download relogit.zip from my web page, and follow the directions in the
readme.txt file.
thanks for the kind words.
Gary King
: 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 (928) 832-7022 :
On Tue, 12 Nov 2002, Kisangani Emizet wrote:
> Dear Professor King:
>
> Your argument criticizing "fixed effects" advocated by Green, Kim, and
> Yoon was a time and "sample" saver. I tried to run "relogit" with
> Stata7, but couldn't. What should I do to download or run it?
> Thanks
> Kisangani Emizet
>
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Thanks for your note. The best way to fix the two forms of bias in rare
events logistic regression is to use one of the techniques we discussed in
the paper you cite. Weighting so that they have a 50:50 distribution
would not help since you'd have to weight it back down (using what we call
prior correction or weighting) to get unbiased estimates.
the point that is easy to confuse is that there are 2 things going on.
first is in case-control data, you must correct for the fact that you're
sampling retrospectively. Then whether or not you have case-control data
or prospectively collected data, "rare events" is defined as the fraction
of y's in the population, not in your sample. With rare events, logistic
regression (or logistic regression with a correction for case-control
sampling) underestimates Pr(Y=1). the corrections we discuss will fix
this problem.
Gary King
David Florence Professor of Government
Director, Harvard-MIT Data Center
http://GKing.Harvard.Edu, King(a)Harvard.Edu
Direct (617) 495-2027, Assistant (617) 495-9271
Data Center (617) 495-4734, eFax (928) 832-7022
On Mon, 11 Nov 2002, Siwik, Thomas (DE - Duesseldorf) wrote:
> Bitte beachten Sie zunächst die Informationen am Ende dieser E-Mail / at
> first please note the information at the end of this email
> ----------------------------------------------------------------------------
>
>
>
> Dear Mr. King,
>
> I found at your HP the interesting paper:
> Logistic Regression in Rare Events Data
> Gary King & Langche Zeng
>
> I have to evaluate an logistic regression, in which
> the rare events are weighted equally to the frequent events
> to avoid the problem of bias of coefficients.
>
> May I allowed to ask an expert on that field two simple question:
> - Is a 50%/50%-weighting an appropriate method to avoid bias?
> - Aren't the drawbacks even worse biased betas and the risk
> of overfitting the rare events?
>
> I cannot find any reliable reference emphasizing this method.
> However, may be it makes sense as an easy to apply rule of thumb.
>
> Forth following I have attached the short discussion I have initiated
> at the s-news-list.
>
> Thank you & Best regards
> Thomas Siwik
> ________________________________________________
>
> Dr. Thomas Siwik
> Deloitte & Touche
> Financial Risk Solutions
> Bahnstrasse 16
> 40212 Duesseldorf
> Germany
>
> eMail: tsiwik(a)deloitte.de
> Fon: ++49.(0)211.8772 - 147 / - 133
> Fax: ++49.(0)211.8772 - 443
> http: www.deloitte.de/Dienstl/Bran-fr1.htm
> ________________________________________________
>
>
> -----Original Message-----
> From: Siwik, Thomas (DE - Duesseldorf) [mailto:tsiwik@deloitte.de]
> Sent: Montag, 4. November 2002 20:24
> To: 'Hongjiew(a)aol.com'
> Cc: 's-news(a)lists.biostat.wustl.edu'
> Subject: Re: [S] general statistical issue: weighting observations in
> logi
>
> > Statistician (1999). One of the nice properties of logistic
> > regression (not sure it carries over to general logit models)
> > is that if oversample is done based on the response variable,
> > the coefficients estimates of the predictors are not changed.
> > Only the intercept needs to be adjusted. There are researches
>
> I understand your point. If one gives weight lambda to the
> observations with Y=1 the odds-ratio is - heuristically speaking -
> changed by lambda as well. That results in an adjustment of the
> intercept.
>
> However, couldn't it be an asympthotic property of the
> predictors? I tried to find your assertion in the normal equation:
> lambda*Sum(P(Y=0|x_i)*x_i;i|y_i=1) = Sum(P(Y=1|x_i)*x_i;i|y_i=0)
> If this equation is re-written with the adjusted P(Y) there
> remains still a term, which vanishes only for T->infinity. Maybe
> I put it wrong, but additionally I ran an example in S+ showing
> different estimates for all coefficients.
>
> My intuition tells me that the overweighting of rare events
> causes overfitting and high sensibility to rare events. It
> seems to me to be not an appropriate method to reduce a possible
> bias of predictors of rare events.
>
> I found a very readable paper illustrating the problem of
> rare events:
> Logistic Regression in Rare Events Data
> Gary King & Langche Zeng
> http://gking.harvard.edu
>
> Thomas
>
> > -----Original Message-----
> > From: Hongjiew(a)aol.com [mailto:Hongjiew@aol.com]
> > Sent: Donnerstag, 31. Oktober 2002 17:48
> > To: fharrell(a)virginia.edu; dcts(a)dcts.de
> > Cc: s-news(a)lists.biostat.wustl.edu
> > Subject: Re: [S] general statistical issue: weighting observations in
> > logit-regression
> >
> >
> > I agree that if any weighted sampling is used, the parameters
> > need to be adjusted to make valid inference on the original
> > population. But there might be practical reasons to use
> > response based sampling. In the area I am in (database
> > marketing), we frequently encounter situation where the
> > occurrences of events are very "rare" or E(Y=1)<=0.01 for
> > example. There will be computational problems associated with
> > the prediction, see "Predictive performance of the binary
> > logit model in unbalanced samples" by J. S Cramer in "The
> > Statistician (1999). One of the nice properties of logistic
> > regression (not sure it carries over to general logit models)
> > is that if oversample is done based on the response variable,
> > the coefficients estimates of the predictors are not changed.
> > Only the intercept needs to be adjusted. There are researches
> > on the area of comparing statistical efficiency between
> > multiple sampling schemes in logistic regression setting. For
> > example, if N (overall population) =100K where 10% of them
> > Y=1.One may take a response based sample (so #y=1 is close to
> > #y=0) and one may make a true random sample. The first sample
> > usually can be much smaller than the second one to generate
> > comparable estimates (see " The effect of sample size and
> > proportion of buyers in the sample on the performance of list
> > segmentation equations generated by regression analysis" by
> > Berger and Magliozzi in Journal of direct marketing.
> >
> >
> >
> >
> >
> > In a message dated 10/30/2002 8:27:15 PM Eastern Standard
> > Time, fharrell(a)virginia.edu writes:
> >
> > >
> > >
> > > On Wed, 30 Oct 2002 23:22:05 +0100
> > > DCTS <dcts(a)dcts.de> wrote:
> > >
> > > >
> > > > I am confronted with a Logit-regression, in which y=0 is
> > much less frequent
> > > > than y=1. It is argued that the less frequent
> > observations with y=0 should
> > > > receive higher weights in the regression, such that the
> > proportion is
> > > > balanced between Ys being 0 and 1.
> > >
> > > Who argues that? No, you don't want to distort the data.
> > If your sample is a random sample from the population to
> > which you want to infer, then rely on maximum likelihood to
> > give good parameter estimates. You weight observations if
> > you oversampled a segment of the population and you want to
> > represent the original population [even then don't always
> > weight as this reduces efficiency when compared with
> > covariate adjustment for oversampling factors].
> > >
> > > Frank Harrell
> > >
> > > >
> > > > To my knowledge there are usually two motivations to use
> > weights others than
> > > > unity:
> > > > - prior knowledge of the probability of y=0
> > > > - optimisation of a cost function (in the example above
> > y=0 is much more
> > > > expensive and should be predicted with higher attention)
> > > >
> > > > In my limited econometric library and in the internet I
> > wasn't able to find
> > > > a discussion on the issue of weighting observations. If
> > someone has a good
> > > > hint to a source or could sketch the ideas of
> > consequences, pros and cons I
> > > > would be very pleased.
> > > >
> > > >
> > > > Thank you,
> > > > Thomas
> > > >
> > > >
> > --------------------------------------------------------------------
> > > > This message was distributed by
> > s-news(a)lists.biostat.wustl.edu. To
> > > > unsubscribe send e-mail to
> > s-news-request(a)lists.biostat.wustl.edu with
> > > > the BODY of the message: unsubscribe s-news
> > >
> > >
> > > --
> > > Frank E Harrell Jr Prof. of Biostatistics & Statistics
> > > Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
> > > U. Virginia School of Medicine
> > http://hesweb1.med.virginia.edu/biostat
> > > --------------------------------------------------------------------
>
> ----------------------------------------------------------------------------
>
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We show empirically and theoretically that Pr(Y=1)=p is underestimated in
logistic regression (at the stage of computing the coefficients and again
at the stage of computing p given the coefficients). this also implies
that 1-p is overestimated. the two cancel each other out in your
calculation, which means that the calculation doesn't bear on the issue of
bias.
Gary King
: 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 (928) 832-7022 :
On Mon, 11 Nov 2002, Harald Scheule wrote:
> Dear professor King,
>
> I am working at the business faculty of the University of Regensburg,
> Germany and we are estimating the probabilities of corporate defaults using
> logistic regression models. With this background I have read your article
> "Logistic regression in Rare Events Data" with great interest.
>
> In Chapter 5: Rare Event, Finite Sample Corrections you argue that the
> probability for an event is underestimated because of rare events and
> randomness of the estimated paramter.
>
> What I do not understand is: If I run a logistic regression e.g. with PROC
> LOGISTIC in SAS and estimate the default probabilities, their sum equals the
> observed sum of events. If probabilities are underestimated, shouldn't their
> sum be lower that the observed number of events?
>
> I would be very thankful if you could help me to solve my problem
>
>
> Harald Scheule_________________
>
> Harald Scheule
> Dipl.-Kfm.
> Lehrstuhl für Statistik
> Universität Regensburg
> 93040 Regensburg
> Germany
>
> Tel.: +49 (0)941/943-2287
> Fax.: +49 (0)941/943-4936
> ________________
>
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