How to do the post-hoc analysis for three predictors (two factor variables and one numeric variable)

Question

I'm using a linear mixed effects model to analyze the reaction time of learners of English as a Second Language (ESL). I have two factor variables: grammaticality (grammatical v.s. ungrammatical) and finiteness (finite v.s. nonfinite), as well as one numeric variable: proficiency.

I'd like to analyze how their proficiency may affect their sensitivity to grammaticality and finiteness, so I built the model like this:

fitnonnative7 <- lmer(data = nonnative, 
                      formula = RT ~ Grammaticality * Finiteness * Proficiency + (Grammaticality|subject) + (Grammaticality|item))

I got a marginal interaction between grammaticality and finiteness as well as a a marginal interaction between grammaticality, finiteness, and proficiency. How am I supposed to do the post-hoc analysis?

The result of the linear mixed effect model can be found here. I also tried the marginaleffects package to estimate the three-way interaction. Details of this package can be found here. This is what I have have so far:

• The result from the marginaleffects package

• The plot of the contrast in Grammaticality from low to high proficiency

• The plot of the contrast in Finiteness from low to high proficiency

I might have done something wrong, as the result doesn't tell me the interaction between grammaticality and finiteness. How do I analyze the two-way and three-way interactions properly?

Answer 1

Typically, you shouldn't look at the 2-way interactions if you have included a 3-way interaction into the model. I find the emmeans package function emtrends easy to use when unpacking interactions involving categorical and continuous predictors. Try

library(emmeans)
emt<-emtrends(fitnonnative7, ~"Grammaticality*Finiteness", var="Proficiency")
emt

for the 3-way interaction. This gives you the slope coefficients of "Proficiency" for different levels of Grammaticality*Finiteness. You can test differences between slopes at different levels of the interaction by

pairs(emt)   #use this instead of the contrast(emt)

If you want to look at the 2-way interaction and think it'll be fine even with the 3-way interaction included, you can use

em<-emmeans(fitnonnative7, pairwise~Grammaticality|Finiteness)
em$emmeans       #estimated marginal means for the 2-way interaction
em$contrasts     #contrasts between the above emm's