How to obtain Tukey compact letter display from a GLM with interactions - r

Question

I have set of data that I've analyzed with a generalized linear model that has three categorical factors in 3-way interaction (factorA, factorB, factorC) and a fourth continuous factor (factorD) that is simply added in the model. I am trying to obtain a set of Tukey letter groups (ie, compact letter display) from the model but haven't found a way to include the interaction successfully. I'm not interested in including factorD, just the three in the interaction.
I have gotten the Tukey-adjusted pairwise comparisons with this:
lsmeans(my.glm, factorA*factorB*factorC)
But I was not able to figure out how to produce a compact letters display from that. It can be done with multcomp package but I could only find ways to do it with main effects with that package, not interactions.
So then I tried the agricolae package, as this post (https://stats.stackexchange.com/questions/31547/how-to-obtain-the-results-of-a-tukey-hsd-post-hoc-test-in-a-table-showing-groupe) discusses that that should work. However, following the instructions in that answer led to a non-functional response from HSD.test. Specifically, I could get the main effects tests to work fine, e.g. HSD.test(my.glm,"factorA") but I could not get the interactions to work. I tried this:
intxns<-with(my.data, interaction(factorA,factorB,factorC))
HSD.test(my.glm,"intxns",group=TRUE)
But a get an error that indicates the HSD.test function didn't recognize "intxns" as a valid object, it looks like this (also, I checked the intxns object and it looks good and the number of rows matched the number of residuals of my glm):
Name: inxtns
factorA factorB factorC factorD
I get that same error if I just put nonsense into the factor field in the HSD.test function call. I checked the inxtns object and it looks good and the number of rows matched the number of residu
The agricolae notes don't actually cover the use of interactions in HSD.test, but I assume it can work.
Does anyone know how to get HSD.test to work with interactions? Or is there any other function you've gotten to work to produce compact letter displays for a glm with interactions?
I've been working on this for a number of days now and haven't been able to find a solution, hopefully I'm not missing something obvious.
Thanks!

Answer 1

I don't know how you've specified your glm model, but for HSD.test, it's looking to match the particular treatment name with the same name specified in the glm formula as well as the data frame. This is why your main effect, factorA will work, but not the 3-way interaction. For multiple comparison tests on interactions, I find it easiest to generate the interactions separately and add them to the data frame as additional columns. The glm model can then be specified using the new variables which code for the interaction.
For example,
set.seed(42)
glm.dat <- data.frame(y = rnorm(1000), factorA = sample(letters[1:2],
size = 1000, replace = TRUE),
factorB = sample(letters[1:2], size = 1000, replace = TRUE),
factorC = sample(letters[1:2], size = 1000, replace = TRUE))
# Generate interactions explicitly and add them to the data.frame
glm.dat$factorAB <- with(glm.dat, interaction(factorA, factorB))
glm.dat$factorAC <- with(glm.dat, interaction(factorA, factorC))
glm.dat$factorBC <- with(glm.dat, interaction(factorB, factorC))
glm.dat$factorABC <- with(glm.dat, interaction(factorA, factorB, factorC))
# General linear model
glm.mod <- glm(y ~ factorA + factorB + factorC + factorAB + factorAC +
factorBC + factorABC, family = 'gaussian', data = glm.dat)
# Multiple comparison test
library(agricolae)
comp <- HSD.test(glm.mod, trt = "factorABC", group = TRUE)
giving
comp$groups giving
trt means M
1 a.a.a 0.070052189 a
2 a.b.b 0.035684571 a
3 b.a.a 0.020517535 a
4 b.b.b -0.008153257 a
5 a.b.a -0.036136140 a
6 a.a.b -0.078891136 a
7 b.a.b -0.080845419 a
8 b.b.a -0.115808772 a