A comparison of strategies for selecting auxiliary variables for multiple imputation

TL;DR

This paper compares eight strategies for selecting auxiliary variables in multiple imputation, finding that including all variables generally performs best, with LASSO being a promising alternative when full inclusion is infeasible.

Contribution

It provides a comprehensive simulation and case study comparison of auxiliary variable selection strategies for multiple imputation, offering practical guidance.

Findings

Full model outperforms all selection strategies in simulations.

LASSO is the best performing selection method overall.

All strategies yielded similar estimates in the case study.

Abstract

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.