  Widely used methods for analyzing missing data can be biased in small
samples. To understand these biases, we evaluate in detail the situation where
a small univariate normal sample, with values missing at random, is analyzed
using either observed-data maximum likelihood (ML) or multiple imputation (MI).
We evaluate two types of MI: the usual Bayesian approach, which we call
posterior draw (PD) imputation, and a little-used alternative, which we call ML
imputation, in which values are imputed conditionally on an ML estimate. We
find that observed-data ML is more efficient and has lower mean squared error
than either type of MI. Between the two types of MI, ML imputation is more
efficient than PD imputation, and ML imputation also has less potential for
bias in small samples. The bias and efficiency of PD imputation can be improved
by a change of prior.
