Re: st: definition of pseudo R^2 for dprobit or probit

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

At 10:39 AM 10/28/2003 +0000, Ronan Conroy wrote:
> But fundamentally, I agree with Nick Cox: R^2 tells you nothing of the
> utility of the model, either from the theoretical or practical standpoint.
> As a sole criterion for model selection, it should only be used when there
> is no-one in the office capable of formulating a theory (and the cleaners
> have gone home).
Thanks Nick and Ronan.  I have another handout on my web pages entitled 
"The Evils of R^2" (http://www.nd.edu/~rwilliam/xsoc593/lectures/l16.pdf) 
so I am very sympathetic and pretty much in agreement with your arguments.

However, arguing that a particular measure should not be deified or abused 
or the sole criterion used seems to me a different issue than what formula 
best represents the concept the statistic is supposed to measure, in this 
case proportion of variance explained.  That is, if you are going to use an 
R^2 measure, which formula does it best?  All these formulas claim to be 
analogs to OLS R^2, and I've read various things that say McFadden's R^2 is 
the best in that respect and that other measures have various problems with 
them.  I agree that placing too much emphasis on a single number is a bad 
thing, but presenting 5 slightly different numbers that all purport to 
measure the same concept isn't necessarily much of an improvement.  Better 
may be to present 5 different numbers which represent 5 different concepts 
of what should be considered best.

So, use R^2 measures with caution and perhaps avoid using them all 
together, but if you are going to use one, is there any compelling reason 
for preferring something other than McFadden's statistic?  Of course, 
unless there is universal agreement that McFadden's is best and others are 
horribly flawed, it doesn't seem like it would kill Stata to report a few 
others (or at least more clearly label the one that is used so people don't 
have to try to guess or go rummaging through the manual to try to find it!)


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Richard Williams, Associate Professor
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