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Bayesian covariance selection in generalized linear mixed models.

Publication ,  Journal Article
Cai, B; Dunson, DB
Published in: Biometrics
June 2006

The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of predictors that have random effects, random effects selection can be challenging, particularly when outcome distributions are nonnormal. This article proposes a fully Bayesian approach to the problem of simultaneous selection of fixed and random effects in GLMMs. Integrating out the random effects induces a covariance structure on the multivariate outcome data, and an important problem that we also consider is that of covariance selection. Our approach relies on variable selection-type mixture priors for the components in a special Cholesky decomposition of the random effects covariance. A stochastic search MCMC algorithm is developed, which relies on Gibbs sampling, with Taylor series expansions used to approximate intractable integrals. Simulated data examples are presented for different exponential family distributions, and the approach is applied to discrete survival data from a time-to-pregnancy study.

Duke Scholars

Published In

Biometrics

DOI

EISSN

1541-0420

ISSN

0006-341X

Publication Date

June 2006

Volume

62

Issue

2

Start / End Page

446 / 457

Related Subject Headings

  • Time Factors
  • Statistics & Probability
  • Pregnancy
  • Linear Models
  • Humans
  • Female
  • Biometry
  • Bayes Theorem
  • Algorithms
  • Adult
 

Citation

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MLA
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Cai, B., & Dunson, D. B. (2006). Bayesian covariance selection in generalized linear mixed models. Biometrics, 62(2), 446–457. https://doi.org/10.1111/j.1541-0420.2005.00499.x
Cai, Bo, and David B. Dunson. “Bayesian covariance selection in generalized linear mixed models.Biometrics 62, no. 2 (June 2006): 446–57. https://doi.org/10.1111/j.1541-0420.2005.00499.x.
Cai B, Dunson DB. Bayesian covariance selection in generalized linear mixed models. Biometrics. 2006 Jun;62(2):446–57.
Cai, Bo, and David B. Dunson. “Bayesian covariance selection in generalized linear mixed models.Biometrics, vol. 62, no. 2, June 2006, pp. 446–57. Epmc, doi:10.1111/j.1541-0420.2005.00499.x.
Cai B, Dunson DB. Bayesian covariance selection in generalized linear mixed models. Biometrics. 2006 Jun;62(2):446–457.
Journal cover image

Published In

Biometrics

DOI

EISSN

1541-0420

ISSN

0006-341X

Publication Date

June 2006

Volume

62

Issue

2

Start / End Page

446 / 457

Related Subject Headings

  • Time Factors
  • Statistics & Probability
  • Pregnancy
  • Linear Models
  • Humans
  • Female
  • Biometry
  • Bayes Theorem
  • Algorithms
  • Adult