结构方程模型统计检验力分析：原理与方法

doi:10.3724/SP.J.1042.2022.02117

摘要/Abstract

摘要：

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

Abstract:

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

中图分类号:

B841

翟宏堃, 李强, 魏晓薇. (2022). 结构方程模型统计检验力分析：原理与方法. 心理科学进展 , 30(9), 2117-2130.

ZHAI Hongkun, LI Qiang, WEI Xiaowei. (2022). Power analysis in structural equation modeling: Principles and methods. Advances in Psychological Science, 30(9), 2117-2130.

图/表 8

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检验方法所处的类别			具体的检验方法	应用场景	H₀	统计量构成	零假设成立时统计量对应的分布	优点	缺点
基于χ²分布的方法(经典方法)	χ²检验	χ²检验	模型拟合的χ²检验	检验模型拟合	F_ML0 = 0 Σ = Σ₀	(n-1)·F_ML	中心化χ²分布	计算简便; 工具成熟	对样本的分布有较强的假设; 对统计量的构成有一定限制; 面对较为复杂的参数函数(如中介效应)表现不佳
		χ²检验	基于χ²统计量的等效性检验	检验模型拟合	F_ML0 > ε Σ与Σ₀间的差距大于ε	(n-1)·F_ML	非中心χ²分布
		Δχ²检验	嵌套模型比较的Δχ²检验	比较模型优劣	F_ML0B - F_ML0A = 0 Σ_0A = Σ_0B	(n-1)·(F_MLB - F_MLA)	中心化χ²分布
		Δχ²检验	模型参数的似然比检验	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	(n-1)·(F_ML约束 - F_ML无约束)	中心化χ²分布
	基于χ²分布理论的检验	Z检验	Wald检验	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	$\frac{g\left( \text{ }\!\!\theta\!\!\text{ } \right)}{\text{S}{{\text{E}}_{g\left( \text{ }\!\!\theta\!\!\text{ } \right)}}}$	标准正态分布
		Z检验	LM检验	检验特定参数	λ = 0 Σ_0约束 = Σ_0无约束	$\frac{\text{ }\!\!\lambda\!\!\text{ }}{\text{S}{{\text{E}}_{\text{ }\!\!\lambda\!\!\text{ }}}}$	标准正态分布
		χ²分布非中心参数检验	拟合指数的检验	检验模型拟合	δ = 0 Σ = Σ₀	给定的拟合指数	不明, 但临界值与中心化χ²分布有关
		χ²分布非中心参数检验	基于拟合指数的等效性检验	检验模型拟合	δ > δ_k Σ与Σ₀间的差距大于f(δ_k)	给定的拟合指数	不明, 但临界值与非中心χ²分布有关
基于模拟或重抽样技术的方法	基于模拟技术的方法	Monte Carlo法	MC法	检验模型拟合	F_ML0 = 0 Σ = Σ₀	给定的拟合指数(包括χ²统计量)	经验分布	放宽了对样本的假设; 不需讨论目标统计量的理论分布	计算较为困难、计算耗时较长、部分方法要求使用者有编程技术
	基于模拟技术的方法	Monte Carlo法	MC法	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	g(θ)	经验分布	放宽了对样本的假设; 不需讨论目标统计量的理论分布
	基于重抽样技术的方法	Bootstrap法	Bootstrap法	检验模型拟合	F_ML0 = 0 Σ = Σ₀	给定的拟合指数(包括χ²统计量)	经验分布	灵活度高, 对统计量的构造几乎没有限制; 对样本分布要求宽松
	基于重抽样技术的方法	Bootstrap法	Bootstrap法	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	g(θ)	经验分布	灵活度高, 对统计量的构造几乎没有限制; 对样本分布要求宽松

检验方法所处的类别			具体的检验方法	应用场景	H₀	统计量构成	零假设成立时统计量对应的分布	优点	缺点
基于χ²分布的方法(经典方法)	χ²检验	χ²检验	模型拟合的χ²检验	检验模型拟合	F_ML0 = 0 Σ = Σ₀	(n-1)·F_ML	中心化χ²分布	计算简便; 工具成熟	对样本的分布有较强的假设; 对统计量的构成有一定限制; 面对较为复杂的参数函数(如中介效应)表现不佳
		χ²检验	基于χ²统计量的等效性检验	检验模型拟合	F_ML0 > ε Σ与Σ₀间的差距大于ε	(n-1)·F_ML	非中心χ²分布
		Δχ²检验	嵌套模型比较的Δχ²检验	比较模型优劣	F_ML0B - F_ML0A = 0 Σ_0A = Σ_0B	(n-1)·(F_MLB - F_MLA)	中心化χ²分布
		Δχ²检验	模型参数的似然比检验	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	(n-1)·(F_ML约束 - F_ML无约束)	中心化χ²分布
	基于χ²分布理论的检验	Z检验	Wald检验	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	$\frac{g\left( \text{ }\!\!\theta\!\!\text{ } \right)}{\text{S}{{\text{E}}_{g\left( \text{ }\!\!\theta\!\!\text{ } \right)}}}$	标准正态分布
		Z检验	LM检验	检验特定参数	λ = 0 Σ_0约束 = Σ_0无约束	$\frac{\text{ }\!\!\lambda\!\!\text{ }}{\text{S}{{\text{E}}_{\text{ }\!\!\lambda\!\!\text{ }}}}$	标准正态分布
		χ²分布非中心参数检验	拟合指数的检验	检验模型拟合	δ = 0 Σ = Σ₀	给定的拟合指数	不明, 但临界值与中心化χ²分布有关
		χ²分布非中心参数检验	基于拟合指数的等效性检验	检验模型拟合	δ > δ_k Σ与Σ₀间的差距大于f(δ_k)	给定的拟合指数	不明, 但临界值与非中心χ²分布有关
基于模拟或重抽样技术的方法	基于模拟技术的方法	Monte Carlo法	MC法	检验模型拟合	F_ML0 = 0 Σ = Σ₀	给定的拟合指数(包括χ²统计量)	经验分布	放宽了对样本的假设; 不需讨论目标统计量的理论分布	计算较为困难、计算耗时较长、部分方法要求使用者有编程技术
	基于模拟技术的方法	Monte Carlo法	MC法	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	g(θ)	经验分布	放宽了对样本的假设; 不需讨论目标统计量的理论分布
	基于重抽样技术的方法	Bootstrap法	Bootstrap法	检验模型拟合	F_ML0 = 0 Σ = Σ₀	给定的拟合指数(包括χ²统计量)	经验分布	灵活度高, 对统计量的构造几乎没有限制; 对样本分布要求宽松
	基于重抽样技术的方法	Bootstrap法	Bootstrap法	检验特定参数	g(θ) = 0 Σ_0约束 = Σ_0无约束	g(θ)	经验分布	灵活度高, 对统计量的构造几乎没有限制; 对样本分布要求宽松

分析方法	是否需要给出协方差矩阵	对应假设检验的技术路线	假设检验的目的	计算量	程序资源
Satorra-Saris法	是	仅经典方法	均可, 但更适合模型参数检验或嵌套模型比较	较小	power4SEM semPower
MacCallum法	否	仅经典方法	模型拟合检验	最小	power4SEM semPower Preacher在线程序
Monte Carlo法	是	均可	均可	大	Bmem mc_power_med pwrSEM

分析方法	是否需要给出协方差矩阵	对应假设检验的技术路线	假设检验的目的	计算量	程序资源
Satorra-Saris法	是	仅经典方法	均可, 但更适合模型参数检验或嵌套模型比较	较小	power4SEM semPower
MacCallum法	否	仅经典方法	模型拟合检验	最小	power4SEM semPower Preacher在线程序
Monte Carlo法	是	均可	均可	大	Bmem mc_power_med pwrSEM

	1	2	3	4	5	6	7
1. 年龄	36.818
2. 疫情严重程度	-0.194	0.936
3. 疫情相关压力	-0.643	2.788	215.412
4. 情绪创造力	-9.107	0.098	9.321	129.108
5. 领悟社会支持	-3.390	-0.992	0.305	60.613	100.388
6. 情绪调节自我效能感	-1.217	-0.294	2.198	42.998	29.468	31.922
7. 压力后成长	-1.981	-0.275	-6.180	24.855	21.677	11.936	21.294