Re: st: mi impute chained with multilevel data

[Stas Kolenikov <skolenik@gmail.com>]

I think the multilevel imputation model should satisfy the following
properties (on top of everything else):
1. The level-2 imputations must be identical within level-2 units.
2. The level-1 imputations must account for the level-2 effects.

The Marchenko and Eddings FAQ only addresses the second issue. Issue 1
will be addressed in the wide format of the multilevel data (their
approach 3), although that's an unwieldy format to work with.

What this means to me is that the chained imputation model might run as follows:
1. For level-1 variables, run gllamm with the appropriate link function
2. Draw the level-2 imputations using the gllapred, u (and then still
taking a random draw from that distribution). -xtm- postestimation
does not seem to allow drawing these posterior summaries.
3. Draw the level-1 imputations using the just imputed level-2
variable(s), the regression weight of these variables, and the
estimated variability of the level-1 variable on its appropriate
scale.

This is a poor man's attempt to reproduce a multilevel MCMC in Stata.
If you can do a large MCMC properly, you would want to do that.

If you stick with Stata, you would have to write your own rather
complicated code, and then tell Stata that you have -mi- data fully
prepared. That means that you need to study how Stata represents MI
data internally, with all the internal variables, chars, and their
interrelations. (I've done this for one of my projects, and my data
have consistently been failing -mi update- checks, although I could
not pin down the reason why.)


-- Stas Kolenikov, PhD, PStat (SSC)
-- Senior Survey Statistician, Abt SRBI
-- Opinions stated in this email are mine only, and do not reflect the
position of my employer
-- http://stas.kolenikov.name



On Tue, May 7, 2013 at 12:35 PM, Newport-berra, Mchale
<mnewport@jhsph.edu> wrote:
> I am using mi impute chained (Stata 12) to impute data for children nested in schools. I am then using the imputed data to do xtmixed. So far I have been able to do the multiple imputation without taking clustering into account, but  I would really appreciate guidance about how to account for the multi-level structure of the data in the imputation.  I have come across the following possibilities:
>
> One suggestion I have received is doing mi impute chained with a dataset of only the school-level variables, and then merging this with the child-level dataset and imputing the child-level variables.  However, I'm not sure how mi estimate would make sense of the imputed variables from different rounds of imputation.
>
> Han  (2008, Developmental Psychology) used Stata and  assigned the same imputed values for school variables to students from the same school to preserve multilevel data structure in multiple imputation procedures, but I'm not sure how to do this.
>
> I also came across this Stata document: http://www.stata.com/support/faqs/statistics/clustering-and-mi-impute/ which describes the following 3 methods:
>
> 1. Include indicator variables for clusters in the imputation model
> 2. Impute data separately for each cluster.
> 3. Use a multivariate normal model to impute all clusters simultaneously.
>
> Since I have a lot of schools but not a lot of kids in each school, #1 and #2 won't work. I'm not sure if #3 work with mi impute chained.
>
> Has anyone used any of these strategies, or other strategies?  Thank you!
>
>
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