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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   Tue, 16 Mar 2010 14:14:33 -0400

Thanks, Maarten, for the detailed description. I probably did not describe our data very clearly. There are different numbers of founders for each firm. The smallest number is 2, it can be as many as 10 co-founders. As far as I understand, the number of categories need to be fixed in the methods you mentioned. Is that right?

Thanks,

Xiang

Maarten buis wrote:
--- On Tue, 16/3/10, Xiang Ao <xao@hbs.edu> wrote:
We are trying to estimate an equation which has some
constraints by observation.  We are studying founders
of firms.  The dependent variable is the share of the
firm.  We are studying what factors influence the
shares.  We now have a problem:  for each firm,
the shares necessarily sum to one.  We were thinking of
dropping an observation per firm, but it turns out the
results are dependent on which observation to drop. Any suggestions on estimation methods would be helpful.

With this type a data the key distinction is whether you
have 2 or more than 2 categories whose proportions should
add up to 1. In the former case you either use -betafit-
or -glm varlist , link(logit) family(binomial) vce(robust)-.
In the latter case you can use -dirifit- or -fmlogit-.

you can install -betafit-, -dirifit-, and -fmlogit- by typing in Stata:
ssc install betafit
ssc install dirifit
ssc install fmlogit

-betafit-, -glm-, and -dirifit- were discussed in this talk
at the 2006 London Stata Users' Group meeting:
http://ideas.repec.org/s/boc/usug06.html

The -glm- trick is based on this paper:
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.
The -glm- trick is also discussed in the Stata tip:
Christopher F. Baum (2008) "Stata tip 63: Modeling proportions"
The Stata Jouranl, 8(2): 299--303.
http://www.stata-journal.com/article.html?article=st0147

The model implemented in -betafit- was discussed in a number of papers: Ferrari, S.L.P. and Cribari-Neto, F. (2004). "Beta regression for modelling rates and proportions". Journal of Applied Statistics 31(7): 799-815.

Paolino, P. (2001). "Maximum likelihood estimation of models with beta-distributed dependent variables". Political Analysis, 9(4): 325-346. Smithson, M. and Verkuilen, J. (2006) "A better lemon squeezer? Maximum likelihood regression with beta-distributed dependent variables". Psychological Methods, 11(1): 54-71.

-fmlogit- is basically a generalization of the -glm- trick to
multiple categories.

examples can be found here:
http://www.maartenbuis.nl/software/betafit.html
http://www.maartenbuis.nl/software/dirifit.html
http://www.maartenbuis.nl/software/fmlogit.html

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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