Seminar by Jemila Hamid

Multivariate Bilinear Models Useful for Analysis of Longitudinal and Clustered Longitudinal Data

Multivariate growth curve models (GCMs) are bilinear models useful in the analysis of growth curves, dose-response curves as well as other curves associated with continuous variables – hence play important roles in the analysis of longitudinal data, especially in scenarios where sample size is limited. The model is a natural extension of the classical multivariate analysis of variance (MANOVA) model and arises when linear restrictions on the MANOVA model are imposed, here it is referred to as the generalized multivariate analysis of variance (GMANOVA) model. In this presentation, I will first provide a brief overview of the GCMs models and their extensions, highlight the bilinear nature of the models and discuss how the vector operator plays important roles in our understanding of the models and the bilinear projections with respect to the within and between individual design matrices. I will then present our contributions to estimation, hypothesis testing, residual analysis, and model diagnostics. I will also highlight applications in the analysis of longitudinal data including clustered longitudinal data and (if time permits) high-dimensional extensions.