Hi, I have used edgeR for single factor and two factor experiments, but I am confused with 3 factor experiments. my code looks like below:

treat=c(rep("treated",12), rep("untreated",12))
subjects=factor(c(rep(1:12), rep(1:12)))
design <- model.matrix(~subjects+treat+W_1, data=pData(set2))

design <- model.matrix(~subjects+treat+W_1, data=pData(set2))
y <- DGEList(counts=counts(set), group=treat)
y <- calcNormFactors(y, method="upperquartile")
y <- estimateGLMCommonDisp(y, design)
y <- estimateGLMTagwiseDisp(y, design)
fit <- glmFit(y, design)
lrt <- glmLRT(fit, coef=?)

I would like to look for DE genes between "treated" vs "untreated". The W_1 comes from RUVSeq. So what would be my coef here ? as I have 12 subjects, my treatment becomes coef 13 ? or I could simply make my design as  

design <- model.matrix(~subjects+W_1+treat, data=pData(set2))

so that by default, the last factor will be considered.

Thanks in advance.

The default for glmLRT() is to drop the last coefficient when testing significance, in which case you can simply change your design matrix to be

design <- model.matrix(~subjects+W_1+treat, data=pData(set2)) 

and then you don't have to specify which coefficient to test, since the last coefficient will represent treated - untreated.

Or you specify the coef by name, in this case

glmLRT(fit, coef="treatuntreated")

Have a look at colnames(fit).