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Re: st: Interaction terms in a logit model


From   Tim Wade <wadetj@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interaction terms in a logit model
Date   Sun, 20 Mar 2005 09:38:16 -0500

Having not kept on this, I must admit to being surprised by these
issues regarding interactions in logit and other "non linear" models.
Do these issues with non linear models (and I haven't yet read all the
articles cited above so perhaps this is addressed) affect other
traditional ways of evaluating interactions, for example using the
likelihood ratio test instead of the t statistic of the interaction
coefficient to compare a model with interaction terms to a more
restricted model, without interaction terms?

Thanks, Tim



On Sat, 19 Mar 2005 12:20:56 -0800, Daniel Schneider
<daniel.schneider@stanford.edu> wrote:
> I am using it to test the moderating effect of motivations of media use
> on the impact of media use on a dependent variable. So, no, I don't
> think I am testing for group differences (like the Chow test in linear
> models would). In fact, while I used a dummy variable in my example, I
> am interacting two continuous variables, but I wanted to keep the
> example simple.
> 
> (but thanks for the link anyway, I am interested in that for different
> reasons)
> 
> Daniel
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > Hoetker, Glenn
> > Sent: Saturday, March 19, 2005 10:13 AM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: RE: st: Interaction terms in a logit model
> >
> >
> > 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_l
> > ogit.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
> > ghoetker@uiuc.edu
> >
> >
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > Richard Williams
> > Sent: Saturday, March 19, 2005 11:51 AM
> > To: statalist@hsphsun2.harvard.edu
> > 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:  Richard.A.Williams.5@ND.Edu
> > WWW (personal):    http://www.nd.edu/~rwilliam
> > WWW (department):    http://www.nd.edu/~soc
> >
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> >
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