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

机译：缺少数据和辅助变量的SEM的偏差和效率：两阶段鲁棒方法与两阶段ML

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摘要

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.
机译：本文比较了两阶段ML（TSML）和最近开发的用于结构方程模型（SEM）的两阶段鲁棒（TSR）方法的参数估计，其中缺少了数据。在设计中，在包括辅助变量（AV）之后，数据是随机（MAR）丢失的，否则，数据不是随机（MNAR）丢失的。结果表明，当实质变量或AV非正态分布时，TSR最有可能产生比TSML更准确的参数估计值。当所有变量均呈正态分布时，TSML仅比TSR稍微偏爱。 TSML包括正态分布的AV可以减少偏差并提高参数估计的准确性。但是，当AV的尾部比正态分布的尾部重时，将它们包含TSML可能会导致参数估计的准确性降低。当样本大小N为中等到较大时，包括具有TSR的AV，最有可能产生更准确的参数估计值。当N较小时，丢失数据率较低，并且当AV非随机分布时，在MNAR机制下，TSML甚至TSR可以产生比MAR机制更准确的参数估计。

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