Residual analysis in the GMANOVA-MANOVA Model

Abstract

This thesis focuses on the establishment and analysis of residuals in the so called GMANOVA-MANOVA model. The model is a special case of the Extended Growth Curve Model. It has two terms where one term models the profiles (growth curves) and the other the covariables of interest. This model is useful in studying growth curves in short time series in fields such as economics, biology, medicine, and epidemiology. Furthermore, in the literature, residuals have been extensively studied and used to check model adequacy in univariate linear models. This thesis contributes to the extension of the study of residuals in the GMANOVA-MANOVA model. In this thesis, a new pair of residuals is established via the maximum likelihood estimators of the parameters in the model. One residual indicates whether an individual is far away from the group means and a second residual is used to check assumptions about the mean structure. Different properties of these residuals are verified and their interpretation is discussed. Moreover, using parametric bootstrap, the empirical distributions of the extreme elements in the residuals are derived. Finally, testing bilinear restriction in the MANOVA model is considered. One can show that the MANOVA model with bilinear restrictions is nothing more than a GMANOVA MANOVA model. Furthermore, the likelihood ratio test can be shown to be given as a function of the residuals to the GMANOVA-MANOVA model, which can be used to understand the appropriateness of the model and test the bilinear hypothesis.