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Topic: Pseudo-R2 for logistic regression
Replies: 1   Last Post: Aug 21, 2013 5:09 PM

 Johann Hibschman Posts: 5 Registered: 4/16/07
Re: Pseudo-R2 for logistic regression
Posted: Aug 21, 2013 5:09 PM

Rich Ulrich <rich.ulrich@comcast.net> writes:

> On Mon, 19 Aug 2013 13:48:48 -0500, Johann Hibschman
> <jhibschman@gmail.com> wrote:
>

>>I'm just starting to read up on the various distinctions here, but I've
>>seen it claimed[1] that the Cox & Snell version reduces to the OLS
>>R^2, but I can't see how that's the case, since
>>
>> L_normal = Prod_i exp((y - yhat)^2)
>>
>>and L^(2/N) gives something like the harmonic mean of exp((y-yhat)^2),

>
> ... geometric mean?

Er, yes. Thanks, I should have caught that before posting.

> I don't immediately see any problem with your invention,
> and it looks like a fairly natural choice.

Poking around in Regression Modeling Strategies, I eventually found just
that measure as eq 9.54, with references to two papers by Korn & Simon.
I'll look those up, though I miss no longer having a university journal
subscription to my name.

> I have never spent time trying to deal with pseudo R-squared
> in reports -- for cases with marginal p-values, I've been
> satisfied to figure for myself what "real" R-squared would
> give the same p-value for the same d.f.

I'm just using it as a first cut when comparing candidate predictive
models, not as something to report. It has the advantage that I
understand what it's measuring and am confident that it represents the
cost function seen by the model.

> Ray Koopman might have comments when he returns, if
> he has just been gone for the summer.
>
> Some years ago, Frank Harrell used to read these
> usenet groups, and I helped popularize the criticisms of
> stepwise regressions that he posted here. I think you
> might get a response more useful than mine if you send

I'll try to track down those Korn & Simon references [1, 2] and see if
that answers my question. Otherwise, I'll give that a try. Usenet is
pretty quiet these days, but it's just easier than monkeying around
with, e.g., http://stats.stackexchange.com [3]

Thanks,
Johann

[1] Korn & Simon. Measures of explained variation for survival data.
Statistics in Medicine, 9:487-503, 1990.

[2] Korn & Simon. Explained residual variation, explained risk, and
goodness of fit. American Statistician, 45:201-206, 1991.

[3] http://stats.stackexchange.com/questions/11676/pseudo-r-squared-formula-for-glms