Enhancing the Analysis of Linear Mixed Models with a Shiny Application: A Practical Guide to Statistical Tools

Details

Supervisors

Legrand, Catherine ; Bertrand, Aurélie

Faculty

Faculté des sciences

Degree label

Master [120] en statistique, orientation générale, à finalité spécialisée

Abstract

This thesis begins by setting out the scope of use of a linear mixed model, as well as the various nuances that can be found, such as data structure (longitudinal vs. hierarchical), and the difference between fixed and random effects. The model was then constructed, and the parameters of the fixed and random effects were estimated/predicted. An important point in this thesis is the analysis of residuals. Before introducing the types of residuals that can be defined within the framework of a linear mixed model, an introduction was given to classical linear models and their underlying assumptions. Following this introduction, two types of residuals are presented: raw marginal residuals and raw conditonal residuals. Once this stage has been completed, we move on to a presentation of the shiny tool that has been developed and an example that allows us to compare a classical linear model and a mixed linear model.