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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:

Continuing this sidelight - I give several formulas for OLS and their logical Pseudo R^2 analogs atFunny. 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.

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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**Follow-Ups**:**RE: st: Validity of R Square with -nl- Regressions***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**References**:**st: Validity of R Square with -nl- Regressions***From:*"Matthias Flueckiger" <matthias.flueckiger@gmx.ch>

**Re: st: Validity of R Square with -nl- Regressions***From:*Maarten buis <maartenbuis@yahoo.co.uk>

**RE: st: Validity of R Square with -nl- Regressions***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

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