The statistical analysis of count data / El análisis estadístico de los datos de recuento

Abstract

This monograph provides an overview of the various regression models used to analyse count response models. We begin by defining counts and the methods used to model count data. We then discuss the basic count model — Poisson regression — focusing on the nature of equi-dispersion, which occurs when the mean and variance are identical in value. Equi-dispersion is a distributional assumption of the Poisson model. We examine how to determine when this assumption is violated, which results in extra-dispersion; i.e., either under- or overdispersion. Extra-dispersion biases the Poisson model standard errors, leading us to accept or reject a model when we should not. The negative binomial model is generally used to model generic overdispersion, but if we know the cause of the overdispersion we can select an alternative count model that appropriately adjusts for it. The same is the case with under-dispersion. Aside from looking at the Poisson and negative binomial models, we also evaluate models such as generalized Poisson, Poisson inverse Gaussian, two-part hurdle models, zero-inflated mixture models and other varieties of count model. Finally, we provide a brief look at Bayesian count models, showing how to estimate a Bayesian negative binomial model.