Variance Inflation Factor (VIF)

In multiple regression, the variance inflation factor (VIF) is used as an indicator of multicollinearity. Computationally, it is defined as the reciprocal of tolerance: 1 / (1 - R²). All other things equal, researchers desire lower levels of VIF, as higher levels of VIF are known to affect adversely the results associated with a multiple regression analysis. In fact, the utility of VIF, as distinct from tolerance, is that VIF specifically indicates the magnitude of the inflation in the standard errors associated with a particular beta weight that is due to multicollinearity.

For example, a VIF of 8 implies that the standard errors are larger by a factor of 8 than would otherwise be the case, if there were no inter-correlations between the predictor of interest and the remaining predictor variables included in the multiple regression analysis.

Various recommendations for acceptable levels of VIF have been published in the literature. Perhaps most commonly, a value of 10 has bee recommended as the maximum level of VIF (e.g., Hair, Anderson, Tatham, & Black, 1995; Kennedy, 1992; Marquardt, 1970; Neter, Wasserman, & Kutner, 1989). The VIF recommendation of 10 corresponds to the tolerance recommendation of .10 (i.e., 1 / .10 = 10). However, a recommended maximum VIF value of 5 (e.g., Rogerson, 2001) and even 4 (e.g., Pan & Jackson, 2008) can be found in the literature. It would appear that researchers can use which ever criterion they wish to help serve their own purposes.

See also

● Tolerance
● Multicollinearity

References

● Hair, J. F. Jr., Anderson, R. E., Tatham, R. L. & Black, W. C. (1995). Multivariate Data Analysis (3rd ed). New York: Macmillan.

● 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.

● Neter, J., Wasserman, W. & Kutner, M. H. (1989). Applied Linear Regression Models. Homewood, IL: Irwin.

● Pan, Y, & Jackson, R. T. (2008). Ethnic difference in the relationship between acute inflammation and and serum ferritin in US adult males. Epidemiology and Infection, 136, 421-431.

● Rogerson, P. A. (2001). Statistical methods for geography. London: Sage.

Further reading

● O'Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41, 673-690.

● Stine, R. A. (1995). The graphical interpretation of variance inflation factors. The American Statistician, 49(1), 53-56