ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors

For the analysis of longitudinal data with multiple characteristics, we are devoted to providing additional tools for multivariate linear mixed models in which the errors are assumed to be serially correlated according to an autoregressive process. We present a computationally flexible ECM procedure for obtaining the maximum likelihood estimates of model parameters. A score test statistic for testing the existence of autocorrelation among within-subject errors of each characteristic is derived. The techniques for the estimation of random effects and the prediction of further responses given past repeated measures are also investigated. The methodology is illustrated through an application to a set of AIDS data and two small simulation studies.