Score Tests for Overdispersion in Marginalized Zero‐Inflated Poisson Regression Based on Marginalized Zero‐Inflated Generalized Poisson Model

ABSTRACT A marginalized zero‐inflated Poisson (MZIP) model has been developed to allow practitioners to make direct inferences about the marginal mean of count data while accounting for the excess zeros in the data. Overdispersion is a well‐documented issue in models that include the Poisson distribution, such as the traditional zero‐inflated Poisson (ZIP) and MZIP models. When both zero‐inflation and overdispersion are present in count data, alternative models like the marginalized zero‐inflated negative binomial (MZINB) and marginalized zero‐inflated generalized Poisson (MZIGP) can be employed. In choosing between models, the score test has an advantage over the likelihood ratio and Wald tests, as it only requires estimating the parameter of interest under the null hypothesis. Building on the work of Inan et al., which developed a score test for overdispersion in MZIP compared to the MZINB‐2 model and inspired by Yang et al., this paper proposes score tests for overdispersion in MZIP regression based on MZIGP models. It also demonstrates that the score statistic derived based on the MZIGP‐2 model is identical to that based on the MZINB‐2 model. A simulation stud