Summary: In a 1992 Technometrics paper, {\it D. Lambert} [Technometrics 34, 1--14 (1992;

Zbl 0850.62756)] described zero-inflated Poisson (ZIP) regression, a class of models for count data with excess zeros. In a ZIP model, a count response variable is assumed to be distributed as a mixture of a Poisson$(\lambda)$ distribution and a distribution with point mass of one at zero, with mixing probability $p$. Both $p$ and $\lambda$ are allowed to depend on covariates through canonical link generalized linear models. In this paper, we adapt Lambertâ€™s methodology to an upper bounded count situation, thereby obtaining a zero-inflated binomial (ZIP) model. In addition, we add to the flexibility of these fixed effects models by incorporating random effects so that, e.g., the within-subject correlation and between-subject heterogeneity typical of repeated measures data can be accommodated. We motivate, develop, and illustrate the methods described here with an example from horticulture, where both upper bounded count (binomial-type) and unbounded count (Poisson-type) data with excess zeros were collected in a repeated measures designed experiment.