Fixed effects models, random effects models, mixed models or multilevel models: properties and implementation of modeling of the heterogeneity in presence of clustered data

This document presents the different ways to model heterogeneity in case of clustering, such pupils achievement in classroom or schools. In the linear framework, it essentially discusses the pertinence of fixed or random effects assumptions depending upon the goal pursued and the empirical evidence displayed by data. Statistical assumptions of the different models are introduced and successively discussed, as well as the properties of the estimators that are derived. For each model, SAS code is provided. Hausman tests, and their use to choose models, are explained. Beyond the linear framework, binary models are presented in the last chapter.