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

[Tove Jansson]

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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