Statistical Inference in Marginalized Zero-inflated Poisson Regression Models with Missing Data in Covariates

Abstract

The marginalized zero-inflated poisson (MZIP) regression model quantifies the effects of an explanatory variable in the mixture population. Also, in practice the variables are usually partially observed. Thus, we first propose to study the maximum likelihood estimator when all variables are observed. Then, assuming that the probability of selection is modeled using mixed covariates (continuous, discrete and categorical), we propose a semiparametric inverse-probability weighted (SIPW) method for estimating the parameters of the MZIP model with covariates missing at random (MAR). The asymptotic properties (consistency, asymptotic normality) of the proposed estimators are established under certain regularity conditions. Through numerical studies, the performance of the proposed estimators was evaluated. Then the results of the SIPW are compared to the results obtained by semiparametric inverse-probability weighted kermel-based (SIPWK) estimator method. Finally, we apply our methodology to a dataset on health care demand in the United States.