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Re: st: an estimation method question


From   xiang ao <xao@hbs.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: an estimation method question
Date   Wed, 17 Mar 2010 22:29:34 -0400

Thanks a lot, Maarten.  That's very helpful.

Best,

Xiang

Maarten buis wrote:
--- On Wed, 17/3/10, Xiang Ao wrote:
I am thinking whether we can do a maximum likelihood with
some constraints by observation.  That is, assume each
share conforms to beta distribution, for example, then
within each firm, the shares add up to one.  Would that
be valid?

That distribution is called a Dirichlet distribution. The
basic version is implemented in -dirifit-. In your case you want to allow for different number of categories and add the possibility that variables may have different values across categories, but add the constraint that the effects are constant across categories.

Before you start on such a programming excersise it is good (i.e. absolutely crucial) to know what to expect. So you need to fit a simpler model using existing software that is halfway reasonable. Going with the -xtgee- or -glm- suggestion I proposed earlier would be such a way. It won't enforce the sum to one constraints, but in my experience that is almost never
a problem: if the model is halfway reasonable then the
predicted proportions will almost always add up to a
number very close to 1. Adding that constraint later
on, will thus add only a little bit of extra information, and thus make the standard errors a bit smaller, but I would not expect much more improvement than that. So you might want to consider if such small gains are worth the effort of programming a new procedure. The smaller standard error aren't the only pay-off though: programming is fun!!(but try selling that to your employer...)

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


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