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Re: st: Dirifit help


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Dirifit help
Date   Sat, 8 Nov 2008 09:30:22 +0000 (GMT)

--- Murali Kuchibhotla <muralik@iastate.edu> wrote:
> What I would like is some help in locating materials that describe
> the statistical theory behind this estimation.

I wrote it just as an extension to -betafit-, the method of estimation
is straightforward maximum likelihood. The difficulty with these
multivariate models is that you no longer only model the mean and the
variance, but also the covariances between the dependent variables.
-dirifit- enforce a rather restrictive covariance structure, as is
shown here:

http://home.fsw.vu.nl/m.buis/presentations/UKsug06.pdf

The Dirichlet distribution forces these covariances to be negative.
This can make sense in a lot of situations: if you spent more time in
some category than there is less time left for the others. But
sometimes you expect positive covariances: those who spent more time
cooking are also more likely to spent more time doing the groceries.
-dirifit- does not allow for these positive dependencies. For a
critical discussion along this line of using the Dirichlet distribution
to model compositional data see:

Aitcheson, John. 2003. The Statistical Analysis of Compositional Data.
Blackburn Press.

> Also, is there a article out there(maybe in the Stata Journal??) that
> describes the dirifit module in detail? 

There should be, but it will have to wait as I am finishing my
dissertation right now (and those who have been on the list a while,
will have noticed that I am finishing that d**n thing for quite some
time now)

-- Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


      
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