Ordinary logit is a likelihood technique and so the value of the
likelihood at the maximum is reported. Relogit is an unbiased estimator,
unlike ordinary logit, and although it is estimating the same model and
although the likleihood is computed as one of the steps in calculating
relogit estimators, it is not a likelihood technique. As such, there is
no value that corresponds to the max of the likelihood under relogit.
In fact, relogit estimators fit the in sample data worse than logit
models, and so if we rigged up a pesudo-R^2 statistic (something that
isn't of much use even in ordinary logit or even regression by the way),
it would drop from ordinary logit to relogit. Why, you might ask, would
anyone switch to the model that fits worse? The answer is that the model
that fits worse in this case is unbiased and the model that fits better is
biased (another reason why R^2 measures are of little use). The same is
true in numerous other areas of statistics. E.g., WLS has lower R^2 than
OLS, but we prefer WLS because it is more efficent (and we don't report
R^2 for WLS).
Best of luck with your research.
Gary
: Gary King, King(a)Harvard.Edu
http://GKing.Harvard.Edu :
: Center for Basic Research Direct (617) 495-2027 :
: in the Social Sciences Assistant (617) 495-9271 :
: 34 Kirkland Street, Rm. 2 HU-MIT DC (617) 495-4734 :
: Harvard U, Cambridge, MA 02138 eFax (617) 812-8581 :
On Tue, 6 Apr 2004, Helmut Fryges wrote:
Dear Professor King,
I found the programme relogit for rare events logit regression on your
homepage. I applied your model to estimate foreign market exit in a
sample of German and UK high-technology firms.
In this context, I have the following question:
When displaying the results, it is common practice to display the value
of the log-likelihood function. However, the relogit programme doesn't
save a value of the log-likelihood function. Is it correct to use the
log-likelihood function from the ordinary logit, although the latter
regression is biased? Or do I have to adjust the value of the
log-likelihood, for example by putting the relogit estimator of beta in
the formula of the log-likelihood?
Answering this question probably also determines, in which way I have
to calculate the Pseudo R2 to be displayed in my paper.
Thank you for your efforts (and happy Easter!).
Helmut Fryges
***************************************************************
Helmut Fryges
Centre for European Economic Research (ZEW)
Department of Industrial Economics and
International Management
L 7,1 ; 68161 Mannheim
P.O. Box 10 34 43 ; 68034 Mannheim
Germany
Phone: +49(0)621/1235-189
Fax: +49(0)621/1235-170
E-mail: fryges(a)zew.de
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