Hello, I am running a glm analysis with edgeR on 64 biologically independent samples, with 3 factors. I have sex (M and F), age (P0, P7, P15, P30), and genotype (Control, KO). I have two separate questions, 1) I would like to look at the main effect of genotype over time. 2) I would like to look at the interaction between sex and genotype. I started by pasting all the factors together to use as a single factor without an intercept. I am having trouble understanding what exactly each coefficient means and which contrasts can be used to answer my questions.

design<-model.matrix(~0 + grouping)
> colnames(design)
 [1] "groupingControl0F."  "groupingControl0M."  "groupingControl15F." "groupingControl15M." "groupingControl30F." "groupingControl30M."
 [7] "groupingControl7F."  "groupingControl7M."  "groupingKO0F."       "groupingKO0M."       "groupingKO15F."      "groupingKO15M."     
[13] "groupingKO30F."      "groupingKO30M."      "groupingKO7F."       "groupingKO7M."      
> 

For example: if I contrast groupingControl0F. and groupingControl0M. does this mean I am holding genotype and age constant and looking at the main effect of sex?

Any help you can provide would be greatly appreciated!

You are fitting what I was taught to call a cell means model, meaning you are simply computing the mean of each 'cell' or group of samples. So for example, groupingControl0F is simply the female controls at P0. And given that you can make any comparisons you want.

For instance, let's say you want to know if there are any differences between male and female controls at P0. In that case you want

groupingControl0M - groupingControl0F

And the contrast matrix for that would be

> matrix(c(-1,1,rep(0,12)), ncol = 1)
      [,1]
 [1,]   -1
 [2,]    1
 [3,]    0
 [4,]    0
 [5,]    0
 [6,]    0
 [7,]    0
 [8,]    0
 [9,]    0
[10,]    0
[11,]    0
[12,]    0
[13,]    0
[14,]    0

Because the first two coefficients are those of interest, and you want to zero out the others. This is all just simple algebra. If you want the interaction of KO and gender at P0, it's (groupingKO0M - groupingControl0M) - (groupingKO0F - groupingControl0F), which is the same thing as groupingKO0M - groupingControl0M - groupingKO0F + groupingControl0F; you just construct a column of your contrast matrix so you have two 1s and two -1s at the correct position to make that comparison (noting that the rows of your contrast matrix correspond to the columns of your design matrix). So

> matrix(c(1,-1,rep(0,6),-1,1,rep(0,6)), ncol = 1)
      [,1]
 [1,]    1
 [2,]   -1
 [3,]    0
 [4,]    0
 [5,]    0
 [6,]    0
 [7,]    0
 [8,]    0
 [9,]   -1
[10,]    1
[11,]    0
[12,]    0
[13,]    0
[14,]    0
[15,]    0
[16,]    0

And to make sure you're getting what you want, you can do silly things like

> z <- colnames(design)
>  zz <- matrix(c(1,-1,rep(0,6),-1,1,rep(0,6)), ncol = 1)
> paste0(zz[as.logical(zz)], z[as.logical(zz)])
[1] "1groupingControl0F"  "-1groupingControl0M" "-1groupingKO0F"   
[4] "1groupingKO0M" 

Which confirms that the specified contrast column does the comparison I wanted.