[R-sig-ME] interpreting interactions
baron at psych.upenn.edu
Tue Apr 8 16:09:27 CEST 2014
THIS WAS A MISTAKE! SORRY!
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On 04/08/14 10:00, Jonathan Baron wrote:
> REMOVE ME
> 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)
> R-sig-mixed-models at r-project.org mailing list
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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