LIKELIHOOD RATIO TEST FOR THE REDUNDANCY IN A MULTIVARIATE GROWTH CURVE MODEL

This paper is concerned with a multivariate growth curve model for observations obtained by simultaneously measuring m response variables at each of p time points, on samples from multiple groups. The objective is to develop a test for determining whether the m2 = m − m1 response variables carry no additional information (are redundant) for a comparison between the groups, given the presence of the first m1 response variables. We obtain some equivalent hypotheses for redundancy by extending the technique of Rao (1970). The likelihood ratio (LR) test is discussed. However, because its null distribution is complicated, we propose a more practical approximate test using a conditional LR criterion.