On the analysis of multivariate growth curves

Growth curve data arise when repeated measurements are observed on a number of individuals with an ordered dimension for occasions. Such data appear frequently in almost all fields in which statistical models are used, for instance in medicine, agriculture and engineering. In medicine, for example, more than one variable is often measured on each occasion. However, analyses are usually based on exploration of repeated measurements of only one variable. The consequence is that the information contained in the between-variables correlation structure will be discarded.  In this study we propose a multivariate model based on the random coefficient regression model for the analysis of growth curve data. Closed-form expressions for the model parameters are derived under the maximum likelihood (ML) and the restricted maximum likelihood (REML) framework. It is shown that in certain situations estimated variances of growth curve parameters are greater for REML. Also a method is proposed for testing general linear hypotheses. One numerical example is provided to illustrate the methods discussed. Received: 22 February 1999