[R-sig-ME] Multiple contrasts and what data to include when writing up a three-way interaction in lmer?

[Tim Meehan]

Hi Tove,

The visreg package [visreg()] and languageR package [plotLMER.fnc()] can
sometimes be helpful for wrapping your head around interactions.

Best,
Tim

On Thu, Feb 12, 2015 at 4:09 AM, Tove Jansson <tove.jansson at gmail.com>
wrote:

> Hi,
>
> I have a question about three-way (or any) interaction data. Perhaps my
> question is more conceptual than allowed on this list - but I hope it can
> still be considered relevant - I am very new to mixed models and it has
> been difficult for me to find an answer for questions regarding
> interactions with continuous predictors.
>
> Brief background:
>
> Our lmer model has a significant three-way interaction. Our DV is
> continuous and we have three predictors. One predictor is categorical
> (three levels) and the other two predictors are continuous.
>
> To view all possible contrasts within the highest order interaction we
> have been using a custom contrast matrix, in a similar way as to what was
> done here:
> http://stats.stackexchange.com/questions/43664/mixed-model-multiple-comparisons-for-interaction-between-continuous-and-categori
> <
> http://stats.stackexchange.com/questions/43664/mixed-model-multiple-comparisons-for-interaction-between-continuous-and-categori
> >
>
> To correct our alpha correction for multiple comparisons, we have been
> using the default single-step adjustment in the glht function in multcomp
> package.
>
> The problem:
>
> To minimize the adjustment for multiple comparisons, I limited my glht
> contrasts to the highest order interaction (the three-way).
>
> But in order to understand the interaction, I need to also look at the
> simple effects for the categorical predictor. For example, it’s important
> for me to know if there was a significant difference at the original
> intercept value of a certain predictor so that I can know if an effect is
> a) emerging on account of an interaction or b) becoming stronger on account
> of the same interaction. However, if I include these simple effects in the
> contrasts, then I am forced to make adjustments to the alpha.
>
> How is this typically handled? Is there a way to present the simple
> effects without further penalty to my p values? Or am I thinking about this
> the wrong way - does the mere fact that I want to look at them mean that I
> must correct my alpha more? Apologies if this should be perfectly obvious.
>
> Also - can anyone recommend a good way of plotting three-way interactions
> for lmer output? I have been using plot() and effect() to create trellis
> plots, as seen below, but I find it difficult and confusing trying to
> control the parameters. For example, I have not found a way to manually
> select the values for Pred2 (incremental, select values are selected by
> default for the trellis plots) and I have not found a way to indicate
> confidence intervals. If anyone can direct me to a good source that
> explains how to use plot() with these sorts of objects, please do so.
> ggplot2 does not seem to work for effects objects.
>
> Thanks in advance.
>
> #plot multiline
> p0 <- effect(“condition:Pred1:Pred2", testTotalRegion2_lmer14)
> p1 <- plot(p0,
>         multiline=TRUE,
>         main="Region2",
>         xlab=“Pred1",
>         ylab="FD (logged + residualalized)",
>         key.args=list(x=1,y=1,corner=c(x=.8, y=1))
>         )
> p1
>
>
>
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>
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