I have read that the distribution for the random effects estimator in lme4 is highly skewed and for this reason standard errors are not reported. I wonder if anyone can provide a reference for this ? I have access to the book by Bates and Pinherio, but not Raudenbush and Bryk. A published paper would also be fine. Thanks !
I don't know of anything offhand, aside from Doug Bates' books and his postings on various online forums. That should be sufficient to justify why you don't report them. But if you want to try and quantify uncertainties, I might try a Bayesian approach, i.e., simulating from posterior distributions of variance parameters using MCMC. Maybe look at: