On estimation and prediction for temporally correlated longitudinal data

Abstract

In this paper, from a Bayesian point of view, we consider estimation of parameters and prediction of future Values for the longitudinal model proposed by Diggle (1988. Biometrics 44. 959-971). This model, called the repeated measures linear model, incorporates group mean, variability among individuals, serial correlation within an individual, and measurement error. Two different: priors are employed by the Bayesian approach, one is the noninformative prior and the other is composed of inverse gamma distributions. Given the noninformative prior, it is shown that the resulting approximate estimates of the regression coefficients are the same as those derived by the restricted maximum likelihood estimation. Markov chain Monte Carlo methods are also used to obtain more accurate Bayesian inference for parameters as well as prediction of future values. For parameter estimation and prediction of future values, the advantages of the Bayesian approach over the maximum likelihood method and the restricted maximum likelihood method are demonstrated by both real and simulated data. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 62F15; 62F10.