Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study
Article first published online: 24 MAY 2004
Volume 56, Issue 4, pages 1030–1039, December 2000
How to Cite
Hall, D. B. (2000), Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study. Biometrics, 56: 1030–1039. doi: 10.1111/j.0006-341X.2000.01030.x
- Issue published online: 24 MAY 2004
- Article first published online: 24 MAY 2004
- Received September 1999. Revised March 2000. Acceoted April 2000.
- Excess zeros;
- EM algorithm;
- Generalized linear mixed model;
- Mixed effects;
- Repeated measures
Summary. 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(λ) distribution and a distribution with point mass of one at zero, with mixing probability p. Both p and λ 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 (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.