st: Multicollinearity diagnostics

[Richard Williams <Richard.A.Williams.5@nd.edu>]

I've made the mistake of trying to update my course notes on 
multicollinearity and find that I'm bogged down when it comes to 
eigenvalues and condition indices.  Specifically, I've been comparing the 
results produced by SPSS's -collin- parameter on its -regression- command 
and the results produced by -collin- in Stata (which is an add-on module; 
type -findit collin-).  What I am finding is that

* If I first center the variables in SPSS (i.e. subtract the mean from each 
variable) both Stata and SPSS produce identical results.

* If I don't center, SPSS gives me very different results. (Stata doesn't 
change whether I center or not.)

* If I am reading the ado file right, Stata -collin- computes eigenvalues, 
etc. from the correlation matrix of the X's.  Spss, on the other hand, 
presents "the eigenvalues of the scaled and uncentered cross-products matrix."

* In SPSS's favor, it computes the same condition number as William Greene 
does in his analysis of the Longley data (Econometric Analysis, 4th 
Edition, p. 258).

* But in Stata collin's favor, it just seems terribly counter-intuitive to 
me that adding or subtracting a constant from a variable is going to change 
my conclusions about multicollinearity.

Now, I've read that there are different ways of computing the eigenvalues 
and condition indices; can anybody offer any insights as to what should 
generally be preferred or when you should prefer one approach over 
another?  Another text I have says that centered predictor variables are 
typically used, but that isn't what SPSS is doing and it isn't what Greene 
seems to be doing if I understand him right.  Thanks for any info.

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