Bayesian analysis of multivariate t linear mixed models with missing responses at random

Abstract

The multivariate t linear mixed model (MtLMM) has been recently proposed as a robust tool for analysing multivariate longitudinal data with atypical observations. Missing outcomes frequently occur in longitudinal research even in well controlled situations. As a powerful alternative to the traditional expectation maximization based algorithm employing single imputation, we consider a Bayesian analysis of the MtLMM to account for the uncertainties of model parameters and missing outcomes through multiple imputation. An inverse Bayes formulas sampler coupled with Metropolis-within-Gibbs scheme is used to effectively draw the posterior distributions of latent data and model parameters. The techniques for multiple imputation of missing values, estimation of random effects, prediction of future responses, and diagnostics of potential outliers are investigated as well. The proposed methodology is illustrated through a simulation study and an application to AIDS/HIV data.

Keywords:

• conditional conjugate priors
• damped exponential correlation
• data augmentation
• IBF sampler
• missing data

AMS Subject Classification:

• 62F15
• 62J05

Acknowledgments

The authors would like to express their deepest thanks to Chief editor, the Associate editor and one anonymous reviewer for their insightful comments and suggestions that greatly improved this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Ministry of Science and Technology under [Grant no. MOST 103-2118-M-035-001-MY2] and [MOST 103-2118-M-005-001-MY2] of Taiwan.