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RE: st: Differences in regression slopes


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Differences in regression slopes
Date   Thu, 21 Feb 2008 11:55:48 -0500

At 11:39 AM 2/21/2008, Lachenbruch, Peter wrote:
The 3.29 appears to be pi^2/3 which is the standard deviation of a
standard logistic distribution.
Correct. My point is that, in an OLS regression, if you add vars, the residual variance goes down. Take away vars, and the residual variance goes up. But in logit and probit, no matter what you do, the residual variance always stays the same. The coefficients are identified by fixing the residual variances. This potentially zaps cross-group comparisons, because if residual variances differ across groups the coefficients get standardized in different ways across groups.

This also complicates comparisons of coefficients across models, because, in effect, the underlying y* variable keeps on getting rescaled as you add variables to the model, hence potentially distorting comparisons of coefficients across models. See

http://www.nd.edu/~rwilliam/xsoc73994/L05.pdf

http://www.nd.edu/~rwilliam/xsoc73994/L06.pdf




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Richard Williams, Notre Dame Dept of Sociology
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