A BAYESIAN MODEL FOR GROWTH CURVE ANALYSIS

An experiment involves K subjects where for subject i, n(i) values y(i 1), Y-i2, ..., Y-in, of a random variable Y are observed at times t(i1 ), t(i2),..., t(ini). Assume that y(ij) - F(i,t(ij)) + e(ij) where {e( ij)} are independently and identically distributed (i.i.d.) N(O, sigma (2)). We consider the estimation of the function F and the testing of the homogeneity hypothesis that, for i not equal j, F(i, t) - F(j, t) does not depend on t. The function F(i, t) is modelled as a Gaussian p rocess which seeks to quantify the notions that for each i, F(i, t) is a slowly changing function of t and that for i not equal j, F(i, t), and F(j, t) are in some sense similar. We propose to estimate F(i, t) by its posterior mean given all of the data. This Bayes estimate is sh own to be equivalent to a particular form of penalised likelihood esti mation. We consider data-based methods for setting the parameters of t he Gaussian process prior, develop a test of the homogeneity hypothesi s, report the results of a Monte Carlo study illustrating the effectiv eness of the proposed methodology, and apply the methods to a study of variations in temperature and blood pressure over the course of the m enstrual cycle.