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

• NCJ Number: 69814
• Journal: American Journal of Sociology Volume: 85 Issue: 4 Dated: (January 1980) Pages: 870-891
• Author(s): J F Nelson
• Date Published: 1980
• Length: 22 pages
• Grant Number(s): 75-SS-99-6029
• Sponsoring Agency: National Criminal Justice Information and Statistics Service
• Publication Format: Article
• Publication Type: Report (Study/Research)
• Language: English
• Country: United States of America

Annotation

Poisson and negative binomial models are applied to the number of multiple victimizations reported in the National Crime Surveys, with the negative binomial not the Poisson model shown to be compatible with data.

Abstract

The simple Poisson model is based on the assumptions that the probability of being victimized is the same for all persons (businesses, households) and the probability of being victimized does not depend on the number of previous victimizations. Under this model, persons who have experienced a high number of victimizations are merely unlucky. The negative binomial model states that if either the probability of being victimized is the same for all persons but depends on the number of prior victimizations or the probability of being victimized remains constant over time but is not necessarily the same for all persons, then the number of victimizations for the total population follows the negative binomial distribution. The negative binomial model's interpretation can be used to estimate the probability of being victimized, depending 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. The parameters of the negative binomial model may be used to show how rates are inflated by persons, households, or businesses suffering an unusually high number of victimizations, how the number of vicitimizations can be transformed to create a distribution closer to the normal distribution than the original distribution, and how the variance of victimization rates can be estimated. Twenty-two references and illustrative material are included. (Author abstract modified--mhp)