RE: st: Differences in regression slopes

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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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