Comparison of Test Statistic for Zero-Inflated Negative Binomial against Zero-Inflated Poisson Model

In this study, the existence of score test and alternative tests were studied for testing the overdispersion parameter after including covariates in ZINB against ZIP models. The power of the three tests for different degrees of overdispersion parameter and various sample sizes were also obtained through Monte Carlo simulation. We have also presented the power of the three tests to detect the overdispersion problem in ZINB regression model. From the simulation result, it was observed that, the score test is more effective than the LRT and Wald test for ZINB regression model because of its higher empirical power. The simulation result also showed that the ZIP model is more appropriate when the value of overdispersion is small while ZINB regression model is more appropriate for dataset that contain high overdispersion values. However, the AIC and BIC were included to choice these two models.