Score tests for zero-inflation and overdispersion in two-level count data

In a Poisson regression model in which observations are either clustered or represented by repeated measurements of counts, the number of observed zero counts is sometimes greater than the expected frequency by the Poisson distribution and overdispersion may remain even after modeling excess zeros. The zero-inflated negative binomial (ZINB) mixed regression model is suggested to analyze such data. Previous studies have proposed score statistics for testing zero-inflation and overdispersion separately in correlated count data. Here, we also deal with simultaneous score tests for zero-inflation and overdispersion in two-level count data by using the ZINB mixed regression model. Score tests are suggested for (1) zero-inflation in the presence of overdispersion, (2) overdispersion in the presence of zero-inflation, and (3) zero-inflation and overdispersion simultaneously. The level and power of score test statistics are evaluated by a simulation study. The simulation results indicate that score test statistics may occasionally underestimate or overestimate the nominal significance level due to variation in random effects. This study proposes a parametric bootstrap method to overcome this problem. The simulation results of the bootstrap test indicate that score tests hold the nominal level and provide good power.