grad-sem
用 SEM 結合 CFA 和路徑分析，檢驗潛在構念的因果結構與模型適配度
中文翻譯
--- name: "grad-sem" description: "用結構方程模型（SEM），結合測量模型（CFA）和結構模型（路徑分析），檢驗假設的因果結構。當使用者需要驗證潛在構念、檢驗中介或調節路徑、用 CFI/TLI/RMSEA/SRMR 評估模型適配度，或問到「這些變數形成因果鏈嗎」「怎麼檢驗我的理論模型」「我的測量模型有效嗎」時，就用這個 skill。" metadata: category: "WP-31 量化方法" tags: ["SEM", "structural-equation-modeling", "CFA", "path-analysis", "model-fit", "latent-variable"] --- # SEM 結構方程模型 ## Overview 結構方程模型（SEM）同時估計測量模型（觀察指標如何對應到潛在構念）和結構模型（構念之間的方向性路徑）。它把驗證性因素分析和路徑分析整合起來，檢驗經驗資料是否和假設的理論結構一致。 ## When to Use - 檢驗一個有潛在構念和方向性路徑的完整理論模型 - 評估有多個中介變數的中介鏈（X → M → Y） - 評估問卷題項是否適當反映其預期的構念（CFA） - 在同一份資料上比較替代的理論模型 ## When NOT to Use - 樣本數低於 200（或每個估計參數少於 10 個個案） - 沒有事先理論模型的探索性研究 - 所有變數都是觀察變數，模型只是簡單迴歸 - 資料嚴重非常態，而且你沒有穩健的估計方法 ## 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. ``` 關鍵假設： 1. 模型設定正確，遺漏路徑或構念會讓估計產生偏誤 2. ML 估計需要多變量常態性（或使用穩健估計方法） 3. 樣本數夠大（經驗法則是 N ≥ 200） 4. 指標之間沒有過度的共線性 ## Methodology ### Step 1 — Specify the Measurement Model 定義潛在構念及其觀察指標。跑 CFA 來確認因素負荷量，評估收斂效度（AVE ≥ 0.50）和區辨效度。 ### Step 2 — Assess Measurement Model Fit 評估適配度指標：CFI ≥ 0.90、TLI ≥ 0.90、RMSEA ≤ 0.08、SRMR ≤ 0.08。謹慎檢視修正指標，只有在有理論依據時才重新設定模型。 ### Step 3 — Specify and Estimate the Structural Model 根據理論，加入潛在構念之間的方向性路徑。估計路徑係數及其顯著性。用卡方差異檢定比較巢套模型。 ### Step 4 — Report and Interpret 報告標準化路徑係數、內生構念的 R²，以及整體適配度。如果假設有中介，就討論間接效果。數學記號和估計細節見 `references/estimation.md`。 ## Output Format ```markdown ## SEM Analysis: [Study Title] ### Measurement Model (CFA) | 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] | ### Structural Paths | Path | Std. β | S.E. | p-value | Supported? | |------|--------|------|---------|------------| | X → M | x.xx | x.xx | x.xx | [Yes/No] | ### Key Findings - [Interpretation of results] ### Limitations - [Note any assumption violations] ``` ## Gotchas - 一定存在適配度相同、但因果方向不同的等價模型，SEM 無法區分它們 - 修正指標會誘使人做資料驅動的重新設定，利用的是機運 - 把題項打包（parceling）會掩蓋測量模型的設定錯誤 - N > 500 時，卡方檢定過度敏感，要靠近似適配度指標 - 非常態的資料需要用 MLR 或 bootstrapping，不要用預設的 ML - 只報告顯著的路徑，沒有完整的假設模型，是選擇性報告 ## 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.
英文原文
--- name: "grad-sem" description: "Apply Structural Equation Modeling (SEM) to test hypothesized causal structures by combining measurement models (CFA) and structural models (path analysis). Use this skill when the user needs to validate latent constructs, test mediation or moderation paths, assess model fit with CFI/TLI/RMSEA/SRMR, or when they ask 'do these variables form a causal chain', 'how do I test my theoretical model', or 'is my measurement model valid'." metadata: category: "WP-31 量化方法" tags: ["SEM", "structural-equation-modeling", "CFA", "path-analysis", "model-fit", "latent-variable"] --- # SEM 結構方程模型 ## 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. ## 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 ## 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 ## 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: 1. Correct model specification — omitted paths or constructs bias estimates 2. Multivariate normality for ML estimation (or use robust estimators) 3. Sufficiently large sample size (N ≥ 200 as rule of thumb) 4. No excessive multicollinearity among indicators ## Methodology ### Step 1 — Specify the Measurement Model Define latent constructs and their observed indicators. Run CFA to confirm factor loadings, assess convergent validity (AVE ≥ 0.50), and discriminant validity. ### Step 2 — Assess Measurement Model Fit Evaluate fit indices: CFI ≥ 0.90, TLI ≥ 0.90, RMSEA ≤ 0.08, SRMR ≤ 0.08. Examine modification indices cautiously — only respecify with theoretical justification. ### Step 3 — Specify and Estimate the Structural Model Add directional paths among latent constructs based on theory. Estimate path coefficients and their significance. Compare nested models using chi-square difference test. ### Step 4 — Report and Interpret 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. ## Output Format ```markdown ## SEM Analysis: [Study Title] ### Measurement Model (CFA) | 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] | ### Structural Paths | Path | Std. β | S.E. | p-value | Supported? | |------|--------|------|---------|------------| | X → M | x.xx | x.xx | x.xx | [Yes/No] | ### Key Findings - [Interpretation of results] ### Limitations - [Note any assumption violations] ``` ## 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 ## 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.