ABSTRACT
This chapter considers an attempt (Hodges 1998) to adapt linear model theory to mixed linear models using the constraint-case formulation described in Section 2.1. Here, as in linear model theory, the purpose is to do the following: • Seek discrepant features of the data; linear model theory does this using residuals. • Seek deviations from model assumptions; linear model theory uses residuals to
check for non-linearity in the mean structure and non-constant error variance, and to consider transformations of the outcome y that are better suited to a homoscedastic linear model. • Seek observations with a large influence on estimates; linear model theory uses
case influence. • Assess evidence for adding predictors; linear model theory uses added variable
plots. • Understand ill-determined estimates, i.e., competition among predictors (regres-
sors, right-hand-side variables, effects) to capture variation in the outcome y; in linear model theory, the relevant ideas are collinearity, confounding, and variance inflation.
