Eric M. ChiGregory C. Reinsel2014-09-122014-09-121989-06Journal of the American Statistical Association, June 1989, Vol.84 No.406http://hdl.handle.net/123456789/5667For 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 explicil maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregrcssive) AR{!) 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(i) errors model are also considered. A numerical example is presented to illustrate these methods.enAutoregressive modelEmpirical Bayes estimateMaximum likelihood estimationPredictionScore testArticle