Hello,

I am removing a batch effect from my data using limma's removeBatchEffect. The variable of interest should not be removed, hence I include it in the design matrix. Should the design matrix include an intercept term? Does it matter?

The design matrix is just the usual design matrix that you would naturally use in an analysis without the batch effect, regardless of whether you like to use ~0 in your model formula or not.

The design matrix does has the span the intercept term, but it can do so implicitly rather than explicitly. Suppose that Condition is a factor of interest and you are planning ot use

y2 <- removeBatchEffect(y,batch=Batch,design=design)

You could use

design <- model.matrix(~Condition)

or

design <- model.matrix(~0+Condition)

and both of these are exactly the same from a mathematical point of view and will produce the same result.

However you could not remove the intercept by

design <- model.matrix(~Condition)
design <- design[,-1]

because then the design matrix would not span the intercept term.