Generalized linear models with random effects; a Gibbs sampling approach

Scott L. Zeger, M. Rezaul Karim

Research output: Contribution to journalArticlepeer-review

632 Scopus citations


Generalized linear models have unified the approach to regression for a wide variety of discrete, continuous, and censored response variables that can be assumed to be independent across experimental units. In applications such as longitudinal studies, genetic studies of families, and survey sampling, observations may be obtained in clusters. Responses from the same cluster cannot be assumed to be independent. With linear models, correlation has been effectively modeled by assuming there are cluster-specific random effects that derive from an underlying mixing distribution. Extensions of generalized linear models to include random effects has, thus far, been hampered by the need for numerical integration to evaluate likelihoods. In this article, we cast the generalized linear random effects model in a Bayesian framework and use a Monte Carlo method, the Gibbs sampler, to overcome the current computational limitations. The resulting algorithm is flexible to easily accommodate changes in the number of random effects and in their assumed distribution when warranted. The methodology is illustrated through a simulation study and an analysis of infectious disease data.

Original languageEnglish (US)
Pages (from-to)79-86
Number of pages8
JournalJournal of the American Statistical Association
Issue number413
StatePublished - Mar 1991


  • Bayesian
  • Correlation
  • Heterogeneity
  • Logistic regression
  • Monte Carlo
  • Overdispersion
  • Regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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