A Study on the Effect of Dispersion Parameter in a Zero-inflated Generalized Poisson Regression Model

In this study, we examine the influence of overdispersion on statistical inference in a zero-inflated generalized Poisson regression model by simulation experiments and real data analysis. In the simulation study, simulated data are generated from the zero-inflated generalized Poisson regression model, and the regression coefficients in the zero-inflated Poisson regression and the zero-inflated generalized Poisson regression models are estimated. The simulation experiment results show that the regression coefficient estimates for the mean and zero-inflation probability of the zero-inflated Poisson regression to ignore overdispersion underestimate the true value when overdispersion exists, and this underestimation problem becomes more severe as the overdispersion increases. In addition, the standard errors of the regression coefficient estimates of the zero-inflated Poisson regression model are more underestimated as the overdispersion increased. Ultimately, the zero-inflated Poisson regression model, which ignores the overdispersion despite its existence, shows a larger nominal significance level in the hypothesis test for the true value of the regression coefficient, and this problem of the nominal significance level becomes more severe as the overdispersion increased. The results of this simulation experiment could be confirmed through the analysis of real data on the number of boat trips to Lake Somerville in eastern Texas in the United States in 1980.