Re: st: logit with sample selection

["R.E. De Hoyos" <redeho@hotmail.com>]

Nishant,

Lee (1984) shows that Heckman's model can be generalized to other 
selectivity problems. The trick is to take the linear prediction of the 
logit (or the multinomial logit, or any other model with a non-normal 
distribution), and make a transformation to normal. Doing this, you are back 
into Heckman's bivariate normal distribution, hence you are able to compute 
and use the Mill's ratio in your objective function.

Your SE still have to account for the two-step procedure involved.

I hope this helps,
Rafa
_______________________
Rafael E. De Hoyos
DEC Prospects Group
The World Bank
Washington, DC 20433

----- Original Message ----- 
From: "Nishant Dass" <nishant_dass@yahoo.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, September 25, 2006 11:44 AM
Subject: Re: st: logit with sample selection



> Hi Ian, Jean, Anders, and Maarten,
>
> Thank you everyone for responding to my query.
>
> I am quite sure that the formula suggested by Ian wouldn't
> work because, as indicated by Maarten, it would have to be
> something that reflects the bivariate logistic
> distribution.  I am aware of the bivariate normal formula
> mentioned below but it wouldn't apply for a logit model.
>
> I was only wondering whether there is something similar for
> a logit model because I had found this link in the
> archives, which shows the IMR calculation for -mlogit- (but
> not for -logit- explicitly.)  Check this:
> http://www.stata.com/statalist/archive/2003-04/msg00465.html
>
> As for Jean's suggestion about -heckprob-: I didn't want to
> use that because 1) I have already tried it and it's taking
> forever to converge, and 2) -logit- fits my data better
> than -probit- and so, I wanted to use something like
> "heckman + logit".
>
> Finally, Anders' suggestion: it is not immediately clear to
> me how -gllamm- is applicable in my case but I will check
> again.
>
> In any case, thanks a lot for the discussion.
>
> If anyone can check the above link and add something for
> -logit-, that'd be great.
>
> Thanks,
>
> Nishant
>
>
>
> --- Ian Watson <iangwatson@gmail.com> wrote:
>
> > Nishant
> >
> > The approach you outline will work. The steps in Stata
> > are straightforward.
> >
> > For example, if participation has two outcomes (working
> > or not working),
> > and you want an inverse mills ratio for the working
> > outcome:
> >
> > logit work  age edu children region
> > capture drop phat
> > capture drop imr
> > predict phat if e(sample), xb
> > gen imr = normden(phat)/norm(phat)
> >
> >
> > (Note that the capture drop lines are only needed if you
> > insert this
> > code into a do file which runs multiple times).
>
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