It is my understanding that when making comparisons both within and between groups with paired samples, but there are a differing number of samples for each condition, the model matrix must be adjusted as such: C: DESeq2 paired and multi factor comparison

I am confused as to what removing elements from the model matrix means. Does this mean that I am losing information from paired samples that don't have a counterpart in the other condition? Am I throwing away information?

I apologize if my question is phrased poorly--I'm pretty confused and would appreciate any clarification. Thank you!

What's happening is that you are removing columns, corresponding to coefficients to estimate which have no samples for which to estimate those coefficients. Hence, the model matrix has a column of zeros. Ones in the column correspond to samples which will be given a 'beta' in the formula.

So it's definitely not throwing away information. If you tried to fit the model without removing those columns, the software would stop and say some version of: "I can't fit this model because there are no samples to estimate one or more coefficients."