Bayesian estimation for longitudinal data in a joint model with HPCs

In longitudinal data analysis, linear models are typically utilized. However, deriving the Bayesian estimation with respect to the misspecification of the correlation structure is a challenging task. In this article, we construct a joint mean-covariance model with angles or hyperspherical coordinates (HPCs) for which we then present a Bayesian framework. Based on the connection with the semipartial correlations (SPCs), we focus on the selection (sparsity) priors on these angles. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for the proposed model, and the positive definiteness of the correlation matrix in posterior computation is automatically guaranteed by our method. Ultimately, we compare the performance of our joint model with some recent methods focusing only on the correlation matrix by using simulations and clinical trial data on smoking.