Random effect models for repeated measures of zero-inflated count data

• Published in: Statistical modelling Vol. 5; no. 1; pp. 1 - 19
• Main Authors: Min, Yongyi, Agresti, Alan
• Format: Journal Article
• Language: English
• Published: Thousand Oaks, CA SAGE Publications 01.04.2005; Sage Publications Ltd
• Subjects: Binomial distribution; Linear equations; Mathematical models; Poisson distribution; Statistical analysis; Studies; negative binomial model; nonparametric mixture model; hurdle model; cumulative logit model; zero-inflated Poisson model; generalized linear mixed model
• ISSN: 1471-082X; 1477-0342
• DOI: 10.1191/1471082X05st084oa

For count responses, the situation of excess zeros (relative to what standard models allow) often occurs in biomedical and sociological applications. Modeling repeated measures of zero-inflated count data presents special challenges. This is because in addition to the problem of extra zeros, the correlation between measurements upon the same subject at different occasions needs to be taken into account. This article discusses random effect models for repeated measurements on this type of response variable. A useful model is the hurdle model with random effects, which separately handles the zero observations and the positive counts. In maximum likelihood model fitting, we consider both a normal distribution and a nonparametric approach for the random effects. A special case of the hurdle model can be used to test for zero inflation. Random effects can also be introduced in a zero-inflated Poisson or negative binomial model, but such a model may encounter fitting problems if there is zero deflation at any settings of the explanatory variables. A simple alternative approach adapts the cumulative logit model with random effects, which has a single set of parameters for describing effects. We illustrate the proposed methods with examples.