Multiple Imputation for Mixed Effects models I stumbled accross this related question from 2010, and I wonder if there has been any progress on using multiple imputation for mixed effects models ? I prefer to use R, though Stata is also available to me.
 A: This is a partial answer at best, but it is too long for a comment.
The asymptotic distribution of the variance estimates will also be normal, but asymptotics here is in terms of the number of clusters (level-2 units, PSUs, whatever your discipline calls them). To get a nice normal distribution, you need to have several hundreds, or better thousands, of them. While this may work out for some social/economic surveys that may have 10K+ individuals followed over time, biostat applications may have a few dozens, which is insufficient. So all in all, this is a matter of trust in asymptotic normality. I would assess the distribution by a simulation with any given sample size, and make a judgement call based on it.
I gather that R developers preferred to enforce their caution regarding the finite sampling distributions, most likely because in their typical biomedical application, sample sizes are not sufficiently large. Stata developers did not have such reservations, because in their typical econometric applications, sample size may not be a badly pressing issue.
A: This is an interesting area, I am working on as well. Similar hospital data. But my difficulty has been on choosing between mixed effect modelling and GEE for a prediction model with multiple imputation. Even though naturally mixed effect model will the first choice, considering the number of " clusters" (patients-12000) with multiple admissions but with smaller cluster size(2-10), the mixed effect model seems to computationally take long (6-12 hours) and the effect sizes seem to be over etsimated.The GEE on the other hand has better estimates and performance (especially calibration).
Mathematically yet to prove this but seems the best solution at hand for a large database, with multiple imputation, 1000s of clusters and with small cluster size.
