How to code contrasts in lme4 or nlme?

Question

I am looking for the most efficient way to run contrasts in R when using lme4. I have been working with a stats consultant that I really trust and she has given me the following code. I have contrasts between 6 treatments and I run these contrasts for 6 different years. So I end up writing 90 contrasts out. Now I am about to include another factor (sampling depth) in the model which will result in me writing 450 contrasts.

There must be a better way?

I have been reading ways to run contrasts in R, but haven't turned up much related to lme4 . nlme would work for me too, but it is also not clear to me how it works with contrasts.

Here is my data:

https://www.dropbox.com/s/2ho6phfxhz6xlsy/Root%20biomass%2C%20whole%20core.csv

Here is the simplest form of the code, for just one year:

lm1 <- lmer(mass_sum ~ block.f+ trt + (1|block.f:trt), data = roots2)
coefs <- fixef(lm1)
varb <- vcov(lm1)

##CC vs CCW
c1 <- as.matrix(c(0,0,0,0,1,0,0,0,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccvccw <- (1-pt(abs(t1), df = 15))*2

##CC vs CS
c1 <- as.matrix(c(0,0,0,0,0,1,0,0,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccvcs <- (1-pt(abs(t1), df = 15))*2

##CC vs P
c1 <- as.matrix(c(0,0,0,0,0,0,1,0,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccvp <- (1-pt(abs(t1), df = 15))*2

##CC vs PF
c1 <- as.matrix(c(0,0,0,0,0,0,0,1,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccvpf <- (1-pt(abs(t1), df = 15))*2

##CC vs SC
c1 <- as.matrix(c(0,0,0,0,0,0,0,0,1))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccvsc <- (1-pt(abs(t1), df = 15))*2

##CCW vs CS
c1 <- as.matrix(c(0,0,0,0,1,-1,0,0,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccwvcs <- (1-pt(abs(t1), df = 15))*2

##CCW vs P
c1 <- as.matrix(c(0,0,0,0,1,0,-1,0,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccwvp <- (1-pt(abs(t1), df = 15))*2

##CCW vs PF
c1 <- as.matrix(c(0,0,0,0,1,0,0,-1,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccwvpf <- (1-pt(abs(t1), df = 15))*2

##CCW vs SC
c1 <- as.matrix(c(0,0,0,0,1,0,0,0,-1))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
ccwvsc <- (1-pt(abs(t1), df = 15))*2

##CS vs P
c1 <- as.matrix(c(0,0,0,0,0,1,-1,0,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
csvp <- (1-pt(abs(t1), df = 15))*2

##CS vs PF
c1 <- as.matrix(c(0,0,0,0,0,1,0,-1,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
csvpf <- (1-pt(abs(t1), df = 15))*2

##CS vs SC
c1 <- as.matrix(c(0,0,0,0,0,1,0,0,-1))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
csvsc <- (1-pt(abs(t1), df = 15))*2

##P vs PF
c1 <- as.matrix(c(0,0,0,0,0,0,1,-1,0))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
pvpf <- (1-pt(abs(t1), df = 15))*2

##P vs SC
c1 <- as.matrix(c(0,0,0,0,0,0,1,0,-1))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
pvsc <- (1-pt(abs(t1), df = 15))*2

##PF vs SC
c1 <- as.matrix(c(0,0,0,0,0,0,0,1,-1))
est1 <- t(c1)%*%coefs
varc1 <- t(c1)%*%varb%*%c1
t1 <- as.numeric(est1/sqrt(varc1))
pfvsc <- (1-pt(abs(t1), df = 15))*2

ccvccw
ccvcs
ccvp
ccvpf
ccvsc
ccwvcs
ccwvp
ccwvpf
ccwvsc
csvp
csvpf
csvsc
pvpf
pvsc
pfvsc

Answer 1

For all pairwise contrasts, this site is helpful: http://www.ats.ucla.edu/stat/r/faq/testing_contrasts.htm

For example:

library(multcomp)
HUC04_model = lmer(Mean_Wr ~ HUC04 + (1|FIN), data, REML=F)
test = glht(HUC04_model,linfct=mcp(HUC04="Tukey"))
summary(test)