Collinearity, Heteroscedasticity and Outlier Diagnostics in Regression. Do They Always Offer What They Claim?

Germà Coenders and Marc Saez

In this article, some classic collinearity, heteroscedasticity and outlier diagnostics in multiple regression models are reviewed. Some major problems are described in the Breusch-Pagan test, the condition number and the critical values for the studentized deleted residual and cook's distance. Alternatives are suggested which consist of computing the condition number of the correlation matrix instead of the rescaled moment matrix, using the NR2 statistic for the Breusch Pagan test, setting global-risk-based critical values for the studentized deleted residual, and drawing graphical displays for Cook's distance. Very large differences between the original and alternative diagnostics emerge both on simulated data and on real data from a work absenteeism study.