Quality & Quantity

, Volume 41, Issue 5, pp 673–690

A Caution Regarding Rules of Thumb for Variance Inflation Factors

Article

Abstract

The Variance Inflation Factor (VIF) and tolerance are both widely used measures of the degree of multi-collinearity of the ith independent variable with the other independent variables in a regression model. Unfortunately, several rules of thumb – most commonly the rule of 10 – associated with VIF are regarded by many practitioners as a sign of severe or serious multi-collinearity (this rule appears in both scholarly articles and advanced statistical textbooks). When VIF reaches these threshold values researchers often attempt to reduce the collinearity by eliminating one or more variables from their analysis; using Ridge Regression to analyze their data; or combining two or more independent variables into a single index. These techniques for curing problems associated with multi-collinearity can create problems more serious than those they solve. Because of this, we examine these rules of thumb and find that threshold values of the VIF (and tolerance) need to be evaluated in the context of several other factors that influence the variance of regression coefficients. Values of the VIF of 10, 20, 40, or even higher do not, by themselves, discount the results of regression analyses, call for the elimination of one or more independent variables from the analysis, suggest the use of ridge regression, or require combining of independent variable into a single index.

Keywords

multi-collinearity tolerance variance inflation factors variance of regression coefficients 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Belsley D.A. (1984). Demeaning conditioning diagnostics through centering. The American Statistician 38: 73–82CrossRefGoogle Scholar
  2. Belsley D.A., Kuh E. Welsch R.E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York, WileyGoogle Scholar
  3. Chatterjee S. Price B. (1991). Regression Analysis by Example, 2nd edn. New York, WileyGoogle Scholar
  4. Cook R.D. (1984). Comment on demeaning conditioning diagnostics through centering. The American Statistician 38: 78–79CrossRefGoogle Scholar
  5. Freund R.J. Wilson W.J. (1998). Regression Analysis: Statistical Modeling of a Response Variable. San Diego, Academic PressGoogle Scholar
  6. Fox J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. Thousand Oaks, CA: SageGoogle Scholar
  7. Goldberger A.S. (1991). A Course in Econometrics. Cambridge MA, Harvard University PressGoogle Scholar
  8. Gordon R.A. (1968). Issues in multiple regression. American Journal of Sociology 73: 592–616CrossRefGoogle Scholar
  9. Gordon R.A. (1987). Citation-classic – issues in multiple regression. Current Contents/Social and Behavioral Sciences 36: 18–18Google Scholar
  10. Greene W.H. (1993). Econometric Analysis, 2nd edn. New York, MacmillanGoogle Scholar
  11. Gunst R.F. (1984). Toward a balanced assessment of collinearity diagnostics. The American Statistician 38: 79–82CrossRefGoogle Scholar
  12. Hair J.F. Jr., Anderson R.E., Tatham R.L. Black W.C. (1995). Multivariate Data Analysis, 3rd edn. New York, MacmillanGoogle Scholar
  13. Johnston J. (1984). Econometric Methods. New York, McGraw-HillGoogle Scholar
  14. Judge G.G., Griffths W.E., Hill E.C., Lutkepöhl H. Lee T.C. (1985). The Theory and Practice of Econometrics, 2nd edn. New York, WileyGoogle Scholar
  15. Kennedy P. (1992). A Guide to Econometrics. Oxford, BlackwellGoogle Scholar
  16. Marquardt D.W. (1970). Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics 12: 591–256CrossRefGoogle Scholar
  17. Mason R.L., Gunst R.F. Hess J.L. (1989). Statistical Design and Analysis of Experiments: Applications to Engineering and Science. New York, WileyGoogle Scholar
  18. Menard S. (1995). Applied Logistic Regression Analysis: Sage University Series on Quantitative Applications in the Social Sciences. Thousand Oaks CA, SageGoogle Scholar
  19. Neter J., Wasserman W. Kutner M.H. (1989). Applied Linear Regression Models. IL, IrwinGoogle Scholar
  20. Obenchain R.L. (1977). Classical F-tests and confidence intervals for ridge regression. 19: 429–439Google Scholar
  21. Snee R.D. Marquardt D.W. (1984). Collinearity diagnostics depend on the domain of prediction, and model, and the data. The American Statistician 38: 83–87CrossRefGoogle Scholar
  22. StataCorp (1997). Reference Manual A-F (Release 5). College Station, TX: Stata Press.Google Scholar
  23. Wood F.S. (1984). Effect of centering on collinearity and interpretation of the constant. The American Statistician 38: 88–90CrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of SociologyUniversity of OregonEugeneUSA

Personalised recommendations