Good day 'listers':
I have been thinking about this selection based multinomial response model for a while, as this is a rather common occurrence in applied microeconomics data, and probably in many other places (one of my graduate students wanted to use this within part of their thesis, as a logical extension to the knowledge that is out there). At the time, I agreed. However, in retrospect, I do not really think it is applicable. Taking a standard economics view. If such a simple solution were available, it is likely that someone would have published it by now...
...It seems to me that if the sample selected outcomes (say, j=1,2,3) are determined within a random utility framework, then the hazard rates would need to be included within each measure of random utility, such that the hazards would be netted out when the model is estimated relative to a base outcome, due to the fact that the base outcome would also include the hazard rate. In other words, unless you could calculate outcome specific hazards, the suggested 'heckman-style' correction does not appear to be practical.
I guess the two-bit question is whether or not it is possible to calculate hazards for each outcome, separately. Maybe the nested mnl is fine... although I am less sure on this front.
Steve
Prof SF Koch
Department of Economics
University of Pretoria
Republic of South Africa
>>> "Thuilliez Josselin" <[email protected]> 06/11/07 12:35 PM >>>
Thank you very much for this answer Maarteen.
o yes, the use of the inverse mills ratio is derived from the
assumption that both the error in the selection equation and in the
equation of interest are normal. That is why I was thinking about
using a Probit model and next a mprobit model instead of a Logit to
have normal joint distribution of the error terms.
o I wil take a look at the stata journal vol 6-2.
o The paper by Paul Glewwe is in "The Three-Choice Multinomial Probit
with Selectivity Corrections - Econometric Theory, Vol. 8, No. 2
(Jun., 1992), pp. 302-304".
o you are right, I have a double selection process going on. I didn't
think about it and it seems better to specify it as you did. But even
in this case, it doesn't seem easier to estimate the model of
interest.
Thank you very much again. It helps me a lot to have your opinion.
Josselin
2007/6/10, Maarten buis <[email protected]>:
> I have a couple of comments, but no ready to use solution:
> o If I remember correctly the use of the inverse mills ratio is derived
> from the assumption that both the error in the selection equation and
> in the equation of interest are normal. In that case I wouldn't use
> the IMR with -mlogit-.
> o You don't give a proper citation for the ``paper by Glewwe'', so I
> can't look it up and give you advise on that.
> o Models that deal with similar problems have been discussed in the
> special issue of the Stata Journal in 2006 on simulated maximum
> likelihood, The Stata Journal volume 6 issue 2.
> o multinomial probit relaxes the IIA assumption if you allow for
> correlation between error terms, but these models are typically
> harder
> to estimate, so I would start with multinomial logit and only move to
> multinomial probit if necesary.
> o Are you sure you don't have a double selection process going on?
> Selecetion equation 1: is there a fever? Selection equation 2: Do you
> have acces to modern healthcare? (if not there isn't much of choice)
> Finally the model of interest: do you go to public, private, or other
> healthcare institutions?
>
> Hope this helps,
> Maarten
>
> --- Thuilliez Josselin <[email protected]> wrote:
>
> > Dear list-members,
> >
> > I would like to estimate a multinomial logit or multinomial probit
> > model with
> > sample selection. The selection equation is based on a simple Logit
> > or Probit
> > model. I have 3 questions.
> >
> > Firstly, since there is only Heckprob in Stata I was wondering
> > whether
> > it would be correct to do the following:
>ate the inverse Mill's ratio
> > c- use the IMR as a regressor in the second-stage multinomial logit
> > or
> > probit model
> >
> > Secondly, if this is incorrect: how can I do? Is there a stata
> > program
> > that allow to take into account selection bias in multinomial models?
> > I have seen a paper of Glewwe (3-choice multinomial probit with
> > selectivity corrections) but it does not provide any solution for
> > programing this in Stata.
> >
> > Thirdly, if there is a way to solve this problem, is it better to use
> > the multinomial Logit or the multinomial Probit. Is it possible for
> > instance, to relaxe the IIA assumption using the multinomial probit
> > and at the same time correcting for the selection bias?
> >
> > The object of the study is to determine the determinants of
> > healthcare
> > seeking behaviour for children with fever in developing countries.
> > My data looks like:
> > First choice: Dummy variable for fever: 0 (no fever) / 1(fever)
> > Second choice:
> > 0 No acces to modern healthcare (reference category)
> > 1 Public health facility
> > 2 Private health facility
> > 3 Other medical facility
> >
> > I'd greatly appreciate any suggestions.Thank you in advance.
> >
> > Josselin
> > *
> > * For searches and help try:
> > * http://www.stata.com/support/faqs/res/findit.html
> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> >
>
>
> -----------------------------------------
> Maarten L. Buis
> Department of Social Research Methodology
> Vrije Universiteit Amsterdam
> Boelelaan 1081
> 1081 HV Amsterdam
> The Netherlands
>
> visiting address:
> Buitenveldertselaan 3 (Metropolitan), room Z434
>
> +31 20 5986715
>
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
>
>
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--
Josselin THUILLIEZ
Allocataire de Recherche CES-TEAM-CNRS
MSE, 106-112 Bd de l'Hôpital
75647 Paris Cedex 13
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