Re: st: linear probability model vs. probit/logit

[Kenneth Flamm <kflamm@mail.utexas.edu>]

"Now, some experiments revealed that linprob and 
logit use the same observations, because for the
observations that are dropped by logit the 
correlation between the perfect predictor and hat is one,
and variables causing multicollinearity should be 
dropped by linear regression as well."

Could you explain? Since the linear probability 
model is not constrained to produce predicted 
values that lie in the [0,1] range, how can there 
be a correlation of 1 between the "perfect 
predictor" and the predicted probability? Your 
linprob routine must be dropping all observations 
with predicted probabilities outside the [0,1] 
range, which is not generally done with LPM 
models. Is this written up anywhere?

Also, robust standard errors are another means of 
dealing with the heteroskedasticity problem.


At 09:15 AM 10/5/2006, Tamas Bartus (tbartus) wrote:

> Hi,
>
> The previous discussion seemed to assume that the linear probability model is
> a simple regression model.
>
> However, the linear probability model should be 
> a two-step weighted regression, that is,
> first estimate the regression, then save the 
> predicted value (hat), calculate hat*(1-hat),
> then reestimate the model with analytic weight N/hat*(1-hat).
>
> This procedure is implemented in my old and 
> simple LINPROB (downloadable from my website)
>
> Now, some experiments revealed that linprob and 
> logit use the same observations, because for the
> observations that are dropped by logit the 
> correlation between the perfect predictor and hat is one,
> and variables causing multicollinearity should 
> be dropped by linear regression as well.
>
> Hope this helps,
>
> Tamas
>
> ------------------------------------------------
>
> Tamas Bartus, PhD
> Associate Professor, Institute of Sociology and Social Policy
> Corvinus University, Budapest
> 1093 Budapest, Fovam ter 8.
> Phone: +36-1-482-5290         Fax:   +36-1-482-5226
> Homepage: www.uni-corvinus.hu/bartus
>
>
> ----- Eredeti �zenet -----
> Felad�: Joseph Coveney <jcoveney@bigplanet.com>
> D�tum: Szerda, Okt�ber 4, 2006 7:31 de
> T�rgy: Re: st: linear probability model vs. probit/logit
>
> > Ronnie Babigumira wrote (excerpted):
> >
> > Does it make sense that Stata drops a variable that predicts
> > perfectly and
> > then goes ahead to drop the observations even when it does not use the
> > problem variable in the regression? Any insights into what is going
> > on.
> > --------------------------------------------------------------------
> > ------------
> >
> > Take a look at _Release 9 Reference K-Q_ Page 98. This is in the entry
> > for -logit-.  At the top of the page, you'll see output of a logistic
> > regression using the auto dataset, and with a variable dropped and 10
> > observations omitted.
> >
> > The paragraphs beneath the printout, including the technical note
> > at the
> > bottom of the page, give the reasoning behind omitting observations
> > aftera perfectly predicting variable (but not after a collinear
> > predictor) has
> > been dropped from the list of candidate predictors.
> >
> > Joseph Coveney
> >
> >
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