Linear Combinations in DESeq2 design

[R_Beth]

Hello,

I have an RNAseq experiment where I am studying longterm effects from a pregnancy condition in mice. Although there are expression similarities between littermates (observed on my bioplot and sample-to-sample dendrograms), long-term metabolic responses within a litter vary. I would like to know what genes are changes with the pregnancy condition but regress out the changes due to different litters. Because the group is a pregnancy condition, “MNR” and controls cannot be in the same litter, resulting in two of my variables being a linear combination.

The summarized experiment is the following:
ID Group Litter_alph
C1 Control b
C3 Control c
C7 Control c
C6 Control d
C4 Control d
C8 Control d
C5 Control e
C2 Control e
I9 MNR a
I5 MNR f
F2 MNR f
T6 MNR g
F3 MNR g
T3 MNR h
T7 MNR i
T5 MNR i
I1 MNR i
T4 MNR j
T2 MNR k
I6 MNR k
F4 MNR l
I2 MNR l
I3 MNR l
I4 MNR l
I7 MNR m
T1 MNR n
F1 MNR n
T8 MNR n
I8 MNR o

Here is an example of that command:
> design(ddsMF) <- formula(~ Litter_alph + Group)

Error in checkFullRank(modelMatrix) :
the model matrix is not full rank, so the model cannot be fit as specified.
One or more variables or interaction terms in the design formula are linear
combinations of the others and must be removed.

I’ve tried to work around this by (see http://seqanswers.com/forums/showthread.php?t=47881)

> m <- model.matrix(~ID:Litter_alph + Group, se)
> m_use <- m[ , colSums(m) > 0]
> design(dds) <- ~ Group
> dds <- estimateSizeFactors(dds)
> dds <- estimateDispersionsGeneEst(dds, modelMatrix=m_use)

Error in eval(expr, envir, enclos) : inv(): matrix seems singular

Is there anyways to work around these issue and regress out litter effects? Any help would be appreciated!