Overdispersion and Poisson Regression

• NCJ Number: 223857
• Journal: Journal of Quantitative Criminology Volume: 24 Issue: 3 Dated: September 2008 Pages: 269-284
• Author(s): Richard Berk; John M. MacDonald
• Date Published: September 2008
• Length: 16 pages
• Publication Format: Article
• Publication Type: Report (Study/Research)
• Language: English
• Country: United States of America

Annotation

Given criminology’s widespread use of regression models for count data, this paper revisits the foundations of such models, whether or not the conditional Poisson distribution or the conditional negative binomial distribution is used.

Abstract

The typical justifications for using the negative binomial formulation for count data go far beyond the standard critiques of regression. They involve a response to important features of these critiques. The claim has been made that by using the negative binomial distribution instead of the Poisson, significant errors in how a model is specified can be fixed. This claim is a focus of the discussion in this paper. The paper concludes that if apparent “overdispersion” (more variability around the model’s fitted values than is consistent with a Poisson formulation) results from specification errors in the systematic part of the Poisson regression model, resorting to the negative binomial distribution does not help. It can make matters worse by giving a false sense of security when the fundamental errors in the model remain. If there is true overdispersion as a result only of specification errors in the stochastic part of the Poisson regression model, attempting to correct those errors can be useful; however, arriving at the proper fix is difficult. There is no necessary connection between the reasons for the misspecification and one or more alternatives to the conventional Poisson distribution. Automatically turning to the negative binomial model can lead to a false confidence in the inferences from the results. Therefore, in criminology applications, it is reasonable to focus on getting the systematic structure correct. Only after a convincing case has been made for the correctness of the systematic structure should a researcher turn to concerns about the structure of the stochastic component. 6 figures, 1 table, and 31 references