Zero‐Inflated Poisson and Binomial Regression with Random Effects: A Case Study

TLDR

Zero‑inflated Poisson regression models count data with excess zeros by mixing a Poisson distribution with a point‑mass at zero, linking both parameters to covariates through generalized linear models. The study extends Lambert’s zero‑inflated Poisson framework to upper‑bounded counts, developing a zero‑inflated binomial model. Random effects are incorporated into the zero‑inflated binomial and Poisson models to capture within‑subject correlation and between‑subject heterogeneity, and the approach is demonstrated on a repeated‑measures horticultural experiment. The methods are illustrated on horticultural data, showing how the zero‑inflated binomial and Poisson models with random effects can accommodate excess zeros and repeated measures.

Abstract

In a 1992 Technometrics paper, Lambert (1992, 34, 1-14) 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 Lambert's methodology to an upper bounded count situation, thereby obtaining a zero-inflated binomial (ZIB) 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.