Linear Models and Time-Series Analysis

3Introduction to Random and Mixed Effects Models

Section 2.1, in the previous chapter on fixed effects ANOVA models, provided some introductory remarks on the distinction between fixed and random effects. This chapter is dedicated to random effects models, abbreviated as REMs, but also briefly touches on the mixed model case. In fixed effects ANOVA, interest is on least squares estimates associated with the treatments, testing their equality, and assessing which ones are statistically different. For example, with a two‐way ANOVA without interaction, there are parameters (the grand mean , the error variance, and the treatment parameters), albeit with sum restrictions. With REMs, there are only (besides the grand mean) variance components. For example, in a so‐called two‐way nested model with both effects random, no matter how many levels of factors A and B, there are three variance components—the error variance , and the variances from the two factors, and —and thus only four model parameters ...