A bridge between PLS path modeling and ULS-SEM

1. A bridge between PLS path modeling and ULS-SEM Michel Tenenhaus

2. SEM Component-based SEM (Score computation) Covariance-based SEM (CSA) (Model validation) H. Hwang Y. Takane GSCA (2004) K. Joreskog (LISREL, 1970) Herman Wold NIPALS (1966) PLS approach (1975) H. Hwang VisualGSCA 1.0 (2007) J.-B. Lohmöller LVPLS 1.8 (1984) Svante Wold Harald Martens PLS regression (1983) R. McDonald(1996) M. Tenenhaus (2001) W. Chin PLS-Graph C. Ringle SMART-PLS Chatelin-Esposito Vinzi Fahmy-Jäger-Tenenhaus XLSTAT-PLSPM (2008) SIMCA-P The Unscrambler A SEM tree Generalized Structured Component Analysis (ALS)

3. Covariance-basedStructural Equation Modeling Latent Variables : Structural model (Inner model):

4. MV MV LV Structural Equation Modeling Measurement model (outer model) : LV Exogenous Endogenous

5. Structural Equation Modeling Mixing Structural and measurement models : Residual variances are diagonal matrices

6. Structural Residual variance Measurement Residual variance Exogen. LV Cov. Outer model Inner model Structural Equation Modeling Covariance matrix for manifest variables :

7. PCA Generalization Covariance-based SEM ULS algorithm : S = Observed covariance matrix for MV Goodness-of-fit Index (Jöreskog & Sorbum):

8. Image Loyalty Customer Expectation Customer Perceived satisfaction value . Perceived Complaints quality Path model describing causes and consequences of Customer Satisfaction: The inner model

9. First Roderick McDonald’s idea (1996) Measurement residual variances are canceled: Use of AMOS 6.0 Méthod = ULS This is a computational trick: Residual variances are passed to errors and can always be computed afterwards.

10. Covariance-based SEM ULS algorithm with the McDonald’s constraints: S = Observed covariance matrix for MV Goodness-of-fit Index (Jöreskog & Sorbum):

11. Use of AMOS 6.0 - Méthod = ULS - Measurement residual variances = 0

12. Outer LV Estimates: 2nd McDonald’s idea + Fornell’s idea • PLS estimate of LV: • Mode A • LV inner estimate = theoretical LV • LV inner estimate computation is useless. Results GFI = .869

13. Cross-validation by bootstrap

14. Cross-validation by bootstrap

15. Comparison between the Fornell-ULS and Fornell-PLS standardized weights

16. Comparison between the Fornell-ULS and Fornell-PLS standardized weights and all Cor(LVFornell-ULS , LVFornell-PLS) > .99

17. First particular case : Factor Analysis and Principal Component Analysis

18. a posteriori computation .08 .15 .21 .42 .36 .36 First particular case : FA and PCA Factor Analysis Reflective mode Principal component Analysis Formative mode AVE = .74 AVE = .69

19. FA vs PCA : Variance reconstruction FA does not care for variance reconstruction FA (reflective mode) yields to better covariances reconstruction than PCA (formative mode). PCA cares for variance reconstruction

20. Reflective mode (multiple effect) Formative mode (multiple cause) MIMIC mode (with this new approach) (Multiple effect indicators for multiple causes)

21. MIMIC mode (usual in CSA) ? ? Reflective mode (multiple effect) Formative mode (multiple cause)

22. MIMIC mode (usual in CSA) ? Reflective mode (multiple effect) Formative mode (multiple cause)

23. Proposal: Compute a global score as MIMIC mode (better) • PCA oriented vs the dependent block Reflective mode (multiple effect) Formative mode (multiple cause) (Same than before)

24. Second particular case : Multi-block data analysis

25. 3 Appellations 4 Soils 4 blocks of variables X3 Illustrative variable Sensory analysis of 21 Loire Red Wines (J. Pagès) X1 X2 X4 X1 = Smell at rest, X2 = View, X3 = Smell after shaking, X4 = Tasting

26. PCA of each block: Correlation loadings

27. PCA of each block: Correlation loadings GFI = .301

28. VIEW SMELL AT REST SMELL AT REST SMELL AFTER SHAKING TASTING Multi-block data analysis = Confirmatory Factor Analysis GFI = .849

29. First dimension Using MV with significant loadings

30. First global score 2nd order CFA GFI = .973

31. Validation of the first dimension Correlations Rest1 View Shaking1 Tasting1 Rest1 1 View .621 1 Shaking1 .865 .762 1 Tasting1 .682 .813 .895 1 Score1 .813 .920 .942 .944

32. Second dimension

33. 2nd global score GFI = .905

34. Validation of the second dimension Correlations Rest2 Shaking2 Tasting2 Rest2 1 Shaking2 .789 1 Tasting2 .782 .803 1 Score2 .944 .904 .928

35. Score 2 unrelated with quality Score 1 related with quality Mapping of the correlations with the global scores

36. Correlation with global quality New result. Not obtained with other multi-block data analysis methods, nor with factor analysis of the whole data.

37. Wine visualization in the global score space Wines marked by Appellation

38. Wine visualization in the global score space Wines marked by Soil

39. Visualization of wine variability among the blocks Star-plot of the “best wine” – 2DAM SAUMUR 3,0 2,8 2,6 2,4 2DAM GLOBAL SCORE Tasting 2,2 Smell after shaking View 2,0 Smell at rest 2,25 2,50 2,75 3,00 3,25 3,50 DAM = Dampierre-sur-Loire

40. A soft, warm, blackberry nose. A good core of fruit on the palate with quite well worked tannin and acidity on the finish; Good length and a lot of potential. DECANTER (mai 1997) (DECANTER AWARD ***** : Outstanding quality, a virtually perfect example) Cuvée Lisagathe 1995

42. Third particular case : Analysis of covariance between two blocks of binary variables (with C. Guinot et E. Mauger (CERIES)) Data  = Sun exposure  = Sun protection A = Gender (A1 = Men, A2 = Women) Model 2 < 3? 1 < 0?  = 0+1A1+2 *A1+3 *A2+ (1)

43.   W  W M M   No gender effect  Gender main effect Interaction *gender Theory: background  = 0+1A1+2 *A1+3 *A2+ (1) 1 = 0, 2 = 3 1  0, 2 = 3 2  3

44. Score for sun exposure Score for sun protection Theory: background X1Sun exposure during lifetime (4) X2Sun exposure during mountain sports (2) X3Sun exposure during nautical sports (2) X4 Sun exposure during hobbies (2) X5Practice of naturism (1) YSun protection behavior over the past year (6) A Gender

45. Equation (1) is replaced by: Yc = 0+1A1+2Xw*A1+3Xw*A2+ (2) = 0+1A1+2(X*A1)w+3(X*A2)w+ (3) Theory: background  = 0+1A1+2 *A1+3 *A2+ (1) Question: How to estimate and test the parameters w, c, 0 , 1,2,3 ?

46. No group effect on the measurement model Theory: methods Covariance based SEM with constraints X1*A1 Y1 w1 c1 w2 2 X2*A1 X*A1 c2 w3 Y Y2 c3 X3*A1 3 Y3 1 X1*A2 w1 A1 w2 X2*A2 X*A2 w3 X3*A2

47. We have applied the ULS-SEM to a study on sun-exposure behavior in 8,084 French adults. Development of skin cancers Premature skin ageing. Data came from the SU.VI.MAX study* *Hercberg S.et al. Arch Intern Med. 2004;164:2325-42 Application: material

48. Use of AMOS method = ULS

49. Confidence Interval (Bootstrap) [.64, .89] [1.12, 1.38] [-.20, -.14] Sun exposure of body and face . Sun exposure of body and face AMOS results Sun exposure between 11am and 4 pm Sun exposure between 11am and 4 pm 2.82 2.82 GFI = .870 Basking in the sun is important or very important Basking in the sun is important or very important 2.30 . 2.30 Intensity of sun exposure moderate or severe Intensity of sun exposure moderate or severe 1.46 1.46 3.91 Sun exposure during practice of mountain sports 3.91 Sun exposure during practice of mountain sports 2.13 Sun expo. (M) Sun expo. (W) 2.13 Nb of days of mountain sport actvities > 200 days Nb of days of mountain sport actvities > 200 days 1.00 1.00 1.23 Sun exposure during practice of nautical sports Sun exposure during practice of nautical sports 1.23 .64 Nb of days of practice of nautical activites > 400 days Men .64 Nb of days of practice of nautical activites > 400 days 2.67 2.67 Sun exposure during practice of hobbies Sun exposure during practice of hobbies .75 1.24 1.35 1.35 -.17 .62 Nb of days of lifetime hobbies > 900 days Nb of days of lifetime hobbies > 900 days .62 d Practice of naturism during lifetime Practice of naturism during lifetime Sun Protection . 1.00 .62 Product used for face with SPF > 15 While sun tanning .40 .82 Product used for body with SPF > 15 While sun exposure .90 .45 Product used besides voluntarily sun exposure periods Several times while sun exposure .

50. Results: AMOS ULS  = 0+1M+2*M+3*W+ Conclusion • Women tend to protect themselves from the sun more than men (1 < 0). • This difference between men and women increases as lifetime sun exposure increases (3 - 2 > 0)