P.Mean: Formula for multiple imputation (created 2009-07-24).

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 (rk) and m standard errors (sk) 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

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.

Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 United States License. This page was written by Steve Simon and was last modified on 2010-04-12. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Modeling issues.