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A Two-Stage Approach to Missing Data: Theory and Application to Auxiliary Variables

机译：丢失数据的两阶段方法：理论和辅助变量的应用

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摘要

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a familiar function while being only marginally less efficient than the full information ML (FIML) approach. Additional advantages of the TS approach include that it allows for easy incorporation of auxiliary variables and that it is more stable in smaller samples. The main disadvantage is that the standard errors and test statistics provided by the complete data routine will not be correct. Empirical approaches to finding the right corrections for the TS approach have failed to provide unequivocal solutions. In this article, correct standard errors and test statistics for the TS approach with missing completely at random and missing at random normally distributed data are developed and studied. The new TS approach performs well in all conditions, is only marginally less efficient than the FIML approach (and is sometimes more efficient), and has good coverage. Additionally, the residual-based TS statistic outperforms the FIML test statistic in smaller samples. The TS method is thus a viable alternative to FIML, especially in small samples, and its further study is encouraged.
机译：使用缺失数据进行结构方程建模的一种众所周知的即席方法是获得总体协方差矩阵的饱和最大似然（ML）估计，然后在完整数据ML拟合函数中使用该估计来获得参数估计。这种2阶段（TS）方法之所以吸引人，是因为它使熟悉的功能最小化，而其效率仅比完全信息ML（FIML）方法略低。 TS方法的其他优点包括，它允许轻松合并辅助变量，并且在较小的样本中更稳定。主要缺点是，完整数据例程提供的标准错误和测试统计信息将不正确。为TS方法找到正确校正的经验方法未能提供明确的解决方案。在本文中，开发并研究了TS方法的正确标准误和测试统计数据，其中随机完全丢失而随机正态分布数据完全丢失。新的TS方法在所有条件下均表现良好，其效率仅比FIML方法略低（有时效率更高），并且具有良好的覆盖范围。此外，在较小样本中，基于残差的TS统计量优于FIML测试统计量。因此，TS方法是FIML的可行替代方法，尤其是在小样本中，因此值得进一步研究。

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  • 来源
    《Structural equation modeling》 |2009年第3期|477-497|共21页
  • 作者

    Victoria Savalei; Peter M. Bentler;

  • 作者单位

    Department of Psychology, University of British Columbia, 2136 West Mall, Vancouver, BC V6T 1Z4, Canada;

    University of California, Los Angeles;

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