Focussed Model Selection for Longitudinal Data

Abstract

Longitudinal data arise when repeated measurements are taken on individuals over time. Commonly used models for such data are multivariate linear models, linear mixed effect models and generalised linear mixed models. This thesis begins by providing a detailed overview of these classes of models within the context of longitudinal data. Attention is then turned to model selection for such data. When selecting between models, one typically aims to come as close as one may to the underlying truth, without regard to the particular questions of interest. In contrast, the focussed information criterion (FIC) (Claeskens and Hjort 2003) approaches model selection with the goal of answering specific questions as accurately as possible. In this thesis, a multivariate slightly misspecified framework is put forward, within which the FIC is applicable as a covariate selector for multivariate linear models, linear mixed effect models, and generalised linear mixed models. Alternative approaches to focussed model selection for multivariate linear models and a selection of quantities of interest are also formulated.