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

["JVerkuilen (Gmail)" <jvverkuilen@gmail.com>]

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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