You really need to read the Aitchison book Maarten cited. Get the 2003 edition, which has an extra chapter in the back.
How well a model like -dirifit- or the logistic-normal that Aitchison prefers can cope with boundaries is tricky. Much depends on the meaning of the zero or one observation. If it is due to rounding error, the procedure recommended by Aitchison is to shrink everything into the simplex uniformly by a small amount, eps. This turns out to work quite well and does very little damage to your estimates, though if you are not caeful Aitchison's model will end up with outliers if you pick a bad value of eps.
If it represents something qualitatively different than an observation of eps > 0, you have a bigger problem.
-----Original Message-----
From: "Murali Kuchibhotla" <[email protected]>
To: [email protected]
Sent: 11/10/2008 5:02 PM
Subject: Re: st: Dirifit help
Thank you Maarten. It turns out that the dependent variables that I am trying to
model(which are in the nature of proportions) take values which include 0 and 1.
So dirifit seems inappropriate for this particular application. In your
presentation however, you show that the fractional logit model can handle this
constraint for the single dependent variable case. Does this also hold when
modelling multiple dependent variables?
Murali
> --- Murali Kuchibhotla <[email protected]> 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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>
Murali Kuchibhotla
Department of Economics
Iowa State University
Office:75,Heady
Phone:515-294-5452
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