Longitudinal Data Analysis Using t Linear Mixed Models with Autoregressive Dependence Structures

The t linear mixed model with AR(p) dependence structure is pro- posed for the analysis of longitudinal data in which the underlying repeated measures contain thick tails and serial correlations simultaneously. For pa- rameter estimation, I develop a hybrid maximization scheme that combines the stability of the Expectation Conditional Maximization Either (ECME) algorithm with the rapid convergence property of the scoring method. Em- pirical Bayes estimation of random effects and prediction of future values for the proposed model are also considered. The proposed methodologies are applied to a real example from a tumor growth study on twenty-two mice. Numerical comparisons indicate that the proposed model outperforms the normal model from both inferential and predictive perspectives.