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Approximate uniform shrinkage prior for a multivariate generalized linear mixed model

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  • Chen, Hsiang-Chun
  • Wehrly, Thomas E.

Abstract

Multivariate generalized linear mixed models (MGLMM) are used for jointly modeling the clustered mixed outcomes obtained when there are two or more responses repeatedly measured on each individual in scientific studies. Bayesian methods are widely used techniques for analyzing MGLMM. The need for noninformative priors arises when there is insufficient prior information on the model parameters. The main aim of the present study is to propose an approximate uniform shrinkage prior for the random effect variance components in the Bayesian analysis for the MGLMM. This prior is an extension of the approximate uniform shrinkage prior proposed by Natarajan and Kass (2000). This prior is easy to apply and is shown to possess several nice properties. The use of the approximate uniform shrinkage prior is illustrated in terms of both a simulation study and osteoarthritis data.

Suggested Citation

  • Chen, Hsiang-Chun & Wehrly, Thomas E., 2016. "Approximate uniform shrinkage prior for a multivariate generalized linear mixed model," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 148-161.
    • Handle: RePEc:eee:jmvana:v:145:y:2016:i:c:p:148-161
    DOI: 10.1016/j.jmva.2015.12.004
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    1. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    2. Brent A. Coull & Alan Agresti, 2000. "Random Effects Modeling of Multiple Binomial Responses Using the Multivariate Binomial Logit-Normal Distribution," Biometrics, The International Biometric Society, vol. 56(1), pages 73-80, March.
    3. Sean M. O'Brien & David B. Dunson, 2004. "Bayesian Multivariate Logistic Regression," Biometrics, The International Biometric Society, vol. 60(3), pages 739-746, September.
    4. An, Lihua & Nkurunziza, Sévérien & Fung, Karen Y. & Krewski, Daniel & Luginaah, Isaac, 2009. "Shrinkage estimation in general linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2537-2549, May.
    5. D. B. Dunson, 2000. "Bayesian latent variable models for clustered mixed outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 355-366.
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