The Overparameterized Analysis of Variance Model

Analyses of variance (ANOVA) with the general linear model (GLM) in many standard statistical packages use an overparameterized model, a model unfamiliar to most behavioral science researchers. Estimates and significance tests with GLM procedures are calculated by computing generalized inverses and estimates of estimable functions. Using simple examples, the authors discuss the concepts that underlie the solutions for 1-way and 2-way ANOVAs with overparameterized models and illustrate how these models allow one to evaluate the research hypotheses. The authors also extend the discussion of overparameterized models to a more general modeling approach than GLM, the general linear mixed model.