Abstract
Analyses of variance (ANOVA) with the general linear model (GLM) in many standard statistical packages use an Overparameter ized 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. Many students and researchers in the behavioral -ciences routinely conduct analyses of variance <ANOVAs) using the general linear model procedure in SAS (1997) or SPSS (1998; GLM, as named in both packages). Unbeknownst to many of these students and researchers, both GLM procedures use Overparameterized models to compute ANOVAs. These GLM users may occasionally suffer some minor discomfort when the procedure produces mysterious messages about matrices being singular, gener
Published Version
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