[S] VIF's and Tolerance in Multiple Regression

Marc R. Feldesman (feldesmanm@pdx.edu)
Thu, 07 May 1998 07:21:33 -0700

Thanks to all who responded to my question about computing the VIF
(variance inflation factor) and/or tolerance (reciprocal of VIF) for a
multiple regression model with potentially highly correlated predictors.

This spawned three basic types of response:

1. the decomposition techniques used by SPLUS are "modern" and are less
affected by collinearity than other techniques. Therefore VIF &/or
tolerance measures aren't really necessary.

2. there is a very simple way to get both, expressed elegantly in the
following formula:

VIF<-diag(solve(cor(model.matrix(lm1)[,-1]))), where the matrix term [,-1]
removes the intercept from the correlation matrix.

tolerance is simply the reciprocal of VIF.

Several people sent me variants of this, as well as a function to compute
PRESS statistics.

3. Finally, one writer suggested that this was a design problem, not an
analysis problem involving a
matrices of "near linear dependence" or "near rank loss" best handled by
extracting the "d" matrix from a singular value decomposition of the model
matrix from a lm().

Thanks are due to Bill Venables, Brant Deppa, Frank Harrell, SD Byers,
Stephen Weller, and Michael Conklin for sharing insights with me.

Dr. Marc R. Feldesman
email: feldesmanm@pdx.edu
email: feldesman@ibm.net
pager: 503-870-2515
fax: 503-725-3905

"If ignorance is bliss then why aren't there more happy people?" Lawrence

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