  Multiple imputation (MI) is a popular method for handling missing data.
Auxiliary variables can be added to the imputation model(s) to improve MI
estimates. However, the choice of which auxiliary variables to include in the
imputation model is not always straightforward. Including too few may lead to
important information being discarded, but including too many can cause
problems with convergence of the estimation procedures for imputation models.
Several data-driven auxiliary variable selection strategies have been proposed.
This paper uses a simulation study and a case study to provide a comprehensive
comparison of the performance of eight auxiliary variable selection strategies,
with the aim of providing practical advice to users of MI. A complete case
analysis and an MI analysis with all auxiliary variables included in the
imputation model (the full model) were also performed for comparison. Our
simulation study results suggest that the full model outperforms all auxiliary
variable selection strategies, providing further support for adopting an
inclusive auxiliary variable strategy where possible. Auxiliary variable
selection using the Least Absolute Selection and Shrinkage Operator (LASSO) was
the best performing auxiliary variable selection strategy overall and is a
promising alternative when the full model fails. All MI analysis strategies
that we were able to apply to the case study led to similar estimates.

Methodology