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RE: st: RE: Interpretation of quadratic terms


From   Rodolphe Desbordes <rodolphe.desbordes@strath.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
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: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard Williams [Richard.A.Williams.5@ND.edu]
Sent: 10 March 2010 13:40
To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu
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:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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