Multicollinearity diagnostics for multiple regression: A Monte Carlo study
Objectives. To demonstrate the ineffectiveness of some commonly used collinearity diagnostics, and present a more effective method which was developed by David Belsley. Methods. Collinearity is a problem in multiple regression when there is a relationship among the independent variables. When collinearity exists, parameter estimates may be incorrect, and their standard errors may be inflated. Some commonly used methods for diagnosing collinearity (e.g. the correlation matrix) are shown to inadequate. A Monte Carlo study of two widely recommended collinearity diagnostics (variance inflation factors and condition indexes) when three conditions were varied. These conditions were the number of IVs (3, 5 or 7), the presence (or absence) of interaction, and degree of collinearity (weak, moderate, or strong) are varied. This 3 x 2 x 3 factorial ANOVA design yielded 18 models, each of which was replicated 1000 times. Each replication was tested for collinearity using 2 diagnostics. Results. Both VIFs and condition indexes were able to diagnose the presence of collinearity, but condition indexes were more precise. Condition indexes were able to determine which variables were involved in the collinearity, but VIFs were not. The most commonly recommended values for diagnosing collinearity with VIFs appear to be substantially too low. Conclusions. Data which are to be analyzed using multiple regression should be tested for collinearity using condition indexes.
Flom, Peter Leslie, "Multicollinearity diagnostics for multiple regression: A Monte Carlo study" (1999). ETD Collection for Fordham University. AAI9926897.