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Would you please advice me if the dependent variables in edgeR and limma should be used as a raw measurements or should they be log transformed if they are skewed?
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Your question is lacking in details. Can you elaborate on what data you have, what you aim to do with it, and which [if any] errors / issues / problems that you have encountered?
Your question says "dependent variable" but I am guessing that you mean independent variables of a numerical type, i.e., covariates.
There is no blanket rule about whether covariates should be transformed or not. Anything that make sense in the linear model is ok. It depends on the context. A covariate does not have to normally distributed.