Structural equation modeling (SEM) provides an extensive toolbox to analyze the multivariate interrelations of directly observed variables and latent constructs. Multilevel SEM integrates mixed effects to examine the covariances between observed and latent variables across many levels of analysis. However, while it is necessary to consider model fit, traditional indices are largely insufficient to analyze model fit at each level of analysis. The present article reviews (a) the partially saturated model fit approach first suggested by Ryu and West and (b) an alternative model parameterization that removes the multilevel data structure. We next describe the implementation of an algorithm to compute partially saturated model fit for 2-level structural equation models in the open source SEM package, OpenMx, including verification in a simulation study. Finally, an example empirical application evaluates leading theories on the structure of affect from ecological momentary assessment data collected thrice daily for two weeks from 345 participants.

中文翻译：

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多级结构方程模型的模型拟合估计


结构方程模型 (SEM) 提供了一个广泛的工具箱来分析直接观察到的变量和潜在结构的多元相互关系。多级 SEM 集成了混合效应，以检查多个分析级别中观察到的变量和潜在变量之间的协方差。然而，虽然有必要考虑模型拟合度，但传统指标很大程度上不足以分析各个分析层面的模型拟合度。本文回顾了 (a) Ryu 和 West 首先提出的部分饱和模型拟合方法，以及 (b) 消除多级数据结构的替代模型参数化方法。接下来，我们描述了一种算法的实现，用于计算适合开源 SEM 软件包 OpenMx 中的 2 级结构方程模型的部分饱和模型，包括仿真研究中的验证。最后，一个实证应用示例根据生态瞬时评估数据评估了影响结构的主要理论，这些数据为期两周，每天三次，从 345 名参与者那里收集。