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Zero‐Inflated Poisson and Binomial Regression with Random Effects: A Case Study
Author(s) -
Hall Daniel B.
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.01030.x
Subject(s) - count data , mathematics , negative binomial distribution , poisson distribution , zero inflated model , poisson regression , quasi likelihood , statistics , overdispersion , bounded function , random variable , binomial (polynomial) , regression analysis , binomial distribution , mathematical analysis , population , demography , sociology
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.