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Bayesian covariance selection in generalized linear mixed models.

Bo Cai1, David B Dunson

  • 1Biostatistics Branch, MD A3-03, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, North Carolina 27709, USA. cai@niehs.nih.gov

Biometrics
|August 22, 2006
PubMed
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This study introduces a Bayesian method for selecting fixed and random effects in generalized linear mixed models (GLMMs). The approach handles complex data structures and non-normal outcomes, improving model accuracy for correlated and longitudinal data analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Generalized linear mixed models (GLMMs) are crucial for analyzing correlated and longitudinal data by incorporating random effects to account for subject heterogeneity.
  • Selecting relevant predictors with random effects in GLMMs is challenging, especially with non-normal outcome distributions.

Purpose of the Study:

  • To propose a fully Bayesian approach for simultaneous selection of fixed and random effects in GLMMs.
  • To address the challenge of covariance selection induced by integrating out random effects.

Main Methods:

  • A fully Bayesian methodology utilizing variable selection-type mixture priors on a Cholesky decomposition of the random effects covariance.
  • Development of a stochastic search Markov chain Monte Carlo (MCMC) algorithm employing Gibbs sampling and Taylor series expansions for intractable integrals.

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Main Results:

  • The proposed Bayesian approach effectively performs simultaneous selection of fixed and random effects in GLMMs.
  • The method demonstrates applicability across various exponential family distributions and is validated on discrete survival data from a time-to-pregnancy study.

Conclusions:

  • The developed Bayesian framework offers a robust solution for variable selection in GLMMs, particularly for complex data scenarios.
  • This approach enhances the analysis of correlated and longitudinal data by accurately identifying significant predictors and their random effects.