Re: st: oglm and heterogeneous choice models

[Richard Williams <richardwilliams.ndu@gmail.com>]

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.

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/