結構方程模式的準則、 變革 (1)

1. 結構方程模式的準則、變革(1) 周子敬 應用統計資訊學系暨教育研究所 於政治大學 98年統計學術研討會 E-mail: rejoice@zeta.mcu.edu.tw

2. 摘要

3. 隨著時代的演進，結構方程模式（Structural Equation Modeling, SEM）已漸漸的深入到各個領域中，許多國際及國內的期刊也要求投稿者能做到SEM的分析。本研究應用自行編製的國內高中生版幸福感靈性指標問卷來說明在執行結構方程模式或其應用驗證性因素分析（Confirmatory Factor Analysis, CFA）應注意的準則。另一面，本研究介紹一些適配度指標的調整以提醒國外學者最新適用的標準，而舊的標準需加以變革。最後，本研究亦介紹一些結構方程模式應用上的變革，以延伸結構方程模式的彈性使用。

4. 幸福感靈性指標(高中生版) 當初稱存在智慧

5. 最原始稱作SIWB-12 附錄五：徵求Dr. Frey「幸福感心靈指標」使用同意權回函 Hello Rejoice, Thank you for your email. Yes, you may use the SIWB. It is in the public domain. Please reference us in your research and we'd be happy to see any results of your study! Best of luck, Bruce ===================================== Bruce Frey, Ph.D. Assistant Professor, Psychology and Research in Education University of Kansas 1122 West Campus Road, Room 643 Lawrence, KS 66045 785-864-9706 Office 785-864-3820 FAX bfrey@ku.edu ===================================== Source: 呂宜儒(2006)。國內高中生多元智慧與創造力之研究。未出版碩士論文，銘傳大 學應用統計資訊學系。

6. 存在智慧（existential intelligence）是一種能夠去探究關於生存的基本問題的傾向或是能力諸如：我是誰？從何處來？又為什麼活著？這和幸福感（well-being）的心靈感受議題相仿。因此關於存在智慧的量測，本研究採用的工具來自於Frey, Daaleman, & Peyton（2005）所建立的「幸福感心靈指標」，用以測量存在智慧，這裡所指的心靈，沒有跨越到宗教的區域，此量表分為兩個部份，第一個部份是「知覺生活意義感」，第二部份是「自我效能」，分述如下： • 知覺生活意義感：指的是人置身在這個世界裡，如何看待自己的存 • 在價值與生命的意義。 • (2) 自我效能：自我效能是一種信念，當自己面對困難時如何察覺自己 • 的能力，迎向任何一個挑戰並克服困難。 Source: 1.呂宜儒(2006)。國內高中生多元智慧與創造力之研究。未出版碩士論文，銘傳 大學應用統計資訊學系。 2. Freg, B.B., & Daaleman P. T., & Peyton V. （2005）Measuring a dimension of spiritually for health research. Research on aging , 27, 556-577.

7. Source: 呂宜儒(2006)。國內高中生多元智慧與創造力之研究。未出版碩士論文，銘傳大 學應用統計資訊學系。

8. 因素分析-斜交

13. 結論:壁壘分明的兩因 素結構

14. 重要的金三角 For LISREL

16. 先寫CFA 用記事本好

18. Observed Variables exist1 exist2 exist3 exist4 exist5 exist6 exist7 exist8 exist9 exist10 Correlation Matrix * 1.00 .55 1.00 .46 .56 1.00 .42 .49 .65 1.00 .41 .51 .58 .72 1.00 .39 .48 .50 .63 .73 1.00 .30 .34 .37 .37 .45 .49 1.00 .34 .29 .33 .32 .32 .35 .53 1.00 .32 .30 .36 .35 .42 .47 .71 .66 1.00 .29 .30 .35 .34 .37 .43 .69 .58 .78 1.00 Sample Size 673 Latent Variables: LIFEMEAN SELFEFFC Relationships: exist1 exist2 exist3 exist4 exist5 exist6 = LIFEMEAN exist7 exist8 exist9 exist10 = SELFEFFC Number of Decimals = 3 Wide Print Print Residuals path diagram LISREL Output SE TV RS EF MI SS SC WP End of Problem

19. 原始模式

20. 先別高興得太早!!! 最終模式? 準則來了

21. 本研究應用結構方程模式（Structural Equation Modeling, SEM）進行分析，其重要性主要是根據使用SEM在於整合（1）因素分析與（2）路徑分析的統計技巧。SEM處理社會科學研究當中潛在變項的問題，也影響研究設計的原理與測量方法的運用，更可以應用到各種不同的情境中，例如因果關係的統計驗證、測量與評量工具的發展、縱貫資料的分析、跨族群（跨文化）資料分析等等（周子敬，2006）。本研究根據Hair, Black, Babin, & Anderson（2010）所提出6時期結構方程模式進行分析，以下列示6個時期： 時期1：定義個別構念 　　時期2：發展及確認測量模式 　　時期3：設計研究以產生實證結果 　　時期4：評估測量模式效度 　　時期5：確認結構模式 　　時期6：確認結構模式效度 為使整個SEM分析達到完善，本研究亦參考以下國內學者周子敬（2006）所整合的7個步驟加以對照處理： 步驟1：理論模式架構建立 　　步驟2：建立因素變數間因果關係路徑圖 　　步驟3：轉換路徑圖為結構方程式或測量方程式 　　步驟4：選擇分析模式（共變數或相關係數） 　　步驟5：評估模式鑑定 　　步驟6：評估適配度標準 步驟7：模式修改與解釋 新的處理步驟

22. 準則1

23. When a model has scales borrowed from various sources reporting other research, a pretest using respondents similar to those from the population to be studies is recommended to screen items for appropriateness. • Pairwise deletion of missing cases (all-available approach) is a good alternative handling missing data when the amount of missing data is less than 10% and the sample size is 250 or more. • Covariance matrices provide the researcher with far more flexibility due to the relatively greater information content thy contain and are the recommended for m of input to SEM models. • The minimum sample size for a particular SEM model depends on several factors, including the model complexity and the common communalities (average variance extracted among items) in each factor: • SEM models containing five or few constructs, each with more than three items (observed variables), and with high item communalities (0.6 or higher) , can be adequately estimated with samples as small as 100 to 150. • When the number of factors greater than six, some of which have fewer than three measured items as indicators, and multiple low communalities are present, sample size requirements may exceed 500. • No matter the modeling approach, the sample size must be sufficient to allow the model to run, but, more important, it must adequately represent the population of interest.

25. Goodness of Fit Statistics Degrees of Freedom = 34 Minimum Fit Function Chi-Square = 265.883 (P = 0.0) Normal Theory Weighted Least Squares Chi-Square = 283.559 (P = 0.0) Estimated Non-centrality Parameter (NCP) = 249.559 90 Percent Confidence Interval for NCP = (199.536 ; 307.058) Minimum Fit Function Value = 0.396 Population Discrepancy Function Value (F0) = 0.371 90 Percent Confidence Interval for F0 = (0.297 ; 0.457) Root Mean Square Error of Approximation (RMSEA) = 0.105 90 Percent Confidence Interval for RMSEA = (0.0935 ; 0.116) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.000 Expected Cross-Validation Index (ECVI) = 0.484 90 Percent Confidence Interval for ECVI = (0.410 ; 0.570) ECVI for Saturated Model = 0.164 ECVI for Independence Model = 10.317 Chi-Square for Independence Model with 45 Degrees of Freedom = 6912.998 Independence AIC = 6932.998 Model AIC = 325.559 Saturated AIC = 110.000 Independence CAIC = 6988.116 Model CAIC = 441.306 Saturated CAIC = 413.146 Normed Fit Index (NFI) = 0.962 Non-Normed Fit Index (NNFI) = 0.955 Parsimony Normed Fit Index (PNFI) = 0.726 Comparative Fit Index (CFI) = 0.966 Incremental Fit Index (IFI) = 0.966 Relative Fit Index (RFI) = 0.949 Critical N (CN) = 142.691 Root Mean Square Residual (RMR) = 0.0512 Standardized RMR = 0.0512 Goodness of Fit Index (GFI) = 0.922 Adjusted Goodness of Fit Index (AGFI) = 0.874 Parsimony Goodness of Fit Index (PGFI) = 0.570 原始模式

26. Summary Statistics for Standardized Residuals Smallest Standardized Residual = -5.828 Median Standardized Residual = 0.000 Largest Standardized Residual = 8.564 Stemleaf Plot - 4|8432 - 2|59865500 - 0|999549863200000000000 0|8112346888 2|1001119 4|716 6|0 8|6 Largest Negative Standardized Residuals Residual for exist4 and exist2 -2.829 Residual for exist5 and exist1 -4.415 Residual for exist5 and exist2 -3.530 Residual for exist5 and exist3 -4.213 Residual for exist6 and exist3 -5.828 Residual for exist9 and exist4 -4.270 Residual for exist10 and exist4 -2.942 Largest Positive Standardized Residuals Residual for exist2 and exist1 8.564 Residual for exist3 and exist1 3.070 Residual for exist3 and exist2 5.127 Residual for exist4 and exist3 4.717 Residual for exist5 and exist4 2.991 Residual for exist6 and exist5 7.028 Residual for exist7 and exist5 2.986 Residual for exist7 and exist6 5.620 Residual for exist8 and exist1 3.864 Residual for exist9 and exist6 3.098 Residual for exist9 and exist8 3.091

27. 修改模式1

28. Goodness of Fit Statistics Degrees of Freedom = 26 Minimum Fit Function Chi-Square = 166.877 (P = 0.0) Normal Theory Weighted Least Squares Chi-Square = 168.911 (P = 0.0) Estimated Non-centrality Parameter (NCP) = 142.911 90 Percent Confidence Interval for NCP = (105.520 ; 187.801) Minimum Fit Function Value = 0.248 Population Discrepancy Function Value (F0) = 0.213 90 Percent Confidence Interval for F0 = (0.157 ; 0.279) Root Mean Square Error of Approximation (RMSEA) = 0.0904 90 Percent Confidence Interval for RMSEA = (0.0777 ; 0.104) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.000 Expected Cross-Validation Index (ECVI) = 0.308 90 Percent Confidence Interval for ECVI = (0.252 ; 0.375) ECVI for Saturated Model = 0.134 ECVI for Independence Model = 8.911 Chi-Square for Independence Model with 36 Degrees of Freedom = 5970.317 Independence AIC = 5988.317 Model AIC = 206.911 Saturated AIC = 90.000 Independence CAIC = 6037.923 Model CAIC = 311.634 Saturated CAIC = 338.029 Normed Fit Index (NFI) = 0.972 Non-Normed Fit Index (NNFI) = 0.967 Parsimony Normed Fit Index (PNFI) = 0.702 Comparative Fit Index (CFI) = 0.976 Incremental Fit Index (IFI) = 0.976 Relative Fit Index (RFI) = 0.961 Critical N (CN) = 184.796 Root Mean Square Residual (RMR) = 0.0424 Standardized RMR = 0.0424 Goodness of Fit Index (GFI) = 0.947 Adjusted Goodness of Fit Index (AGFI) = 0.908 Parsimony Goodness of Fit Index (PGFI) = 0.547 修改模式1

29. Summary Statistics for Standardized Residuals Smallest Standardized Residual = -5.483 Median Standardized Residual = 0.000 Largest Standardized Residual = 6.257 Stemleaf Plot - 4|541 - 2|18755 - 0|997400732000000000 0|113023578 2|012022 4|567 6|3 Largest Negative Standardized Residuals Residual for exist5 and exist3 -4.363 Residual for exist6 and exist3 -5.483 Residual for exist6 and exist4 -3.055 Residual for exist9 and exist4 -4.076 Residual for exist10 and exist4 -2.766 Residual for exist10 and exist5 -2.663 Largest Positive Standardized Residuals Residual for exist3 and exist2 6.257 Residual for exist4 and exist3 5.505 Residual for exist6 and exist5 5.629 Residual for exist7 and exist5 2.969 Residual for exist7 and exist6 5.688 Residual for exist9 and exist6 3.180 Residual for exist9 and exist8 3.175

30. 修改模式2= 最終模式?

31. Goodness of Fit Statistics Degrees of Freedom = 19 Minimum Fit Function Chi-Square = 72.824 (P = 0.000) Normal Theory Weighted Least Squares Chi-Square = 71.657 (P = 0.000) Estimated Non-centrality Parameter (NCP) = 52.657 90 Percent Confidence Interval for NCP = (30.413 ; 82.476) Minimum Fit Function Value = 0.108 Population Discrepancy Function Value (F0) = 0.0784 90 Percent Confidence Interval for F0 = (0.0453 ; 0.123) Root Mean Square Error of Approximation (RMSEA) = 0.0642 90 Percent Confidence Interval for RMSEA = (0.0488 ; 0.0804) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.0637 Expected Cross-Validation Index (ECVI) = 0.157 90 Percent Confidence Interval for ECVI = (0.124 ; 0.202) ECVI for Saturated Model = 0.107 ECVI for Independence Model = 7.088 Chi-Square for Independence Model with 28 Degrees of Freedom = 4747.008 Independence AIC = 4763.008 Model AIC = 105.657 Saturated AIC = 72.000 Independence CAIC = 4807.102 Model CAIC = 199.357 Saturated CAIC = 270.423 Normed Fit Index (NFI) = 0.985 Non-Normed Fit Index (NNFI) = 0.983 Parsimony Normed Fit Index (PNFI) = 0.668 Comparative Fit Index (CFI) = 0.989 Incremental Fit Index (IFI) = 0.989 Relative Fit Index (RFI) = 0.977 Critical N (CN) = 334.959 Root Mean Square Residual (RMR) = 0.0359 Standardized RMR = 0.0359 Goodness of Fit Index (GFI) = 0.974 Adjusted Goodness of Fit Index (AGFI) = 0.951 Parsimony Goodness of Fit Index (PGFI) = 0.514 修改模式2= 最終模式?

32. 真的是最終模式?

33. 按照舊標準是的

34. 新標準表

36. Goodness of Fit Statistics Degrees of Freedom = 19 Minimum Fit Function Chi-Square = 72.824 (P = 0.000) Normal Theory Weighted Least Squares Chi-Square = 71.657 (P = 0.000) Estimated Non-centrality Parameter (NCP) = 52.657 90 Percent Confidence Interval for NCP = (30.413 ; 82.476) Minimum Fit Function Value = 0.108 Population Discrepancy Function Value (F0) = 0.0784 90 Percent Confidence Interval for F0 = (0.0453 ; 0.123) Root Mean Square Error of Approximation (RMSEA) = 0.0642 90 Percent Confidence Interval for RMSEA = (0.0488 ; 0.0804) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.0637 Expected Cross-Validation Index (ECVI) = 0.157 90 Percent Confidence Interval for ECVI = (0.124 ; 0.202) ECVI for Saturated Model = 0.107 ECVI for Independence Model = 7.088 Chi-Square for Independence Model with 28 Degrees of Freedom = 4747.008 Independence AIC = 4763.008 Model AIC = 105.657 Saturated AIC = 72.000 Independence CAIC = 4807.102 Model CAIC = 199.357 Saturated CAIC = 270.423 Normed Fit Index (NFI) = 0.985 Non-Normed Fit Index (NNFI) = 0.983 Parsimony Normed Fit Index (PNFI) = 0.668 Comparative Fit Index (CFI) = 0.989 Incremental Fit Index (IFI) = 0.989 Relative Fit Index (RFI) = 0.977 Critical N (CN) = 334.959 Root Mean Square Residual (RMR) = 0.0359 Standardized RMR = 0.0359 Goodness of Fit Index (GFI) = 0.974 Adjusted Goodness of Fit Index (AGFI) = 0.951 Parsimony Goodness of Fit Index (PGFI) = 0.514 修改模式2= 最終模式?

37. 修改模式2= 最終模式

38. 再看SEM 注意LISREL

39. Observed Variables exist1 exist2 exist3 exist4 exist5 exist6 exist7 exist8 exist9 exist10 Correlation Matrix * 1.00 .55 1.00 .46 .56 1.00 .42 .49 .65 1.00 .41 .51 .58 .72 1.00 .39 .48 .50 .63 .73 1.00 .30 .34 .37 .37 .45 .49 1.00 .34 .29 .33 .32 .32 .35 .53 1.00 .32 .30 .36 .35 .42 .47 .71 .66 1.00 .29 .30 .35 .34 .37 .43 .69 .58 .78 1.00 Sample Size 673 Latent Variables: LIFEMEAN SELFEFFC Relationships: exist1 exist2 exist3 exist4 exist5 exist6 = LIFEMEAN exist7 exist8 exist9 exist10 = SELFEFFC SELFEFFC=LIFEMEAN Number of Decimals = 3 Wide Print Print Residuals path diagram LISREL Output SE TV RS EF MI SS SC WP End of Problem

40. SELFEFFC=LIFEMEAN CFASEM

41. SEM= 因果關係

42. Goodness of Fit Statistics Degrees of Freedom = 34 Minimum Fit Function Chi-Square = 265.883 (P = 0.0) Normal Theory Weighted Least Squares Chi-Square = 283.559 (P = 0.0) Estimated Non-centrality Parameter (NCP) = 249.559 90 Percent Confidence Interval for NCP = (199.536 ; 307.058) Minimum Fit Function Value = 0.396 Population Discrepancy Function Value (F0) = 0.371 90 Percent Confidence Interval for F0 = (0.297 ; 0.457) Root Mean Square Error of Approximation (RMSEA) = 0.105 90 Percent Confidence Interval for RMSEA = (0.0935 ; 0.116) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.000 Expected Cross-Validation Index (ECVI) = 0.484 90 Percent Confidence Interval for ECVI = (0.410 ; 0.570) ECVI for Saturated Model = 0.164 ECVI for Independence Model = 10.317 Chi-Square for Independence Model with 45 Degrees of Freedom = 6912.998 Independence AIC = 6932.998 Model AIC = 325.559 Saturated AIC = 110.000 Independence CAIC = 6988.116 Model CAIC = 441.306 Saturated CAIC = 413.146 Normed Fit Index (NFI) = 0.962 Non-Normed Fit Index (NNFI) = 0.955 Parsimony Normed Fit Index (PNFI) = 0.726 Comparative Fit Index (CFI) = 0.966 Incremental Fit Index (IFI) = 0.966 Relative Fit Index (RFI) = 0.949 Critical N (CN) = 142.691 Root Mean Square Residual (RMR) = 0.0512 Standardized RMR = 0.0512 Goodness of Fit Index (GFI) = 0.922 Adjusted Goodness of Fit Index (AGFI) = 0.874 Parsimony Goodness of Fit Index (PGFI) = 0.570 Goodness of Fit Statistics Degrees of Freedom = 34 Minimum Fit Function Chi-Square = 265.883 (P = 0.0) Normal Theory Weighted Least Squares Chi-Square = 283.559 (P = 0.0) Estimated Non-centrality Parameter (NCP) = 249.559 90 Percent Confidence Interval for NCP = (199.536 ; 307.057) Minimum Fit Function Value = 0.396 Population Discrepancy Function Value (F0) = 0.371 90 Percent Confidence Interval for F0 = (0.297 ; 0.457) Root Mean Square Error of Approximation (RMSEA) = 0.105 90 Percent Confidence Interval for RMSEA = (0.0935 ; 0.116) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.000 Expected Cross-Validation Index (ECVI) = 0.484 90 Percent Confidence Interval for ECVI = (0.410 ; 0.570) ECVI for Saturated Model = 0.164 ECVI for Independence Model = 10.317 Chi-Square for Independence Model with 45 Degrees of Freedom = 6912.998 Independence AIC = 6932.998 Model AIC = 325.559 Saturated AIC = 110.000 Independence CAIC = 6988.116 Model CAIC = 441.305 Saturated CAIC = 413.146 Normed Fit Index (NFI) = 0.962 Non-Normed Fit Index (NNFI) = 0.955 Parsimony Normed Fit Index (PNFI) = 0.726 Comparative Fit Index (CFI) = 0.966 Incremental Fit Index (IFI) = 0.966 Relative Fit Index (RFI) = 0.949 Critical N (CN) = 142.691 Root Mean Square Residual (RMR) = 0.0512 Standardized RMR = 0.0512 Goodness of Fit Index (GFI) = 0.922 Adjusted Goodness of Fit Index (AGFI) = 0.874 Parsimony Goodness of Fit Index (PGFI) = 0.570 SEM CFA

43. 最終模式推論 CFA=SEM(刪除變數、適配度)

44. 準則2

45. As model become more complex, the likelihood of alternative models with equivalent fit increases. • Multiple fit indices should be used to assess a model’s goodness-of-fit and should include: • The χ2 value and the associated df. • One absolute fit index (i.e., GFI, RMSEA, or SRMR) • One incremental fit index(i.e., CFI or TLI) • One goodness-of-fit index(GFI, CFI, TLI, etc.) • One badness-of-fit index (RMSEA, SRMR, etc.) • No single “magic” value for the fit indices separates good from poor models, and it is not practical to apply a single set of cutoff rules to all measurement models and for that matter to all SEM models of any type. • The quality of fit depend heavily on model characteristics including sample size and model complexity: • Simple models with small samples should be held to strict fit standards, even an insignificant p-value for a simple model may not be meaningful. • More complex models with large samples should be held to the same strict standards, and so when samples are large and the model contains a large number of measured variables and parameter estimates, cutoff values of 0.95 on key GOF measures are unrealistic.