What Ai and Norton (2003) are saying is that interaction terms in
nonlinear models do not give you the 'marginal effect' because the
magnitude and significance level are not provided by the value of the
coefficient and standard erros on the interaction terms.
If you are interested in the marginal effect of one of the variable
that is part of the interaction effect, you can bootstrapp your
equation and get the distribution of the marginal effect and its
significance level. Ai and Norton propose to use the Delta Method. In
my point of view, bootstrapping is much easier to implement and gives
you the same type of information.
If you are interested in predicted probabilities, you can simply
predict using the average of prediction strategy. Mentioning clearly
that you rely on average predictions and not marginal effects. Then
you can estimate the standard errors around your predictions to get
the significance levels, relying once again on the bootstrapping
technique.
France Priez
The University of North Carolina at Chapel Hill
On Sun, 20 Mar 2005 14:33:28 -0800, Daniel Schneider
<[email protected]> wrote:
> As far as I understand most of the papers quoted, there is in fact a
> problem with the LR test approach as well, because it basically uses the
> same mechanisms. The authors argue that interaction effects vary across
> probabilities in strength and significance.
>
> My main problem is finding a way to discuss the substantial content of
> my data analysis and not just saying that they are sometimes significant
> and sometimes not. I tried to use -predict- and changing the values of
> my variables (similar to what -prvalue- or -prgen- do), and then make
> some nice graphs showing how the predicted value changes with the
> different values for my variables. The problem is, that I am just not
> sure if the Ai & Norton (2000) basically says "you can't do that" and if
> this is true, what else I can do to demonstrate the effect of the
> variables in my model.
>
> Another interesting article on that topic is
>
> Chi Huang / Todd G. Shields (2000): "Interpretation of Interaction
> Effects in Logit and Probit Analyses: Reconsidering the Relationship
> Between Registration Laws, Education, and Voter Turnout", American
> Politics Research, Vol. 28, No. 1, 80-95
>
> Because they also work on the problem and use graphical procedures to
> illustrate effects like I am trying to do. I will probably just follow
> their example...
>
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf Of Tim Wade
> > Sent: Sunday, March 20, 2005 6:38 AM
> > To: [email protected]
> > Subject: Re: st: Interaction terms in a logit model
> >
> >
> > 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
> > <[email protected]> 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: [email protected]
> > > > [mailto:[email protected]] On Behalf
> > Of Hoetker,
> > > > Glenn
> > > > Sent: Saturday, March 19, 2005 10:13 AM
> > > > To: [email protected]
> > > > 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 [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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