I have a paired design, two groups, two time points and two conditions. Participants are nested within groups. Time points are nested within conditions.

Here it is:

group   ind.n   when    time
A   1   A   A
A   1   A   B
A   1   A   C
B   1   A   A
B   1   A   B
B   1   A   C
A   2   A   A
A   2   A   B
A   2   A   C
A   3   A   A
A   3   A   B
A   3   A   C
A   4   A   A
A   4   A   B
A   4   A   C
B   2   A   A
B   2   A   B
B   2   A   C
B   3   A   A
B   3   A   B
B   3   A   C
A   5   A   A
A   5   A   B
A   5   A   C
A   6   A   A
A   6   A   B
A   6   A   C
A   7   A   A
A   7   A   B
A   7   A   C
A   8   A   A
A   8   A   B
A   8   A   C
A   9   A   A
A   9   A   B
A   9   A   C
B   4   A   A
B   4   A   B
B   4   A   C
A   1   B   A
A   1   B   B
A   1   B   C
B   1   B   A
B   1   B   B
B   1   B   C
A   2   B   A
A   2   B   B
A   2   B   C
A   3   B   A
A   3   B   B
A   3   B   C
A   4   B   A
A   4   B   B
A   4   B   C
B   2   B   A
B   2   B   B
B   2   B   C
B   3   B   A
B   3   B   B
B   3   B   C
A   5   B   A
A   5   B   B
A   5   B   C
A   6   B   A
A   6   B   B
A   6   B   C
A   7   B   A
A   7   B   B
A   7   B   C
A   8   B   A
A   8   B   B
A   8   B   C
A   9   B   A
A   9   B   B
A   9   B   C
B   4   B   A
B   4   B   B
B   4   B   C
A   10  A   A
A   10  A   B
A   10  A   C
A   11  A   A
A   11  A   B
A   11  A   C
A   12  A   A
A   12  A   B
A   12  A   C
A   13  A   A
A   13  A   B
A   13  A   C
A   14  A   A
A   14  A   B
A   14  A   C
A   15  A   A
A   15  A   B
A   15  A   C
A   16  A   A
A   16  A   B
A   16  A   C
A   17  A   A
A   17  A   B
A   17  A   C
A   18  A   A
A   18  A   B
A   18  A   C
A   19  A   A
A   19  A   B
A   20  A   A
A   20  A   B
A   20  A   C
A   21  A   A
A   21  A   B
A   21  A   C
B   5   A   A
B   5   A   B
B   5   A   C
A   10  B   A
A   10  B   B
A   10  B   C
A   11  B   A
A   11  B   B
A   11  B   C
A   12  B   A
A   12  B   B
A   12  B   C
A   13  B   A
A   13  B   B
A   13  B   C
A   14  B   A
A   14  B   B
A   14  B   C
A   15  B   A
A   15  B   B
A   15  B   C
A   16  B   A
A   16  B   B
A   16  B   C
A   17  B   A
A   17  B   B
A   17  B   C
A   18  B   A
A   18  B   B
A   18  B   C
A   19  B   A
A   19  B   B
A   20  B   A
A   20  B   B
A   20  B   C
A   21  B   A
A   21  B   B
A   21  B   C
B   5   B   A
B   5   B   B
B   5   B   C

For group A: I want to test the difference of the difference:

(GroupA.WhenB.TimeB-GroupA.WhenB.TimeA) - (GroupA.WhenA.TimeB-GroupA.WhenA.TimeA)

For group B: then same thing:

(GroupB.WhenB.TimeB-GroupB.WhenB.TimeA) - (GroupB.WhenA.TimeB-GroupB.WhenA.TimeA)

Then, I want the difference between the difference of difference:

((GroupB.WhenB.TimeB-GroupB.WhenB.TimeA) - (GroupB.WhenA.TimeB-GroupB.WhenA.TimeA)) - ((GroupA.WhenB.TimeB-GroupA.WhenB.TimeA) - (GroupA.WhenA.TimeB-GroupA.WhenA.TimeA))

NB! Subject 19 is missing two libraries, one at for WhenA.TimeC and one at WhenB.TimeC.

So, how do I make my design matrix, correcting for paired samples? I have tried this:

full.m <- model.matrix(~ Group + Group:ind.n + Group:Time:When, dt.ss)
ss1 <- which(apply(full.m, 2, sum) == 0)
full.m <- full.m[,-ss1]
colnames(full.m)

library(caret)
findLinearCombos(full.m) # Remove linear combinations
full.m <- full.m[,-c(37:38)]

dds <- DESeqDataSetFromMatrix(countData = as.matrix(d.ss),
                              colData = dt.ss,
                              design = ~ 1)

dds <- DESeq(dds, full=full.m, parallel=TRUE, betaPrior=FALSE)

Questions:
1) How do I specify the wanted results?
2) Why did I have to remove terms 37 and 38? How do I now specify them?

Here an attempt:

results(dds, contrast=list("GroupB.timeB.whenB","GroupB.timeB.whenA"))

results(dds, contrast=list("GroupA.timeB.whenB","GroupA.timeB.whenA"))

Thus, I think I got the first order interactions. However, how do I get the second order interaction?:

results(dds, contrast=list(c("GroupB.timeB.whenB","GroupB.timeB.whenA"),  c("GroupA.timeB.whenB","GroupA.timeB.whenA")) ???????

hi,

You have a complex experimental design, and so I would strongly recommend you to collaborate with a statistician on how to set up the design and how to combine coefficients using the design formula and coefficients that R produces.

I think you need all the interactions here, e.g. if you didn't have individual, you would use

~group + cond + time + cond:time + group:cond + group:time + group:cond:time

This gives all the standard interactions you would expect, and the last coefficient is the difference in the interaction across group.