An Approach to Addressing Multiple Imputation Model Uncertainty Using Bayesian Model Averaging

Abstract

This paper considers the problem of imputation model uncertainty in the context of missing data problems. We argue that so-called “Bayesianly proper” approaches to multiple imputation, although correctly accounting for uncertainty in imputation model parameters, ignore the uncertainty in the imputation model itself. We address imputation model uncertainty by implementing Bayesian model averaging as part of the imputation process. Bayesian model averaging accounts for both model and parameter uncertainty, and thus we argue is fully Bayesianly proper. We apply Bayesian model averaging to multiple imputation under the fully conditional specification approach. An extensive simulation study is conducted comparing our Bayesian model averaging approach against normal theory-based Bayesian imputation not accounting for model uncertainty. Across almost all conditions of the simulation study, the results reveal the extent of model uncertainty in multiple imputation and a consistent advantage to our Bayesian model averaging approach over normal-theory multiple imputation under missing-at-random and missing-completely-at random in terms of Kullback-Liebler divergence and mean squared prediction error. A small case study is also presented. Directions for future research are discussed.