[R-sig-ME] Interpreting three-way interaction with categorical predictors and binary outcome (GLMER)

[Francesco Romano]

Dear Emmanuel, thanks for sharing your expertise with me. Unfortunately I
can't seem to understand several details in your explanation but I do
appreciate this work can be done manually. At this time I realize the
question is ill-placed within this R-sig so I am closing the ticket and
asking the question elsewhere. Apologies for cross-posting.

On Fri, Feb 26, 2016 at 1:47 PM, Emmanuel Curis <
emmanuel.curis at parisdescartes.fr> wrote:

> 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 µ by
> ln odds in that case], lmer...
>
> Exemple, for a 2-way 2×2 design with interaction, with cell means
>
>    A    B
> 1  µ1A  µ1B
>                   and comparison to do let's say (µ2A - µ1B) =?  (µ1A-µ1B)
> 2  µ2A  µ2B
>
> Using the default contrats with a reference cell (A,1), the
> coefficients in the model are µ0, dB, d2, d2:B with
>   µ1A = µ0
>   µ1B = µ0 + dB
>   µ2A = µ0 + d2
>   µ2B = µ0 + d2 + dB + d2:B
>
> Then, you're comparison is
>  (µ2A - µ1B) - (µ1A-µ2B) =
>  ((µ0 + d2) - (µ0 + dB)) -( (µ0) - (µ0 + d2 + dB + d2:B) ) =
>  d2 - dB - d2 + dB - d2:B =
>  d2:B
>
> and your « contrast » to use to write your test is
>  µ0  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
>



-- 
Frank Romano Ph.D.

Tel. +39 3911639149

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