Heterogeneity in the Frequency Distribution of Crime Victimization

TLDR: In this article, Latent class analysis is used to explore the probable, latent distributions of individual property crime and personal crime victimization matrices that express the frequency and type of victimization that are self-reported by respondents over the survey recall period.

Abstract: Tests the idea that the frequency distribution typically observed in crosssectional crime victimization data sampled from surveys of general populations is a heterogeneously distributed result of the mixing of two latent processes associated, respectively, with each of the tails of the distribution. Datasets are assembled from a number of samples taken from the British Crime Survey and the Scottish Crime Victimization Survey. Latent class analysis is used to explore the probable, latent distributions of individual property crime and personal crime victimization matrices that express the frequency and type of victimization that are self-reported by respondents over the survey recall period. The analysis obtains broadly similar solutions for both types of victimization across the respective datasets. It is demonstrated that a hypothesized mixing process will produce a heterogeneous set of local sub-distributions: a large sub-population that is predominantly not victimized, a very small ‘chronic’ sub-population that is frequently and consistently victimized across crime-type, and an ‘intermediate’ sub-population (whose granularity varies with sample size) to whom the bulk of victimization occurs. Additionally, attention is paid to the position of very high frequency victimization within these sub-populations. The analysis supports the idea that crime victimization may be a function of two propensities: for immunity, and exposure. It demonstrates that zero-inflation is also a defining feature of the distribution that needs to be set alongside the significance that has been attached to the thickness of its right tail. The results suggest a new baseline model for investigating population distributions of crime victimization.

Figures

Figure 2: Probability (p.) and Frequency (f.) of Crime Victimization

Table 2: Cross‐tabulation of Membership in Five Class and Six Class Models of BCS Property Crime (percentages)

Figure 5: Mean Number of Victimizations by Property Crime Type – Six Class BCS Model

Figure 11: Probability of Membership in the ‘Polar Classes’ Conditional on Frequency of Victimization. BCS Property crime

Figure 3: ABIC Statistics for Models of Property Crime, BCS and SCVS Datasets

Figure 12: Probability of Membership in the ‘Intermediate Classes’ Conditional on Level of Victimization. BCS Property Crime

Frequently asked questions

Q1. What is the main problem with the use of weighting?

The necessary use of weighting to correct for sampling bias raises a basic dilemma with regard to the secondary analysis of data drawn from complex sample designs, since many parametric tests cannot be applied to weighted data. 

Q2. What is the significance of the weight of evidence?

The weight of evidence shows that heterogeneity in the probability of crime victimization is likely to be attributable causally to variables directly or indirectly measuring individuals’ life styles, routine activities and residential circumstances, all of which are held to serve as indicators of the likelihood of exposure to potential offenders (Tseloni, 2006; Miethe and Meier, 1994). 

Q3. what is the true distribution of target population event matrices?

Thus the true distribution of target population event matrices might be the product of a mixture of two probability distributions: the first being the probability of each case being a zero (which could be taken to correspond to the process of immunity), the second being the probability of a positive (non‐zero) count (corresponding to the process of exposure). 

Q4. What can be done to manipulate the components of victimization frequency and prevalence?

This may require analytic approaches, including experimentation and simulation, which can manipulate the separate components of victim‐prevalence and victimization‐frequency hypothetically in order to uncover the latent data generating processes that are embedded within the observable behavior of aggregate crime rates.