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Re: st: Comparing regression coefficients


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Comparing regression coefficients
Date   Thu, 28 Feb 2013 07:27:41 -0500

On Wed, Feb 27, 2013 at 5:54 PM, Mahometa, Michael J
<michael.mahometa@ssc.utexas.edu> wrote:
> Hi all,
>
> The *only* thing different is the use of variable2 over variable1 as a predictor in the model - same outcome, same covariates. Is there a way to compare the impact of variable1 to variable2? Why am I drawing a blank? Is it as simple as saying "the R2 is better for the second model, so variable 2 is better?"
>

I don't think there's an inherently obvious answer in this kind of
situation, but that said I would suggest something such as:

(1) regress outcome, variable1, and variable2 each separately on the
demographics and generate residuals
(2) Compare the R^2 of residual outcome on residual variable1 and on
residual variable2.

So what this is doing is comparing the resulting squared partial
correlations, having removed demographics. However, variable1 and
variable2 may be correlated too, so the R^2 from each regression still
has common variance which you haven't accounted for.

(This assumes the relationships are linear, which they may not be.)



-- 
JVVerkuilen, PhD
jvverkuilen@gmail.com

"It is like a finger pointing away to the moon. Do not concentrate on
the finger or you will miss all that heavenly glory." --Bruce Lee,
Enter the Dragon (1973)

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