Introduction to Random and Mixed Effects Models

This chapter describes the random effects models (REMs), and focuses on the mixed model case. In fixed effects the analysis of variance (ANOVA), interest is on least squares estimates associated with the treatments, testing their equality, and assessing which ones are statistically different. With REMs, there are only variance components. The one-factor REM is the simplest case, and the obvious starting point. It is also an important model, serving to introduce the various concepts and procedures common to all REMs. An REM with two factors can be either crossed, or nested. The setup in the two-factor crossed REM model is the same, but the classes are now random instead of fixed. As in the fixed effects case, the model can be additive in the two effects or include an interaction term. In addition, with more than one factor, some could be fixed and some could be random, giving rise to a mixed model.