A constrained marginal zero-inflated binomial regression model

Zero-inflated models have become a popular tool for assessing relationships between explanatory variables and a zero-inflated count outcome. In these models, regression coefficients have latent class interpretations, where latent classes correspond to a susceptible subpopulation with observations generated from a count distribution and a non susceptible subpopulation that provides only zeros. However, it is often of interest to evaluate covariates effects in the overall mixture population, that is, on the marginal mean of the zero-inflated count. Marginal zero-inflated models, such as the marginal zero-inflated Poisson models, have been developed for that purpose. They specify independent submodels for the susceptibility probability and the marginal mean of the count response. When the count outcome is bounded, it is tempting to formulate a marginal zero-inflated binomial model in the same fashion. This, however, is not possible, due to inherent constraints that relate, in the zero-inflated binomial model, the susceptibility probability and the latent and marginal means of the count outcome. In this paper, we propose a new marginal zero-inflated binomial regression model that accommodates these constraints. We investigate the maximum likelihood estimator in this model, both theoretically and by simulations. An application to the analysis of health-care demand is provided for illustration.