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Re: st: linear, quadratic terms and centering


From   Fabio Zona <fabio.zona@unibocconi.it>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: linear, quadratic terms and centering
Date   Sat, 21 Aug 2010 11:20:22 +0200 (CEST)

Thank you very much Michael!

One more information: I have to make a complex interaction, whereby a linear and a square term are both interacted with a linear (continuous) variable x2:

y = a +   x1 + x1_Square  + x2  +   x2 x1  +   x2 x1_Square


One of my VIF ( the one related to  x2 x1_Square  ) is just above 10 ( it is 10,949),  while the maximum condition index reaches the value of  19,782 (for the same  interaction term  x2  x1_Square ).

Do I have a problem of multicollinearity with this value just above the threshold of 10 ? How can I fix this problem ?

I know there is this command in STATA orthog; how does this command work? I though that I had to calculate the quadratic term and then use orthog between the linear and the quadratic term. However, since you said that (for centering variables) I first center the linear term and then calculate the quadratic term, I get confused also about orthog!
Thanks






----- Messaggio originale -----
Da: "Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>
A: statalist@hsphsun2.harvard.edu
Inviato: Sabato, 21 agosto 2010 10:43:12 GMT +01:00 Amsterdam/Berlino/Berna/Roma/Stoccolma/Vienna
Oggetto: Re: st: linear, quadratic terms and centering

Dear Fabio

   You were correct when you wrote...

Or do I first center the linear term and calculate the square term on the basis of the 
"centered" linear term ?

   Or, in Stata, you can do this (say you want to center -x- around 100)...

generate xcentered = x - 100
regress y c.xccentered##c.xccentered

   That -regress- command will include -xcentered- as well as the squared term.

Hope this helps,

Michael N. Mitchell
Data Management Using Stata      - http://www.stata.com/bookstore/dmus.html
A Visual Guide to Stata Graphics - http://www.stata.com/bookstore/vgsg.html
Stata tidbit of the week         - http://www.MichaelNormanMitchell.com



On 2010-08-21 12.40 AM, Fabio Zona wrote:
> Dear Statalist,
>
> a very simple question: I have
>
> y = c + x0 + x1 + x1square
>
> In order to center x1 and x1square, do I first need to calculate the square term and afterwards to center both the linear and the quadratic term around their respective means?
> Or do I first center the linear term and calculate the square term on the basis of the "centered" linear term ?
>
> I guess that the first alternative works.
>
> Thanks
>
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