A flexible regression model for count data

TL;DR

This paper introduces a flexible regression model based on the COM-Poisson distribution that effectively handles count data with varying dispersion levels, extending traditional Poisson regression.

Contribution

It proposes a generalized COM-Poisson regression model with a GLM framework, including estimation, inference, diagnostics, and a test for model selection over Poisson regression.

Findings

COM-Poisson regression fits over- and under-dispersed data better than Poisson.

The model provides accurate inference and diagnostics for count data.

Application to real datasets demonstrates its practical advantages.

Abstract

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive to Poisson regression. We propose a regression model based on the Conway--Maxwell-Poisson (COM-Poisson) distribution to address this problem. The COM-Poisson regression generalizes the well-known Poisson and logistic regression models, and is suitable for fitting count data with a wide range of dispersion levels. With a GLM approach that takes advantage of exponential family properties, we discuss model estimation, inference, diagnostics, and interpretation, and present a test for determining the need for a COM-Poisson regression over a standard Poisson regression. We compare the COM-Poisson to several alternatives and illustrate its advantages and usefulness using three data sets with varying dispersion.