Additional caution regarding rules of thumb for variance inflation factors: extending O’Brien to the context of specification error

Abstract

Despite the popularity of Variance Inflation Factor (VIF) scores as multicollinearity diagnostics, methodological work has voiced skepticism. In a paper that has become the most highly cited reference regarding the use of VIF scores, O’Brien urged caution when applying VIF thresholds. More recent articles have considered the validity of VIF scores in the presence of regression specification error. These suggest a need for additional caution. In this paper, we present a strategy to incorporate analytic results from the specification error literature directly into the framework developed and employed by O’Brien. We confirm O’Brien’s main result that VIF scores far above thresholds may be benign, but we establish a boundary condition for his original framework: regressions must be perfectly specified. Further, our extension reconciles the O’Brien framework with results from the specification error literature. We conclude that multicollinearity may indeed be the cause of excess type 1 errors regardless of whether VIF scores are high or low.