Thank for all the help guys!!!
I am just surprised that this fractional logit and compositional data analysis appears in stata, but the econometrics behind it is underexplored or not (fully) discussed.
thanks for the reference articles and book.
----------------------------------------
> Date: Mon, 15 Jun 2009 09:55:04 +0000
> From: [email protected]
> Subject: Re: st: The dependent variable is a multi-proportion in actual values
> To: [email protected]
>
>
> --- On Sat, 13/6/09, jverkuilen wrote:
>>> See John Aitchison, 2003, Compositional Data Analysis.
>>> -dirifit- implements the Dirichlet model, which is highly
>>> restrictive. Otherwise you need to transform the proportions
>>> and use a multivariate multiple regression type approach.
>
> --- On Sun, 14/6/09, [email protected] wrote:
>> -fmlogit- by Maarten Buis (downloadable from SSC) does
>> regression on such fractional or compositional data.
>
> To add a bit of context: When you think of linear regression,
> -regress-, you model two elements of the dependent variable:
> the mean (and how it changes over the explanatory variables)
> and the variance conditional on the expalantory variables
> (i.e. the variance of the error term, this is shown in the
> output of -regress- as "root MSE"). You are modeling multiple
> dependent variables (proportion spent on food, on cloths, and
> on recreation), so appart from the mean and the variance you
> also have the covariance between the dependent variables.
>
> -dirifit- assumes that this covariance is always negative
> (For the exact forumula see page 32 of
> http://home.fsw.vu.nl/m.buis/presentations/UKsug06.pdf ).
> This can make sense: if you spent more on clothing then
> there is less income left to spent on recreation or food.
> But this does not necesarily have to be the case: We could
> imagine that "Fun-loving-people" would spent high
> proportions on both clothing and recreation, thus creating
> a positive correlation between the two. The correlation
> structure of -dirifit- does not allow for this possibility
> and can thus be considered to be pretty restricted.
>
> Often (but not always) we only care about the how the means
> (i.e. predicted proportions) changes when the explanatory
> variables change, the variances and covariances are in that
> case just nuisance parameters. If you have a large sample
> than you can use Quasi-likelihood to get correct inference
> even if you mis-specify the model of the nuisance
> parameters. This is what -fmlogit- does. The basic idea
> is discussed in (Papke and wooldridge 1996). A critique
> on quasi-likihood / robust standard errors in general
> can be found in (freedman 2006).
>
> Hope this helps,
> Maarten
>
> Freedman, David A. (2006) On The So-Called "Huber Sandwich
> Estimator" and "Robust Standard Errors", The American
> Statistician, 60(4), pp. 299-302.
>
> Papke, Leslie E. and Jeffrey M. Wooldridge. (1996)
> Econometric Methods for Fractional Response Variables with
> an Application to 401(k) Plan Participation Rates, Journal
> of Applied Econometrics 11(6):619-632.
>
>
> -----------------------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
>
>
>
>
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> * http://www.stata.com/support/statalist/faq
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