BAYESIAN PREDICTION ANALYSIS FOR GROWTH CURVE MODEL USING NONINFORMATIVE PRIORS

GWOWEN SHIEH AND JACK C. LEE

Department of Management Science and Institute of Statistics, National Chiao Tung University, Hsinchu, Taiwan 30050, R.O.C.

(Received November 16, 1998; revised July 17, 2000)

Abstract. We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.

Key words and phrases: Approximations, Metropolis-Hastings, posterior, random coefficient regression, Rao-Blackwellization.