Toward a balanced assessment of collinearity diagnostics

The present investigation is concerned with a review of the foundations upon which regression methodology is based, taking into account a study of regression diagnostics conducted by Belsey et al. (1980). It is found that one of the most difficult and controversial problems facing data analysts is related to redundant predictor variables in a regression analysis. Collinearity diagnostics are only meaningful when interpreted in terms of 'basic variables' which are 'structurally interpretable'. Conflicting perspectives are discussed, giving attention to the role of centering when diagnosing collinearity. The definition of collinearity and collinearity measures are considered along with questions regarding 'structural interpretability' as a universally accepted principle in model formulation, and the importance of the detection of collinearity with the constant term.