Bayesian Joint Semiparametric Mean-Covariance Modeling for Longitudinal Data

Joint parsimonious modeling the mean and covariance is important for analyzing longitudinal data, because it accounts for the efficiency of parameter estimation and easy interpretation of variability. The main potential risk is that it may lead to inefficient or biased estimators of parameters while misspecification occurs. A good alternative is the semiparametric model. In this paper, a Bayesian approach is proposed for modeling the mean and covariance simultaneously by using semiparametric models and the modified Cholesky decomposition. We use a generalized prior to avoid the knots selection while using B-spline to approximate the nonlinear part and propose a Markov Chain Monte Carlo scheme based on Metropolis-Hastings algorithm for computations. Simulation studies and real data analysis show that the proposed approach yields highly efficient estimators for the parameters and nonparametric parts in the mean, meanwhile providing parsimonious estimation for the covariance structure.