Bayesian generalized linear model for over and under dispersed counts

TL;DR

This paper introduces a Bayesian Conway-Maxwell-Poisson generalized linear model capable of handling both over and under dispersed count data, using a Metropolis-Hastings algorithm for inference, with applications and simulation validation.

Contribution

It presents a novel Bayesian count regression model that accommodates both over and under dispersion while maintaining simplicity and interpretability.

Findings

Effective Bayesian inference demonstrated via Metropolis-Hastings algorithm.

Model performs well in real data examples.

Simulation study shows favorable frequentist properties.

Abstract

Bayesian models that can handle both over and under dispersed counts are rare in the literature, perhaps because full probability distributions for dispersed counts are rather difficult to construct. This note takes a first look at Bayesian Conway-Maxwell-Poisson generalized linear models that can handle both over and under dispersion yet retain the parsimony and interpretability of classical count regression models. The focus is on providing an explicit demonstration of Bayesian regression inferences for dispersed counts via a Metropolis-Hastings algorithm. We illustrate the approach on two data analysis examples and demonstrate some favourable frequentist properties via a simulation study.