Pek Jolynn, Wu Hao
Department of Psychology, York University, 322 Behavioural Science Building, 4700 Keele Street, Toronto, ON, M3J 1P3 , Canada.
Department of Psychology, Boston College, Chestnut Hill, MA, USA.
Psychometrika. 2015 Dec;80(4):1123-45. doi: 10.1007/s11336-015-9461-1. Epub 2015 Apr 30.
Structural equation models (SEM) are widely used for modeling complex multivariate relationships among measured and latent variables. Although several analytical approaches to interval estimation in SEM have been developed, there lacks a comprehensive review of these methods. We review the popular Wald-type and lesser known likelihood-based methods in linear SEM, emphasizing profile likelihood-based confidence intervals (CIs). Existing algorithms for computing profile likelihood-based CIs are described, including two newer algorithms which are extended to construct profile likelihood-based confidence regions (CRs). Finally, we illustrate the use of these CIs and CRs with two empirical examples, and provide practical recommendations on when to use Wald-type CIs and CRs versus profile likelihood-based CIs and CRs. OpenMx example code is provided in an Online Appendix for constructing profile likelihood-based CIs and CRs for SEM.
结构方程模型（SEM）被广泛用于对测量变量和潜在变量之间的复杂多变量关系进行建模。尽管已经开发了几种用于结构方程模型区间估计的分析方法，但缺乏对这些方法的全面综述。我们回顾了线性结构方程模型中流行的 Wald 型方法和鲜为人知的基于似然的方法，重点是基于轮廓似然的置信区间（CIs）。描述了用于计算基于轮廓似然的置信区间的现有算法，包括两种扩展用于构建基于轮廓似然的置信区域（CRs）的新算法。最后，我们通过两个实证例子说明这些置信区间和置信区域的使用，并就何时使用 Wald 型置信区间和置信区域与基于轮廓似然的置信区间和置信区域提供实用建议。在线附录中提供了 OpenMx 示例代码，用于构建基于轮廓似然的结构方程模型置信区间和置信区域。
