Understanding the Effect of "random Repeats": Statistical Review of Repeat Victimization Studies

UNDERSTANDING THE EFFECT OF "RANDOM REPEATS": STATISTICAL REVIEW OF REPEAT VICTIMIZATION STUDIES

Abstract The notion of repeat victimization has been a growing interest of crime prevention studies and portrayed as a practical solution to prevent crimes more effectively and efficiently. One stochastic characteristic of repeat victimization, however, has not been fully considered in understanding and interpreting the distribution of victimizations: random repeats which indicate that victimizations are concentrated on a small portion of population even when there is no risk heterogeneity and event dependence. This lack of consideration results in misleading interpretation of victimization data and provides erroneous arguments related to the rate of repeat victimization, time windows effect, and time-course of repeat victimization. The present paper investigates the statistical characteristics of random repeats and reviews the arguments of previous studies on repeat victimization. The policy implication for allocating crime prevention resource and the application toward crime place (hot spot) studies are also discussed.

Keywords Repeat victimization, Rate of repeat victimization, Time windows effect, Time-course of repeat victimization, Crime concentration, Random repeats

1. INTRODUCTION

Victimizations do not happen randomly and tend to be concentrated on a relatively small portion of the population (Farrell et al., 2005; Farrell & Pease, 1993; Gottfredson, 1984; Tilley & Laycock, 2002); therefore, prior victimization information is a good predictor of future victimization (Lauritsen & Davis-Quinet, 1995; Osborn et al., 1996; Osborn & Tseloni, 1998; Pease 1998). This notion of repeat victimization has been receiving more attention in crime prevention studies since the 1980s (Deams, 2005; Farrell, 2003) and some scholars argued that one of the most promising areas of research in criminology is the understanding and reducing of repeat victimization (Davis et al 2006). The growth of academic interest in this area has produced a large amount of policy-driven literature about repeat victimization (Deams, 2005; Farrell, 2003; Farrell, 2005; Farrell & Pease, 2001; Pease, 1998; Tilley & Laycock, 2002; Trickett et al., 1992). Repeat victimization has been portrayed as a practical solution to prevent crimes more effectively and efficiently (see Farrell, 2005; Pease, 1998). Especially in England and Wales, the phenomenon of repeat victimization has influenced criminal justice policies and become the backbone of their crime prevention practices (Farrell & Pease, 2001).

Despite significant progress in the study of repeat victimization, one stochastic characteristic of repeat victimization has not been fully considered. Victimization can be considered as the stochastic process of sampling with replacement (Winkelmann, 2008). When one individual is selected for victimization, he is not excluded from the victimization pool and has the same probability to be selected for the next victimization. Therefore, even when victimizations happen randomly and independently, each person has the same probability to be chosen for every victimization and some people can be selected more than once by chance. For this reason, victimization incidents are to be concentrated on a small portion of the population without any other non-random factor.

This stochastic characteristic of repeat victimization does not negate the existence of non-random factors such as risk heterogeneity and event dependence in the population. Considering the real context of victimization, it is more realistic to assume that individuals have an uneven risk of victimization (flags) and event dependence where the previous victimization boosts the risk of future victimization (Gottfredson, 1984; Hindelang et al., 1978; Ousey et al., 2008; Sparks et al, 1977; Tseloni & Pease, 2003; 2004). The stochastic characteristic of random concentration, however, implies that the concentration of victimizations is caused by three intertwined reasons: (1) random concentration, (2) risk heterogeneity, and (3) event dependence. While studies on repeat victimization have focused on the latter two reasons and achieved meaningful progress in clarifying their effects (i.e. Ousey et al. 2008; Tseloni and Pease 2003; 2004), little attention was given to the effect of random concentration of victimizations.

This omission has caused misleading interpretations of victimization data and also provided erroneous arguments on related issues such as the rate of repeat victimization, time windows effect, and time-course of repeat victimization. The consideration of random concentration is also important for increasing the effectiveness of crime prevention efforts. The allocation of crime prevention resources on repeat victims without considering random concentration may result in limited effectiveness and efficiency of crime prevention efforts. The present study designates this random concentration of victimizations as random repeats and tries to fill this omission by; (1) investigating the statistical characteristics of random repeats, (2) reviewing the related previous arguments, and (3) discussing the policy implications for allocating crime prevention resources and the suggestions for crime place studies.

2. RANDOM REPEATS

Random repeats are the natural results from the stochastic process of victimization. While there have been few studies on the effect of random repeats, the count statistical models which have been employed for analyzing repeat victimization - such as Poisson and Negative binomial regressions - are mathematically designed to consider the effects of random repeats (Winkelmann, 2008). Studies on repeat victimization reveal the existence of non-random repeat victimizations by testing whether or not the distribution of victimization fit the Poisson distribution, (Farrell & Pease, 1993; Hindelang et al., 1978; Nelson, 1980; Short et al, 2009; Sparks et al., 1977).

If victimization happens randomly and independently, the frequencies of incidents are distributed following the Poisson distribution (Hindelang et al., 1978; Nelson, 1980; Short et al, 2009; Sparks et al., 1977; Winkelmann, 2008). A Poisson process describes how events, like victimization, are generated under the assumption of random and independent occurrence at rate . The Poisson distribution is a special case of stochastic processes with the following probability function:

where (1)

Here, indicates the rate of incidence occurrence while shows the number of incidents. The mean and variance of the Poisson distribution are the same and given by (2)

To clarify