In Chapter 2, Univariate and Multivariate Tests for Equality of Means, we discussed mixed effects models in the context of the analysis of variance (ANOVA). These models arise when we have a mixture of fixed and random effects. Fixed effects are associated to standard coefficients that appear in every regression problem, and random effects are variance components that govern shocks that are shared by members of the same groups. For example, the grades of any student can be thought of as the sum of how many hours the student spent studying (this would be the fixed effect) and a random shock that is shared across all students from the same school. The idea is to capture that students belonging to the same school to have correlated grades.