[Limdep Nlogit List] A selection qeustion--a quick follow-up

[Christer.Thrane at hil.no]

Thanks everybody! Bottom line: Since I do not know anything about Bayesian 
statistics, I can't adjust my multinomial regression model for samlpe 
selection. This also means that my best approach probably is to go on as 
if selection is not a problem?

BR,

Christer



Fred Feinberg <feinf at umich.edu> 
Sent by: limdep-bounces at limdep.itls.usyd.edu.au
18.10.2007 21:53
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Re: [Limdep Nlogit List] A selection qeustion--a quick follow-up





Agreed completely on all this.

Bayesians (I'm one, sort of) like to trumpet the superiority of their 
methods for
*high-dimensional* models. For example, models involving heterogeneity are 
is
very, very difficult to estimate classically outside of certain specific 
instances
(e.g., Bryk-Raudenbush HLM territory), and are especially tough in 
discrete choice
settings. Prof. Greene is right that, for homogeneous models, you're only 
going to
get suspect classical results if your sample is very small. [One other 
case is
when you are estimating a bounded parameter, and want to rely on dividing 
the
estimate by its standard error... but that's just faulty reasoning, and 
nothing
intrinsically wrong with classical estimation.]

As for the standard errors being off sometimes, this is actually what 
Puhani found
-- unless I'm misremembering -- using certain classical estimators, 
especially so
two-steps for Heckman-type set-ups. I'd also point out that Bayesian 
approaches
not only provide the marginal densities of any parameters of interest, but 
also
give the joint density of all unknown quantities, which are sometimes 
legitimate
objects of inquiry of their own.

Sorry if I came across as a Bayesian cultist.

FF

William Greene wrote:

> Fred (and all).  The Terza JAE (2002) paper is a FIML estimator for
> the MNL model with selection that was queried in the first email. The
> use of the Taylor series in this paper was to describe an alternative
> approach by Mullahy and Sindelar.  I am current working on an 
implementation
> of the model in LIMDEP, but am not ready to say it is complete. The
> Terza and Kenkel (2001) paper is a formal sample selection model for
> counts that derives the appropriate conditional mean function for the
> Poisson variable under selection, and estimates it by nonlinear least
> squares. It does not use an IMR approach.  Terza and I developed the
> FIML estimator for this model simultaneously (to some extent, jointly)
> in the early 1990s.  It is currently fully implemented in LIMDEP; 
however,
> being a model for counts, it is not helpful to this discussion.
>   The Boyes, Hoffman and Low paper describes the bivariate probit model
> with sample selection that has been fully implemented in LIMDEP since
> about 1992.  Likewise the Poirier model on partial observability, which
> is one of several forms of this model.  The LIMDEP manual contains
> extensive documentation on all of these models.  FIML estimators for all
> of them are incorporated in LIMDEP.  They do not use IMRs.  On the other
> hand, neither are these helpful; they are not the model that was queried
> about.  As Fred points out, the modeling of the joint distribution of 
the
> disturbances that is used in the probit and Heckman linear models does 
not
> carry over to the multinomial logit model, so the problem remains.
>    The business of the standard errors of MLEs in these models relying
> on suspect asymptotic results is a canard.  The idea that the Bayesian
> estimators somehow get everything right and the MLE doesn't has two 
flaws,
> notwithstanding all the other problems listed: (1) If the sample is
> at all large, and that does not have to be excessively so, though the
> typical application does use a big sample, then the asymptotics for 
these
> models are fine, and, in fact, they are very well behaved.  I and many
> others have been using them for a couple decades.  Moreover, even in a
> moderately sized sample, unless one has a very strong prior - and that
> would taint the results - the Bayesian estimates are generally close
> to identical to the MLEs (a theorem of Bernstein and von Mises is at 
work).
> Indeed, it is a signal that something is wrong when the Bayesian
> estimate deviates too much from the MLE.  After all, if the sample is
> relatively large, the log likelihood is nearly symmetric and unimodal
> (central limit theorem), so the mode (MLE) and the mean (posterior mean)
> coincide.
> (2) If the sample is so
> small that these criticisms would have any relevance -- and we would be
> talking about small 2 digit sample sizes, then the fact that the 
Bayesian
> estimators have exact small sample properties is a flaw not a virtue. 
The
> results are posterior to just the sample data, and can't be extended 
beyond
> the small sample in hand. But, it is a heroic (and very classical) 
assumption
> that somehow this small sample tells you the story about the whole
> population you are trying to characterize.
>
> /Bill Greene

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