Bayesian Inference for Zero-inflated Poisson Regression Models

Count data with excess zeros are common in social science research and can be considered as a special case of mixture structured data. We exploit the flexibility of the Bayesian analytic approach to model the mixture data structure inherent in zero-inflated count data by using the zero-inflated Poisson (ZIP) model. We discuss the importance of modelling excess-zero count data in social sciences and review the distributional properties of zero-inflated count data, with special attention given to its mixture data structure in the context of Bayesian modelling. We illustrate the methodology using data from the Americans’ changing lives (ACL) survey on cigarette smoking. Results from predictive checks suggest that the proposed Bayesian ZIP model provides a good fit to the HUI LIU and DANIEL A. POWERS 156 specific case of zero-inflated count data. Simulation studies suggest that the proposed Bayesian method performs better than the maximum likelihood approach to estimate the ZIP model, with larger coverage probabilities and smaller bias, as measured by the root mean squared error (RMSE). This is especially true for small samples and in cases of very high or very low incidence of excess zero outcomes.