[R-sig-ME] interpreting interactions

[Jonathan Baron]

THIS WAS A MISTAKE! SORRY!

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Jon

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.
> 
> http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3267935/
> 
> 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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> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> 
> -- 
> 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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-- 
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)