Efficiency Gains from Using Auxiliary Variables in Imputation

Imputation models sometimes use auxiliary variables that, though not part of the planned analysis, can improve the accuracy of imputed values and the efficiency of point estimates. A recent article, using evidence from simulations, argued that the use of auxiliary variables in imputation did not improve efficiency. We review the simulation results and find that the use of auxiliary variables did improve efficiency; under some conditions the efficiency gain was equivalent to increasing the sample size by a quarter. We give an example from our own research where the efficiency gained from auxiliary variables was equivalent to increasing the sample size by three quarters, and pushed some estimates from statistical insignificance to significance. For auxiliary variables to make a difference, there must be a lot of missing data, some estimates must be near the border of significance, and the auxiliary variables must be excellent predictors of the missing values.