Generalized Collinearity Diagnostics for Factorial ANOVA and Polynomial Regression

• In Event: Linear, Nonlinear, Latent, and Machine Learning Modeling for Educational Research

Abstract

Fox and Monette (1992) introduced the Generalized Variance Inflation Factor (GVIF) as a means of assessing multicollinearity for models containing related sets of regressors including: 1) a set of coding scheme variables that represent independent groups (i.e., one-way between-subjects ANOVA designs) or 2) variables that are functions of each other as in polynomial and interaction terms. Despite this important development, GVIF rarely appears in the statistical literature or statistical software. The purpose of this paper is to: reintroduce GVIF using Fox & Monette’s (1992) approach; conceptualize GVIF as a function of multivariate regression models; present approaches to computing GVIFs in popular statistical software that only report standard collinearity diagnostics; and explore the complications of estimating GVIF in Factorial ANOVA.

Author

• T. Mark Beasley, University of Alabama - Birmingham