[R-sig-ME] interpreting interactions

[Jonathan Baron]

Again, sorry for this. I thought I was replying to the third spam from
the same person and was getting annoyed. In fact I was in my
"postponed mail". I postponed sending my comment because I wanted to
look at the Ai/Norton paper.

I have now looked at the Ai/Norton paper again, and it is NOT the same
issue as described in the Wagenmaker et al. paper that I cited. In the
Ai/Norton paper, probability of participation is what is truly of
interest. And the problem raised by Ai and Norton does not have to do
with interactions that are removable by transforming the dependent
variable.

However, I still think that the Wagenmaker et al. paper should be
required reading for psychologists.

Jon

On 04/08/14 10:09, Jonathan Baron wrote:
> THIS WAS A MISTAKE! SORRY!
> 
> (The message is not finished.)
> 
> 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 ...
> > > 
> > > _______________________________________________
> > > R-sig-mixed-models at r-project.org mailing list
> > > 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)
> > 
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > 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)
> 
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> 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)