When using multiple imputation to handle missing data, one must, if not immediately, but eventually, decide how many imputations to base inferences on. The validity of inferences does not rely on how many imputations are used, but the statistical efficiency of the inference can be increased by using more imputations. Moreover, we may want our results to be reproducible to a given precision, in the sense that if someone were to re-impute the same data using the same number of imputations but with a different random number seed, they would obtain the same estimates to the desired precision. For a great summary on considerations on how many imputations to use, see the corresponding section from Stef van Buuren’s book.

In this post I provide a small bit of R code which, given a pooled analysis after performing imputation using the mice package in R, calculates the so called Monte-Carlo standard error of the multiple imputation point estimates. Stata has really nice functionality for doing this built into mi estimate.