  Multiple imputation (MI) is a method for repairing and analyzing data with
missing values. MI replaces missing values with a sample of random values drawn
from an imputation model. The most popular form of MI, which we call posterior
draw multiple imputation (PDMI), draws the parameters of the imputation model
from a Bayesian posterior distribution. An alternative, which we call maximum
likelihood multiple imputation (MLMI), estimates the parameters of the
imputation model using maximum likelihood (or equivalent). Compared to PDMI,
MLMI is less computationally intensive, faster, and yields slightly more
efficient point estimates.
  A past barrier to using MLMI was the difficulty of estimating the standard
errors of MLMI point estimates. We derive, implement, and evaluate three
consistent standard error formulas: (1) one combines variances within and
between the imputed datasets, (2) one uses the score function, and (3) one uses
the bootstrap to estimate variance components due to sampling and imputation.
Formula (1) modifies for MLMI a formula that has long been used under PDMI,
while formulas (2) and (3) can be used without modification under either PDMI
or MLMI. We have implemented MLMI and the standard error estimators in the mlmi
and bootImpute packages for R.
