Score tests for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models

Hall (2000) has described zero-inflated Poisson and binomial regression models that include random effects to account for excess zeros and additional sources of heterogeneity in the data. The authors of the present paper propose a general score test for the null hypothesis that variance components associated with these random effects are zero. For a zero-inflated Poisson model with random intercept, the new test reduces to an alternative to the overdispersion test of Ridout, Demetrio & Hinde (2001). The authors also examine their general test in the special case of the zero-inflated binomial model with random intercept and propose an overdispersion test in that context which is based on a beta-binomial alternative.