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Re: st: Sequential Probit


From   <[email protected]>
From   Maarten buis <[email protected]>
To   <[email protected]>
Subject   Re: st: Sequential Probit
Date   Thu, 17 Mar 2011 14:35:00 -0000
Date   Wed, 16 Mar 2011 08:20:54 +0000 (GMT)

- --- On Wed, 16/3/11, Elin Vimefall wrote:
> If I want to do the sequential probit and control for the
> correlated unobserved  heterogenity (for example the
> ability of the child), then it is the same thing as doing a
> trivariat probit with sample selection?

Not quite, you are than loosing the sequential nature of the
model. In a sequential logit/probit you are looking at the
probability of passing a transition given that you are at 
risk. In a multivariate probit you are looking at the 
probability of attaining a level. 

> If so; is there some way to do this in stata?

Lorenzo Cappellari and Stephen P. Jenkins (2006) "Calculation 
of multivariate normal probabilities by simulation, with 
applications to maximum simulated likelihood estimation" The
Stata Journal, 6(2): 156--189.
<http://www.stata-journal.com/article.html?article=st0101>

> I assume the heckprob command is what I would use if I had
> two steps, but is there some way to extend this into three 
> steps?

That is yet again a subtly different model...

Hope this helps,
Maarten
===============

Thanks for plug. (Elin missed the self-citation in my original response.)

I disagree with Maarten. I think a form of multivariate probit model with selection can account for the sequential aspect he refers to.  Suppose there are 3 education levels: A, B, C

The model I have in mind is:
Pr(reach A) as function of stuff, where risk set is all starting education
Pr(reach B) as function of stuff, where risk set is those finishing A
Pr(reach C) as function of stuff, where risk set is those finishing B
And the errors of the latent outcomes are trivariate normal.

The standard bivariate probit model with selection (-heckprob- in Stata) could be applied to the 2 level case.

A paper that applies this approach is "Selection Bias in Educational Transition Models: Theory and Empirical Evidence" by Anders Holm and Mads Meier Jæger, unpublished paper, Center for research in compulsory schooling, University of Aarhus, Tuborgvej 164, DK-2400 Copenhagen NV  Denmark (email: [email protected] or email: [email protected]) 

One is asking a lot from these models given the data available, so they can be hard to fit and might be rather fragile.

Maarten's own approach to examining the impact of unobserved heterogeneity in these models in his -seqlogit- (on SSC) assumes a different type of model (I think). That is (I think) he assumes the same univariate normal frailty distribution for the errors of the latent outcomes in each equation (i.e. perfect correlation across equations). [His likelihood function accounts for the selection arising from the sequential nature of the problem.]  However, rather than /estimating/ the variance of the normal frailty distribution, he allows the researcher to assume different values for that variance and to inspect what happens to the estimates of the other model parameters with different assumptions. So, note: compared to the MV probit with selection approach, there is a different underlying model (for the frailty and link functions).  His approach might be more robust -- I don't know -- but that is partly bought by his assumptions implicit in his specification.  

Stephen
------------------
Professor Stephen P. Jenkins <[email protected]>
Department of Social Policy and STICERD
London School of Economics and Political Science
Houghton Street, London WC2A 2AE, UK
Tel: +44(0)20 7955 6527
Survival Analysis Using Stata: http://www.iser.essex.ac.uk/survival-analysis
Downloadable papers and software: http://ideas.repec.org/e/pje7.html



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