Solved – Post-hoc testing in multcomp::glht for mixed-effects models (lme4) with interactions

Question

I am performing post-hoc tests on a linear mixed-effects model in R (lme4 package). I am using multcomp package (glht() function) to perform the post-hoc tests.

My experimental design is repeated-measures, with a random block effect. The models are specified as:

mymod <- lmer(variable ~ treatment * time + (1|block), data = mydata, REML = TRUE)

Rather than attaching my data here, I am working off of the data called warpbreaks within the multcomp package.

data <- warpbreaks
warpbreaks$rand <- NA

I have added an extra random variable to mimic my "block" effect:

warpbreaks$rand <- rep(c("foo", "bar", "bee"), nrow(warpbreaks)/3)

This mimics my model:

mod <- lmer(breaks ~ tension * wool + (1|rand), data = warpbreaks) 

I am aware of the the example in the "Additional Multcomp Examples- 2 Way Anova" This example leads you to a comparison of levels of tension within the levels of wool.

What if I want to do the opposite – compare the levels of wool within the levels of tension? (In my case, this would be comparing the levels of treatment (two – 0, 1) within the levels of time (three – June, July, August).

I have come up with the following code to do so, but it doesn't seem to work (see error message below).

First, from the example (with wool and tension swapped places):

tmp <- expand.grid(wool = unique(warpbreaks$wool), tension = unique(warpbreaks$tension))
X <- model.matrix(~ tension * wool, data = tmp)
glht(mod, linfct = X)

Tukey <- contrMat(table(warpbreaks$wool), "Tukey")

K1 <- cbind(Tukey, matrix(0, nrow = nrow(Tukey), ncol = ncol(Tukey)))
rownames(K1) <- paste(levels(warpbreaks$tension)[1], rownames(K1), sep = ":")

K2 <- cbind(matrix(0, nrow = nrow(Tukey), ncol = ncol(Tukey)), Tukey)
rownames(K2) <- paste(levels(warpbreaks$tension)[2], rownames(K2), sep = ":")

From here to bottom, my own code:

K3 <- cbind(matrix(0, nrow = nrow(Tukey), ncol = ncol(Tukey)), Tukey)
rownames(K2) <- paste(levels(warpbreaks$tension)[3], rownames(K3), sep = ":")

K <- rbind(K1, K2, K3)
colnames(K) <- c(colnames(Tukey), colnames(Tukey))

> summary(glht(mod, linfct = K %*% X))
Error in summary(glht(mod, linfct = K %*% X)) : 
  error in evaluating the argument 'object' in selecting a method for function 'summary': Error in K %*% X : non-conformable arguments

Answer 1

It is a lot easier to do using the lsmeans package

library(lsmeans)
lsmeans(mod, pairwise ~ tension | wool)
lsmeans(mod, pairwise ~ wool | tension)