Interpreting three-way interaction with categorical predictors and binary outcome (GLMER)

If you're patient, you may use the tedious but sure way of
 1) check how the model is defined exactly
 2) write each cell mean using this model
 3) write down the exact comparison you want in term of cell means
 4) using 2), rewrite this comparison in term of the model
    coefficients
  ==> this will give you the linear combination to test (using
 multcomp:glht for instance).

This apply for any model that has a linear part: lm, glm [replace ? by
ln odds in that case], lmer...

Exemple, for a 2-way 2?2 design with interaction, with cell means

   A    B
1  ?1A  ?1B
                  and comparison to do let's say (?2A - ?1B) =?  (?1A-?1B)
2  ?2A  ?2B

Using the default contrats with a reference cell (A,1), the
coefficients in the model are ?0, dB, d2, d2:B with
  ?1A = ?0
  ?1B = ?0 + dB
  ?2A = ?0 + d2
  ?2B = ?0 + d2 + dB + d2:B

Then, you're comparison is
 (?2A - ?1B) - (?1A-?2B) =
 ((?0 + d2) - (?0 + dB)) -( (?0) - (?0 + d2 + dB + d2:B) ) =
 d2 - dB - d2 + dB - d2:B =
 d2:B

and your ? contrast ? to use to write your test is
 ?0  dA  d2  d2:B
 0    0   0     1

This is quite tedious with a three-way interaction and several levels,
and you need to known how were defined each coefficient in the model,
but at least you're certain of what you're testing in the end...

On Fri, Feb 26, 2016 at 12:28:37PM +0100, Francesco Romano wrote:
? One more question regarding the interpretation of interactions.
? I am having difficulty finding information on how to obtain a specific
? contrast in a 3-way interaction of three categorical variables, syntax
? (levels s and of), animacy (levels +AN -AN and -AN +AN), and group (int,
? adv, ns), predicting a binary outcome (correct or inversion).
?
? The anova yielded a significant effect for animacy and an interaction
? between syntax:group. Everything else was non-significant. As I am
? interested in comparing two cells at a time from the three-way table, I
? kept all 3 predictors and their interactions within the model. The best
fit
? was given by inclusion of random intercepts for participants and items
only.

--
                                Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html