[R-sig-ME] interpreting interactions

Jonathan Baron baron at psych.upenn.edu
Tue Apr 8 16:00:23 CEST 2014


An additional problem with interactions is described in this excellent
paper, which is about "removable" interactions, i.e., those that can
be removed by a transformation of the dependent variable.


I don't know about econometrics either, but in psychology this is a
huge problem because most of the dependent variables are not
necessarily linear functions of the underlying variable that they are
trying to measure.

I tried to read the recommended paper, but I did not get far enough to
write the kind of very helpful summary that is below. From that, it
sounds like it is about a special kind of removable interaction.

On 04/08/14 00:50, Ben Bolker wrote:
> Joshua Hartshorne <jkhartshorne at ...> writes:
> > 
> > A colleague recently made the argument that interaction terms in logistic
> > regression are uninterpretable, citing Ai & Norton (2003)
> >  Interaction terms
> > in logit and probit models. On reading the paper, it seems to make the
> > weaker claim that interaction terms of continuous predictors may be
> > calculated incorrectly in 2003-era STATA, and that one should take care to
> > calculate them correctly.
> > 
> > But this did make me wonder whether there are any issues in interpreting
> > interpreting interaction terms for 'binomial' models in lmer. Can anyone
> > comment?
> > 
> > Josh
>   This topic was new to me.  As far as I can tell from my reading of
> the paper, it's extremely important to make the distinction between
> interaction _terms_ and interaction _effects_.  Again as far as I can
> tell, the interaction _terms_ correspond exactly to the estimated
> coefficients, and are relevant on the scale of the linear predictor
> (where everything is indeed linear).  The interaction _effects_,
> in contrast, seem to be defined on the response scale. Because there
> is a nonlinear transformation between these scales, there is
> not necessarily an intuitive correspondence between expected 
> differences-in-difference (cross derivatives) on the linear predictor
> scale (terms) and the response scale (effects).
>   Not being an applied econometrician, I don't really understand why
> one would want to do a statistical test of an interaction _effect_
> rather than an interaction _term_.  To me it makes most sense to
> do statistical tests on the scale of the linear predictor where
> everything is linear and (relatively) simple ...
>   As far as how this applies to GLMMs; I don't know, but
> there is an additional level of variation and/or averaging that may raise
> issues depending on whether you're trying to understand 
> population-level, conditional, or marginal effects ...
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Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)

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