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


From   Ángel Rodríguez Laso <angelrlaso@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Can multicollinearity problems be resolved by using residuals from another regression?
Date   Fri, 9 Nov 2012 18:01:48 +0100

Dear A. Shaul,

Sorry if I'm missing some important point but I don't understand why
you attribute the loss of significance when introducing x2 to
collinearity. It just means that the previous significant effect of x1
on y you found is explained by the confounding effect of x2.

What collinearity produces is impossibility of fitting the model or
very large standard errors, and there are specific commands to check
for it -collin-.

Best regards,

Angel Rodriguez-Laso

2012/11/9 A. Shaul <3c5171@gmail.com>:
> 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
>
> Although I get the expected estimates of b1 and b2, they are
> insignificant. They are, however, significant if I exclude x2. I
> believe this is the result of collinearity between x1 and x2 because
> x1 is affected by x2. I have tried to resolve the problem by first
> running the regression
>
>    (2)   x2 = x1 + constant
>
> and then generating the variable x2_res consisting of the residuals
> from regression (2). I have then modified regression model (1) by
> substituting x2 with x2_res, i.e. I then estimate the model:
>
>    (3)   y = b1*x1 + b2*(x1)^2 + b3*x2_res + constant
>
> The coefficients b1 and b2 are now significant. This is also the case
> if I used an n>2 degree polynomial in x1 in model (2).
>
> My thinking is that controlling for x2_res corresponds to controlling
> for the part of the variation of x2 that is not affecting x1.
>
> Does this make sense?
>
> In order not to flood the list, I would like to thank you very much in
> advance for your answers! Thank you!
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