Hi All,

I am attempting to create a MF design that will allow me to analyze paired samples (mouse) when testing different conditions, i.e. contrast(c("condition", "E", "D")) . When I attempt to create the dds file I receive this error whether or not I include or exclude the first two samples (B10 and B6):

> dds.Spe = phyloseq_to_deseq2(physeq, ~condition + mouse)
converting counts to integer mode
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.
See the section 'Model matrix not full rank' in vignette('DESeq2')

I have seen answers to this similar problem on bioconductor and read the manual/vignette, but cannot apply them to my specific case (I apologize in advance). Any help would be greatly appreciated.

My Design:

The problem here is that you don't really have a paired analysis. Just because have some blocking structure to your experiment doesn't make it a paired design. And if you have a blocking structure that doesn't have enough replication, then you don't have enough observations to estimate all the coefficients you need to model the experiment (which is what the problem is).

This is the same thing you learn in algebra class - you can solve a single equation with one unknown, but if you have two unknowns, you need two equations, three equations for three unknowns, etc. If you have two unknowns and one equation, there are infinite solutions, so neither x nor y are 'identifiable'. You don't have enough equations for the unknowns you are trying to solve for.

You could do a paired design if you eliminate mice 1-3 and 7, which would result in a full rank design matrix. Or you could hypothetically just remove mice 1-2, use voom() to convert to something you can do conventional statistics on, and then fit a glm using duplicateCorrelation() to estimate the within-mouse correlation structure.

Unfortunately you have a really flawed experimental design, so you are not likely to be able to make all the comparisons you hoped for.