If your dummy variable does in fact reflect that you are looking at
differences across groups, you really need to read Allison's 1999 piece
cited below. Partially building on Allison's piece, I have a paper in
which I test whether cross-group differences in residual variation
really matter (as opposed to being a theoretical concern without
practical impact). Monte Carlo simulations indicate that even small
differences in residual variation can indeed invalidate cross-group
comparisons. Using interaction terms to model different groups in logit
models ends up being particularly risky--you can even end up with
significant results in the opposite direction! Allison's tests, while
they have some limitations, are a definite improvement on common
practice.
If you are interested, the paper is at
http://www.business.uiuc.edu/ghoetker/documents/Hoetker_comp_logit.pdf.
You can install the Stata code it discusses from within Stata:
net from http://www.business.uiuc.edu/ghoetker
and carry on as normal from there. Please be aware that the software is
work in progress. In particular, there is absolutely no sanity
checking.
As far as I know, so long as you aren't using the interaction term to
model cross-group differences (which is what introduces the potential
for differences in residual variation), you should be okay.
Glenn
Glenn Hoetker
Assistant Profess of Strategy
College of Business
University of Illinois at Urbana-Champaign
[email protected]
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Richard
Williams
Sent: Saturday, March 19, 2005 11:51 AM
To: [email protected]
Subject: Re: st: Interaction terms in a logit model
At 10:00 PM 3/18/2005 -0800, Daniel Schneider wrote:
>Dear List,
>
>I have read the articles by Norton, Wang, Ai (2004) as well as their
>more theoretical paper (Ai & Norton (2000)) and I am aware of other
>literature describing the same problem. I think I understood the
>theoretical problems and reasoning behind their approach, but
>unfortunately I really have a hard time of really understanding what I
>have to do when I use interaction terms in a logit regression.
Daniel, could you provide more precise citations for the articles you
are
mentioning? I'd be curious to read more about what they say.
Not having read these papers, I don't know specifically what your
concern
is, but Paul Allison's "Comparing Logit and Probit Coefficients Across
Groups," SOCIOLOGICAL METHODS & RESEARCH, Vol. 28 No. 2, November 1999
186-208, may be worth a look. Here is the abstract:
"In logit and probit regression analysis, a common practice is to
estimate
separate models for two or more groups and then compare coefficients
across
groups. An equivalent method is to test for interactions between
particular
predictors and dummy (indicator) variables representing the groups. Both
methods may lead to invalid conclusions if residual variation differs
across groups. New tests are proposed that adjust for unequal residual
variation."
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
FAX: (574)288-4373
HOME: (574)289-5227
EMAIL: [email protected]
WWW (personal): http://www.nd.edu/~rwilliam
WWW (department): http://www.nd.edu/~soc
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