Overdisp: A stata (and mata) package for direct detection of overdispersion in poisson and negative binomial regression models

Abstract

Stata has several procedures that can be used in analyzing count-data regression models and, more specifically, in studying the behavior of the dependent variable, conditional on explanatory variables. Identifying overdispersion in countdata models is one of the most important procedures that allow researchers to correctly choose estimations such as Poisson or negative binomial, given the distribution of the dependent variable. The main purpose of this paper is to present a new command for the identification of overdispersion in the data as an alternative to the procedure presented by Cameron and Trivedi [5], since it directly identifies overdispersion in the data, without the need to previously estimate a specific type of count-data model. When estimating Poisson or negative binomial regression models in which the dependent variable is quantitative, with discrete and non-negative values, the new Stata package overdisp helps researchers to directly propose more consistent and adequate models. As a second contribution, we also present a simulation to show the consistency of the overdispersion test using the overdisp command. Findings show that, if the test indicates equidispersion in the data, there are consistent evidence that the distribution of the dependent variable is, in fact, Poisson. If, on the other hand, the test indicates overdispersion in the data, researchers should investigate more deeply whether the dependent variable actually exhibits better adherence to the Poisson-Gamma distribution or not.