Beta-binomial/gamma-Poisson regression models for repeated counts with random parameters

TL;DR

This paper introduces a beta-binomial/gamma-Poisson regression model for repeated multivariate count data, addressing overdispersion and covariance, with estimation via maximum likelihood and comparison to existing models.

Contribution

It proposes a novel beta-binomial/gamma-Poisson model that overcomes limitations of previous models by handling overdispersion and covariance in repeated count data.

Findings

The gamma-Poisson model effectively captures overdispersion.

Maximum likelihood estimation is feasible with a Newton-Raphson algorithm.

The model outperforms previous models in practical data examples.

Abstract

Beta-binomial/Poisson models have been used by many authors to model multivariate count data. Lora and Singer (Statistics in Medicine, 2008) extended such models to accommodate repeated multivariate count data with overdipersion in the binomial component. To overcome some of the limitations of that model, we consider a beta-binomial/gamma-Poisson alternative that also allows for both overdispersion and different covariances between the Poisson counts. We obtain maximum likelihood estimates for the parameters using a Newton-Raphson algorithm and compare both models in a practical example.