Actually, the CI index and VIF are just a start.  It is best to look at what they call a matrix of "variance proportions" (found in SAS and a few other places...)--which hardly anyone understands (including the SAS folks).  It is a matrix of estimates of what the variences of the regression coefficients would be if you could figure them out in the first place.  It shows which factors dominate over others IN THE PARTICULAR SETUP you are analyzing.  The matrix is often calculated using eigenvalues, but is best done with Singular Value Decomposition techniques (you don't have to have a square matrix, and you maintain better precision).  Analysts will say that it can display an unstable system -- which is correct, but they generally say that, if its true, you have bad data and should throw it out--or collect more.  I suggest care, because it may be illustrating the nature of the system you are studying.

The only decent reference that I know of is a little book (hard to read) that I can't remember off the top of my head.  Have to look it up.

Timothy E. Paysen, Phd
Research Forester (ret.)




________________________________
From: John Sorkin <jsorkin@grecc.umaryland.edu>
To: Alex Roy <alexroy2008@gmail.com>; r-help@r-project.org
Sent: Tuesday, July 21, 2009 4:19:11 AM
Subject: Re: [R] Collinearity in Linear Multiple Regression

I suggest you start by doing some reading about Condition index (CI) and variation inflation factor (VIF). Once you have reviewed the theory, a search of search.r-project.org (under the help menu in a windows-based R installation) for VIF will help you obtain values for VIF, c.f. http://finzi.psych.upenn.edu/R/library/HH/html/vif.html 
John

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

>>> Alex Roy <alexroy2008@gmail.com> 7/21/2009 7:01 AM >>>
Dear all,
                  How can I test for collinearity in the predictor data set
for multiple linear regression.

Thanks

Alex

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