Zero-inflated Poisson and binomial regression with random effects: a case study.
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.
Hall
D B
DB
Department of Statistics, University of Georgia, Athens, Georgia 30602-1952, USA. dhall@stat.uga.edu
D000818:Animals; D001699:Biometry / Q000379:methods; D004175:Diptera; D015233:Models, Statistical; D010944:Plants; D016012:Poisson Distribution; D011336:Probability; D012044:Regression Analysis