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Re: st: oglm and heterogeneous choice models


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: oglm and heterogeneous choice models
Date   Sat, 23 Jul 2011 17:03:06 -0500

At 03:33 PM 7/23/2011, Rourke O'Brien wrote:
I am currently running logit models predicting success (dichotomous)
with sex and income as main predictors.  I understand that with
potential unequal variances across groups I should explore
heterogeneous choice models. See:
http://www.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf

Also see the followup Stata Journal article, a pre-publication version of which appears here:

http://www.nd.edu/~rwilliam/oglm/oglm_Stata.pdf

when I run --oglm success male income, het(male)-- the lnsigma on male
is significant. Yet, when I include the interaction (which is my main
interest) ---oglm male income maleXincome, het(male)-- lnsigma is no
longer significant. How should I interpret this? Does this mean that
the inclusion of the interaction effectively modeled the source of the
unequal variances across groups? If so, do I need to use oglm on
models that include the interaction?

Even though I wrote oglm, I think life is simpler when you can get by without using a hetero choice model. As both of my articles point out, there are multiple and very different interpretations of what the hetero parameters may mean. With some models, you can also run into estimation and identification problems. But with just about any method (I think) the appearance of hetero may be due to the fact that important variables have been left out of the model. Include those variables, and the hetero may go away. See, for example, the first 2 pages of this handout, in particular the example on p. 2 about subpopulation differences in effects:

http://www.nd.edu/~rwilliam/stats2/l25.pdf

In short, if the model with interaction terms and no hetero term makes sense, I would probably go with it. You could still note that you had tested for hetero with oglm and concluded it didn't seem to be a problem.

As a sidelight, the preferred syntax for your model is

oglm success i.male income i.male#c.income, het(i.male)

It won't change your estimation results, but it will make it easy to use the -margins- command afterwards.


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Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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