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RE: st: Validity of R Square with -nl- Regressions


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Validity of R Square with -nl- Regressions
Date   Fri, 20 Jun 2008 09:17:31 -0400

At 08:24 AM 6/20/2008, Nick Cox wrote:
Funny. Maarten sees this definition as "obvious", and I do understand
why.

I was brought up an old-fashioned way with lots of correlation before
regression and still tend to see the definition of R-square as the
square of the correlation between observed and fitted as the "obvious"
one.

No doubt there are now people who see a definition in terms of
likelihood results as the "obvious" one.
Continuing this sidelight - I give several formulas for OLS and their logical Pseudo R^2 analogs at

http://www.nd.edu/~rwilliam/xsoc73994/L04.pdf

For OLS, the formulas all give the same results, but the Pseudo R^2 stats all give different numbers. Counter to the claims of some, I don't think logic alone clearly favors one Pseudo R^2 measure over another.

One thing I do find kind of remarkable is that the Maximum Likelihood R^2 (aka Cox-Snell) isn't just a logical analog - it is the exact same formula for OLS R^2 and Pseudo R^2. That might be why, as Nick says, some may think this is the "obvious" measure.

I'm not quite sure why McFadden's Pseudo R^2 came to be blessed by Stata, but I suppose it is as good as any.


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Richard Williams, Notre Dame Dept of Sociology
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EMAIL: Richard.A.Williams.5@ND.Edu
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