  Imputing missing values is an important preprocessing step in data analysis,
but the literature offers little guidance on how to choose between different
imputation models. This letter suggests adopting the imputation model that
generates a density of imputed values most similar to those of the observed
values for an incomplete variable after balancing all other covariates. We
recommend stable balancing weights as a practical approach to balance
covariates whose distribution is expected to differ if the values are not
missing completely at random. After balancing, discrepancy statistics can be
used to compare the density of imputed and observed values. We illustrate the
application of the suggested approach using simulated and real-world survey
data from the American National Election Study, comparing popular imputation
approaches including random forests, hot-deck, predictive mean matching, and
multivariate normal imputation. An R package implementing the suggested
approach accompanies this letter.
