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.
