When I'm running a GLM I will sometimes need to rescale predictors (e.g. take z-scores) to make the coefficients of different predictors easier to compare to each other. My understanding is that this doesn't and shouldn't change anything about the model fit except the scale of the coefficient. When I do this in DESeq2, I find that it changes not only the log2FC estimates, but also the p-values (before adjustment). I don't understand how or why that would be happening, or what to do about it.
Does anyone understand this? Is it expected behaviour? What should I do about it?