Marginalized Zero-Inflated Bell Regression Models for Overdispersed Count Data

Zero-inflated models are statistical tools that can be used to assess the relationships between covariates and a count result that contains an excessive number of zero-inflated counts. However, these models do not allow analysis of the effects of the covariates on the overall population of the mixture, namely on the marginal mean of the zero-inflated count. For this purpose, marginal zero-inflated models, such as marginal zero-inflated Poisson models, have been developed. Most often, these models are restricted to data whose overdispersion is due solely to the high proportion of zeros they contain. In this paper, we propose a new marginal zero-inflated Bell (MZIBell) regression model that allows the analysis of highly overdispersed count data whose overdispersion is partly caused by the excessive number of zeros. The asymptotic properties (consistency, asymptotic normality) of the MZIBell estimator are established under certain regularity conditions. Also, the performances of the proposed estimators are evaluated by Monte Carlo simulations. An analysis of real healthcare demand data is presented for illustrative purposes, and a comparative study based on this real data suggests that that MZIBell is better suited to modeling these data than other zero-inflated regressions commonly used in practice.