Bayesian inference for generalized linear mixed models

Youyi Fong, Haavard Rue, Jon Wakefield*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

135 Scopus citations

Abstract

Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.

Original languageEnglish (US)
Pages (from-to)397-412
Number of pages16
JournalBiostatistics
Volume11
Issue number3
DOIs
StatePublished - Jul 1 2010

Keywords

  • Integrated nested Laplace approximations
  • Longitudinal data
  • Penalized quasi-likelihood
  • Prior specification
  • Spline models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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