Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects
Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects
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DOI：
10.1080/10705511.2011.582408
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发表时间：
2011-01-01
影响因子：
6
通讯作者：
West, Stephen G.
中科院分区：
文献类型：
--
作者：
Kelava, Augustin;Werner, Christina S.;West, Stephen G.
到目前为止，潜变量模型中的相互作用和二次效应很少在实践中得到检验。传统的产品指标方法需要创建产品指标(例如，x(1)(2)、x(1)x(4))作为每个非线性潜在结构的指标。这些方法需要使用复杂的非线性约束和额外的模型规范，并且不直接处理产品项的非正态分布。相比之下，最近开发的、易于使用的分布分析方法不使用产品指标，而是直接对所测量指标的非线性多变量分布进行建模。本文概述了分布解析隐含缓和结构方程(LMS；Klein&Moosbrogger，2000)和拟最大似然(QML；Klein&Muten，2007)估计的理论性质。将LMS和QML的特性与产品指标法的特性进行了比较。一项小型的模拟研究比较了这两种方法，并说明了随着多重共线性的增加，特别是在具有多个非线性项的复杂模型中，分布分析方法的优势。一个来自工作压力领域的经验例子将LMS和QML应用到一个具有交互作用和两个平方效应的模型中。提供了使用这两种方法进行分析的示例语法。
Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x(1)(2), x(1)x(4)) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthen, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches. A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided.