Bias and Efficiency for SEM With Missing Data and Auxiliary Variables: Two-Stage Robust Method Versus Two-Stage ML

This article compares parameter estimates by 2-stage ML (TSML) and a recently developed 2-stage robust (TSR) method for structural equation modeling (SEM) with missing data. In the design, data are missing at random (MAR) after an auxiliary variable (AV) is included, and they are missing not at random (MNAR) otherwise. Results indicate that, when either the substantive variables or the AV is nonnormally distributed, TSR most likely yields more accurate parameter estimates than TSML; TSML is only slightly preferred to TSR when all variables are normally distributed. Including normally distributed AVs with TSML reduces the bias and improves the accuracy in parameter estimates. However, when the distribution of AVs has heavier tails than that of the normal distribution, including them with TSML could result in less accurate parameter estimates. When the sample size N is medium to large, including AVs with TSR most likely yields more accurate parameter estimates. When N is small, missing data rate is low, and when the AV is nonnromally distributed, TSML or even TSR could yield more accurate parameter estimates under MNAR mechanism than under MAR mechanism.