Joint mean-covariance random effect model for longitudinal data.

In this paper, we consider the inherent association between mean and covariance in the joint mean-covariance modeling and propose a joint mean-covariance random effect model based on the modified Cholesky decomposition for longitudinal data. Meanwhile, we apply M-H algorithm to simulate the posterior distributions of model parameters. Besides, a computationally efficient Monte Carlo expectation maximization (MCEM) algorithm is developed for carrying out maximum likelihood estimation. Simulation studies show that the model taking into account the inherent association between mean and covariance has smaller standard deviations of the estimators of parameters, which makes the statistical inferences much more reliable. In the real data analysis, the estimation of parameters in the mean and covariance structure is highly efficient.