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Also, I'm facing a slight conundrum where I'm comparing between four groups (two at a time) but depending on what continuous covariate I'm adding, the number of DE genes can change, and the change is different between different comparisons.
From the sounds of it, you're getting DE genes in each comparison, regardless of the model.
Given that they're both working, I wouldn't bother fitting a different model for each comparison.
The more concerning issue is if either of the continuous covariates are confounded with age; if so, then this will also compromise detection of the age response, as any genuine increase in expression due to age can be absorbed into the covariate's coefficient and lost. I think I better understand how the design matrix works now.
I do agree that given the continuous covariate is age, it wouldn't make sense to compare the intercept between group1 and group2.
But if I were to create a design matrix: , and perform the same comparison between group1 and group2, would that give a same result?