Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers

The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is v...

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Published inJournal of multivariate analysis Vol. 105; no. 1; pp. 300 - 310
Main Authors Wang, Wan-Lun, Fan, Tsai-Hung
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.02.2012
Elsevier
Taylor & Francis LLC
SeriesJournal of Multivariate Analysis
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ISSN0047-259X
1095-7243
DOI10.1016/j.jmva.2011.10.006

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Abstract The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Owing to the introduction of too many hidden variables in the model, the conventional Markov chain Monte Carlo (MCMC) method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formulas (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for future values are also investigated. The proposed methodologies are illustrated with a real example from an AIDS clinical trial and a careful simulation study.
AbstractList The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Owing to the introduction of too many hidden variables in the model, the conventional Markov chain Monte Carlo (MCMC) method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formulas (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for future values are also investigated. The proposed methodologies are illustrated with a real example from an AIDS clinical trial and a careful simulation study.
The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great flexibility for modeling the between- and within-subject correlation among multi-outcome repeated measures, the underlying normality assumption is vulnerable to potential atypical observations. We present a fully Bayesian approach to the multivariate t linear mixed model (MtLMM), which is a robust extension of MLMM with the random effects and errors jointly distributed as a multivariate t distribution. Owing to the introduction of too many hidden variables in the model, the conventional Markov chain Monte Carlo (MCMC) method may converge painfully slowly and thus fails to provide valid inference. To alleviate this problem, a computationally efficient inverse Bayes formulas (IBF) sampler coupled with the Gibbs scheme, called the IBF-Gibbs sampler, is developed and shown to be effective in drawing samples from the target distributions. The issues related to model determination and Bayesian predictive inference for future values are also investigated. The proposed methodologies are illustrated with a real example from an AIDS clinical trial and a careful simulation study. [PUBLICATION ABSTRACT]
Author Wang, Wan-Lun
Fan, Tsai-Hung
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Issue 1
Keywords 91-08
Conditional conjugate priors
MCMC
62H12
Hierarchical models
Inverse Bayes formulas
62F15
Multivariate longitudinal data
Language English
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Snippet The multivariate linear mixed model (MLMM) has become the most widely used tool for analyzing multi-outcome longitudinal data. Although it offers great...
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SubjectTerms Bayesian analysis
Conditional conjugate priors
Conditional conjugate priors Hierarchical models Inverse Bayes formulas MCMC Multivariate longitudinal data
Hierarchical models
Inverse Bayes formulas
Markov analysis
MCMC
Monte Carlo simulation
Multivariate analysis
Multivariate longitudinal data
Studies
Title Bayesian analysis of multivariate t linear mixed models using a combination of IBF and Gibbs samplers
URI https://dx.doi.org/10.1016/j.jmva.2011.10.006
http://econpapers.repec.org/article/eeejmvana/v_3a105_3ay_3a2012_3ai_3a1_3ap_3a300-310.htm
https://www.proquest.com/docview/912942123
Volume 105
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