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Bayesian zero-inflated generalized Poisson regression model: estimation and case influence diagnostics

Count data with excess zeros arises in many contexts. Here our concern is to develop a Bayesian analysis for the zero-inflated generalized Poisson (ZIGP) regression model to address this problem. This model provides a useful generalization of zero-inflated Poisson model since the generalized Poisson distribution is overdispersed/underdispersed relative to Poisson. Due to the complexity of the ZIGP model, Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the considered model. Additionally, some discussions on the model selection criteria are presented and a Bayesian case deletion influence diagnostics is investigated for the joint posterior distribution based on the Kullback–Leibler divergence. Finally, a simulation study and a psychological example are given to illustrate our methodology.