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Re: st: Can multicollinearity problems be resolved by using residuals from another regression?

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: Can multicollinearity problems be resolved by using residuals from another regression? Date Mon, 26 Nov 2012 19:46:50 -0500

```Sorry for coming late to this topic.

I wanted to point out that ridge regression, a family of methods for
remediating
multicollinearity, is implemented by -ridgereg- (SSC).

For background, see the following reference, listed in the -help-:
Evagelia, Mitsaki (2011) "Ridge Regression Analysis of Collinear Data",
http://www.stat-athens.aueb.gr/~jpan/diatrives/Mitsaki/chapter2.pdf

Steve

On Sat, Nov 10, 2012 at 12:16 PM, JVerkuilen (Gmail)
<jvverkuilen@gmail.com> wrote:
> On Thu, Nov 8, 2012 at 9:36 PM, A. Shaul <3c5171@gmail.com> wrote:
>> Dear Statalist,
>>
>> I expect a non-linear effect of an exogenous variable, x1, on a
>> dependent variable, y. The variable x1 is affected by another
>> exogenous variable, x2. The variable x2 affects x1 directly and also y
>> directly. The variable x1 does not affect x2. I am only interested in
>> the partial effect of x1 on y while controlling for x2 --- or at least
>> while controlling for the part of the variation in x2 that affects y
>> directly.
>>
>> I have the following regression equation:
>>
>>    (1)   y = b1*x1 + b2*(x1)^2 + b3*x2 + constant
>
> I'm not 100% sure what you're doing but when you have polynomial terms
> like this collinearity is inevitable. Before doing anything odd,
> center x1 and then compute x1^2, and regress on the centered
> variables. (You may want to rescale x1 as well but centering does the
> work.) This will give you a statistically equivalent model that breaks
> the collinearity between x1 and x1^2.
>
> Usually though you're not interpreting x1 terms directly anyhow, so
> whether x1 or x1^2 is statistically significant individually is
> irrelevant. Certainly the linear term for x1 is irrelevant if the term
> for x1^2 is significant. You can test for x1 effects as a block using
> -testparm-.
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```