Model selection with the linear mixed effects model for longitudinal data.

Abstract

Model building or model selection with linear mixed models (LMM) is complicated by the presence of both fixed effects and random effects. The fixed effects structure and random effects structure are co-dependent, so selection of one influences the other. Most presentations of LMM in psychology and education are based on a multi-level or hierarchical approach in which the variance-covariance matrix of the random effects is assumed to be positive definite with non-zero values for the variances. When the number of fixed effects and random effects is not known, the predominant approach to model building is a step-up procedure in which one starts with a limited model (e.g., few fixed and random intercepts) and then additional fixed effects and random effects are added based on statistical tests. A procedure that has received less attention in psychology and education is top-down model building. In the top-down procedure, the initial model has a single random intercept but is loaded with fixed effects (also known as an ”over-elaborate” model). Based on the over-elaborate fixed effects model, the need for additional random effects is determined. Once the number of random effects is selected, the fixed effects are tested to see if any can be omitted from the model. There has been little if any examination of the ability of these procedures to identify a true population model (i.e., identifying a model that generated the data). The purpose of this dissertation is to examine the performance of the various model building procedures for exploratory longitudinal data analysis. Exploratory refers to the situation in which the correct number of fixed effects and random effects is unknown before the analysis.