Zero-inflated Poisson and binomial regression with random effects: a case study

Biometrics. 2000 Dec;56(4):1030-9. doi: 10.1111/j.0006-341x.2000.01030.x.


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.

MeSH terms

  • Animals
  • Biometry / methods
  • Diptera
  • Models, Statistical*
  • Plants
  • Poisson Distribution*
  • Probability
  • Regression Analysis*