Bayesian analysis of joint mean and covariance models for longitudinal data

• Published in: Journal of applied statistics Vol. 41; no. 11; pp. 2504 - 2514
• Main Authors: Xu, Dengke, Zhang, Zhongzhan, Wu, Liucang
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.11.2014; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Cholesky decomposition; Computer simulation; Covariance; Covariance matrix; Data analysis; Data processing; Decomposition; Estimates; Gibbs sampler; joint mean and covariance models; Markov analysis; Mathematical models; Metropolis-Hastings algorithm; Monte Carlo simulation; Parameter estimation; Regression analysis; Studies
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/02664763.2014.920778

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. If misspecification occurs, it may lead to inefficient or biased estimators of parameters in the mean. One of the most commonly used methods for handling the covariance matrix is based on simultaneous modeling of the Cholesky decomposition. Therefore, in this paper, we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a fully Bayesian inference for joint mean and covariance models based on this decomposition. A computational efficient Markov chain Monte Carlo method which combines the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard deviation estimates. Finally, several simulation studies and a real example are presented to illustrate the proposed methodology.