Objective Bayes testing of Poisson versus inflated Poisson models

TL;DR

This paper develops an objective Bayesian testing framework to compare Poisson and zero-inflated Poisson models, including covariate adjustments, with applications demonstrating its effectiveness.

Contribution

It introduces a new Bayesian testing approach for Poisson versus ZIP models using objective priors, extending to regression with covariates.

Findings

Effective Bayesian test for Poisson vs. ZIP models

Objective priors have desirable properties for model comparison

Applications show practical utility in count data analysis

Abstract

The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a zero-inflated Poisson (ZIP) distribution is often proposed. This article addresses testing a Poisson versus a ZIP model, using Bayesian methodology based on suitable objective priors. Specific choices of objective priors are justified and their properties investigated. The methodology is extended to include covariates in regression models. Several applications are given.