A Note on the Use of Missing Auxiliary Variables in Full Information Maximum Likelihood-Based Structural Equation Models

Abstract

Recent missing data studies have argued in favor of an “inclusive analytic strategy” that incorporates auxiliary variables into the estimation routine, and Graham (2003) outlined methods for incorporating auxiliary variables into structural equation analyses. In practice, the auxiliary variables often have missing values, so it is reasonable to ask whether the inclusion of such variables will improve the estimation of model parameters. Simulation results indicated that the proportion of missing data and the missing data mechanism of the auxiliary variables had little impact on bias. Even when an auxiliary variable was missing not at random, bias was relegated to the auxiliary variable portion of the model, and did not propagate into the model of substantive interest. The study results suggest that the inclusion of an auxiliary variable is beneficial, even if the auxiliary variable has a substantial proportion of missing data.

Notes

¹The education example is unrealistic, because it is not possible to verify whether a particular variable is related to the cause of missingness. In practice, the selection of auxiliary variables relies heavily on substantive expertise and familiarity with the data collection process.