Setting contrasts for three way interaction using multcomp

Question

I have a BACI experiment with measures before (2007) and after (2011) at three sites. Having trouble setting up the contrasts so I see whether the effect of year differs for treatments (cf the control) at each of the three sites.

I've tried to extend the example in the vignette with no success. Have also tried the lsmeans package.

Example df and code below, as well as the explicit contrasts I'd like to test.

library(nlme)
library(multcomp)
require(lsmeans)

# I have these versions:
# R version 3.2.4 Revised (2016-03-16 r70336)
# Platform: x86_64-w64-mingw32/x64 (64-bit)
# Running under: Windows 7 x64 (build 7601) Service Pack 1
# nlme_3.1-126
# multcomp_1.4-4 



exdf <- expand.grid(Site = c("Z",  "Y", "X"), 
                   Plot = 1:30,
                   Year = c("2007", "2011"), 
                   Treatment = c("Control", "A", "B", "A+B"))
exdf$Site <- factor(exdf$Site)
exdf$Plot <- factor(exdf$Plot)
exdf$Year <- factor(exdf$Year)
exdf$Treatment <- factor(exdf$Treatment)
exdf$Treatment <- relevel(exdf$Treatment, ref = "Control")

exdf$Response <- rnorm(mean = 1150, sd = 130, n = nrow(exdf))

mod1 <- lme(data = exdf,
            fixed =  Response ~ Year * Treatment * Site,
            random = ~1|Plot)


## would like to test (obviously that's not actual code)

## How do the treatments A, B, A+B differ in their interaction with 
## year, compared to the control treatment (ie do the slopes differ)

SiteX:Year:TreatmentControl - SiteX:Year:TreatmentA == 0
SiteX:Year:TreatmentControl - SiteX:Year:TreatmentB == 0
SiteX:Year:TreatmentControl - SiteX:Year:TreatmentA+B == 0

SiteY:Year:TreatmentControl - SiteY:Year:TreatmentA == 0
SiteY:Year:TreatmentControl - SiteY:Year:TreatmentB == 0
SiteY:Year:TreatmentControl - SiteY:Year:TreatmentA+B == 0

SiteZ:Year:TreatmentControl - SiteZ:Year:TreatmentA == 0
SiteZ:Year:TreatmentControl - SiteZ:Year:TreatmentB == 0
SiteZ:Year:TreatmentControl - SiteZ:Year:TreatmentA+B == 0

## Also potentially - does the interaction between site and year
## differ across sites? 
SiteX:Year:TreatmentA - SiteY:Year:TreatmentA == 0
SiteZ:Year:TreatmentA - SiteY:Year:TreatmentA == 0
SiteZ:Year:TreatmentA - SiteX:Year:TreatmentA == 0

SiteX:Year:TreatmentB - SiteY:Year:TreatmentB == 0
SiteZ:Year:TreatmentB - SiteY:Year:TreatmentB == 0
SiteZ:Year:TreatmentB - SiteX:Year:TreatmentB == 0

SiteX:Year:TreatmentA+B - SiteY:Year:TreatmentA+B == 0
SiteZ:Year:TreatmentA+B - SiteY:Year:TreatmentA+B == 0
SiteZ:Year:TreatmentA+B - SiteX:Year:TreatmentA+B == 0


## Started doing the example from 
#https://cran.r-project.org/web/packages/multcomp/vignettes/multcomp-examples.pdf
# Got a bit stuck

tmp <- expand.grid(Year = levels(exdf$Year),
                   Treatment = levels(exdf$Treatment),
                   Site = levels(exdf$Site))
X <- model.matrix(~ Year * Treatment * Site, data = tmp)
glht(mod1, linfct = X)


## Gives all the interactions not in the form I want..
tt <- lsmeans(mod1, specs = ~Year:Treatment|Site)
comps <- pairs(tt, interaction = TRUE)
summary(comps,  adjust = "holm")

Answer 1

Let's build it up in steps. First, you want to get differences of the two years for each combination of the other factors. This is easily done in lsmeans using

tt = lsmeans(mod1, specs = ~ Year | Treatment:Site)
dd = pairs(tt, reverse = TRUE)   # (2011) - (2008) for each T*S comb
summary(dd, by = NULL)

You can now compare these differences as you like:

pairs(dd, by = "Site")
pairs(dd, by = "Treatment")

... or compare them marginally:

pairs(lsmeans(dd, "Treatment"))
pairs(lsmeans(dd, "Site"))