On the difference between ML and REML estimators in the modelling of multivariate longitudinal data

A random effects model is examined in the multivariate setting where more than one characteristics are measured at each time point. ML and REML estimators are obtained under the restriction that estimates of variance matrices being at least p.s.d. It is shown that REML has greater probability of giving full rank estimates of variance components matrices but as regards the efficiency in the estimation of the location parameter, correct specification of the number of random effects is needed. In general, REML provides larger estimates of variance of model parameters than ML.