Poisson-Based Regression Analysis of Aggregate Crime Rates

• Published in: Journal of quantitative criminology Vol. 16; no. 1; pp. 21 - 43
• Main Author: Osgood, D. Wayne
• Format: Journal Article
• Language: English
• Published: New York Kluwer Academic/Plenum Publishers 01.03.2000; Springer Nature B.V
• Subjects: Aggregate Data; Arrest rates; Arrests; Binomials; Censuses; Crime; Crime Rates; Criminal offenses; Criminal statistics; Criminology; Elaboration; Juvenile Offenders; Methodology (Data Analysis); Minors; Modeling; Offenses; Per capita; Poisson distribution; Population; Population size; Regression Analysis; Robbery; Statistical variance; Variables; United States > US; Pennsylvania
• ISSN: 0748-4518; 1573-7799
• DOI: 10.1023/A:1007521427059

This article introduces the use of regression models based on the Poisson distribution as a tool for resolving common problems in analyzing aggregate crime rates. When the population size of an aggregate unit is small relative to the offense rate, crime rates must be computed from a small number of offenses. Such data are ill-suited to least-squares analysis. Poisson-based regression models of counts of offenses are preferable because they are built on assumptions about error distributions that are consistent with the nature of event counts. A simple elaboration transforms the Poisson model of offense counts to a model of per capita offense rates. To demonstrate the use and advantages of this method, this article presents analyses of juvenile arrest rates for robbery in 264 nonmetropolitan counties in four states. The negative binomial variant of Poisson regression effectively resolved difficulties that arise in ordinary least-squares analyses.