A Bayesian Approach for Zero-Inflated Count Regression Models by Using the Reversible Jump Markov Chain Monte Carlo Method and an Application

Abstract

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors.

Keywords:

• Bayesian posterior estimates
• Gibbs sampling
• Hierarchical modeling
• Log-gamma distribution
• Metropolis-Hastings algorithm
• Potential scale reduction factor
• Zero-inflation
• Zoological data

Mathematics Subject Classification:

• 62F15
• 62J12

Acknowledgments

The authors thank Professor. I. Erdem for his careful reading of the manuscript and his suggestions. They also greatly acknowledge Professor. N. Balakrishnan for his valuable encouragement.

Notes

*These zeros denote structural zeros. The others denote sampling zeros.

*Acceptance ratio in the implementation the RJMCMC method.

*Conditional odds ratio.