Thanks to Kit Baum, there is a new package available for
download on SSC, -dirifit- by Maarten Buis, Nick Cox and
Stephen Jenkins. dirifit fits by maximum likelihood a
Dirichlet distribution to a set of variables. Usually these
variables are proportions, e.g. proportions of the budget
of municipalities spent on categories school, police, and
other. These proportions can be made dependent on covariates,
e.g. political orientation of ruling parties, and whether or
not the municipality is urban.
-dirifit- is closely related to -betafit-, just as the
Dirichlet distribution is closely related to the beta
distribution. Both model proportions, but -betafit- can
handle only one dependent/explained/y variable, while
-dirifit- can handle multiple dependent variables. Using the
example above: -betafit- could model the proportion of city
budget spent on e.g. police, while -dirifit- can model the
proportions spent on all categories simultaneously. Another
way to think about it is that -betafit- and -dirifit- have
a lot in common just as -logit- and -mlogit- have a lot in
common.
-dirifit- has two parameterization, just as -betafit-: one
in terms of only scale parameters, and one in terms of
location parameters and one scale parameter. The latter
allows one to model the odds of one category versus the
reference category, and should be most useful if one has
covariates, while the former conforms more to the
conventional way a Dirichlet distribution is written and
should be most useful when no covariates are used.
Maarten
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z214
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
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