A Score Test For Overdispersion In Marginalized Zero-inflated Poisson Regression Model

Zero-inflated regression models have been widely used in social economy,medical statistics,disease research and many other aspects.Zero-inflated Poisson model is the most commonly used zero-inflated count regression models.Zero-inflated negative binomial regression model and zero-inflated generalized Poisson model can solve the problem of excessive dispersion in ZIP regression model.However,the traditional zero-inflated regression models are not suitable for direct inference on overall exposure effects,especially for quantifying the effects of variables on the whole population.In view of this situation,the existing zero-inflated regression models cannot analyze the characteristics of the counting data more accurately,so we use the marginal zero-inflated regression models to solve this problem.The marginal model directly models the marginal mean.In addition to pointing out the components of the zero-inflated probability,the marginal model also specifies the components of the regression model of the marginal mean,which provides a direct explanation for the estimation of the parameters of the covariates on the marginal mean.In this paper,the ZIGP regression model is extended according to the MZIP regression model,and a new marginal model that MZIGP regression model is proposed,and a Score test is performed for the over dispersion of the MZIP regression model.The research shows that the MZIGP regression model and the MZINB regression model are equivalent to the over-dispersion Score statistic of the MZIP regression model,and the MZIGP regression model can simultaneously solve the problem of over dispersion and under dispersion in the MZIP regression model.In the numerical simulation analysis,the Score test statistic T was studied by the Monte Carlo stochastic simulation method.UnderH₀,T asymptotically obeys the standard normal distribution.Under₁H,the power of T increases with the increase of sample size and zero expansion coefficient.