Date: Wed, 19 Sep 2007 09:02:52 -0700
Reply-To: "Ornelas, Fermin" <FOrnelas2@azdes.gov>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: "Ornelas, Fermin" <FOrnelas2@azdes.gov>
Subject: Re: Regression, centering and collinearity
In-Reply-To: A<200709190902.l8J509qA032242@mailgw.cc.uga.edu>
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When you fit a model without an intercept the collinearity diagnostics
will give you a lower condition index. To me this is not a good idea
since most often the final model will include an intercept in the
regression function.
I may reply to the second part later... but brushing up on linear
algebra will help you understand how x'x and xy are being affected.
-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of
Mike Ford
Sent: Wednesday, September 19, 2007 2:03 AM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Re: Regression, centering and collinearity
Thank you for the responses. I should have made clear that I was not
talking
about perfect collinearity.
Having seen centering suggested as a method to reduce moderate
collinearity
in a number of sources, I have used it and thought it worked because of
a
change in the condition indices of models when I use centered variables.
For
example, with this makey-up toy data...
y x1 x2
68 4.1 73.6
71 4.6 17.4
62 3.8 45.5
75 4.4 75.0
58 3.2 45.3
60 3.1 25.4
67 3.8 8.8
68 4.1 11.0
71 4.3 23.7
69 3.7 18.0
68 3.5 14.7
67 3.2 47.8
63 3.7 22.2
62 3.3 16.5
60 3.4 22.7
63 4 36.2
65 4.1 59.2
67 3.8 43.6
63 3.4 27.2
61 3.6 45.5
The condition index of the model = 21.7, which I would worry about if I
got
with real data. However if I center the DV and IVs and do the regression
(with no constant) the condition index for the model of the centered
data
=
1.2.
Obviously the beta, SE beta values etc. are the same for IVs in both
cases.
So, to my understanding the condition indices are saying that the model
with
the centered data is better than the model with the original data. Given
the
responses I have got to my posting, this change in the condition indices
confuses me even more now.
It must relate to a change in the cross products and sums of squares but
I
don't really understand.
Thank you!
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