Multiple Victimization in American Cities: A Statistical Analysis of Rare Events

Poisson and negative binomial models are applied to the number of multiple victimizations reported in the National Crime Surveys. The negative binomial but not the Poisson models is shown to be compatible with the data. The negative binomial model is consistent with the hypothesis that the probability of being victimized is constant over time and does not depend upon the number of prior victimizations, but that not all persons, businesses, and households have the same probability of being victimized. This interpretation can be used to estimate the probability of being victimized conditional upon the number of victimizations experienced in an observation period and to estimate the maximum correlation between independent variables and the number of victimizations experienced in a given time interval. Regardless of the interpretation, the analysis shows that victimization rates are not unduly affected by small numbers of persons having unusually high rates. Researchers using large data sets are likely to find similar patterns between victimization counts and independent variables using either rates or probabilities to measure victimization.