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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.

Robert Long
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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.

StasK
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  • thank you. I have approx 220 level 2 units, with around 750,000 unique level 1 observations. There is a lots of missing data, but the hard work of MI (predeictor matrix etc) had been done by someone else but for a fixed effects model. This is a biostat application and the outcome is binary. The data are patients (L1) within hospitals (L2), or possibly a multiple membership structure with patients within years within hospitals. Thanks again. – Robert Long Apr 23 '12 at 17:41
  • Well, as I said, I would run a simulation to see how the variance components look like for the pattern of regressors at both levels, as well as the relation with the outcomes. My gut feeling is that if you have outcomes that are strongly associated with particular clusters, and/or rare events, with whatever pattern, then I would imagine that you will have bad sampling distributions of the variance estimates for this sample size. – StasK Apr 24 '12 at 02:01
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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.

Krish
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    Welcome to the site, @Krish. I'm not sure how much this answers the OP's question, which seems to be about progress in using multiple imputation. Would you mind editing your answer to draw out the connection more explicitly? – gung - Reinstate Monica Jan 04 '13 at 18:21