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Component based SEM Comparison between various methods Michel Tenenhaus

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2 A Component-based SEM tree Chatelin-Esposito Vinzi Fahmy-Jäger-Tenenhaus XLSTAT-PLSPM (2007) W. Chin PLS-Graph Herman Wold NIPALS (1966) PLS approach (1975) J.-B. Lohmöller LVPLS 1.8 (1984) SEM Component-based SEM (Score computation) Covariance-based SEM (CSA) (Model estimation) H. Hwang Y. Takane GSCA (2004) H. Hwang VisualGSCA 1.0 (2007) (AMOS 6.0, 2007) Score computed using block MV loadings Path analysis on the structural model defined on the scores For good blocks (High Cronbach ): - Score = 1st PC - Score = MV’s When all blocks are good, all the methods give almost the same results. M. Tenenhaus : Component-based SEM Total Quality Management, 2008 ALL BLOCK REFLECTIVE When the blocks are heterogeneous, GSCA is too close to PCA. PLS and SEM give almost the same results. PLS Path-Scale Path-PCA ULS-SEM GSCA

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3 The ECSI model

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4 Fairly good blocks

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5 Outer weights (Fornell normalization)

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6 Comparison between the LVs coming from the 5 methods PCA ULS-SEM SCALE PLS GSCA When all blocks are good, all the methods give almost the same results.

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7 ECSI model with noise Noise variables are highly correlated (>.99) and uncorrelated with Customer Satisfaction MVs. For this new block: - Noise = 1 st PC - Customer Satisfaction = 2 nd PC

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8 Fornell weights when the augmented Customer Satisfaction block is heterogeneous and reflective GSCA is trapped !!!!

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9 Why GSCA is trapped The GSCA criterion PCA MSEV, Glang (1988) MSEV = Maximum Sum of Explained Variance

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10 For reflective blocks, GSCA seems to be too close to PCA Fornell weights for original ECSI model

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11 Fornell weights when the augmented Customer Satisfaction block is heterogeneous and formative GSCA is still trapped !!!!

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12 A Component-based SEM tree ALL BLOCK FORMATIVE Herman Wold PLS approach (1975) Mathes (1994) Component-based SEM (Score computation) H. Hwang VisualGSCA 1.0 (2007) M. Glang MSEV (1988) = Glang and Hwang criteria are equivalent. Computational practice: PLS Maximum PLS Critical points

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13 B + Centroid

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14 B + Factorial

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15 GSCA R2=.263 R2=.313 R2=.301 R2=.380 R2=.691 R2=.491

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16 Comparison between PLS, GSCA and CCA

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17 Comparison between methods * * * * Criterion optimized by the method Practice supports “theory”

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18 Comparison between the LVs coming from the 3 methods B + Centroid B + Factorial GSCA When all blocks are good, all the methods give almost the same results.

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19 Economic inequality and political instability (Russet) GINI FARM RENT GNPR LABO Agricultural inequality (X 1 ) Industrial development (X 2 ) ECKS DEAT D-STB D-INS INST DICT Political instability (X 3 ) 11 22 3

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20 Use of XLSTAT-PLSPM Mode B + Centroid scheme Y 1 = X 1 w 1 Y 2 = X 2 w 2 Y 3 = X 3 w 3

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21 Use of XLSTAT-PLSPM Mode B + Factorial scheme Y 1 = X 1 w 1 Y 2 = X 2 w 2 Y 3 = X 3 w 3

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22 Use of GSCA (All formative) When there is only one structural equation and when all blocks are formative,GSCA is equivalent to a canonical correlation analysis.

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23 Use of XLSTAT-PLSPM for two blocks Mode B Canonical Correlation Analysis

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24 Comparison between methods * * * * * Criterion optimized by the method Practice supports “theory”

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25 Conclusion When the blocks are good (or moderately good) all methods seems to give almost the same LV scores. When some blocks are heterogeneous, PLS and ULS-SEM seems to give better results than GSCA. For all formative blocks : GSCA criterion is a more natural criterion than the PLS ones. For all formative blocks : PLS give good results for multiblock data analysis.

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Final conclusion « All the proofs of a pudding are in the eating, not in the cooking ». William Camden (1623)

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