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Re: st: Gof for ologit/oprobit


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: Gof for ologit/oprobit
Date   Tue, 30 Oct 2007 23:24:16 -0500

At 09:54 PM 10/30/2007, Clive Nicholas wrote:
Dan Weitzenfeld wrote:

> What is the best way to communicate to non-statisticians the Goodness
> of Fit (gof) of an ordered logit/ordered probit model?
>
> For OLS, there is the trusty R2, letting you tell a non-statistician,
> "I can explain X% of the variation in the dependent variable."
>
> For logit/probit, I've used the probability of correct classification,
> type I and type II error rates as my go-to metric for gof.

Personally speaking, I've never thought the 'percentage correctly
classified' summary statistic (which I think you're referring to) to
be particularly meaningful, since it can hardly fail when Y=1 in more
than 50% of the observations. No doubt I'll get lynched for saying
this.
Indeed you will. :) If, say, 55% of the cases are 1, you could still mis-classify 45% of the cases. The adjusted count R^2 is better because it tells you how much better you are doing than by just always picking whichever category is in the majority. This, and some other measures of fit, are discussed here:

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

The count measures can be pretty much useless when one outcome is rare, e.g. only 10% get a zero, because it will then often be the case that every case gets predicted as a 1.

In general, I agree with your other comments though. Of course, the original question was, How do I explain this stuff to the masses? That is tough. If the masses insist on some sort of pseudo R^2, you need to explain that pseudo R^2 stats are generally much lower than OLS R^2 stats.

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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EMAIL: Richard.A.Williams.5@ND.Edu
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