these variables, language ability and racial heterogeneity, were expected to be related to the level of crime, as they would affect the realization of common goals in neighborhoods. Hindered communication and social ties among neighborhood residents would be likely to affect the level of social control in neighborhoods. While limited language ability may hinder the establishment of a common value system in neighborhoods, concentration of a particular ethnic group there fosters the formulation of common (sub-cultural) value systems. That is, while racial heterogeneity is an index of heterogeneity, language ability can be considered an index of homogeneity. The importance of language ability and immigrant concentration for explaining the level of crime in neighborhoods was noted by Shaw and McKay (1942; 1969). The fact that these two variables, racial heterogeneity and language ability, varied in their effects on the level of crime was also interesting, as the effects of language ability on crime based on global regression models were somewhat minimal. That is, when global regression models provided results as averaged association across space, the models failed to capture spatially varying patterns of association between the level of crime and language ability. It is important to note that the results of GWR are not necessarily random, statistical artifacts. For example, a subsequent analysis was conducted by estimating the coefficient estimate for racial

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heterogeneity in the western and eastern regions of Philadelphia separately in a spatial lag regression model (i.e. global regression). The results indeed indicated that the effect of racial heterogeneity on the level of crime was negative in the western region, while it was positive in the eastern region (results not shown). Nonetheless, the negative association between racial heterogeneity and the level of crime was surprising from the standpoint of social disorganization theory. As social disorganization theory predicts that racial heterogeneity hinders social ties among residents and the realization of common goals, which subsequently increases the level of crime in neighborhoods, alternative linkages need to be specified between racial heterogeneity and the level of crime. Several possible explanations can be offered. For example, criminally conducive value systems among juveniles might be more effectively transmitted and shared in racially homogeneous neighborhoods. That is, if neighborhoods had conditions that increased frustrated wants to begin with, such frustrated wants might be more easily shared with others in racially homogeneous neighborhoods than heterogeneous neighborhoods. Furthermore, Shaw and McKay (1942; 1969) noted that criminally conducive value systems were transmitted across generations in high crime neighborhoods. Such transmission of value systems, whether they were conforming or illicit ones, could be more efficiently done in homogeneous neighborhoods. Moreover, as the analysis in the next chapter indicates, property offenders might actually prefer racially homogenous neighborhoods in order to reduce their visibility. Thus, although it might be true that racial heterogeneity reduces informal social control among neighborhood residents and increases the level of crime, different processes might be in operation in different neighborhoods. Second, of four types of violent and property offences, the effect of socio-economic disadvantage varied significantly only for property offences (residential burglary and auto theft). Although both negative and positive associations between socio-economic disadvantage and the level of crime would hardly be predicted by social disorganization theory, such results, in fact, provided support for routine activities theory. Routine activities theory predicts an increase in the level of crime if target attractiveness increases or if the level of guardianship decreases. Oftentimes, the increase in income level can be considered as either or both increased attractiveness (e.g., heightened perceived

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payoffs from crime) and increased guardianship (e.g., stronger security measures). By estimating location specific associations, GWR found neighborhoods that were high in socio-economic status and weak in guardianship, as well as neighborhoods that were high in socioeconomic status and strong in guardianship. This was particularly notable, as the effects of socio-economic disadvantage varied only for property offences, which are considered more opportunistic and rational than violent offences. Identifying locally specific associations and uncovering the mechanisms of specific neighborhood characteristics that contribute to the increased level of crime will be useful in developing crime prevention strategy for each neighborhood. Third, place specific associations were also detected for variables, mainly based on routine activities theory. Such findings were anticipated at the start of the analysis, as routine activities theory often provides explanations based at the place level, while social disorganization theory explanations are often based at the neighborhood level. In particular, the results of the global regression model for aggravated assault indicated that the effect of the percent youth was negative. The geographically weighted regression results indicated, however, that the effect of the variable on the level of aggravated assault was positive in downtown areas, possibly capturing the high levels of physical confrontations occurring at business establishments serving alcohol. Furthermore, the effect of the percentage of public transportation users varied for robbery. Although the variable was expected to be positively associated with higher levels of robbery because of increased vulnerability, the variable had different patterns of association between downtown and other areas. This may be due to the fact that census data measure characteristics of people living in neighborhoods. As the percentage of public transportation users was measured for each block group if residents were using public transportation to go to work, it was not surprising that the percentage of public transportation users was not high among residents living downtown to begin with. Nonetheless, the level of robbery was inherently high due to unique characteristics. The results of spatially varying association between the percent public transportation usage and the level of robbery captured such structurally different patterns of association for downtown and other areas. Fourth, although spatial heterogeneity has often been taken into account by controlling for downtown and elsewhere, the results of this

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analysis indicated that spatial variation could occur in different areas. For example, the effects of racial heterogeneity and language ability varied between western and eastern regions. Such findings also pointed out that geographically weighted regression models could be used for exploratory purposes in order to identify spatial heterogeneity of data, prior to running global regression models.

CHAPTER 4

A Spatial Analysis of Criminal Offenders’ Target Selection

INTRODUCTION Research on neighborhoods and crime has often relied on information about the neighborhoods in which offenders commit crimes. Such a research design cannot capture individuals’ movements, including those of criminals, between neighborhoods. Some criminals may commit crimes in their own neighborhoods due to convenience, while others may travel longer distances in search of suitable opportunities. In fact, the non-random distribution of crime over space is largely due to the non-random distribution of suitable opportunities for crime (Groff and La Vigne 2001; Hakim et al. 2001; Ratcliffe 2002; Ratcliffe 2006). Routine activities theory contends that opportunity structures for crime in communities are created by temporally and spatially dynamic movements of potential victims, motivated offenders, and guardians (Brantingham and Brantingham 1981a; Cohen and Felson 1979; Felson and Clarke 1998; Ratcliffe 2002; Ratcliffe 2006). In order to fully understand the types of neighborhood contexts that allow motivated criminals to act, it is necessary to consider the viewpoint of offenders. Although the spatial analysis of crimes has been a popular research topic in criminology, such analyses have followed three separate lines of research (Bernasco and Nieuwbeerta 2005). First, many studies have examined neighborhood and place characteristics where crimes are reported. Analytical interests of this line of research have ranged from explaining variation in individual victimization to assessing neighborhood differences in the level of crime (Miethe and Meier 1990; Miethe and Meier 1994; Morenoff and Sampson 1997; Rountree et al. 1994; Sampson and Groves 1989; Shaw and McKay 1942). This 113

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type of research has been facilitated by the increasing availability of geographic information systems (GIS), as well as the development of appropriate statistical models, such as spatial regression models and multilevel models (Anselin et al. 2000; Anselin et al. 2004; Oberwittler 2004; Rountree and Land 2000; Rountree et al. 1994; Smith and Jarjoura 1989). Social disorganization theory and routine activities theory often provide the theoretical foundation for these studies (Cohen and Felson 1979; Kubrin and Weitzer 2003a; Shaw and McKay 1942; Shaw and McKay 1969). A disadvantage of this line of research is that studies do not have any information regarding who offenders are and where they live (Bernasco and Nieuwbeerta 2005). The second line of research investigates the distance that offenders travel, or the “journey to crime” (Rengert et al. 1999; Wiles and Costello 2000). This line of research typically shows there is a distance decay function with respect to criminal offenders’ target selection and distance. That is, the probability of offending becomes smaller as the distance between offenders’ residences and potential victims becomes larger. These studies treat the distance that offenders travel as the dependent variable and include offender characteristics, such as race and age, as their independent variables. Thus, characteristics of neighborhoods being targeted by offenders are typically ignored in this line of research. The third line of research is qualitative studies of criminals through in-depth interviews (Decker et al. 1993; Walsh 1986; Wright and Decker 1994). By uncovering the decision making process of offenders, these studies typically illustrate the rationality of criminal offenders. Rational choice theory also points out that decision making by criminal offenders involves a multi-stage process, from deciding to become involved in illegal activities to selecting particular targets for their crimes (Cornish and Clarke 1986b). Although these qualitative studies provide rich information that cannot be captured in statistical analysis, quantitative data are needed for conclusions which can be generalized. Very few studies have simultaneously examined where offenders live, where they commit their crimes, and why they select a particular neighborhood as their target, rather than other locations. As past quantitative studies only incorporated characteristics of neighborhoods that were targeted, and did not assess characteristics of other neighborhoods that could have been chosen, it cannot be assessed “in which ways the chosen target differs from the potential targets that

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were forsaken” (Bernasco and Nieuwbeerta 2005: 301). If the assumption is made that criminal offenders are rational actors (i.e., they select a target neighborhood based on the costs and benefits of a location), then neighborhoods with certain characteristics should be more likely to be selected as targets. Thus, an appropriate model for assessing criminal offenders’ target selection should incorporate characteristics of both chosen and alternative neighborhoods. Among a few studies that investigated target selection, Bernasco and Nieuwbeerta (2005) found that the probability of a neighborhood being targeted by offenders was heightened by the neighborhoods’ ethnic heterogeneity, percentage of single-family households, and proximity to offenders’ houses. As an analytical model, Bernasco and Nieuwbeerta used McFadden’s conditional logit model (1973) to examine criminal offenders’ target selection. The model is attractive for testing target selection because it can incorporate characteristics of chosen and alternative neighborhoods in one regression model, which allows an assessment of how chosen neighborhoods are different from neighborhoods that could have been targeted. Furthermore, the model can incorporate characteristics of offenders, such as age and race, allowing for richer hypothesis tests. This study builds on Bernasco and Nieuwbeerta’s study (2005) by partly replicating their hypotheses, as well as following their suggestions for future research to test criminal offenders’ target selection using social disorganization theory, routine activities theory, and rational choice theory. NEIGHBORHOOD CHARACTERISTICS AND CRIME Studying the associations between neighborhood characteristics and the level of crimes has been a classic topic in criminology. Studies based upon social disorganization theory typically have found there is more crime in neighborhoods characterized by socio-economic disadvantage, residential instability, and racial heterogeneity (Kubrin 2000; Kubrin and Stewart 2006; Sampson and Groves 1989; Shaw and McKay 1942; Shaw and McKay 1969). Social disorganization theory links these neighborhood characteristics and the level of crime through limited informal social control and frustrated wants (Agnew 1999; Bursik 1988; Bursik and Grasmick 1993b; Kornhauser 1978). Residential mobility inhibits residents from establishing vested interests in

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addressing neighborhood problems. Racial heterogeneity often hinders the realization of common goals among neighborhood residents. Socio-economic disadvantage contributes to creating criminal motivation. There are several approaches to empirically testing social disorganization theory. Using the number of crimes known to police as the dependent variable, and socio-demographic characteristics from the census as independent variables, studies confirm the importance of neighborhood characteristics in explaining varying levels of crime over space (Cahill and Mulligan 2003; Kubrin 2000; Kubrin and Weitzer 2003a; Messner and Tardiff 1985; Miethe and Meier 1994). Methodological developments in spatial econometrics have also fostered analysis of the spatial dynamics of crime (Anselin 1988; Anselin et al. 2000; Baller et al. 2001; Cohen and Tita 1999; Messner et al. 1999; Morenoff et al. 2001). Although social disorganization has focused on the importance of space in explaining the level of crime since the original study by Shaw and McKay, statistical methods that have been developed in the past decade provide a more accurate assessment of the spatial dynamics of neighborhoods and crime. Routine activities theory gives an alternative view of what causes crime by focusing on suitable opportunities for crimes across time and space (Cohen and Felson 1979; Felson and Clarke 1998; Felson and Cohen 1980; Groff and La Vigne 2001; Ratcliffe 2002; Ratcliffe 2006). In particular, routine activities theory postulates that a crime occurs when a motivated offender and a suitable target converge in time and space in the absence of capable guardians (Cohen and Felson 1979). The theory predicts an increase in crime as target attractiveness increases. Target attractiveness can be evaluated based upon the acronyms VIVA (value, inertia, visibility, accessibility) and CRAVED (concealable, removable, available, valuable, enjoyable, and disposable) (Clarke and Eck 2005; Cohen and Felson 1979; Felson 2006). Based upon these criteria, money ranks as the most desirable item to steal because of its value and portability, while refrigerators and washing machines rank low despite their high value. Interestingly, according to routine activities theory, the volume of crime can change without an increase in the number of targets or offenders, if the behavioral patterns of these actors change in space and time (Wilcox et al. 2003). For example, an increased frequency in converging suitable targets and motivated offenders can result in an

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increase in the number of crimes. This also indicates that changing behavioral patterns can be a crime prevention strategy. That is, as routine activities theory considers opportunity a necessary, if not sufficient, condition for a crime to occur (Felson and Clarke 1998), changing opportunity structures can be a very effective crime prevention tactic. Despite its theoretical argument that crime occurs as a result of three elements (i.e., motivated offenders, suitable targets, and capable guardians) intersecting over space and time, many empirical tests of routine activities theory have focused on either one or two elements. Oftentimes, studies have looked at how victims’ demographic characteristics and behavioral patterns affect their victimization risk (Miethe and McDowall 1993; Miethe and Meier 1990; Miethe and Meier 1994; Miethe et al. 1987; Rountree et al. 1994). These studies typically support the expectations of routine activities theory, as an increase in guardianship reduces victimization risk, while exposure to motivated offenders increase the likelihood of being victimized. Regression models based upon routine activities theory often have very high R-squared values (i.e., a high percentage of variance in the dependent variable is explained by independent variables), indicating the superiority of the theory in explaining crime. Probably due to limited data availability, however, empirical tests of the role of motivated offenders in generating crime have been rare, despite the theory’s focus on criminal offenders. Although social disorganization theory provides a strong explanation for varying levels of crime at the neighborhood level, the theory does not provide scenarios or sequences of how each specific criminal incident occurs. In that respect, routine activities theory provides a theoretical link between offenders’ motivation and crime incidents. Nonetheless, the role of criminal offenders has not been fully tested via quantitative analysis in the context of routine activities theory. JOURNEYS TO CRIME An analysis of journeys to crime treats the distance that criminal offenders travel for the commission of crimes as the dependent variable of interest. This line of research consistently indicates that criminal

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offenders do not travel a long distance for their crimes (Rengert et al. 1999; Wiles and Costello 2000). In terms of probability, the likelihood of offending becomes smaller as the distance between offenders’ houses and potential victims becomes larger. This phenomenon is known as a distance decay function. The precise functional form of the distance decay function varies by crime types (e.g., property offenses vs. violent offenses), individual characteristics of offenders (e.g., sex and race), and the urban structure of a city (e.g., a densely populated city vs. a sparsely populated rural county) (Levine 2004). In addition to offenders’ residences and victims’ locations, Brantingham and Brantingham (1981b; 1993; 2001) argue that awareness space is important in criminal target selection. They argue that conventional activities of individuals are anchored at select locations, such as residences, work sites, leisure sites, and shopping sites. Individuals form their awareness spaces in areas around these locations (nodes) and roads connecting these locations (paths). As criminals are not committing crimes all the time, they also form awareness spaces based upon their daily lives. As offenders are likely to have a good idea of the types of people living within their awareness spaces, it is argued that criminal offenders select targets for their crimes from their awareness spaces. Extending these ideas, Rossmo (2004) developed a criminal investigation technique, known as geographic profiling, that calculates a probability estimate of where an offender’s residence is based upon the locations of known crime series. The geographic profiling has also been developed and evaluated by several scholars (Canter et al. 2000; Levine 2004; Paulsen 2006; Paulsen 2007; Rich and Shively 2004). Descriptive studies of journeys to crimes provide an alternative perspective on crime incidents. These studies typically treat the distance that offenders travel as the dependent variable and only include offender characteristics, such as race and age, as their independent variables. Such an analytic strategy neglects the characteristics of neighborhoods being targeted by offenders. That is, journeys to crime research does not necessarily explain why offenders targeted a particular neighborhood out of other potential choices. Although theoretical arguments outlined by Brantingham and Brantingham are plausible, empirical tests have been limited, as precise data on awareness spaces are often not readily available.

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TARGET SELECTION AS RATIONAL CHOICE While there are many theories devoted to explaining why individuals have criminal motivations (e.g., strain theories and social learning theories), routine activities theory takes criminal motivation for granted. In order to explain criminal events, routine activities theory assumes that human behaviors are a product of rational choice. Thus, criminal behavior can be predicted based on the costs and benefits involved in the commission of a crime. The costs and benefits involved in crime vary depending on situations and targets. For example, while targets in close proximity to motivated offenders’ houses are convenient (benefit), the likelihood of being detected (cost) becomes high. Targets with high monetary values (benefit) are also likely to have strong guardianship (cost). Routine activities theory and rational choice theory argue that offenders act on suitable opportunities for crime based upon cost/benefit calculation. Whether criminologists hold the assumption of rationality among criminals may depend on their philosophical beliefs on human behavior. Nonetheless, ethnographic studies of criminals typically support the idea that criminals are guided by a certain degree of rationality, especially for property crimes (Decker et al. 1993; Hakim et al. 2001; Taylor and Nee 1988; Walsh 1986; Wright and Decker 1994). For example, burglars often prefer houses located on a corner, rather than in the middle of a street segment, and they avoid lights and open ground. A primary motive for committing burglaries is money. Furthermore, interviews with robbers found a substantial number of them considered the accessibility and visibility of money (e.g., a person counting money in front of an ATM machine), an easy get away after the crime, and perceived low risk of detection when they selected targets (Feeney 1986). It is also important to note, however, that offenders typically do not weigh all relevant factors (e.g., time, location, modus operandi, objective risk of arrest, presumed monetary gains, etc.) when they commit their offense, and other seemingly irrelevant factors (e.g., mood, alcohol and drug consumptions, peer pressure, laziness, etc.) often shape their judgments. That is, criminal offenders are said to be equipped with limited rationality, as they process only limited information in making decisions regarding their criminal activities. The rational choice perspective looks at crime as an event whereby a motivated offender makes a decision to attack a certain target in order

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to maximize his/her gains and minimize the possibilities of apprehension. That is, it is assumed that crime is not a random event committed by an individual who is propelled to get involved in illegal behavior by his/her criminal predispositions. Instead, opportunity theories of crime hold that an offender considers a variety of situational factors (i.e., vulnerability of a target, possible gains from the crime, and possibility of detection) in a cost/benefit analysis. The decision making process and the degree of rationality, however, may be different across individuals, especially by age. Although one of the primary motives for property crimes is monetary, other factors can be at work, such as excitement, thrill seeking, and peer pressure. Such secondary motives for crimes can be particularly strong for young offenders. As crimes committed by youths are typically group behaviors, peer pressure and proving masculine status may become important criteria for young offenders’ decision making (Warr 2002). As young offenders are more likely to be impulsive and present-oriented, they may fail to consider the possible consequences of their actions (Gottfredson and Hirschi 1990). Older criminals, on the other hand, may be more responsive to the potential consequences of committing a crime and evaluate costs and benefits differently from youths. For example, older offenders may have an increased stake in social order (e.g., employment and family relationships) and wider experiences (e.g., prior experience with apprehension and confinement). A SUMMARY OF LITERATURE REVIEW Spatial analysis is an important and popular topic in criminology. Among a variety of methods used in approaching the spatial analysis of crimes, a large number of studies have examined varying levels of crime across neighborhoods, based on social disorganization theory. Despite its theoretical argument for the importance of criminal offenders in shaping criminal incidents, studies based on routine activities theory have typically focused on victims. This line of research that examines crime rates based on neighborhood characteristics, however, attempts to explain the reported levels of crime as its dependent variable and does not take into account where offenders are coming from.

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The second line of research shifts its attention to criminal offenders and investigates the distance that criminal offenders travel to commit their crimes. These studies may include demographic characteristics of offenders (e.g., sex and race), as well as crime types (e.g., violent vs. property offenses), as independent variables for descriptive analysis. This line of research, however, does not necessarily explain why criminal offenders select a particular target among other potential choices. Third, discussions of rationality among criminals have largely been theoretical and/or qualitative. Although the rich descriptions culled from interviews with offenders are definitely important for deepening our understanding of crime, quantitative studies are also needed to establish generalizable conclusions. By merging these separate lines of research, this chapter takes a quantitative approach to testing criminal offenders’ target selection. Both social disorganization theory and routine activities theory contend that situational contexts are important in explaining criminal incidents. That is, some neighborhood and situational characteristics are conducive to crime, while others deter motivated offenders to commit criminal acts. By quantitatively incorporating criminal offenders’ movements in the analysis, this research overcomes the limitation of the previous research on the spatial analysis of crime. Assuming criminal offenders are rational decision makers who attempt to maximize benefits and minimize costs, this chapter examines why criminal offenders select a particular target from available options. HYPOTHESES Based on social disorganization theory, rational choice theory, and routine activities theory, this chapter examines what neighborhood characteristics raise the likelihood of being targeted by criminal offenders. In particular, as ethnographic studies of criminal offenders’ target selection are richer for burglaries than any other offense (Cromwell and Olson 2006; Hakim et al. 2001; Hakim and Shachmurove 1996; Steffensmeier and Ulmer 2005; Walsh 1986; Wright and Decker 1994), this study examines burglars’ target selection. The following hypotheses are developed to facilitate the quantitative analysis of target selection.

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H1 (Proximity/Accessibility): The probability of being targeted by a burglar decreases as the distance between a neighborhood and the offender’s home increases. Based on the assumption of rationality and cost/benefit analysis in criminal offending (Cornish and Clarke 1986a; Wright and Decker 1994), a distance decay function is hypothesized for the probability of offenders’ committing crimes and proximity between their home and a crime location. The distance to travel for commission of a crime can be considered a cost, while the monetary reward from the crime can be considered a benefit. It is assumed that criminal offenders are less likely to travel to the other side of a city just to obtain $20 from a burglary. H2 (Proximity/Accessibility): Young people (younger than 16 years old) are especially likely to target neighborhoods that are close to their homes because they are less geographically mobile (they do not have access to a car). This hypothesis is mainly related to the availability of cars. Individuals are eligible for a license when they are sixteen in the state of Arizona where the burglars’ data were collected. Although the distance decay hypothesis (H1) is still true across age groups, the effect is hypothesized to be stronger for youths, who are assumed to not have access to cars. Furthermore, the journey to crime for young offenders are expected to shorter than older offenders as young offenders’ are assumed to be equipped with more limited rationality and to commit crimes for reasons other than money (e.g., seek for excitement). H3 (Attractiveness): Neighborhoods with higher median housing values are more likely to be targeted by burglars because they are potentially more profitable. According to routine activities theory (Cohen and Felson 1979), target attractiveness can be evaluated by target value, portability, visibility, and access. For residential burglars, attractiveness can be approximated by housing values. An assumption here is that affluent households have valuable goods. Based on this assumption, there should be a positive association between the likelihood of victimization and housing values. Several ethnographic studies of burglars have also illustrated that burlars’ primary motivation for breaking into houses is monetary rewards (Cromwell and Olson 2006; Wright and Decker 1994).

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H4 (Visibility/Accessibility): The likelihood of being targeted by burglars increases as the racial composition of neighborhoods becomes more heterogeneous. Social disorganization theory argues that racially and ethnically heterogeneous neighborhoods tend to have lower levels of social control, as social ties and the realization of common goals are hindered (Bursik and Grasmick 1993b; Kornhauser 1978; Kubrin and Weitzer 2003a; Sampson and Groves 1989). As lower levels of informal social control lead to lower levels of guardianship, racial heterogeneity of neighborhoods is expected to increase criminal opportunities. For offenders coming from outside a neighborhood, it may be easier to blend into racially heterogeneous neighborhoods than racially homogeneous neighborhoods. H5 (Guardianship): Neighborhoods with higher residential mobility are more likely to be targeted by burglars. High residential mobility weakens the surveillance ability of neighborhood residents and lowers the level of guardianship, which in turn leads to higher crime rates. When people are constantly moving in and out, neighborhood residents may have a harder time distinguishing residents from possible intruders. Furthermore, those who are not planning to stay in a neighborhood for long may not be interested in improving neighborhood conditions and they may not care about neighborhood disorder. H6 (Guardianship): Neighborhoods with a higher proportion of renter-occupied housing units are more likely to be targeted by burglars. Similar to the logic given for H5, persons living in renter-occupied housing are likely to move their residency, reducing the informal social control of neighborhoods. H7 (Guardianship): Neighborhoods with a higher proportion of labor force participation by adult household members are more likely to be targeted by burglars. A decrease in employment rates can be criminogenic in that joblessness causes economic strain, which results in an increase in the number of motivated offenders. However, from the perspective of routine activities theory, an increase in the employment rate indicates an increase in non-household activities. Thus, an increase in employment is hypothesized to be associated with lower levels of guardianship and, subsequently, higher crime rates. Female labor force

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participation has been used as an indicator of household guardianship (Miethe et al. 1991; Miethe and Meier 1990). The argument, based on routine activities theory, is that an increase in female labor force participation is associated with an increased number of homes left unguarded during the day. H8 (Guardianship): Neighborhoods with a higher proportion of one person households are more likely to be targeted by residential burglars. Similar to the logic given for H7, single households are hypothesized to have a higher victimization risk due to low levels of guardianship. H9 (control): Neighborhoods with larger numbers of occupied housing units are more likely to be targeted by residential burglars. Routine activities theory argues that the amount of crime is a function of the number of motivated offenders, suitable targets, and levels of guardianship (Cohen and Felson 1979). It is predicted that crime increases without an increase in potential offenders if the number of suitable targets increases or the level of guardianship decreases. Thus, this hypothesis states that neighborhoods with larger numbers of occupied housing units are more likely to suffer from crime victimization simply because of a larger number of potential targets. Additionally, in this research, variation in target selection based on individual characteristics is examined. In particular, attention is given to how target selection varies with offender’s age and the presence of co-offenders. Assuming age is a proxy for rationality, it is expected that adult offenders will consider a variety of neighborhood characteristics when choosing a residence to burglarize. If young offenders are likely to have secondary motives for their crimes other than money, such as peer pressure and excitement, the effect of housing values on their target selection may be weaker than for older offenders. Furthermore, if young offenders have more limited rationality than older offenders, certain neighborhood characteristics, such as the level of guardianship, may matter less for their target selection than older offenders. Similarly, it is expected that the decision making process of single offenders and group-offenders will vary. For example, as co-offenders provide more lookouts during the commission of crimes, groupoffenders may think they can conquer difficult, but lucrative houses. In such a case, the level of guardianship of neighborhoods may matter less

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for group-offenders than for single offenders. On the other hand, it is also possible that the presence of co-offenders limits rational decision making if secondary motives, such as peer pressure, are in operation. If so, the effects of neighborhood characteristics may be weaker for group-offenders than for single offenders, as the former lacks rational decision making when selecting targets for their crimes. Furthermore, as journeys to crime may originate from locations other than offenders’ own residences, if a co-offender is present the effect of distance from one’s residence may be weaker for group-offenders’ target selection than for single offenders. DATA Burglars’ Characteristics In order to analyze target selection, data on criminal offenders who had been arrested for any criminal offense more than once by the Glendale (Arizona) Police Department were obtained. The arrested offender data included offenders arrested between 1996 and 2003. Arrest records are especially useful for the analysis of criminal offenders’ target selection because they include information about both where criminal offenders live and where they committed their crimes. Thus, unlike many previous studies, the distance that offenders have traveled in order to commit their crimes could be determined. Having identified offenders’ residences and their target locations, this study treated 157 block groups in Glendale, Arizona, as offenders’ alternative choices in order to assess which neighborhood characteristics increase the likelihood of being targeted by offenders. Although the primary focus of this study was to identify neighborhood characteristics that raise the likelihood of being targeted by burglars, this study also investigated how offenders’ target selection varies by offenders’ individual characteristics. Thus, basic demographic characteristics of offenders, such as age and race, were included in the analysis. The data included 354 burglary incidents committed by 270 burglars. Among the burglars included in these data, 53% were White (N=143). Additionally, there were 91 Hispanic offenders (34%) and 36 African American offenders (13%). The burglars were predominantly male (88%). Not surprisingly, the

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majority of offenders were young offenders. The median and mean ages of the offenders were 18 and 21, respectively. Although the offenders’ ages ranged from 10 to 51, older offenders were relatively rare. The distance offenders traveled to commit their crimes was highly positively skewed. The median distance that these offenders traveled was 0.6 miles, while the mean distance was 1.6 miles. Neighborhood Characteristics A series of neighborhood characteristics that were identified based on social disorganization theory and routine activities theory were extracted from 2000 Census block group data. First, a measure of 2 racial heterogeneity was calculated as 1 − ∑ pi , where pi is the proportion of each of the following racial groups: non-Hispanic Caucasian, African American, Hispanic, Asian, and Other. This index of racial heterogeneity ranged from 0 (complete homogeneity with one racial group dominating a block group) to 0.8 (complete heterogeneity with each of the five racial groups comprising 20%). Additionally, in order to assess the effect of the proportion of each racial group separately, proportions of non-Hispanic Caucasian, African American, and Hispanic were also included in the analysis. In addition to these demographic characteristics, a number of housing characteristics were used, as the focus of the study was burglars’ target selection. These characteristics included: 1) residential mobility, measured as the percentage of the population ages five and over who changed their address in the past five years; 2) the percentage of single households (one household member); 3) the percentage of employed adult household members, defined as the percentage of employed single householders and employed married families; 4) the percentage of detached housing, defined as the percentage of single unit housing structures; 5) median housing values; 6) median age (years) of the housing units; and 7) the number of occupied housing units. The descriptive statistics for these neighborhood characteristics are presented in Table 4.1. The city of Glendale is located in Maricopa County, Arizona, and is a northeastern suburb of Phoenix. Figure 4.1 shows a map of Glendale neighborhoods, along with residential burglary rates. The downtown area, located in the southeastern corner of the map, has

Table 4.1 Descriptive Statistics for Neighborhood Characteristics Mean Std. Dev Min Max Heterogeneity 0.41 0.16 0.00 0.69 % White 64.98 22.30 0.00 1.00 % African American 4.27 4.82 0.00 0.25 % Hispanic 23.25 19.60 0.00 0.94 % Residential Mobility 56.88 20.45 0.00 1.00 % Single Household 18.75 14.41 0.00 0.64 % Adult Employed 41.77 28.38 0.00 0.90 % Detached House 78.11 30.72 0.00 1.00 % Renter-occupied 27.72 28.08 0.00 1.00 Occupied Houses 438.46 273.20 0.00 2102.00 Median Housing Value 110.45 52.85 0 253.10 Median Age of Housing 1947 258 0 1999

Figure 4.1 Spatial Distribution of Burglary Rates per 1,000 Households

Offender A’s Choice

Offender A’s Alternative Choices

Figure 4.2 A Criminal Offender’s Choice and Alternatives

Table 4.2 Data Structures of a Conditional Logit Model (Hypothetical Data) Offender Housing ID Target Neighborhood Value Distance 1 1 A 100 10 1 0 B 200 23 1 0 C 300 45 1 0 D 400 69 2 0 A 100 52 2 1 B 200 18 2 0 C 300 25 2 0 D 400 30 3 0 A 100 10 3 0 B 200 23 3 0 C 300 45 3 1 D 400 12

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higher residential burglary rates, although the levels of burglary vary considerably over space. METHOD This study examines how burglars choose a particular neighborhood as their target from available alternatives. Figure 4.2 provides an illustration of the research question. The light gray cell indicates offender A’s residence and the dark gray cell indicates the crime incident location. That is, the light gray cell represents the origin of the offender’s journey to crime, while the dark gray cell represents the destination. The right panel of the figure illustrates, however, that the offender could have chosen any other neighborhood as his/her target. Each neighborhood is likely to vary in its socio-demographic characteristics. Some neighborhoods may be racially heterogeneous with low levels of social control, while others may be homogeneous and socially cohesive. Some neighborhoods may consist of many owner-occupied residences, while other neighborhoods may be predominantly apartment complexes with high residential mobility. Given such variability in neighborhood characteristics, what are the neighborhood characteristics that raise the likelihood of offender A selecting a particular neighborhood as his target? In order to examine offenders’ target selection as a spatial location choice, this study employs a variant of logistic regression, the conditional logit model. The conditional logit model was originally developed by McFadden (1973) for his analysis of travel mode choices. For example, given that a person could travel by car, bus, or subway, and that travel time and cost vary by mode of transportation, McFadden analyzed the factors that influence a person’s choice of transportation. One advantage of the conditional logit model for the analysis of offenders’ target selection can be illustrated with hypothetical data (see Table 4.2). Notice that, unlike the structure of typical social science data with one row per case, there are as many rows as alternative choices (neighborhoods in this example) for each offender. Additionally, the data have two variables, median housing values of neighborhoods and distances from offenders’ residence to each neighborhood. Median housing value is a neighborhood-specific variable that varies by neighborhoods (i.e., alternative choices). On the

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other hand, distance is an offender-specific variable, often called a case-specific variable, and it varies by offenders. That is, each neighborhood offers different levels of attractiveness as well as accessibility that affect offenders’ target selection. Assuming that individuals are utility seekers who attempt to maximize benefits and minimize costs, a conditional logit model examines what characteristics affect the offenders’ choice of crime target. The conditional logit model has several advantages for modeling offenders’ target selection. First, the model’s underlying assumption of individual choice behavior is compatible with rational choice theory; rational choice theory assumes that individuals are utility seekers who attempt to maximize benefits and minimize costs. Given this compatibility with the assumption of rational choice theory, the conditional logit model is suitable for the research question that this study pursues. Second, the conditional logit model is flexible enough to incorporate both neighborhood characteristics (alternative-specific characteristics) and offender characteristics (case-specific characteristics). In order to assess which neighborhood characteristics affect the risk of being targeted by offenders, an analytic model needs to incorporate characteristics of not only chosen neighborhoods, but also alternative neighborhoods. The unique data structure of the conditional logit model can incorporate characteristics of all potential choices. Furthermore, the conditional logit model can incorporate individual characteristics of criminal offenders, such as sex, age, and race, for the analysis of target selection. Such model flexibility enriches the types of hypothesis that can be tested. Third, as the conditional logit model is a variant of the logit model, coefficient estimates can be interpreted as odds ratios. Therefore, interpretation of the results is intuitive. Exponentiated logit coefficients indicate a multiplicative change in the odds of neighborhoods being selected by offenders, per unit change in an independent variable. Taking advantage of these unique features of the conditional logit model, this study examines criminal offenders’ target selection. The series of hypotheses identified from social disorganization theory, routine activities theory, and rational choice theory are tested using arrested burglars’ data.

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RESULTS The results of the conditional logit models that assessed the effects of neighborhood characteristics on the probability of neighborhoods being targeted by offenders are reported in Table 4.3. The first model includes characteristics of both chosen and alternative neighborhoods as predictors of target selection. The results indicated that the Table 4.3 Conditional Logit Models of Offenders’ Target Selection Predicted by Neighborhood Characteristics Neighborhood Neighborhood Characteristics and Characteristics Distance Distance (.5 mile) Heterogeneity

0.523** (0.043) 1.164 0.299+ (0.625) (0.192) Residential Mobility 1.017 0.977 (10%) (0.037) (0.051) % Single Household 0.934 0.888+ (10%) (0.058) (0.063) % Adult Employed 1.061* 1.066+ (10%) (0.031) (0.040) % Detached Housing 1.311** 1.217** (10%) (0.070) (0.074) % Renter-occupied 1.348** 1.233** (10%) (0.069) (0.066) Median Housing Value 0.989** 0.996* ($1,000) (0.002) (0.002) Median Year 1.003 1.006 (10 years) (0.004) (0.004) Occupied Housing 1.113** 1.176** (100 units) (0.015) (0.028) Note: Odds ratios are reported as coefficient estimates. Standard errors are reported in parentheses. + p<0.10, * p<0.05, ** p<0.01

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likelihood of neighborhoods being targeted by offenders was significantly increased by higher percentages of employed members in families, higher percentages of detached housing units, higher percentages of renter-occupied housing units, lower median housing values, and higher numbers of occupied housing units. Similar to the logit model, the exponentiated coefficient estimates of the conditional logit model could be substantively interpreted as odds ratios. For example, a 10 % increase in employed family members was predicted to increase the odds of a neighborhood being selected by a factor of 1.06. Equivalently, this meant that a 10% increase in the percentage of employed family members resulted in a 6% increase in the odds that a neighborhood would be selected by offenders. Such interpretation facilitated the assessment of the relative importance of detached and renter-occupied housing units. For example, a 10% increase in the percentage of detached housing units and the percentage of renter-occupied housing units increased the odds of a neighborhood being targeted by offenders by 31% and 35%, respectively. Although these directions of association supported the theoretical expectations of routine activities theory, the negative association between median housing values and the probability of being selected was not consistent with rational choice theory. A negative association between the socio-economic status of neighborhoods and crime has been found in other studies, however (Bernasco and Luykx 2002; Bernasco and Nieuwbeerta 2005). From a routine activities perspective, such a negative association may be explained as low housing values represent low levels of guardianship (e.g., limited security measures). In addition to neighborhood characteristics, the second model considered distance from offenders’ residences to each potential target as a predictor. As hypothesized, distance was strongly and negatively associated with target selection. In particular, the model indicated that each 0.5 mile increase in the distance between an offender’s residence and a neighborhood decreased the odds of the offender selecting the neighborhood by 48% (or equivalently, an additional 0.5 mile increase in the distance decreased the odds by a factor of 0.52). This finding strongly supports the theoretical expectations of both routine activities theory and rational choice theory. A neighborhood was more likely to be targeted by burglars when known offenders lived in close proximity. Although distance plays a strong role in offenders’ decision

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making, neighborhood characteristics still affect target selection. Neighborhood characteristics that were statistically significant in the previous model remained the same in both direction and relative strength of association. Interestingly, however, when the effect of distance was taken into account in the target selection model, the effects of racial heterogeneity and the percentage of single households (i.e., one person households) became significant. The direction of association for these variables was the opposite of theoretical expectations. That is, the offenders were more likely to target neighborhoods characterized by racial homogeneity and higher proportions of single households. Although it was expected that heterogeneity would help offenders blend into neighborhoods when scouting a target, the results of the conditional logit model indicated the possibility that homogeneity might actually foster offenders’ confidence that they can blend into target neighborhoods. As the effect of homogeneity was likely to depend on offenders’ race, however, the next analysis model considered the effect of neighborhood racial composition on offenders’ target selection. Instead of an index of heterogeneity, the conditional logit models presented in Table 4.4 included the racial composition of neighborhoods as a predictor. The results for the first model indicated that the percentage of Hispanics in neighborhoods was positively associated with offenders’ target selection. In particular, each 10% increase in Hispanic residents increased the odds of offenders selecting the neighborhood by 54%. As three racial composition variables (the percentages African American, Hispanic, and White) were relatively highly correlated, separate analyses were conducted by including each measure of racial composition, one at a time, in order to deal with multi-collinearity. As the pattern of association remained the same, the results for the conditional logit models with all three measures of racial composition in the model are presented. As for other neighborhood characteristics, the percent family members employed, the percent detached housing, the percent renter-occupied, and the number of housing units were significantly associated with offenders’ target selection. In order to further investigate variation in target selection by offenders’ race, interaction terms between offenders’ race and the racial composition of neighborhoods were included in the conditional logit models (Table 4.4). The results indicated that both Hispanic and White

Table 4.4 Conditional Logit Models of Offenders’ Target Selection using Racial Characteristics of Neighborhoods and Offenders

Distance (.5 mile) Residential Mobility (10%) % Single Household (10%) % Adult Employed (10%) % Detached Housing (10%) % Renter-occupied (10%) Median Housing Value ($1,000) Median Year (10 years) Occupied Housing (100 units)

% White (10%) % African American (10%) % Hispanic (10%)

Racial Composition of Neighborhoods

Offenders' Race

0.537** (0.042) 0.964 (0.052) 0.939 (0.072) 1.083+ (0.044) 1.115+ (0.068) 1.104+ (0.065) 0.998 (0.002) 0.988 (0.009) 1.147** (0.029)

0.548** (0.042) 0.986 (0.054) 0.916 (0.070) 1.083* (0.043) 1.077 (0.063) 1.071 (0.062) 0.997 (0.002) 0.989 (0.012) 1.148** (0.029)

1.310 (0.220) 1.103 (0.301) 1.542** (0.258)

African American 1.283 (0.295) 2.625* (1.062) 1.242 (0.294)

Hispanics 0.876 (0.101) 0.268** (0.100) 1.241+ (0.148)

Whites 1.216 (0.372) 0.323* (0.178) 1.286 (0.402)

Note: Odds ratios are reported as coefficient estimates. Standard errors are reported in parentheses. + p<0.10, * p<0.05, ** p<0.01

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offenders avoided neighborhoods composed of African Americans, while African American offenders were likely to target such neighborhoods. In particular, a 10% increase in the percentage of African Americans in neighborhoods increased the odds of African American offenders selecting the neighborhood by 2.5 times. The same amount of change in the percentage of African American residents in neighborhoods, however, deterred Hispanic and White offenders as the odds of selecting the neighborhood decreased by a factor of 0.27 and 0.32, respectively (or equivalently, 73% and 68% reduction in the odds). Changes in the proportion of Hispanic residents only affected Hispanic offenders’ target selection, while changes in the proportion of White residents did not affect the target selection of any offenders. The results indicated that a 10% increase in the percentage of Hispanic residents in a neighborhood increased the odds of burglars targeting the neighborhood by 24%. Overall, the results indicated that offenders were highly conscious of visibility when committing crimes. Both Hispanic and White offenders avoided neighborhoods composed of African American residents. African American offenders, on the other hand, seemed to be comfortable being in neighborhoods composed of a higher percentage of African American residents. Hispanic offenders were also likely to target neighborhoods composed of Hispanic residents, although such a pattern was not found for White offenders. It may be true that offenders were likely to be living in neighborhoods that were primarily composed of their own race to begin with. It is important to note, however, that the results in Table 4.4 controlled for distances from offenders’ residents to each neighborhood. Thus, if offenders were likely to target adjacent neighborhoods, only the distance should be statistically significant. The results indicated, on the contrary, that both the distance from offenders’ residences to potential targets and the racial composition of neighborhoods were significantly related to offenders’ target selection. Finally, looking at other neighborhood characteristics, the percentage of employed adult family members and the number of occupied housing units were significantly related to offenders’ target selection in expected directions. Significant effects for these two variables supported the theoretical expectations of routine activities theory and rational choice theory, as offenders were expected to target neighborhoods that had many potential targets (i.e., the number of

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occupied housing units) with low levels of guardianship (i.e., higher percentage of employed family members). In order to further examine how offenders’ individual characteristics affected their target selection, the next set of models incorporated offenders’ age as a predictor. In particular, a conditional logit model was run by dividing offenders into youth (ages younger than 15) and adult (ages 15 and over) in order to determine if target selection processes varied by offenders’ age. This age distinction for youth and adult was made mainly because of the accessibility of motor vehicles. As access to cars significantly alters individuals’ behavior space, and subsequently potential target choices, the legal age for individuals to obtain motor vehicle licenses was used as a cutoff point1. As expected, the results of the conditional logit model indicated the effect of distance was stronger for youth offenders than adult offenders, as indicated by the smaller odds ratios for youth offenders (Table 4.5). Each 0.5 mile increase in the distance between offenders’ residences to a neighborhood decreased the odds for youth offenders to target the neighborhood by 65%, while the same amount of change in the distance decreased the odds for adult offenders by only 43%. Thus, this means that youth offenders were a lot more likely to choose targets in close proximity to their residences than adult offenders. Interestingly, for youth offenders, the effect of distance took away most of the effects of neighborhood characteristics in selecting targets for their crimes. Except for the control variable, the number of housing units, only median age of housing structures was significantly related to youth offenders’ target selection. Adult offenders target selection, on the other hand, was affected by a variety of neighborhood characteristics, even after the distance was taken into account. In particular, adult offenders were likely to select neighborhoods that were characterized by racial homogeneity, higher percentages of single households, higher percentages of employed families, higher percentages of detached housing units, higher percentages of renters, lower housing values, and more occupied housing units. These findings suggested that adult offenders were likely to select neighborhoods that were low in guardianship (as indicated by the effects of the percentage of employed families, detached housing, and renter-occupied housing units), while considering their visibility (as indicated by the negative effect of heterogeneity). As the conditional logit model controlled for the effect of distance, such different patterns

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Table 4.5 Conditional Logit Models of Offender Target Selection by Youth and Adult Offenders Youth Offenders Adult Offenders Distance 0.350** 0.573** (.5 mile) (0.082) (0.049) Heterogeneity 0.753 0.224+ (0.729) (0.178) Residential Mobility 0.868 1.020 (10%) (0.106) (0.056) % Single Household 0.971 0.854+ (10%) (0.129) (0.069) % Adult Employed 0.996 1.098* (10%) (0.060) (0.050) % Detached Housing 1.113 1.259** (10%) (0.141) (0.089) % Renter-occupied 1.166 1.266** (10%) (0.118) (0.083) Median Housing Value 0.996 0.995+ ($1,000) (0.004) (0.003) Median Year 1.019** 1.004 (10 years) (0.005) (0.005) Occupied Housing 1.100+ 1.195** (100 units) (0.061) (0.029) Note: Odds ratios are reported as coefficient estimates. Standard errors are reported in parentheses. + p<0.10, * p<0.05, ** p<0.01 of association across age groups might indicate that adult burglars’ crimes were driven more by carefully selecting targets, while young offenders’ crimes were largely based upon convenience. The final analysis considered if target selection differed between single and group-offender groups. The results presented in Table 4.6 indicated that distances from offenders’ home residence to a potential target was negatively associated for burglaries committed by single offenders but not group-offenders. Such different patterns might be explained by the result of data limitations. The data only showed if the

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crimes were committed by co-offenders without links to who the cooffenders were. That is, the analysis could not include distance measures for co-offenders’ residences. Looking at the other characteristics, group-offenders were highly likely to target a neighborhood characterized by racial homogeneity. That is, the results indicated that offenders were more conscious of visibility when committing crimes with their associates. Although the data did not provide information regarding who the co-offenders were for each crime, it might be reasonable to assume that offenders were more likely to hang out with people of the same race. Based on such an assumption, it could be argued that two black offenders scouting White neighborhoods would stand out more than when they were traveling alone. In fact, the results indicated that group-offenders’ only consideration in selecting targets was visibility, while several neighborhood characteristics affected the decision making of single offenders. For single offenders, the odds of selecting a neighborhood increased as the neighborhood’s percentage of detached housing, the percentage of renter-occupied housing units, and the number of occupied housing units increased. SUMMARY This research has quantitatively examined criminal offenders’ target selection using data on arrested offenders. In particular, a series of hypotheses based on routine activities theory, social disorganization theory, and rational choice theory were tested using conditional logit models. Taking advantage of the conditional logit models’ flexibility in analyzing the characteristics of chosen and not-chosen neighborhoods simultaneously, this research identified neighborhood characteristics that increased the risk of being targeted by burglars. Overall, the results were in accord with theoretical expectations of rational choice theory and routine activities theory. First, burglars were likely to target neighborhoods in close proximity to their residences. The strong effect of distance on target selection could be explained by both the cost/benefit of journeys to crime and familiarity with the area. Burglars are less likely to visit a neighborhood on the opposite side of a city just to obtain $50. Burglars are also less likely to be involved in,

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Table 4.6 Conditional Logit Models of Target Selection by Single and Multi-Offenders Single Offenders Multi-Offenders Distance 0.5634** 0.8795 (.5 mile) (0.077) (0.131) Heterogeneity 0.9727 0.1412+ (0.847) (0.156) Residential Mobility 0.9262 1.0897 (10%) (0.080) (0.112) % Single Household 0.9676 0.8736 (10%) (0.105) (0.114) % Adult Employed 1.0635 1.0031 (10%) (0.051) (0.061) % Detached Housing 1.3237** 0.8776 (10%) (0.108) (0.093) % Renter-occupied 1.3109** 0.9085 (10%) (0.096) (0.085) Median Housing Value 0.9971 0.9975 ($1,000) (0.004) (0.005) Median Year 1.0023 1.0058 (10 years) (0.006) (0.009) Occupied Housing 1.1840** 0.9934 (100 units) (0.037) (0.043) Note: Odds ratios are reported as coefficient estimates. Standard errors are reported in parentheses. + p<0.10, * p<0.05, ** p<0.01 illegal activities in an area which is unfamiliar to them. Offenders’ awareness space based on their daily activities, on the other hand provides a list of potential targets. It is important to note that offenders also need to fence stolen items. It is not reasonable to think that offenders travel into an unfamiliar area, commit an illegal activity, and carry a stolen item for a long distance and time. The present analysis quantitatively confirmed that offenders’ target selection was largely affected by their awareness spaces, or neighborhoods they were familiar with (Brantingham and Brantingham 1981a)

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Second, offenders were likely to target neighborhoods that were low in guardianship. Neighborhoods characterized by higher proportions of employed family members become attractive targets with limited guardianship because residents are less likely to be at home during the day. Employment provides highly structured activities where residents leave early in the morning and come back late in the afternoon. Such structured activities make the behavior of residents predictable. As the biggest concern of offenders’ is whether they will encounter residents after breaking into their homes, predictable patterns of behavior by residents provide fruitful opportunities for burglars. Renter-occupied housing was also an important predictor of burglars’ target selection. As renters are less likely to be concerned about the property than home owners, renter-occupied housing units may have limited security measures, hence low levels of guardianship. Limited interest in the property is also likely to affect disorder in the surrounding environment. Renters may be less likely to address the physical deterioration of neighborhoods, although such neighborhood disorder may actually send cues to potential offenders that the areas are suitable targets. The analysis also indicated that burglars are likely to target neighborhoods characterized by a high percentage of detached housing units. Detached housing units can also be evaluated based on the level of guardianship. Oftentimes, detached housing units emit signs of occupancy (and vacancy) that are easily read by offenders. For example, a car may be parked in the driveway. Newspapers may be left in front of doors. Intruders can also determine occupancy from windows located on all sides of detached housing units. Although cars and newspapers may also be present at apartment complexes, it is harder to determine which apartment unit is empty based on cars parked in a parking lot. Offenders may also fear that residents of nearby apartment units may come back during their break in and enter. Compared to detached housing units, apartment complexes may provide a limited number of entry points. While single story detached housing units may be easily accessible for break-in and enter, multistory apartment buildings are only accessible through front doors. Furthermore, apartment complexes often provide supervision by apartment maintenance and office staff during the day. Third, the analysis indicated that visibility played a strong role in selecting targets. Although racial heterogeneity is often a key predictor

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of the level of crime, according to social disorganization theory, when the analysis takes into account offenders’ points of view, it was found that homogeneity was a predictor of where offenders commit crimes. Although heterogeneity may hinder the development of social ties and the realization of common goals among neighborhood residents, such latent constructs are not visible to offenders. When offenders are selecting targets, their concern is likely to be whether they blend into neighborhoods. As skin color is a highly visible characteristic, offenders are likely to consider the racial composition of neighborhoods. The results were strongest for comparisons with the percentage of African American residents in neighborhoods and offenders’ race, supporting such a claim. While Hispanic and White offenders were less likely to target African American neighborhoods, the opposite was true for African American offenders. The strong effect of race on target selection held, even after controlling for the distance from offenders’ residences to potential targets. Fourth, in addition to offenders’ racial characteristics, the analysis indicated target selection processes varied by age and the presence of co-offenders. The effect of distance was stronger for youth offenders than adult offenders. First of all, for youths, the effect of distance may simply be due to a limited access to motor vehicles. It is important to note, however, that neighborhood characteristics affected adult offenders’ target selection in addition to the distance, although distance was the primary predictor of young offenders’ target selection. That is, adult offenders considered not only convenience and familiarity, as indicated by distance, but also opportunity structures of neighborhoods. This may indicate that offenders’ rationality varies by age, which subsequently affects the cost/benefit calculation of target selection. Variation in the degree of rationality by age may be supported as various neighborhood characteristics affected the target selection of older offenders, while neighborhood characteristics had scarcely any association with younger offenders’ target selection. Furthermore, target selection processes varied by the presence of co-offenders. Such a finding is important as criminal activities, especially among youth, are typically group behaviors (Warr 2000). When co-offenders were present, the key predictor of the offenders’ target selection was the racial homogeneity of neighborhoods. Assuming that offenders are likely to hang out with people of the same race, offenders may be considering their visibility more seriously in

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selecting targets when committing crimes with partners. In fact, the effect of homogeneity was so strong that the variable was the only significant predictor of multi-offenders’ target selection. Previous studies on crime from a spatial perspective can be categorized into two types. The first focused on the level of reported crime as a dependent variable and neighborhood characteristics as independent variables. The limitation of this line of research is that these studies did not take into account where offenders lived and where they came from. The second line of spatial analysis of crime focused on offenders’ mobility by examining their journeys to crime. This line of research, however, typically ignored characteristics of neighborhoods that offenders targeted. Thus, based on previous studies, it was not clear how offenders’ mobility and target selection were affected by neighborhood characteristics and individual characteristics (e.g., race and age). Furthermore, previous studies did not distinguish how characteristics of neighborhoods targeted by offenders were different from other neighborhoods that could have been targeted by offenders. In order to overcome these limitations of the previous studies, this book proposed an alternative point of view by incorporating offenders’ target selection. Based on social disorganization theory, rational choice theory, and routine activities theory, a series of hypotheses was tested. In particular, the current research developed several hypotheses that had not been addressed in previous studies, such as variation in target selection by individual characteristics (e.g., race, age, and the presence of co-offenders). Using arrest data and the conditional logit model as an analytical strategy, the results supported the overall expectations of rational choice theory and routine activities theory. The support for social disorganization theory seemed to be minimal when the viewpoint of offenders was taken into account. While it is expected that the results found in this study are generalizable to other cities, a potential limitation of the study due to its use of arrest data needs to be recognized. For example, the analysis was conducted using offenders who had been caught by the police. Thus, it is not clear if the results of this study also apply to target selection by active offenders who have avoided apprehension. It is possible that active offenders have avoided apprehension because they have been more careful and rational in selecting their targets. If so, the results of this study might have underestimated the effects of

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neighborhood characteristics on burglars’ target selection. Furthermore, by using arrested burglars’ data, the results of this study might have overemphasized the effects of distance on target selection, as offenders who travel a short distance might be more likely to be caught than those who travel a long distance.

CHAPTER 5

Conclusion

WHAT IS SPECIAL ABOUT SPACE IN CRIMINOLOGY? In this book, I conducted a series of studies on crime, incorporating a spatial and temporal perspective. The importance of space in criminology has been recognized for a long time. Starting with Shaw and McKay’s original study of juvenile delinquency in Chicago (1942; 1969), many studies have found that crimes are not randomly distributed over space. Instead, high crime areas tend to be spatially clustered in select neighborhoods within cities. Shaw and McKay also found that high crime neighborhoods maintain their high volume of crimes over time. In order to conduct empirical analyses of crime across space and time, this book used social disorganization theory and routine activities theory as theoretical foundations. Social disorganization theory argues that neighborhood characteristics, rather than types of neighborhood residents, are important for explaining the spatial distribution of crime. A control variant of social disorganization theory hypothesizes that the limited ability of neighborhood residents to realize common goals prohibits them from exercising effective social control to reduce the level of crime. According to the control variant of social disorganization theory, structural characteristics of neighborhoods, such as residential mobility and racial heterogeneity, affect the types and extent of social ties among neighborhood residents, which subsequently influences the effectiveness of informal social control in neighborhoods. A strain variant of social disorganization theory, on the other hand, links structural characteristics of neighborhoods and the level of crime via the frustrated wants of neighborhood residents. Neighborhoods characterized by socio-economic disadvantage provide limited means for residents to achieve positively valued goals. Routine activities theory, on the other hand, postulates that crime occurs when a motivated offender and an attractive target intersect in 145

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time and space in the absence of a capable guardian. While routine activities theory takes the supply of motivated offenders for granted and is not concerned with the source of criminal motivation, the theory provides an explanation for how offenders translate their criminal motivation into action. According to routine activities theory, the spatial concentration of crime can be explained by the distribution of suitable opportunities for crime. For example, certain places tend to lack parental supervision, but are good places for youths to congregate, such as skateboard parks and vacant lots/buildings. Furthermore, crime hot spots may also be generated if certain places draw criminally prone individuals, such as bars and liquor stores. By articulating that suitable opportunities in time and space are necessary for a crime to occur, routine activities theory incorporates space and time in explaining crime. Thus, for substantive reasons, space is an important concept/variable in explaining crime. Additionally, from a methodological perspective, spatial analysis requires particular attention to two types of spatial effects, spatial dependency and spatial heterogeneity. Although ordinary least squares (OLS) regression is a powerful analytical tool for examining multivariate associations between independent variables and a dependent variable, spatial dependency causes problems. As spatial dependency means the value of a variable depends on the value of the same variable in close proximity, observations on spatial units (e.g., neighborhoods) are hardly independent. As spatial dependency often causes the residuals of OLS regression to be correlated (i.e., not independent), the failure to take into account spatial dependency results in biased coefficient estimates and statistical tests, depending on underlying spatial processes (i.e., spatial lag of the dependent variable or spatial correlation of error). Substantively, the spatial clustering of crime (i.e., spatial dependency of crime) can occur as the same offenders commit multiple offenses in their activities space. Furthermore, it can also occur if the underlying social processes generating crime, such as illegal drug markets and gang turf, go beyond the units of analysis, such as the administrative boundaries of census data. The second type of spatial effect, spatial heterogeneity, indicates that structural relationships between variables may change in strength and possibly in direction across space. For example, spatial heterogeneity implies that the relationship between a neighborhood

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characteristic (e.g., racial heterogeneity) and the level of crime varies in strength. Although the relationship may be positive across the study area (i.e., high racial heterogeneity is associated with a high level of crime), the relationship may be stronger in neighborhoods if they are also surrounded by racially heterogeneous neighborhoods. Changing relationships across space can also be interpreted as a conditional effect. For example, the effect of racial heterogeneity on the level of crime may depend on the socio-economic disadvantage of neighborhoods. Furthermore, as the downtown area is the center of business activities and draws both criminally prone and law abiding individuals alike, it may exhibit unique social processes of generating crimes that are different from other areas. It is important to note that neighborhoods exist in continuous space and that dummy coding areas into downtown vs. other areas neglects the continuity of spatial data. Finally, an analysis of space has important practical applications. For example, a lot of law enforcement activities, such as daily patrol routines, are based on police beats divided by areas of a city. Furthermore, the police often conduct crackdowns on select offenses, such as prostitution and drug dealing, based on the concentration of these crimes in select areas of a city. In fact, one study has shown that places are much more predictive of future crimes than the identities of known offenders (Sherman 1995). A small fraction of street addresses/places tend to produce the majority of calls for service in a city (Sherman et al. 1989). Finally, the locations of crime hot spots are also of interest for law abiding persons in reducing their risk of victimization. Based on a recognition of the importance of space in criminology, I conducted three studies to contribute to the body of knowledge in criminology. As neighborhood level social processes have been predominantly examined using cross-sectional data, the first study examined the longitudinal nature of changes in the level of crime and neighborhood characteristics. In order to capture the spatial dynamics of relationships between neighborhood characteristics and the level of crime, the second analysis explicitly considered both spatial dependency and spatial heterogeneity. Finally, the third study examined criminal offenders’ target selection using data on arrested burglars.

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THEORETICAL IMPLICATIONS OF THE LONGITUDINAL ANALYSIS OF CRIME The level of crime in the United States rapidly increased after 1960. The empirical analysis in chapter two found there was considerable variability across neighborhoods in both the initial level of crime and rate of change over time. In particular, the initial level of crime was higher and the rate of increase was faster in socially disorganized neighborhoods. It was also notable that the effects of each characteristic of social disorganization on growth curve parameters varied. When the characteristics of trajectories were divided into three parts (the initial level and rates of linear and non-linear change), racial heterogeneity and residential mobility predicted the initial level of crime. Socio-economic disadvantage, on the other hand, strongly predicted the linear rate of increase for all crime types, while the effects of racial heterogeneity and residential mobility on change were minimal. Furthermore, socio-economic disadvantage was not related to the subsequent non-linear decreases for homicide and robbery, indicating that disadvantaged neighborhoods maintained high levels of crime for a prolonged period of time. When neighborhood characteristics were treated as time-invariant predictors, however, the trajectories of crime were not significantly related to variables from routine activities theory. When the growth curve analysis included neighborhood characteristics of social disorganization and routine activities as timevariant predictors, changes in opportunity structures were associated with changes in the level of crime. For example, increases in the percentage of employed females increased the level of burglary and auto theft at each time point. Furthermore, in support of the hypothesis that an increase in exposure to motivated offenders increases the level of robbery, the percentage of public transportation users was associated with an increase in robbery. It is important to also note that the neighborhood characteristics of social disorganization measured in 1960 were still predictive of the overall trajectories, controlling for changes in neighborhood characteristics over time. In particular, the effects of disadvantage measured in 1960 were consistently associated with faster increases in the levels of all crime types. Higher levels of residential mobility and racial heterogeneity measured in 1960 were also associated with faster increases in robbery and burglary.

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Furthermore, the results of the spatial panel model were largely in accord with social disorganization theory and routine activities theory, even after controlling for the spatial arrangement of census tracts. Overall, the results of the growth curve models that did not control for spatial effects, and the results of spatial panel analysis that did control for them, were relatively the same. Thus, it was concluded that the results of aspatial growth curve models were likely to be valid, even though the models were not designed to treat spatial effects. Overall, these results indicate that neighborhood characteristics are very predictive of longitudinal changes in crime rates. In particular, characteristics of neighborhoods derived from social disorganization theory are important predictors of crime rate trajectories decades later, even though the neighborhood characteristics were measured many years prior (1960). Predictors from routine activities theory, on the other hand, were likely to have time specific effects, meaning the level of crime in neighborhoods was also susceptible to temporally specific opportunities for crime. That is, although overall trajectories seemed to be predicted by characteristics of social disorganization theory, changes in routine activity patterns at each time point affected how neighborhoods deviated from the overall trajectories. Thus, the results of the longitudinal analysis of crime at the neighborhood level indicate that routine activities theory may be a more temporally dynamic theory than social disorganization theory. Social disorganization theory seems to explain general trends in crime over time. In that respect, social disorganization theory may be a more general theoretical explanation of crime, because of its ability to characterize the overall shape of crime trajectories. Routine activities theory, on the other hand, can explain and predict changes in crime rates at a specific time period. The pattern of routine activities may change quickly as a result of changes in the urban infrastructure (e.g., the presence/absence of bars/taverns and changes in bus routes). Changes in routine activities affect opportunity structures for crime, which may increase or decrease the level of crime, depending on how the three elements of the crime triangle (the motivated offender, attractive target, and capable guardian) intersect in time and space. Based on routine activities theory, suitable opportunities for crime are time period specific and are likely to change over time. Neighborhood characteristics of social disorganization, on the other hand, may be less susceptive to change than routine activities.

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For example, the socio-economic disadvantage of neighborhoods may not be easily alleviated. Residents of disadvantaged neighborhoods may leave these neighborhoods as soon as they achieve the financial means to move, while the structural characteristics of neighborhood disadvantage remain unchanged. The racial composition of neighborhoods, on the other hand, is not likely to change dramatically over time. Neighborhoods tend to be racially and ethnically segregated. Housing owners are not likely to move frequently, which increases the stability of the racial composition of neighborhoods. Additionally, new comers to a neighborhood may select their residences based on the racial composition of neighborhoods. Thus, because the characteristics of social disorganization are stable, social disorganization theory may not adequately explain rapid changes in crime over time. When longitudinal changes in crime are examined at the neighborhood level, this study has illustrated the importance of considering both neighborhood social disorganization and criminal opportunities. From the viewpoint of social disorganization theory, the overall trajectory of crime can be predicted. Predictions from routine activities theory are also important to consider, as routine activities theory seems to be a more temporally dynamic theory that can incorporate time specific opportunities for crime. THEORETICAL IMPLICATIONS OF THE ANALYSIS OF SPATIAL DEPENDENCY AND SPATIAL HETEROGENEITY The global regression models that produced the overall association between neighborhood characteristics and the level of crime were mainly in accord with both social disorganization theory and routine activities theory. For example, higher levels of robbery, residential burglary, and auto theft were predicted in neighborhoods characterized by higher racial heterogeneity. Furthermore, socio-economic disadvantage had a positive effect on aggravated assault, robbery, and residential burglary. The effect of residential mobility seemed to be minimal, however, as it was only significant in the expected direction for residential burglary. The results for variables based on routine activities theory indicated the effect of suitable opportunities for crime was crime specific. For example, the percentage of public transportation users

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was significantly related to aggravated assault, robbery, and residential burglary, although the effects were much stronger for the first two crime types. The findings were consistent with theoretical expectations. The number of public transportation users was assumed to represent the frequency of exposure to motivated offenders. Furthermore, the percentage of employed females was positively related to the level of property crimes (residential burglary and auto theft), indicating that a decreased level of guardianship led to an increase in property crimes. Finally, it should be noted that these results were based on regression models that took into account the spatial arrangement of data. Based on the statistical tests, proper model specifications were evaluated in order to incorporate the spatial dependency of observations in the analysis. The results of the spatial regression models indicated that the coefficient estimates of spatial terms (either the spatial lag of crime or spatial error) were highly significant, which supported the importance of considering the spatial structure of data in the analysis. When the analysis took spatial heterogeneity into account by examining spatially varying regression coefficients, the results indicated the association between neighborhood characteristics and the level of crime varied considerably over space. From the standpoint of social disorganization theory, such findings are problematic, as the association between indicators of social disorganization and the level of crime should not differ across space. The results from the analysis of spatial heterogeneity suggest there is something important about space that social disorganization theory does not consider. For example, the spatially varying association between racial heterogeneity and crime is not consistent with the initial expectation of the research. The association between racial heterogeneity and the level of crime was consistently negative in the western region of Philadelphia, while the association was positive in the eastern region. Such results indicate there is something peculiar to these areas where the level of crime is increased because of racial homogeneity. In order to explain such spatial variability in the associations between neighborhood characteristics and the level of crime, explanations might need to go beyond social disorganization theory. This book focused on the structural characteristics of neighborhoods in explaining the level of crime across space (Bursik and Grasmick 1993b; Kornhauser 1978; Sampson and Groves 1989).

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Focusing on the structural characteristics of neighborhoods, however, neglects the role of neighborhood culture in shaping an individual’s behavior (Kubrin and Weitzer 2003a; Kubrin and Weitzer 2003b). While the influence of culture on behavior was originally incorporated in the works of Shaw and McKay (1942; 1969), the subsequent reformulation of the theory focused almost entirely on the structural explanation of crime (Bursik and Grasmick 1993b; Kornhauser 1978; Sampson and Groves 1989). Although racial heterogeneity might hinder the development of social ties among residents, which subsequently reduces informal social control, racial homogeneity might facilitate sharing values, even if the sub-cultural values are criminogenic. The role of neighborhood sub-cultures conducive to criminal acts has been vividly described by various ethnographic studies, including Elijah Anderson’s study in Philadelphia (1994; 1999). Through his field work in disadvantaged neighborhoods, Anderson identified a code of the streets that facilitated violence among inner-city youths. Although adolescents living in disadvantaged neighborhoods were aware of the mainstream value system that promoted conformity to legal norms, the adolescents were also expected to act tough on the streets and to use physical violence in order to achieve respect from their peers. Anderson argued the three main sources of the code of the streets were socio-economic disadvantage, poor parenting, and peer influence. Economic disadvantage of neighborhoods led to few stable jobs that paid living wages. Drug trafficking and use were often rampant in these neighborhoods. The neighborhoods also offered little hope for the future due to limited resources. Although parents did love their children and often endorsed the mainstream value system, a lack of parenting skills prohibited parents from effectively socializing children. A lack of economic resources often resulted in accumulating bills. Frustrated parents who were under much stress were often verbally abusive and even acted aggressively. Children who witnessed violence in family contexts came to learn that violence was a means to solve problems. Furthermore, when children hung out with other children on the streets, experiences of their family situations were often shared, which reinforced the notion that violence was a solution to problems. Children also witnessed older adolescents who fought on the streets and obtained respect from bystanders and peers when problems arose. Children were often initiated into the code of the streets by these

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daily life experiences. Adolescents’ perceptions of the need to solve problems on their own through violence were also accompanied with general distrust of the police. Although the existence of a subcultural value system that promotes aggressive and illegal behavior within neighborhoods is a topic of debate (see, for example, the discussion in Kubrin and Weitzer 2003a), sharing the oppositional culture among adolescents may be more efficiently done in racially homogeneous neighborhoods. That is, the subcultural value system that is conducive to violence may be more likely to be reinforced in racially homogeneous neighborhoods. Although racial homogeneity in and of itself may not be criminogenic, racial homogeneity coupled with the socio-economic disadvantage that has created frustrated wants and oppositional culture may result in an increase in crime. That is, there might be a conditional effect of racial heterogeneity on crime, in that the effect of racial heterogeneity depends on the socio-economic disadvantage of neighborhoods. The results of GWR highlighted something peculiar about neighborhoods that the global regression models failed to capture. The presence of oppositional culture in the western regions of Philadelphia might be one possible explanation for the negative effect of racial heterogeneity in these neighborhoods. Additionally, the effect of language ability on crime varied over space considerably. In particular, language ability and racial heterogeneity had opposite effects on crime over space. Spatial variation in the effects of language ability and racial heterogeneity is understandable, as language ability is an index of homogeneity, while racial heterogeneity is an index of heterogeneity. Although it was expected that language ability would have a positive effect on crime, as the mixture of immigrants in neighborhoods often creates different value systems that hinder the development of social ties among residents, a negative effect of language ability may represent a tipping point in the concentration of immigrants that actually fosters a common value system in neighborhoods. Furthermore, it is important to note that the results of GWR are not necessarily random, statistical artifacts, as the results of spatial variation in coefficient estimates for racial heterogeneity and language ability were relatively consistent across different crime types. From the viewpoint of routine activities theory, on the other hand, spatially varying coefficient estimates of GWR highlight varying

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opportunity structures for crime across space. For example, the effect of socio-economic disadvantage on residential burglary was negative in select neighborhoods in the northwest region of Philadelphia. That is, in these neighborhoods, an increase in residential burglary was predicted by a decrease in socio-economic disadvantage (or equivalently, an increase in socio-economic status). These neighborhoods might represent attractive targets for burglars as the perceived benefits from committing crimes in these neighborhoods were high. Furthermore, the negative effect of racial heterogeneity on residential burglary could also be reasonably interpreted from the perspective of routine activities theory. Racially homogeneous neighborhoods might represent low levels of guardianship against intruders from outside neighborhoods, as homogeneity helps offenders of the same race blend into the neighborhoods. In fact, racial homogeneity could increase the likelihood of being targeted by residential burglars, as the analysis of burglars’ target selection in Chapter 4 found. Overall, the results of GWR indicate that both social disorganization theory and routine activities theory need to be more sophisticated in order to fully understand crimes at the neighborhood level. Quite unexpectedly from the perspective of social disorganization theory, the associations between the structural characteristics of neighborhoods and the level of crime varied considerably across space. Although social disorganization theory assumes simple linear relationships between the structural characteristics of neighborhoods and the level of crime, the association might not be so simple. Furthermore, characteristics of criminal opportunity structures had spatially varying effects on the level of crime. Although, for routine activities theory, the spatially varying results were not as difficult to explain as for social disorganization theory, such results still imply the theory needs to be more specific and sophisticated in order to explain how neighborhood characteristics lead to increases/decreases in the level of crime.

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THEORETICAL IMPLICATIONS FOR CRIMINAL OFFENDERS’ TARGET SELECTION The third study of this book examined offenders’ target selection by merging ecological studies of crime with rational choice theory. The assumption of “reasoning criminals” seemed to be supported in the analysis, as neighborhood characteristics that represented suitable opportunities for burglary were associated with the likelihood of selecting targets in the expected direction. For example, the percentage of employed adult members of households in a neighborhood was positively related to the likelihood of offenders selecting the neighborhood, as houses were likely to be unattended. Structured activities, such as going to work in the early morning and coming back in the late afternoon, imply predictability for offenders to decide when to commit burglaries. As detached housing units provide more entry points and more signs of occupancy/nonoccupancy, increasing the number of detached housing units in a neighborhood increases the likelihood that burglars select the neighborhood. As the effects of residential mobility and racial heterogeneity seemed to be limited, on the other hand, predictions by social disorganization theory might not be supported when examining offenders’ target selection. Instead, opportunity theories of crime were in accord with the empirical findings. To a large extent, offenders’ target selection was predicted not only by distance from their residences, but also by housing characteristics. Another important finding of the quantitative analysis of target selection was that offenders’ rational choices were affected by their individual characteristics, such as race, age, and the presence of cooffenders. As younger offenders were likely to have secondary motives for crimes, such as peer pressure and thrill seeking, their target selection seemed to be less rational than older offenders. Younger offenders also had (presumably) limited access to cars, which restricted movements for scouting targets. Furthermore, the limited rationality of younger offenders might also be due to their mindset (e.g., more present-oriented and less concerned about possible consequences) and lack of experience. It was also found that burglars were conscious of their visibility in scouting targets, as their target selection was highly affected by their skin color. In particular, both White and Hispanic burglars avoided neighborhoods composed of predominantly African

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American residents, while African American burglars preferred such neighborhoods. Hispanic offenders seemed to prefer neighborhoods characterized by high percentages of Hispanic residents, while White offenders seemed to be the most mobile, as their target selections were not affected by the composition of White nor Hispanic residents. Finally, the results of the target selection analysis indicated that offenders’ consciousness of visibility was especially pronounced when a co-offender was present. While these findings, which highlight the importance of criminal opportunities in explaining offenders’ target selection, provide support for rational choice theory and routine activities theory, they point to a limitation of social disorganization theory. Social disorganization theory tends to focus on the residents living in neighborhoods to explain the level of crime. This tendency is particularly evident in the strain variant of social disorganization theory that links neighborhood social disorganization to the level of crime through the frustrated wants of neighborhood residents. Economic deprivation not only creates criminal motivation, but also limits legitimate means to achieve positively valued goals. Although it is important to consider the source of criminal motivation, criminal motivation itself is not a sufficient condition for explaining criminal incidents. Suitable opportunities are necessary for a crime to occur. When considering criminal opportunities, it is important to take into account the mobility of criminals, as rational offenders are expected to commit crimes in neighborhoods that require less effort to accomplish their illegitimate goals. Considering how the characteristics of a neighborhood affect people living in that neighborhood, as social disorganization theory tends to focus on, is not enough to explain offenders’ target selection. Disadvantaged neighborhoods may create and fuel the frustrated wants of residents. This does not mean, however, that the strained residents commit crime in their own neighborhood. The socio-economic disadvantage of neighborhoods cannot necessarily explain high crime rates if residents commit crimes in neighborhoods other than their own. If a suitable target is absent in their own neighborhood, motivated offenders are likely to travel to other neighborhoods in order to act out their illicit motivation. This may be particularly true if affluent neighborhoods are adjacent to disadvantaged neighborhoods where the supply of motivated offenders is abundant. While social disorganization theory incorporates the role of offenders in their

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theoretical framework via the source of criminal motivation, its explanation is limited because the presence of criminal motivation cannot necessarily explain where offenders commit their crimes. Suitable opportunities for crime, as postulated by routine activities theory, are important in predicting where offenders commit their crimes. POLICY IMPLICATIONS Several practical implications can be drawn from the series of studies conducted in this book. First, based on the findings of the longitudinal analysis, it is concluded that social disorganization theory predicts the overall trajectory of crime at the neighborhood level for a long period of time, while opportunity structures have temporally specific effects on the level of crime at each time period. These findings imply two different approaches for crime prevention strategies. First, in order to address problems caused by the disorganization of neighborhoods, elected officials need to establish a committed long term policy to alleviate neighborhood disorganization conducive to crime. In particular, the effect of socio-economic disadvantage on increases in crime is tremendous, as the effects were significant for all crime types, while racial heterogeneity and residential instability were only related to the level of crime in 1960 and not to changes over time. Thus, it is particularly important to alleviate economic disadvantage in order to avoid its long term consequences. Tonry and Farrington (1995) argue that politicians tend to support policies that directly tackle crimes, due to their concerns about elections in the near future, while ignoring policies that require a long time before their effects appear. For example, in order to obtain the public’s support, these politicians might back an increase in the number of police officers, which would increase the number of criminals taken off the streets. The general public’s feelings of safety might also result from strengthened law enforcement. At the same time, politicians might think indirect crime prevention strategies that would only show results in the long-run would be less appealing. It is important to note that the incapacitation of problematic individuals by sending them to penal institutions would only temporally divert the problems in disorganized neighborhoods. If neighborhoods remain socially disorganized, these incapacitated criminals would be likely to return to

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the same neighborhoods they grew up in once they are released from prison. For example, a recent multilevel analysis of recidivism indicated that ex-criminals released to disadvantaged neighborhoods were significantly more likely to commit crimes again than those released to neighborhoods with more resources (Kubrin and Stewart 2006). Such research findings, together with the longitudinal analysis presented in this book, indicate that it is very important to consider the long term consequences of neighborhood disadvantage in addressing crime problems. In addition to the first approach to crime prevention, which is based on the long term effects of social disorganization, it is also important to consider a second approach to crime prevention that considers temporally specific criminal opportunities. As the levels of crime were sensitive to opportunity structures specific to each time period, especially property crimes, approaches such as situational crime prevention might be effective in addressing crime problems particular to each time point (Clarke 1995; Clarke and Eck 2005; Clarke 1980; Felson 2006; Felson and Clarke 1998; Lab 2004). From the perspective of criminal opportunity theories, criminal opportunities are highly specific to time and space. With careful analysis of problems, however, reductions in crime can be achieved through small changes in situational opportunities (Clarke and Eck 2005; Goldstein 1990). For example, the presence of convenience stores with payphones can give apparently legitimate reasons for drug dealers to stay around the stores to conduct their illegal business, without raising much suspicion (Clarke and Eck 2005). Small changes, such as taking out the payphones, installing rotary dials to prevent calls to pagers, blocking incoming calls, and limiting calls during night hours, can result in large reductions in crime problems at specific places. Recent studies have also shown that place-focused crime prevention strategies often result in reducing crimes in surrounding areas and crimes other than the ones originally targeted by the strategies (Clarke and Weisburd 1994; Lab 2004; Weisburd et al. 2006). The result of the current research also indicated the pattern of association between neighborhood characteristics and crime was crimespecific, which highlighted a suitable opportunity for a crime did not necessarily indicate a suitable opportunity for another crime. For example, the longitudinal analysis indicated that an increased proportion of public transportation users was associated with an

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increased level of robbery, indicating an increased frequency for motivated offenders and suitable targets to intersect in time and space was an important condition for robbery to occur. Installing brighter street lights and emergency call buttons at bus stops may deter criminals from acting out their illicit motivation in public places. Furthermore, increases in burglary and auto theft were predicted in neighborhoods that experienced increases in female employment and residential mobility. While one cannot easily change the female employment rate or residential mobility, the level of guardianship can be strengthened by target hardening at housing units and by decreasing anonymity among residents. While changing opportunity structures for crime can have a direct impact on crime reduction, the reduction effect can also occur indirectly by prohibiting offenders from realizing their criminal motivations. Although opportunity theories of crime are often criticized for their lack of attention to the source of criminal motivation, as the theories take criminal motivation for granted, several criminologists have argued that the presence of suitable opportunities can fuel criminal motivation (Steffensmeier and Ulmer 2005). That is, coming across a suitable opportunity for crime can make individuals feel they can accomplish a crime without much effort and risk. In Steffenmeier and Ulmer’s words (2005: 6), “being able makes one more willing.” Furthermore, the accomplishment of one crime is likely to lead to further illegal activities, as the behaviors of criminals are likely to be reinforced due to the achievement of positively valued goals (e.g., money and excitement). Reducing criminal opportunities can prevent offenders from realizing their underlying illicit motivation. Thus, targeting opportunities for crime can be very effective in lowering crime and have a much broader impact than the original scope of crime prevention strategies. Geographically weighted regression (GWR) models can also be employed by police departments in order to establish place-focused crime prevention strategies. As represented by the increasing numbers of Weed and Seed projects and problem oriented policing (Clarke and Eck 2005; Goldstein 1990; Sherman et al. 2006), crime prevention activities at the local police department level have often targeted specific neighborhoods. Effectively achieving reductions in crime, however, requires careful planning with the identification of specific problems. As neighborhoods vary considerably in their characteristics,

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different mechanisms might be in operation in increasing the level of crime in each neighborhood. For example, diminished informal social control caused by racial heterogeneity might be responsible for increasing crime and disorder in one neighborhood, while the presence of oppositional culture given rise to by racial homogeneity and economic disadvantage might be responsible for increasing crimes in other neighborhoods. Racial homogeneity might also reduce the level of guardianship against property crimes, as it helps perpetrators blend into neighborhoods and select targets. Thus, although predictions from social disorganization theory and routine activities theory might be unidirectional, it is important to recognize considerable local variability. It is likely that the effects of a neighborhood characteristic on crime might be conditioned by other neighborhood characteristics. Geographically weighted regression (GWR) models can be easily employed by crime analysts at a local police department in order to uncover complex local relationships between neighborhood characteristics and the level of crime. The results would provide cues as to the mechanisms linking the structural characteristics of neighborhoods and crime at the neighborhood level, which subsequently would lead to planning effective crime prevention strategies. Finally, the analysis of criminal offenders’ target selection has several policy implications. By analyzing known offenders’ travel patterns, the results can be applied to support investigation. For example, geographic profiling currently employs built-in algorithms to calculate the likely locations of offenders’ residences based on a series of crimes (Canter et al. 2000; Levine 2004; Rossmo 1999). As the pattern of journeys to crime is likely to be different depending on cities and towns, the algorithms should be fine-tuned based on the journeys to crime patterns of known offenders in the past. As criminal offenders’ target selection is not random, but predictable to some extent, the results of the conditional logit model might be used to calculate a probability surface and map of criminal offenders targeting neighborhoods. Furthermore, the results of the analysis of target selection also have implications for crime prevention strategies. As the results indicated, offenders are mobile agents who travel from one neighborhood to another in search of suitable opportunities for crime, so neighborhood characteristics that have been found significant in this

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study need to be considered for developing effective crime prevention strategies targeting outsiders. In particular, the results indicated housing characteristics, such as employed household members, detached housing units, and renter occupied housing units, strongly predicted the likelihood of being targeted by burglars. Thus, strengthening guardianship with additional security measures is likely to be needed in detached housing units composed of employed family members. Various methods of target hardening that increase the effort needed to accomplish crimes are available, such as installing window bars, strengthening window glass, and removing bushes around buildings to increase visibility from the street. The guardianship of neighborhoods can also be strengthened collectively by organizing block watches. While crime prevention strategies derived from social disorganization theory (especially the strain variant of social disorganization theory) often target adolescents living in neighborhoods, the results of this analysis indicated that suitable opportunities for crime can be important in predicting crimes, even after taking into account distance from offenders’ residences. LIMITATIONS OF THE CURRENT RESEARCH AND DIRECTIONS FOR FUTURE RESEARCH While the starting point of this book was to overcome limitations of previous studies of crime at the neighborhood level, the research conducted in this book was not free from limitations either. The crucial limitation of the current research was its lack of better measures of social disorganization and criminal opportunities. Instead, this book focused on structural characteristics of neighborhoods in order to evaluate social disorganization theory and routine activities theory. While it was true that structural characteristics were important in predicting crime, recent extensions of social disorganization theory have involved the identification of linkages between structural characteristics and the levels of crime in neighborhoods. When social disorganization theory was revitalized in the 1980s and the early 90s by a series of influential studies (Bursik 1988; Bursik and Grasmick 1993b; Kornhauser 1978; Sampson and Groves 1989), the argument was made that structural characteristics affected the extent and strength of social ties and the ability to realize common goals among

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neighborhood residents, which in turn affected the levels of crime in neighborhoods. Some criminologists investigated different types of social ties, for example internal ties among neighborhood residents and external ties to policy makers (Bursik and Grasmick 1993b). The importance of institutions in neighborhoods as anchoring points for social ties, such as schools, churches, and community centers, has also been noted (Triplett et al. 2003). Others have argued that the presence of social ties in and of themselves do not lead to effective social control. Instead, informal social control needs to be conceptualized as a purposive action (Sampson 2004; Sampson et al. 1999; Sampson et al. 2002; Sampson et al. 1997). That is, although social ties may be a necessary factor in creating social control, they are not a sufficient one. Neighborhood residents need to activate social ties and mobilize available resources in order to address crime and disorder in neighborhoods (Kubrin and Weitzer 2003a). Sampson and others argue that collective efficacy, defined as neighborhood residents’ willingness to intervene when problems arise and the presence of mutual trust among residents, is the key aspect for establishing and exercising informal social control. These measures of informal social control and collective efficacy cannot be adequately measured with census data. Additionally, surveys would also provide better measurements of suitable opportunities for crime and appropriate tests of routine activities theory. For example, the target selection analysis included housing values as a proxy of attractiveness. It was hypothesized that high housing values increased the likelihood of being targeted by burglars because of perceived benefits (although the result was statistically insignificant). It is important to note, however, that expensive housing was likely to be equipped with better security measures (i.e., strengthened guardianship). Thus, based upon the measures of the crime triangle from routine activities theory (i.e., motivated offender, attractive target, and guardianship), the results would not be specific enough to distinguish mechanisms of how the level of crime was heightened/lowered. In sum, the predictors included in the analysis in this book are only proxies for the mechanisms of social disorganization theory and routine activities theory. While neighborhood characteristics measured by the census are still strong predictors of neighborhood crime rates, the exact mechanisms by which the structural characteristics of neighborhoods

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create crime conducive environments is not tested in this book. Thus, future research needs to incorporate more appropriate measures of social disorganization and criminal opportunities based on survey data, in order to more appropriately test social disorganization theory and routine activities theory. Additionally, future research may also need to determine the appropriate unit of analysis at which social disorganization and routine activities operate. For example, this book used census tracts for the longitudinal analysis and block groups for the analyses of spatial heterogeneity and target selection. As social disorganization theory postulates contextual effects of neighborhood characteristics, census block groups are used as a proxy for neighborhoods. It is important to note, however, that people’s activity space is not necessarily defined by census boundaries. Furthermore, routine activities theory makes predictions and hypotheses at the place and street level. For example, the presence of bars is related to an increase in crime because criminally prone individuals are likely to be drawn to bars and the consumption of alcohol increases the likelihood of violent confrontations. The presence of convenience stores, bus stops, and skateboard parks also affect the behavioral patterns and activities of individuals, including motivated offenders. Future research may utilize multilevel modeling that incorporates both neighborhood characteristics and place/street characteristics to assess how individual behaviors and victimization risks are conditioned by neighborhood characteristics. Finally, future research may also investigate how the spatial arrangement of independent variables affects the level of crime in neighborhoods and criminal offenders’ target selection. Although this book analyzed the spatial arrangement of dependent variables (i.e. crime) through spatially lagged dependent variables that represented a crime spillover effect, the level of crime in neighborhoods and offenders’ target selection may also be conditioned by neighborhood characteristics of adjacent neighborhoods. For example, if a neighborhood is low in guardianship and adjacent to disadvantaged neighborhoods, this neighborhood is likely to be targeted by motivated offenders coming from disadvantaged neighborhoods. If a disadvantaged neighborhood is surrounded by highly guarded neighborhoods, on the other hand, motivated offenders have no place to commit their crimes other than in their own neighborhoods.

164

Neighborhood Structures and Crime: A Spatial Analysis

Characteristics of surrounding neighborhoods, in addition to the level of crime, need to be examined in future research.

APPENDIX A

Maps of Seattle Data

Maps of descriptive statistics of crime and socio-demographic data in Seattle between 1960 and 2000 are presented in Appendices A.1 through A.12. Maps of predicted values of growth curve parameters are presented in Appendices A.13 through A. 16. As there are three parameters in the quadratic growth curve model, three maps are presented for each crime type. The first panel represents the predicted value of the intercept (i.e., the initial level of crime). The second panel represents the predicted value of the linear term, while the third panel indicates the predicted value of the quadratic term.

Figure A.1. Homicide Rate per 1,000 people

165

166

Appendix A

Figure A.2 Robbery Rate per 1,000 people

Figure A.3 Burglary Rate per 1,000 people

Appendix A

167

Figure A.4 Auto Theft Rate per 1,000 people

Figure A.5 The Proportion of the Foreign Born Population

168

Appendix A

Figure A.6 The Proportion of Children Living with Both Parents

Figure A.7 The Proportion of Public Transportation Users

Appendix A

Figure A.8 The Proportion of Employed Females

Figure A.9 The Proportion of Male Youth (Ages 15-24)

169

170

Appendix A

Figure A.10 Residential Mobility

Figure A.11 Racial Heterogeneity

Appendix A

171

Figure A.12 Socio-economic Disadvantage

Figure A. 13 The Parameter Estimates of Homicide Trajectory

172

Appendix A

Figure A. 14 The Parameter Estimates of Robbery Trajectory

Figure A. 15 The Parameter Estimates of Burglary Trajectory

Appendix A

Figure A. 16 The Parameter Estimates of Auto Theft Trajectory

173

APPENDIX B

Maps of Philadelphia Data

The spatial distribution of crime and socio-demographic variables in Philadelphia data are presented in Appendices B.1 through B.3.

Figure B.1The Spatial Distribution of Crimes in Philadelphia

175

176

Appendix B

Figure B.2 The Spatial Distribution of Demographic Variables in Philadelphia (1)

Appendix B

177

Figure B.3 The Spatial Distribution of Demographic Variables in Philadelphia (2)

APPENDIX C

Maps of Glendale Data

Figures C.1 through C2 illustrate the spatial distribution of sociodemographic characteristics in Glendale, AZ.

Figure C.1 The Spatial Distribution of Socio-Demographic Characteristics in Glendale, AZ (1)

179

180

Appendix C

Figure C.2 The Spatial Distribution of Socio-Demographic Characteristics in Glendale, AZ (2)

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Index

cross-sectional analysis, 21, 50, 65 cross-sectional data, 2, 17, 19, 65, 147 deceleration, 21, 22, 30, 35, 39 degrees of freedom, 50, 51, 54, 56 demographic composition, 15, 17, 25, 86 difference score, 20 diffusion of benefit, 12, 73 distance decay function, 114, 118, 122 ecological fallacy, 70 fixed effect model, 50, 51, 52, 54, 55, 56, 57, 59 Fotheringham, A. Stewart, 3, 13, 71, 76, 81, 84, 94, 97, 99, 183, 187 F-test, 56 geographic profiling, 118, 160 geographically weighted regression, 71, 72, 76, 77, 79, 81, 84, 95, 100, 107, 110, 111 global statistic, 82, 94 growth curve model, 21, 23, 28, 30, 31, 37, 39, 44, 45, 48, 49, 50, 65, 66, 149, 165 guardianship, 1, 2, 9, 10, 11, 13, 16, 18, 23, 25, 48, 62, 63, 78, 79, 86, 108, 109, 117,

acceleration, 30, 33, 35, 39, 65 Anselin, Luc, 2, 3, 49, 53, 55, 56, 57, 59, 70, 72, 73, 74, 75, 80, 90, 114, 116, 181, 182, 189, 190 awareness space, 118, 139 Bayesian Information Criterion, 31 Breusch-Pagan test, 56 Bursik and Grasmick, 2, 7, 8, 13, 15, 18, 19, 20, 21, 28, 30, 49, 65, 74, 115, 123, 151, 161 capable guardian, 9, 19, 78, 116, 117, 146, 149 census, 24, 25, 50, 57, 80, 84, 85, 110, 116, 146, 149, 162, 163 Cohen and Felson, 9, 10, 12, 16, 18, 19, 113, 114, 116, 122, 124 collective efficacy, 8, 162 conditional growth curve model, 23 conditional logit model, 115, 129, 130, 131, 132, 133, 136, 138, 142, 160 continuous spatial process, 76, 81 crime prevention, 4, 12, 73, 110, 117, 157, 158, 159, 160 197

198 119, 123, 124, 132, 136, 140, 151, 154, 159, 160, 161, 162, 163 GWR. see geographically weighted regression Hausman test, 57, 59 incidental parameter problem, 51, 55 independent observations, 12, 70 independently distributed residual, 26, 70, 80, 107 initial level of crime, 17, 22, 28, 30, 35, 39, 44, 65, 66, 148, 165 Kornhauser, 6, 7, 19, 77, 115, 123, 151, 161, 188 Lagrange Multiplier test, 56, 80, 81 least squares dummy variable regression, 51 limited rationality, 119, 122, 124, 155 Local statistics, 82 longitudinal analysis, 3, 14, 16, 20, 50, 58, 65, 66, 67, 149, 157, 158, 163 Miethe, Terance D., 2, 19, 24, 64, 69, 75, 113, 116, 117, 124, 190, 191, 193 Monte Carlo simulation, 56, 82, 94 Moran’s I, 26, 80 motivated offender, 2, 9, 10, 11, 16, 18, 19, 23, 24, 25, 48, 62, 63, 64, 70, 74, 78, 79, 100, 113, 116, 117, 119, 121, 123, 124, 145, 148, 149, 151, 156, 159, 162, 163

Index multilevel model, 28, 71, 114, 163 non-linear, 17, 21, 22, 31, 33, 35, 37, 38, 42, 43, 44, 45, 65, 148 OLS, 3, 4, 12, 26, 27, 31, 49, 51, 56, 70, 72, 79, 80, 81, 87, 88, 89, 90, 107, 146 omitted variables bias, 50 ordinary least squares, see OLS principal component analysis, 24, 85 quadratic trajectory, 30 racial heterogeneity, 6, 19, 24, 25, 43, 45, 48, 49, 62, 63, 66, 67, 77, 86, 91, 94, 95, 100, 107, 108, 109, 111, 115, 123, 126, 133, 140, 145, 147, 148, 150, 151, 152, 153, 154, 155, 157, 160 racial heterogeneity index, 25 random effect, 22, 52, 53, 54, 55, 56, 57, 58, 59, 62, 71 random effect model, 52, 54, 55, 56, 57, 59 rates of change, 17, 20, 22, 28, 30 rational choice, 10, 115, 119, 121, 130, 132, 135, 138, 142, 155, 156 rationality, 114, 119, 120, 121, 122, 124, 141 residential instability, see residential mobility residential mobility, 6, 8, 19, 20, 23, 24, 39, 42, 43, 44, 48, 49, 62, 63, 64, 66, 67, 74, 77, 85, 91, 95, 107, 115, 123, 126, 129, 145, 148, 150, 155, 157, 159

Index residual change score, 19, 20, 50, 65 routine activities theory, 4, 5, 9, 10, 11, 12, 17, 19, 22, 23, 24, 25, 48, 49, 62, 63, 64, 66, 67, 71, 72, 75, 76, 78, 79, 84, 85, 86, 87, 90, 95, 107, 109, 110, 114, 115, 116, 117, 119, 120, 121, 122, 123, 126, 130, 132, 135, 138, 142, 145, 146, 148, 149, 150, 153, 154, 156, 160, 161, 162, 163 Sampson and Groves, 2, 6, 7, 19, 25, 77, 86, 113, 115, 123, 151, 161, 189, 195 Shaw and McKay, 1, 5, 6, 7, 12, 13, 25, 69, 78, 108, 109, 113, 115, 116, 145, 152 social control, 6, 7, 8, 9, 10, 19, 20, 23, 48, 63, 73, 74, 77, 108, 109, 115, 123, 129, 145, 152, 160, 162 social disorganization theory, 3, 4, 5, 6, 7, 8, 9, 12, 17, 19, 20, 22, 24, 31, 42, 45, 48, 49, 62, 63, 64, 66, 67, 70, 71, 72, 75, 76, 77, 78, 81, 84, 85, 86, 87, 90, 91, 94, 95, 100, 107, 108, 109, 110, 115, 116, 117, 120, 121, 126, 130, 138, 141, 142, 145, 149, 150, 151, 154, 155, 156, 157, 160, 161, 162, 163 socio-economic disadvantage, 8, 13, 17, 19, 23, 24, 42, 43, 44, 45, 49, 62, 63, 66, 67, 77, 85, 91, 95, 107, 109, 115, 145, 147, 148, 150, 152, 153, 154, 156, 157 spatial autocorrelation, 26, 55, 80, 81

199 spatial clustering, 55, 70, 72, 73, 146 spatial dependency, 3, 12, 14, 49, 70, 71, 72, 73, 74, 76, 82, 107, 108, 146, 147, 151 spatial econometrics, 4, 12, 59, 74, 76, 116 spatial effect, 3, 12, 14, 26, 49, 53, 54, 55, 57, 58, 62, 70, 71, 72, 74, 91, 107, 146, 149 spatial error model, 54, 55, 57, 59, 74, 80, 81, 90 spatial externalities, 72 spatial heterogeneity, 3, 12, 13, 14, 55, 70, 71, 72, 74, 75, 76, 81, 107, 108, 110, 146, 147, 151, 163 spatial interaction, 53, 72 spatial lag, 53, 54, 55, 57, 59, 74, 80, 81, 90, 109, 146, 151 spatial lag model, 53, 54, 74, 80, 90 spatial multiplier, 53 spatial non-stationarity, 72, 78 spatial panel model, 27, 50, 53, 54, 55, 56, 58, 59, 149 spatial regression model, 4, 70, 72, 74, 76, 79, 80, 90, 107, 108, 114, 151 spatial stationarity, 72, 77, 94 spatial weights matrix, 26, 50, 53, 54, 80 spatially varying associations, 72, 76, 79, 82, 95, 107 strain, 6, 7, 9, 59, 63, 75, 95, 119, 123, 145, 156, 161, 192 suitable target, 9, 11, 79, 116, 117, 124, 140, 156, 159 systemic model, 8

200 target selection, 5, 114, 115, 118, 121, 124, 125, 126, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 147, 154, 155, 156, 160, 162, 163 Tobler’s first law of geography, 73 topologically invariant, 4, 80 trajectories, 17, 20, 21, 22, 31, 33, 35, 37, 45, 49, 58, 65, 66, 67, 148, 149 trend, 11, 16, 17, 18, 21, 22, 28, 30, 31, 33, 35, 65, 149 unconditional growth curve model, 22 Uniform Crime Reports, 2, 11, 15, 24, 58 unobserved heterogeneity, 50, 52, 53, 54, 58, 64 variability, 8, 17, 20, 22, 28, 30, 35, 38, 39, 44, 45, 49, 50, 59, 65, 66, 67, 82, 94, 129, 148, 151, 160

Index