Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models.

TLDR

Regression models for count data are rarely used in psychology, and the basic Poisson model is often misleading due to overdispersion. The article aims to highlight issues with linear regression on count data and to present three alternative regression models. The authors describe two modifications: an overdispersed model that estimates a correction factor, and a negative binomial model that adds a random term for between‑subject variability. The authors compare the advantages of the Poisson, overdispersed, and negative binomial models.

Abstract

The regression models appropriate for counted data have seen little use in psychology. This article describes problems that occur when ordinary linear regression is used to analyze count data and presents 3 alternative regression models. The simplest, the Poisson regression model, is likely to be misleading unless restrictive assumptions are met because individual counts are usually more variable ("overdispersed") than is implied by the model. This model can be modified in 2 ways to accomodate this problem. In the overdispersed model, a factor can be estimated that corrects the regression model's inferential statistics. In the second alternative, the negative binomial regression model, a random term reflecting unexplained between-subject differences is included in the regression model. The authors compare the advantages of these approaches.