Computational Statistics and Data Analysis: Robustness of the Linear Mixed Effects Model to Non-normality of Longitudinal Data.

Abstract

The Linear mixed effects model is based on one of the assumptions, which is that data are normally distributed as the errors and random effects in the model are assumed to have normal distributions; but in practice, longitudinal data are often either slightly or very skewed. Hence, they have non-normal distributions. This thesis is focused on studying the robustness of the linear mixed effects model to non-normality of error distribution. The thesis is structured in this way: in chapter 1, the literature review of the linear mixed effects model is presented. Chapter 2 contains explanations of the statistical tools used in checking the goodness of fit for a fitted model. Chapter 3 contains a description of the research procedures employed in the implementations. Chapter 4 contains the simulations and results. All in all, conclusions are presented in chapter 5.