Lee Sik-Yum, Song Xin Yuan, Poon Wai-Yin
Multivariate Behav Res. 2004 Jan 1;39(1):37-67. doi: 10.1207/s15327906mbr3901_2.
Various approaches using the maximum likelihood (ML) option of the LISREL program and products of indicators have been proposed to analyze structural equation models with non-linear latent effects on the basis of Kenny and Judd's formulation. Recently, some methods based on the Bayesian approach and the exact ML approaches have been developed. This article reviews, elaborates and compares several approaches for analyzing nonlinear models with interaction and/or quadratic effects. A total of four approaches are examined, including the product indicator ML approaches proposed by Jaccard and Wan (1995) and Joreskog and Yang (1996), a Bayesian approach and an exact ML approach. The empirical performances of these approaches are assessed using simulation studies in terms of their capabilities in producing reliable parameter and standard error estimates. It is found that whilst the Bayesian and the exact ML approaches produce satisfactory results in all the settings under consideration, and are in general very reliable; the product indicator ML approaches can only produce reasonable results in simple models with large sample sizes.
基于肯尼和贾德的公式，已经提出了各种使用LISREL程序的最大似然（ML）选项和指标乘积的方法来分析具有非线性潜在效应的结构方程模型。最近，一些基于贝叶斯方法和精确最大似然方法的方法也得到了发展。本文回顾、阐述并比较了几种用于分析具有交互作用和/或二次效应的非线性模型的方法。总共考察了四种方法，包括贾卡德和万（1995年）以及乔雷斯科格和杨（1996年）提出的乘积指标最大似然方法、一种贝叶斯方法和一种精确最大似然方法。通过模拟研究，根据这些方法产生可靠参数和标准误差估计的能力来评估它们的实证表现。研究发现，虽然贝叶斯方法和精确最大似然方法在所有考虑的设置中都产生了令人满意的结果，并且总体上非常可靠；但乘积指标最大似然方法只能在大样本量的简单模型中产生合理的结果。
