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RE: st: RE: Interpretation of quadratic terms
From
Rodolphe Desbordes <[email protected]>
To
"[email protected]" <[email protected]>
Subject
RE: st: RE: Interpretation of quadratic terms
Date
Wed, 10 Mar 2010 17:09:20 +0000
Dear Richard,
My hunch is that high multicollinearity will be detected in any case by very low eigenvalues. However, these diagnostic tests may be very misleading since "better values" may fool a researcher into thinking that his model after rescaling now performs better, e.g.
. collin mpg mpg2
Collinearity Diagnostics
SQRT R-
Variable VIF VIF Tolerance Squared
----------------------------------------------------
mpg 34.69 5.89 0.0288 0.9712
mpg2 34.69 5.89 0.0288 0.9712
----------------------------------------------------
Mean VIF 34.69
Cond
Eigenval Index
---------------------------------
1 2.8654 1.0000
2 0.1334 4.6350
3 0.0013 47.4208
---------------------------------
Condition Number 47.4208
Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
Det(correlation matrix) 0.0288
. gen double mpgm=mpg-`m'
. gen double mpgm2=mpgm^2
. collin mpgm mpgm2
Collinearity Diagnostics
SQRT R-
Variable VIF VIF Tolerance Squared
----------------------------------------------------
mpgm 1.43 1.20 0.6975 0.3025
mpgm2 1.43 1.20 0.6975 0.3025
----------------------------------------------------
Mean VIF 1.43
Cond
Eigenval Index
---------------------------------
1 1.6914 1.0000
2 1.0000 1.3005
3 0.3086 2.3410
---------------------------------
Condition Number 2.3410
Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
Det(correlation matrix) 0.6975
Rodolphe
________________________________________
From: [email protected] [[email protected]] On Behalf Of Richard Williams [[email protected]]
Sent: 10 March 2010 13:40
To: [email protected]; [email protected]
Subject: RE: st: RE: Interpretation of quadratic terms
At 07:34 AM 3/10/2010, Rodolphe Desbordes wrote:
>Dear Rosie, Nick and Roger,
>
>To conclude this thread and summarise the main arguments put forward
>by Nick, Roger and myself:
>
>A) There can be some good reasons for "pre-emptive centering": a) to
>avoid computational issues, which are unlikely to arise with modern
>econometric softwares such as Stata; b) to provide substantive interpretation.
I agree with that, and I may add a sentence like that to my notes in
the future! One other thought that I have had though: Suppose you
are doing tests for collinearity and you have other variables in the
model, so I use something like the -collin- command. Is there an
advantage to minimizing the collinearity involving the variables that
have the squared term? That is, would doing so make me better able
to detect where the collinearity is among other variables? Or would
it make no difference?
For example, suppose x1 is highly collinear with other variables. If
I have x1^squared in the model, I am thinking I might miss the
collinearity because x1 and x1^squared are so highly correlated
(unless I have centered x1 first). This is just idle speculation on
my part, I haven't fiddled around with it to see.
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME: (574)289-5227
EMAIL: [email protected]
WWW: http://www.nd.edu/~rwilliam
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