Something Fishy? Uncovering heterogeneity in the distribution of crime victimisation in general populations Tim Hope and Paul Norris SCCJR (CJ-QUEST) University of Edinburgh December 2008

The Distribution of Property Crime in the BCS Maximum count present in BCS is 27. Based on six crimes capped at 6 incidents per crime. Unweighted BCS Sample: , , , 2003/ , 2006/ , Total

Understanding and Modelling the Distribution of Crime The distribution shown on the previous slide poses two questions :- - Substantive question: What is the data generation process that underpins the distribution? - Statistical question: What kind of dependent variable is best employed to model victimisation?

Theoretical Models of Victimisation Simple Exposure (pure heterogeneity) Mixture Model Simple RV (pure state-dependency) T. Hope and A. Trickett (2004). La distribution de la victimation dans la population, Déviance et Société, 28 (3), Large proportion of the population experience no victimisation - Small proportion of the population experience chronic victimisation - One or more groups for low-level victimisation

Dependent Variable for Victimisation Research Type of crime victimisation –Type of incident –One type verses more generalist victim Frequency of crime victimisation –Nominal (0,1), Ordinal (0, 1, 2+), Count (0-n) –Distribution of count variables – Poisson verses Negative Binomial

Data British Crime Survey - England and Wales (BCS) – 1992, 1996, 2001, 2003/04, 2006/07 Scottish Crime Victimisation Survey (SCVS) –1993, 1996, 2000, 2003, 2006 Crime types –Household Property Crime (6 questions) –Count data (victim screeners, capped at 6)

Latent Class Models Latent Class Analysis (LCA) is analogous to cluster analysis but:Latent Class Analysis (LCA) is analogous to cluster analysis but: -Can handle missing data-Can handle missing data -Can handle non-normal data-Can handle non-normal data -Can be used with longitudinal data-Can be used with longitudinal data

A Simple LCA Model Victim Type Household Theft Victimisation Vandalism VictimisationForced Entry Victimisation ++= Total Victimisation AgeHousehold IncomeNeighbourhood Type LCA indicator considers both level of victimisation and type of crime

Accuracy Verses Parsimony How many groups are required? -range of statistical indicators -substantive interpretation is crucial Within group variation?

Distribution of Victimisation Indicators Count data often modelled using Poisson distribution Victimisation appears to follow Negative Binomial distribution BCS Combined Sample VariableMeanStd. DevVarianceRatio of Variance to Mean Defaced Property (Outside) Stolen Property (Outside) Property Stolen from Home Tried to Gain Entry to Commit Theft/Damage Entered Property and Caused Damage Entered Property and Commited Theft Unweighted BCS Sample: , , , 2003/ , 2006/ , Total What about zero-inflation?

ABIC for BCS Data Lower ABIC figures represent better fit between model and data ABIC suggests six groups should be used Results based on Negative Binomial Distribution. Results using zero-inflated Negative Binomial reveal an identical pattern but exhibit a slightly worse fit to the data

BCS Six Class Solution

Results for Scottish Data Distribution of property crime in Scottish data is very similar to BCS ABIC statistic suggests 4 class solution is optimal Results based on Negative Binomial Distribution. Results using zero-inflated Negative Binomial reveal an identical pattern but exhibit a slightly worse fit to the data

Scottish 4 Class Solution

Summary Overall distribution obscures heterogeneity Heterogeneity of both substantive and statistical interest Most uncertainty occurs around the middle of the distribution Key issues around how solution is affected by sample design, prevalence of incidents and how useful apparent classes are for analysis