For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and AR(1) errors is then derived. Empirical Bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with AR(1) errors model are also considered. Two numerical examples are presented to illustrate these models.
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