Exploring Theories of Victimization Using a Mathematical Model of Burglary

• Author: Shane D. Johnson,Ashley B. Pitcher
• Published date: 01 February 2011
• Date: 01 February 2011
• DOI: http://doi.org/10.1177/0022427810384139
• Subject Matter: Articles

Article

Exploring Theories

of Victimization

Using a

Mathematical

Model of Burglary

Ashley B. Pitcher

1

and Shane D. Johnson

2

Abstract

Research concerned with burglary indicates that it is clustered not only at

places but also in time. Some homes are victimized repeatedly, and the risk to

neighbors of victimized homes is temporarily elevated. The latter type of

burglary is referred to as a near repeat. Two theories have been proposed

to explain observed patterns. The boost hypothesis states that risk is

elevated following an event reflecting offender foraging activity. The flag

hypothesis, on the other hand, suggests that time-stable variation in risk

provides an explanation where data for populations with different risks are

analyzed in the aggregate. To examine this, the authors specify a series of

discrete mathematical models of urban residential burglary and examine

their outcomes using stochastic agent-based simulations. Results suggest that

variation in risk alone cannot explain patterns of exact and near repeats, but

1

Centre d’Analyse et de Mathe

´matique Sociales, Ecole des Hautes Etudes en Sciences

Sociales, Paris, France

2

UCL Jill Dando Institute of Crime Science, University College London, London, United

Kingdom

Corresponding Author:

Shane D. Johnson, UCL Jill Dando Institute of Crime Science, University College London,

Second Floor Brook House, 2–16 Torrington Place, London, WC1E 7HN, United Kingdom

Email: shane.johnson@ucl.ac.uk

Journal of Research in Crime and

Delinquency

48(1) 83-109

ªThe Author(s) 2011

Reprints and permission:

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DOI: 10.1177/0022427810384139

http://jrcd.sagepub.com

that models which also include a boost component show good qualitative

agreement with published findings.

Keywords

burglary, mathematical model, repeat victimization, boost hypothesis, risk

heterogeneity, agent-based simulation

Introduction

Criminologyis a multidisciplinary subject but the application of mathematics

has been fairlylimited in the study of crime patterns(for recent exceptions,see

Short et al. 2008; Short et al. 2010; and, for a special journal issue devoted

to this, see the European Journal of Applied Mathematics,Volume 21, Issues

4-5). The advantages of using a mathematical approach are numerous and

range from the conceptual clarity that arises from using formal expressions

to describe systems, to the abilityto model nonlinear complex systems, to the

possibility of developing control strategies if systems are adequately speci-

fied. In this article, we use mathematical models to examine theories con-

cerned with space–time patterns of victimization at the level of place and

consider how concepts commonly used in mathematics may be helpful in

formalizing and exploring theories of this kind.

Whatever the method, the unit of analysis selected will directly affect the

reliability of inferences drawn. For example, where research concerns

theories of crime concentration, the analysis of data aggregated to large

geographical units will often be inappropriate and invite errors of inference.

A common example is the ecological fallacy (Robinson 1950) of assuming

that patterns observed in the aggregate across an area will apply to all places

within it. Rarely will this be the case. For example, Bowers, Johnson, and

Pease (2005) demonstrate that for domestic burglary irrespective of what

type of area they live in, the type of house (e.g., flats, row homes, and so

on) a resident lives in significantly affects their risk of victimization (see

also, Budd 1999). Likewise, a series of studies demonstrate that regardless

of area-level risks, how connected a block face is to the surrounding street

network significantly influences the risk of burglary to homes located on it

(e.g., Beavon, Brantingham, and Brantingham 1994; Bevis and Nutter

1977; Hillier 2004; Johnson and Bowers 2010). Stated more explicitly, the

importance of place in the study of crime—where places may include mean-

ingful units of analysis such as block faces or individual homes—has been

acknowledged for some time (e.g., Eck and Weisburd 1995).

84 Journal of Research in Crime and Delinquency 48(1)