Analyzing the Relationship Between Variance Inflation Factors and Predictor Variable Redundancy in Regression Models

Posted: Apr 15, 2021

• Evelyn Young
• Maria King
• Noah Rivera

Abstract

Multicollinearity represents one of the most persistent challenges in regression analysis, affecting the stability and interpretability of parameter estimates. The variance inflation factor (VIF) has emerged as the predominant diagnostic tool for detecting multicollinearity, providing a quantitative measure of how much the variance of an estimated regression coefficient increases due to collinearity. Despite its widespread adoption, the mathematical relationship between VIF and the underlying redundancy structure among predictor variables remains incompletely characterized in the statistical literature. Traditional interpretations of VIF often focus on pairwise correlations between predictors, overlooking the complex interplay of higher-order dependencies that contribute to multicollinearity. This research addresses this gap by developing a comprehensive theoretical framework that explicitly links VIF to multidimensional redundancy metrics. Our approach moves beyond conventional pairwise correlation analysis to incorporate information-theoretic measures and spectral decomposition techniques that capture the full complexity of predictor interdependencies. The novelty of our work lies in its systematic exploration of how VIF values respond to different patterns of redundancy, including scenarios where traditional diagnostics may provide misleading guidance. The central research questions guiding this investigation are threefold. First, how can we mathematically characterize VIF as a function of both pairwise and higher-order correlations among predictor variables? Second, what patterns emerge when mapping VIF values against comprehensive redundancy metrics