Savalei Victoria, Rhemtulla Mijke
Department of Psychology, University of British ColumbiaVancouver, BC, Canada.
Department of Psychology, University of California, DavisDavis, CA, USA.
Front Psychol. 2017 May 22;8:767. doi: 10.3389/fpsyg.2017.00767. eCollection 2017.
Structural equation models (SEMs) can be estimated using a variety of methods. For complete normally distributed data, two asymptotically efficient estimation methods exist: maximum likelihood (ML) and generalized least squares (GLS). With incomplete normally distributed data, an extension of ML called "full information" ML (FIML), is often the estimation method of choice. An extension of GLS to incomplete normally distributed data has never been developed or studied. In this article we define the "full information" GLS estimator for incomplete normally distributed data (FIGLS). We also identify and study an important application of the new GLS approach. In many modeling contexts, the variables in the SEM are linear composites (e.g., sums or averages) of the raw items. For instance, SEMs often use parcels (sums of raw items) as indicators of latent factors. If data are missing at the item level, but the model is at the composite level, FIML is not possible. In this situation, FIGLS may be the only asymptotically efficient estimator available. Results of a simulation study comparing the new FIGLS estimator to the best available analytic alternative, two-stage ML, with item-level missing data are presented.
结构方程模型（SEMs）可以使用多种方法进行估计。对于完全正态分布的数据，存在两种渐近有效的估计方法：最大似然法（ML）和广义最小二乘法（GLS）。对于不完全正态分布的数据，一种称为“完全信息”最大似然法（FIML）的ML扩展方法通常是首选的估计方法。GLS到不完全正态分布数据的扩展方法从未被开发或研究过。在本文中，我们定义了不完全正态分布数据的“完全信息”广义最小二乘估计量（FIGLS）。我们还识别并研究了这种新的广义最小二乘方法的一个重要应用。在许多建模情境中，结构方程模型中的变量是原始项目的线性组合（例如，总和或平均值）。例如，结构方程模型经常使用项目包（原始项目的总和）作为潜在因子的指标。如果数据在项目层面缺失，但模型是在组合层面，那么就无法使用完全信息最大似然法。在这种情况下，FIGLS可能是唯一可用的渐近有效估计量。本文给出了一项模拟研究的结果，该研究将新的FIGLS估计量与最佳可用分析替代方法——两阶段最大似然法，针对项目层面存在缺失数据的情况进行了比较。
