A constrained marginal zero-inflated binomial regression model

International audienceZero-inflated models have become a popular tool for assessing the relationships between explanatory variables and a zero-inflated count outcome. In these models, regression coefficients have latent class interpretations, where the latent classes correspond to a susceptible subpopulation with observations generated from a count distribution and a non-susceptible subpopulation that provides only zero counts. 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 response. Marginal zero-inflated models, such as the marginal zero-inflated Poisson and negative binomial 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 the 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 marginal zero-inflated binomial regression model that accommodates these constraints. We construct maximum likelihood estimates of the regression parameters. Their asymptotic properties are established and their finite-sample behaviour is examined by simulations. An application of the proposed model to the analysis of health-care demand is provided for illustration