A Simple and Adaptive Dispersion Regression Model for Count Data

TL;DR

This paper introduces a discrete Weibull regression model that adaptively handles various dispersion types in count data, simplifying model selection and improving practical applicability.

Contribution

It proposes a unified, easy-to-implement regression model that automatically adapts to different dispersion levels in count data, unlike traditional models.

Findings

The model effectively captures overdispersion and underdispersion.

Maximum likelihood estimation is efficient for parameter inference.

The approach performs well on simulated and real datasets.

Abstract

Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically occurs in count datasets. It is highly desirable to have a unified model that can automatically adapt to the underlying dispersion and that can be easily implemented in practice. In this paper, a discrete Weibull regression model is shown to be able to adapt in a simple way to different types of dispersions relative to Poisson regression: overdispersion, underdispersion and covariate-specific dispersion. Maximum likelihood can be used for efficient parameter estimation. The description of the model, parameter inference and model diagnostics is accompanied by simulated and real data analyses.