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SEM 結構方程模型

SEM 结构方程模型

Overview

Structural Equation Modeling (SEM) simultaneously estimates measurement models (how observed indicators map to latent constructs) and structural models (directional paths among constructs). It integrates confirmatory factor analysis with path analysis to test whether empirical data are consistent with a hypothesized theoretical structure.

结构方程模型（SEM）可同时估计测量模型（观测指标如何对应潜变量结构）和结构模型（变量结构间的定向路径）。它整合了验证性因子分析（CFA）与路径分析，用于检验实证数据是否与假设的理论结构一致。

When to Use

Testing a full theoretical model with latent constructs and directional paths
Evaluating mediation chains (X → M → Y) with multiple mediators
Assessing whether survey items adequately reflect their intended constructs (CFA)
Comparing alternative theoretical models on the same data

检验包含潜变量结构和定向路径的完整理论模型
评估包含多个中介变量的中介链（X → M → Y）
检验调查项是否能充分反映其对应的目标结构（CFA）
在同一数据集上比较不同的理论模型

When NOT to Use

Sample size below 200 (or below 10 cases per estimated parameter)
Exploratory research with no a priori theoretical model
All variables are observed and model is a simple regression
Data are severely non-normal and you lack robust estimators

样本量低于200（或每个待估计参数对应的样本量少于10）
无先验理论模型的探索性研究
所有变量均为观测变量且模型为简单回归模型
数据严重非正态且缺乏稳健估计方法

Assumptions

IRON LAW: SEM does NOT prove causation — it tests whether data is CONSISTENT
with a hypothesized causal structure. Good fit does NOT mean the model is
correct; it means the model cannot be rejected.

Key assumptions:

Correct model specification — omitted paths or constructs bias estimates
Multivariate normality for ML estimation (or use robust estimators)
Sufficiently large sample size (N ≥ 200 as rule of thumb)
No excessive multicollinearity among indicators

IRON LAW: SEM does NOT prove causation — it tests whether data is CONSISTENT
with a hypothesized causal structure. Good fit does NOT mean the model is
correct; it means the model cannot be rejected.

关键假设：

模型设定正确——遗漏路径或结构会导致估计偏差
使用ML估计时需满足多元正态性（或使用稳健估计方法）
样本量足够大（经验法则为N ≥ 200）
指标间不存在过度多重共线性

Methodology

Step 1 — Specify the Measurement Model

步骤1 — 设定测量模型

Define latent constructs and their observed indicators. Run CFA to confirm factor loadings, assess convergent validity (AVE ≥ 0.50), and discriminant validity.

定义潜变量结构及其观测指标。运行CFA以确认因子载荷，评估聚合效度（AVE ≥ 0.50）和区分效度。

Step 2 — Assess Measurement Model Fit

步骤2 — 评估测量模型拟合度

Evaluate fit indices: CFI ≥ 0.90, TLI ≥ 0.90, RMSEA ≤ 0.08, SRMR ≤ 0.08. Examine modification indices cautiously — only respecify with theoretical justification.

评估拟合指数：CFI ≥ 0.90、TLI ≥ 0.90、RMSEA ≤ 0.08、SRMR ≤ 0.08。谨慎查看修正指数——仅在有理论依据的情况下重新设定模型。

Step 3 — Specify and Estimate the Structural Model

步骤3 — 设定并估计结构模型

Add directional paths among latent constructs based on theory. Estimate path coefficients and their significance. Compare nested models using chi-square difference test.

基于理论添加潜变量结构间的定向路径。估计路径系数及其显著性。使用卡方差异检验比较嵌套模型。

Step 4 — Report and Interpret

步骤4 — 报告与解读

Report standardized path coefficients, R² for endogenous constructs, and overall fit. Discuss indirect effects if mediation is hypothesized. See

references/estimation.md

for mathematical notation and estimation details.

报告标准化路径系数、内生结构的R²值以及整体拟合度。若假设存在中介效应，需讨论间接效应。有关数学符号和估计细节，请参阅

references/estimation.md

。

Output Format

markdown

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markdown

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SEM Analysis: [Study Title]

Measurement Model (CFA)

Construct	Indicator	Std. Loading	AVE	CR
[name]	[item]	x.xx	x.xx	x.xx

Construct	Indicator	Std. Loading	AVE	CR
[name]	[item]	x.xx	x.xx	x.xx

Model Fit

Index	Value	Threshold	Assessment
CFI	x.xx	≥ 0.90	[pass/fail]
TLI	x.xx	≥ 0.90	[pass/fail]
RMSEA	x.xx	≤ 0.08	[pass/fail]
SRMR	x.xx	≤ 0.08	[pass/fail]

Index	Value	Threshold	Assessment
CFI	x.xx	≥ 0.90	[pass/fail]
TLI	x.xx	≥ 0.90	[pass/fail]
RMSEA	x.xx	≤ 0.08	[pass/fail]
SRMR	x.xx	≤ 0.08	[pass/fail]

Structural Paths

Path	Std. β	S.E.	p-value	Supported?
X → M	x.xx	x.xx	x.xx	[Yes/No]

Path	Std. β	S.E.	p-value	Supported?
X → M	x.xx	x.xx	x.xx	[Yes/No]

Key Findings

[Interpretation of results]

[Interpretation of results]

Limitations

[Note any assumption violations]

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[Note any assumption violations]

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Gotchas

Equivalent models with identical fit but different causal directions always exist — SEM cannot distinguish them
Modification indices tempt data-driven respecification that capitalizes on chance
Parceling items masks misspecification in the measurement model
Chi-square test is overly sensitive with N > 500; rely on approximate fit indices
Non-normal data require MLR or bootstrapping, not default ML
Reporting only significant paths without the full hypothesized model is selective reporting

始终存在拟合度相同但因果方向不同的等效模型——SEM无法区分它们
修正指数可能诱导基于数据的模型重新设定，从而利用偶然因素
项目打包会掩盖测量模型中的设定错误
当N > 500时，卡方检验过于敏感；应依赖近似拟合指数
非正态数据需使用MLR或自助法，而非默认的ML方法
仅报告显著路径而不展示完整假设模型属于选择性报告

References

Kline, R. B. (2016). Principles and Practice of Structural Equation Modeling (4th ed.). Guilford Press.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes. Structural Equation Modeling, 6(1), 1-55.
Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice. Psychological Bulletin, 103(3), 411-423.

Kline, R. B. (2016). Principles and Practice of Structural Equation Modeling (4th ed.). Guilford Press.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes. Structural Equation Modeling, 6(1), 1-55.
Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice. Psychological Bulletin, 103(3), 411-423.