Score tests for overdispersion in zero-inflated Poisson mixed models

This note is motivated by recent works of Xie et al. (2009) and Xiang et al. (2007). Herein, we simplify the score statistic presented by Xie et al. (2009) to test overdispersion in the zero-inflated generalized Poisson (ZIGP) mixed model, and discuss an extension to test overdispersion in zero-inflated Poisson (ZIP) mixed models. Examples highlight the application of the extended results. The extensive simulation study for testing overdispersion in the Poisson mixed model indicates that the proposed score statistics maintain the nominal level reasonably well. In practice, the appropriate model is chosen based on the approximate mean-variance relationship in the data, and a formal score test based on asymptotic standard normal distribution can be employed for testing overdispersion. A case study is provided to illustrate procedures for data analysis.