can a covariate also be a random effect in linear mixed model? I have a problem where I have 5 different patients who have given their blood. And each of these samples is treated with 6 different compounds. These samples are assayed for a panel of 50 proteins and we finally get the protein abundances for each of these samples.
So I am interested in looking at how the protein abundances change with the treatment. My sample size ( no. of donors ) is small, and the variance among them is pretty large, I want to use the donor ID as the random effect. But the same donors are used in obtaining repeated measures at a further time point as well.
So my question is - can I use the donor ID as the covariate as well as the random effect in my model?
abundance ~ treatment + donor + (1|donor)
Does the above model make sense?
Thanks for your help!


abundance ~ treatment + donor + (1|donor)
Does the above model make sense?

No, it doesn't. For one thing, it is unlikely that such a model is identified. For another, it may result in convergence problems.
Either it should be random, or fixed. It can't really be both.
