A PREDICTION OF INDIVIDUAL GROWTH OF HEIGHT ACCORDING TO AN EMPIRICAL BAYESIAN APPROACH

TAKAO SHOHOJI^{1}, KOUJI KANEFUJI^{2}, TAKAHIRO SUMIYA^{1} AND TAO QIN^{2}

1Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima 730, Japan 2Graduate School of Engineering, Hiroshima University, Higashihiroshima 724, Japan

(Received February 27, 1990; revised April 12, 1991)

Abstract. An empirical Bayesian approach is applied to a prediction of an individual growth in height at an early stage of life. The sample has 548 normal growth of Japanese girls whose measurements are available on request. The prior distribution of estimator of the growth parameter vector in a lifetime growth model is obtained conventionally from the least squares estimates of the growth parameters. The choice of prior distributions is discussed from a practical point of view. It is possible to obtain a relevant prediction of growth based upon only measurements during the first six years of life. The lifetime prediction of individual growth at the age of 6 is enough approximation of real measurements obtained. This report deals with the comparison between the least squares estimates and an empirical Bayes estimates of the growth parameters and the characteristic points of the growth curve. We discuss the mean-constant growth curves of the groups classified by the height intervals at the age of 6.

Key words and phrases: Empirical Bayes prediction, fundamental growth model, growth model, height, individual growth, mean-constant growth curve, non-linear regression, prediction, stature.