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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Belsley D.A. (1984). Demeaning conditioning diagnostics through centering. The American Statistician 38: 73–82
Belsley D.A., Kuh E. Welsch R.E. (1980). Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York, Wiley
Chatterjee S. Price B. (1991). Regression Analysis by Example, 2nd edn. New York, Wiley
Cook R.D. (1984). Comment on demeaning conditioning diagnostics through centering. The American Statistician 38: 78–79
Freund R.J. Wilson W.J. (1998). Regression Analysis: Statistical Modeling of a Response Variable. San Diego, Academic Press
Fox J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. Thousand Oaks, CA: Sage
Goldberger A.S. (1991). A Course in Econometrics. Cambridge MA, Harvard University Press
Gordon R.A. (1968). Issues in multiple regression. American Journal of Sociology 73: 592–616
Gordon R.A. (1987). Citation-classic – issues in multiple regression. Current Contents/Social and Behavioral Sciences 36: 18–18
Greene W.H. (1993). Econometric Analysis, 2nd edn. New York, Macmillan
Gunst R.F. (1984). Toward a balanced assessment of collinearity diagnostics. The American Statistician 38: 79–82
Hair J.F. Jr., Anderson R.E., Tatham R.L. Black W.C. (1995). Multivariate Data Analysis, 3rd edn. New York, Macmillan
Johnston J. (1984). Econometric Methods. New York, McGraw-Hill
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, Wiley
Kennedy P. (1992). A Guide to Econometrics. Oxford, Blackwell
Marquardt D.W. (1970). Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics 12: 591–256
Mason R.L., Gunst R.F. Hess J.L. (1989). Statistical Design and Analysis of Experiments: Applications to Engineering and Science. New York, Wiley
Menard S. (1995). Applied Logistic Regression Analysis: Sage University Series on Quantitative Applications in the Social Sciences. Thousand Oaks CA, Sage
Neter J., Wasserman W. Kutner M.H. (1989). Applied Linear Regression Models. IL, Irwin
Obenchain R.L. (1977). Classical F-tests and confidence intervals for ridge regression. 19: 429–439
Snee R.D. Marquardt D.W. (1984). Collinearity diagnostics depend on the domain of prediction, and model, and the data. The American Statistician 38: 83–87
StataCorp (1997). Reference Manual A-F (Release 5). College Station, TX: Stata Press.
Wood F.S. (1984). Effect of centering on collinearity and interpretation of the constant. The American Statistician 38: 88–90
About this article
Cite this article
O’brien, R.M. A Caution Regarding Rules of Thumb for Variance Inflation Factors. Qual Quant 41, 673–690 (2007). https://doi.org/10.1007/s11135-006-9018-6
- variance inflation factors
- variance of regression coefficients