ISSN 1671-3710
CN 11-4766/R

心理科学进展 ›› 2022, Vol. 30 ›› Issue (9): 2117-2130.doi: 10.3724/SP.J.1042.2022.02117

• 研究方法 • 上一篇    下一篇


翟宏堃, 李强, 魏晓薇()   

  1. 南开大学社会心理学系, 天津 300350
  • 收稿日期:2021-10-09 出版日期:2022-09-15 发布日期:2022-07-21
  • 通讯作者: 魏晓薇
  • 基金资助:

Power analysis in structural equation modeling: Principles and methods

ZHAI Hongkun, LI Qiang, WEI Xiaowei()   

  1. Department of Social Psychology, Nankai University, Tianjin 300350, China
  • Received:2021-10-09 Online:2022-09-15 Published:2022-07-21
  • Contact: WEI Xiaowei


结构方程模型是心理学、管理学、社会学等学科中重要的统计工具之一。然而, 大量使用结构方程模型的研究忽视了对该方法的统计检验力进行必要的分析和报告, 在一定程度上降低了这些研究的结果的证明效力。结构方程模型的统计检验力分析方法主要有Satorra-Saris法、MacCallum法与Monte Carlo法三类。其中Satorra-Saris法适用于备择模型清晰、检验对象相对简单、检验方法基于χ2分布的情形; MacCallum法适用于基于χ2分布的模型拟合检验且备择模型不明的情形; Monte Carlo法适用于检验对象相对复杂、采用模拟或重抽样方法进行检验的情形。在实际应用中, 研究者应当首先判断检验的目的、方法以及是否有明确的备择模型, 并根据这些信息选择具体的分析方法。

关键词: 结构方程模型, 统计检验力, 模型拟合检验, 模型参数检验


Structural equation modeling (SEM) is an important statistical tool in psychology, management, and sociology. However, many studies that use SEM lack analyses and reports of statistical power. Studies with low statistical power may result in a waste of labor and material resources; studies may even be led astray because of failure to test real effects, thereby making incorrect conclusions. In addition, low statistical power may cause researchers to mistake poorly fitted models for well-fitted models. Consequently, researchers may draw incorrect conclusions. At present, the Satorra-Saris, MacCallum, and Monte Carlo methods are the three main types of statistical power analysis methods for SEM. The Satorra-Saris and MacCallum methods are based on various important conclusions on the χ2 distribution given by the earlier works of Satorra and Saris. These methods are applicable for analyzing the statistical power of χ2-based tests in SEM. The Monte Carlo method is based on the work of Muthén and Muthén, and it uses simulations to analyze the statistical power, which can be applied to a wide range of test situations in SEM. Among the three types of analytical methods, the MacCallum method is the simplest and least computationally intensive; however, it has the narrowest scope of application. The Monte Carlo method is the most complex and computationally intensive, and it has the widest scope of application. The Satorra-Saris method has moderate complexity, computation intensity, and scope of application. In practice, researchers can choose the appropriate analysis method according to the purpose of the test, test method, availability of alternative models, ease of use of the method, and computational power. The Satorra-Saris method is recommended when the test is based on the χ2 distribution (e.g., the χ2 test, likelihood ratio test, Wald test, and test of model fit index), the alternative model is clear, and the test object is simple; the MacCallum method is recommended if the alternative model is unknown. The Monte Carlo method is recommended when simulation or resampling methods are used, or when the target of the test is complex. In addition, when researchers try to evaluate the model fit for SEM, there is a conjugate relationship between the statistical power analysis and the equivalence test. Therefore, researchers have proposed a new method in recent years to evaluate the model fit of SEM, which can be conditionally interchanged to some extent.

Key words: structural equation model, statistical power, fitting test, test of model parameters