grad-pls-sem

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PLS-SEM 偏最小平方法結構方程模型

PLS-SEM 偏最小平方法结构方程模型

Overview

概述

PLS-SEM (Wold, 1982; Hair et al., 2017) is a variance-based approach to structural equation modeling that estimates composite-based path models. Unlike CB-SEM, it maximizes explained variance in endogenous constructs and readily handles both reflective and formative measurement models.

PLS-SEM（Wold，1982；Hair等人，2017）是一种基于方差的结构方程建模方法，用于估计基于复合变量的路径模型。与CB-SEM不同，它能最大化内生潜变量的解释方差，并且可轻松处理反映型和形成型两种测量模型。

When to Use

适用场景

Formative measurement models are part of the research design
Sample size is small (PLS works with N ≥ 10× the largest number of paths pointing to any construct)
Research goal is prediction and variance explanation rather than theory confirmation
The structural model is complex with many constructs and indicators

研究设计中包含形成型测量模型
样本量较小（PLS适用于样本量N≥指向任意潜变量的最大路径数×10的情况）
研究目标为预测和方差解释，而非理论验证
结构模型复杂，包含多个潜变量和指标

When NOT to Use

不适用场景

Research goal is strict theory testing and model fit assessment
All constructs are reflective and sample size is adequate for CB-SEM
You need global model fit indices (chi-square, CFI, RMSEA)
Circular relationships (non-recursive models) are hypothesized

研究目标为严格的理论检验和模型拟合评估
所有潜变量均为反映型，且样本量足以支持CB-SEM分析
需要全局模型拟合指标（卡方值、CFI、RMSEA）
假设模型存在循环（非递归）关系

Assumptions

假设前提

IRON LAW: PLS-SEM maximizes VARIANCE EXPLAINED, not model fit — it does NOT
test overall model fit like CB-SEM. A high R² does not mean the model
structure is correct.

Key assumptions:

Predictor specification — each construct must be correctly specified as reflective or formative
No circular (non-recursive) relationships in the structural model
Observations are independent (no nested structure without extensions)
Data need not be normally distributed (PLS is distribution-free)

铁律：PLS-SEM最大化的是解释方差，而非模型拟合度——它不会像CB-SEM那样检验整体模型拟合度。高R²值并不代表模型结构正确。

核心假设：

预测变量规范——每个潜变量必须被正确指定为反映型或形成型
结构模型中不存在循环（非递归）关系
观测值相互独立（若无扩展方法，不支持嵌套结构）
数据无需服从正态分布（PLS是无分布假设的方法）

Methodology

方法步骤

Step 1 — Specify Measurement Models

步骤1——指定测量模型

Classify each construct as reflective (arrows from construct to indicators) or formative (arrows from indicators to construct). Formative constructs require at minimum two indicators and a theoretical rationale.

将每个潜变量分类为反映型（箭头从潜变量指向指标）或形成型（箭头从指标指向潜变量）。形成型潜变量至少需要两个指标，且具备理论依据。

Step 2 — Assess Reflective Measurement

步骤2——评估反映型测量模型

Evaluate indicator reliability (loadings ≥ 0.70), internal consistency (CR ≥ 0.70), convergent validity (AVE ≥ 0.50), and discriminant validity (HTMT < 0.90).

评估指标信度（载荷≥0.70）、内部一致性（CR≥0.70）、收敛效度（AVE≥0.50）和区分效度（HTMT<0.90）。

Step 3 — Assess Formative Measurement

步骤3——评估形成型测量模型

Check indicator weights for significance via bootstrapping. Examine VIF among indicators (VIF < 5.0). Assess content validity — dropping a formative indicator changes the construct meaning.

通过自助法（bootstrapping）检验指标权重的显著性。检查指标间的方差膨胀因子（VIF<5.0）。评估内容效度——删除某个形成型指标会改变潜变量的含义。

Step 4 — Evaluate Structural Model

步骤4——评估结构模型

Report path coefficients, R², f² effect sizes, Q² predictive relevance (via blindfolding), and bootstrapped confidence intervals. See

references/

for algorithm details.

报告路径系数、R²、f²效应量、通过盲法（blindfolding）得到的Q²预测相关性，以及自助法得到的置信区间。算法细节详见

references/

目录。

Output Format

输出格式

markdown

undefined

markdown

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PLS-SEM Analysis: [Study Title]

PLS-SEM分析结果：[研究标题]

Reflective Measurement Assessment

反映型测量模型评估

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

潜变量	指标	载荷	CR	AVE	HTMT
[名称]	[项目]	x.xx	x.xx	x.xx	x.xx

Formative Measurement Assessment

形成型测量模型评估

Construct	Indicator	Weight	VIF	p-value
[name]	[item]	x.xx	x.xx	x.xx

潜变量	指标	权重	VIF	p值
[名称]	[项目]	x.xx	x.xx	x.xx

Structural Model

结构模型

Path	β	t-value	p-value	f²	Supported?
X → Y	x.xx	x.xx	x.xx	x.xx	[Yes/No]

路径	β	t值	p值	f²	是否支持？
X → Y	x.xx	x.xx	x.xx	x.xx	[是/否]

Model Quality

模型质量

Endogenous Construct	R²	Q²
[name]	x.xx	x.xx

内生潜变量	R²	Q²
[名称]	x.xx	x.xx

Limitations

局限性

[Note any assumption violations]

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[记录任何违反假设的情况]

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Gotchas

注意事项

PLS-SEM is NOT a silver bullet for small samples — it still requires adequate statistical power
Misspecifying reflective as formative (or vice versa) fundamentally changes results
HTMT is preferred over Fornell-Larcker for discriminant validity in PLS-SEM
PLS overestimates loadings and underestimates path coefficients (consistency at large corrects this)
Blindfolding Q² > 0 shows predictive relevance but does not validate the model structure
Reporting PLS results using CB-SEM criteria (CFI, RMSEA) is methodologically incorrect

PLS-SEM并非小样本的万能解决方案——它仍需要足够的统计效力
将反映型误指定为形成型（反之亦然）会从根本上改变分析结果
在PLS-SEM中，HTMT比Fornell-Larcker准则更适合用于评估区分效度
PLS会高估载荷，低估路径系数（大样本一致性方法可纠正此问题）
盲法得到的Q²>0仅表明模型具有预测相关性，但不能验证模型结构的正确性
使用CB-SEM的标准（如CFI、RMSEA）来报告PLS结果在方法论上是错误的

References

参考文献

Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). A Primer on Partial Least Squares Structural Equation Modeling (2nd ed.). Sage.
Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity. Journal of the Academy of Marketing Science, 43(1), 115-135.
Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report PLS-SEM. European Business Review, 31(1), 2-24.

Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). A Primer on Partial Least Squares Structural Equation Modeling (2nd ed.). Sage.
Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity. Journal of the Academy of Marketing Science, 43(1), 115-135.
Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report PLS-SEM. European Business Review, 31(1), 2-24.