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Re: st: RE: sample size: linear probability vs probit


From   SamL <saml@demog.berkeley.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: sample size: linear probability vs probit
Date   Mon, 7 Feb 2005 14:24:29 -0800 (PST)

Hmm.  I'm not so sure that a linear probability model per se *should*
actually trap such situations.

The LPM does not bound the prediction--that is, the model presumes the
prediction can be larger than one and smaller than zero, indeed, can tend
toward + or - infinity.  Thus, there is no such thing as "perfectly
predict" in the LPM case, at least with respect to a binary outcome.  At
least, that's my understanding of the model.

If that understanding is correct, how could one identify cases that are
"perfectly predicted" (and the associated Xs that "perfectly predict")?

Thanks for any insights.
Sam

On Mon, 7 Feb 2005, Nick Cox wrote:

> I think that -probit- and -logit- have
> special code to trap those situations.
>
> If you are fitting a linear probability
> model by -regress-, that has no sense
> of such special problems with binary outcomes.
>
> (a guess)
>
> Nick
> n.j.cox@durham.ac.uk
>
> David K Evans
>
> > I understand why the probit model drops variables which
> > predict an outcome
> > perfectly even if they aren't perfectly correlated with the
> > outcome (e.g.
> > if X=1 always implies Y=1, even if X=0 may not imply that Y=1).
> >
> > However, the linear probability model does not drop those variables.
>
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