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I'm working on a project that involves multiple imputation, and I may have to program some of the work myself. I can use the R package MICE to generate the imputed data sets, but then I have to use a mixed linear model rather than a linear model. How do I combine the estimates from the multiple imputed data sets? The estimate is just the average of the individual estimates, but what about the standard error?

I found a simple answer in one of my books. If I run the model and get m estimates (r

_{k}) and m standard errors (s_{k}) then the formula for the standard error of the combined estimate is:This is found on page 30 of Allison, P (2002). Missing Data. Sage Publications, Thousand Oaks, CA.

You can find a similar formula at

- Schafer J. Multiple imputation FAQ page. Available at: http://www.stat.psu.edu/~jls/mifaq.html [Accessed July 25, 2009].
Look for the question "How do I combine the results across the multiply imputed sets of data?"

When I have a chance, I'll illustrate how this works with some real data.