Component based SEMComparison between various methodsMichel Tenenhaus

A Component-based SEM treeWhen all blocks are good, all the methodsgive almost the same results.M. Tenenhaus : Component-based SEMTotal Quality Management, 2008ALL BLOCK REFLECTIVEWhen the blocks are heterogeneous,GSCA is too close to PCA. PLS and SEMgive almost the same results.PLSPath-ScalePath-PCAULS-SEMGSCA

The ECSI model

The ECSI modelFairly good blocks

Block correlation

1st eigenvalue

Block correlation

2nd eigenvalue

Cronbach alpha

Image

2.394

0.913

0.723

Customer expectation

1.444

0.903

0.452

Perceived quality

4.040

0.771

0.877

Perceived value

1.700

0.300

0.824

Customer satisfaction

2.082

0.518

0.779

Customer loyalty

1.561

0.983

0.472

Customer loyalty (without item 2)

1.542

0.458

0.703

Outer weights (Fornell normalization)

Outer model

Parameter

ULS-SEM

PLS

GSCA

PCA

SCALE

x11

(

Image

0.220

0.208

0.218

0.218

.200

x12

(

Image

0.180

0.183

0.169

0.170

.200

x13

(

Image

0.156

0.153

0.174

0.175

.200

x14

(

Image

0.229

0.229

0.225

0.223

.200

x15

(

Image

0.214

0.227

0.214

0.214

.200

x21

(

Customer expectation

0.364

0.363

0.389

0.384

.333

x22

(

Customer expectation

0.336

0.325

0.349

0.347

.333

x23

(

Customer expectation

0.300

0.312

0.262

0.269

.333

x31

(

Perceived quality

0.156

0.163

0.150

0.150

.143

x32

(

Perceived quality

0.116

0.110

0.123

0.122

.143

x33

(

Perceived quality

0.152

0.152

0.145

0.146

.143

x34

(

Perceived quality

0.139

0.136

0.148

0.147

.143

x35

(

Perceived quality

0.142

0.138

0.142

0.143

.143

x36

(

Perceived quality

0.142

0.138

0.147

0.148

.143

x37

(

Perceived quality

0.153

0.164

0.145

0.144

.143

x41

(

Perceived value

0.459

0.448

0.500

0.500

.500

x42

(

Perceived value

0.541

0.551

0.500

0.500

.500

x51

(

Customer satisfaction

0.320

0.314

0.321

0.322

.333

x52

(

Customer satisfaction

0.327

0.318

0.345

0.344

.333

x53

(

Customer satisfaction

0.353

0.368

0.334

0.334

.333

x71

(

Customer loyalty

0.401

0.363

0.446

0.439

.500

x72

(

Customer loyalty

0.095

0.106

0.103

0.117

0

x73

(

Customer loyalty

0.505

0.531

0.451

0.445

.500

Comparison betweenthe LVs coming from the 5 methodsPCAULS-SEMSCALEPLSGSCAWhen all blocks are good, all the methodsgive almost the same results.

IMAGE

CUSTOMER EXPECTATION

PERCEIVED QUALITY

PERCEIVED VALUE

CUSTOMER SATISFACTION

LOYALTY

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

Fornell weights when the augmented Customer Satisfaction block is heterogeneous and reflective

Outer model

Parameter

ULS-SEM

PLS

GSCA

x11

(

Image

0.206

0.208

0.218

x12

(

Image

0.163

0.181

0.169

x13

(

Image

0.202

0.155

0.174

x14

(

Image

0.244

0.230

0.225

x15

(

Image

0.184

0.226

0.214

x21

(

Customer expectation

0.318

0.362

0.388

x22

(

Customer expectation

0.329

0.326

0.348

x23

(

Customer expectation

0.353

0.313

0.263

x31

(

Perceived quality

0.131

0.163

0.150

x32

(

Perceived quality

0.130

0.110

0.124

x33

(

Perceived quality

0.170

0.153

0.146

x34

(

Perceived quality

0.135

0.135

0.147

x35

(

Perceived quality

0.122

0.139

0.142

x36

(

Perceived quality

0.137

0.137

0.147

x37

(

Perceived quality

0.174

0.164

0.144

x41

(

Perceived value

0.512

0.445

.500

x42

(

Perceived value

0.488

0.555

.500

x51

(

Customer satisfaction

0.234

0.251

0.006

x52

(

Customer satisfaction

0.359

0.254

0.016

x53

(

Customer satisfaction

0.393

0.293

0.037

x54

(

Noise 1

0.003

0.041

0.189

x55

(

Noise 2

0.003

0.038

0.188

x56

(

Noise 3

0.003

0.042

0.188

x57

(

Noise 4

0.003

0.041

0.188

x58

(

Noise 5

0.003

0.040

0.188

x71

(

Customer loyalty

0.442

0.363

0.445

x72

(

Customer loyalty

0.138

0.099

0.105

x73

(

Customer loyalty

0.421

0.538

0.450

Why GSCA is trappedThe GSCA criterionMSEV, Glang (1988)MSEV = Maximum Sum of Explained Variance

For reflective blocks, GSCA seemsto be too close to PCAFornell weightsfor originalECSI model

ULS-SEM vs PCA

PLS vs PCA

GSCA vs PCA

0.011817

0.025221

0.000373

_1276674946.unknown

Outer model

Parameter

GSCA

PCA

GSCA - PCA

x11

(

Image

0.218

0.218

0

x12

(

Image

0.169

0.17

-0.001

x13

(

Image

0.174

0.175

-0.001

x14

(

Image

0.225

0.223

0.002

x15

(

Image

0.214

0.214

0

x21

(

Customer expectation

0.389

0.384

0.005

x22

(

Customer expectation

0.349

0.347

0.002

x23

(

Customer expectation

0.262

0.269

-0.007

x31

(

Perceived quality

0.15

0.15

0

x32

(

Perceived quality

0.123

0.122

0.001

x33

(

Perceived quality

0.145

0.146

-0.001

x34

(

Perceived quality

0.148

0.147

0.001

x35

(

Perceived quality

0.142

0.143

-0.001

x36

(

Perceived quality

0.147

0.148

-0.001

x37

(

Perceived quality

0.145

0.144

0.001

x41

(

Perceived value

0.5

0.5

0

x42

(

Perceived value

0.5

0.5

0

x51

(

Customer satisfaction

0.321

0.322

-0.001

x52

(

Customer satisfaction

0.345

0.344

0.001

x53

(

Customer satisfaction

0.334

0.334

0

x71

(

Customer loyalty

0.446

0.439

0.007

x72

(

Customer loyalty

0.103

0.117

-0.014

x73

(

Customer loyalty

0.451

0.445

0.006

Fornell weights when the augmented Customer Satisfaction block is heterogeneous and formative

Outer model

PLS

GSCA

Parameter

Weight

Loading

Weight

Loading

x11

(

Image

0.301

0.745

0.315

0.742

x12

(

Image

0.262

0.601

0.244

0.577

x13

(

Image

0.219

0.577

0.251

0.591

x14

(

Image

0.327

0.768

0.324

0.765

x15

(

Image

0.325

0.744

0.309

0.730

x21

(

Customer expectation

0.523

0.772

0.550

0.789

x22

(

Customer expectation

0.469

0.688

0.493

0.708

x23

(

Customer expectation

0.448

0.610

0.372

0.534

x31

(

Perceived quality

0.213

0.803

0.198

0.791

x32

(

Perceived quality

0.144

0.637

0.163

0.653

x33

(

Perceived quality

0.200

0.784

0.192

0.769

x34

(

Perceived quality

0.177

0.769

0.195

0.779

x35

(

Perceived quality

0.182

0.756

0.188

0.752

x36

(

Perceived quality

0.180

0.775

0.194

0.776

x37

(

Perceived quality

0.215

0.780

0.191

0.762

x41

(

Perceived value

0.486

0.904

0.543

0.921

x42

(

Perceived value

0.598

0.938

0.543

0.921

x51

(

Customer satisfaction

0.356

0.772

0.288

0.467

x52

(

Customer satisfaction

0.254

0.781

0.260

0.481

x53

(

Customer satisfaction

0.572

0.902

0.620

0.262

x54

(

Noise 1

0.114

0.125

0.630

-0.730

x55

(

Noise 2

-0.763

0.117

-0.814

-0.729

x56

(

Noise 3

0.011

0.130

-0.165

-0.729

x57

(

Noise 4

0.318

0.126

0.211

-0.724

x58

(

Noise 5

0.364

0.124

0.156

-0.728

x71

(

Customer loyalty

0.450

0.813

0.549

0.864

x72

(

Customer loyalty

0.132

0.220

0.128

0.203

x73

(

Customer loyalty

0.660

0.917

0.556

0.873

A Component-based SEM treeALL BLOCK FORMATIVE

Mode

Criterion maximized

Centroid

Factorial

_1276677324.unknown

_1276677461.unknown

Criterion minimized

_1276678908.unknown

Criterion maximized

_1277794187.unknown

B + Centroid

B + Factorial

GSCAR2=.263R2=.313R2=.301R2=.380R2=.691R2=.491

Comparison between PLS, GSCA and CCA

Endogenous latent variables

R

PLS (B+Centroid)

PLS (B+Factorial)

GSCA

CCA

Customer expectation

0.254

0.254

.263

.269

Perceived quality

0.316

0.312

.313

.340

Perceived value

0.379

0.379

.380

.392

Customer satisfaction

0.696

0.700

.691

.736

Complaint

0.294

0.293

.301

.314

Loyalty

0.491

0.490

.491

.514

Sum

2.430

2.428

2.439

2.565

FIT = Sum/6

0.405

0.405

0.407

0.428

Comparison between methods***Practice supports theory

Mode B + Centroid scheme

Mode B + Factorial scheme

GSCA

6.927

6.926

6.903

4.158

4.159

4.128

0.405

0.405

0.407

_1277653798.unknown

_1277654046.unknown

_1277653706.unknown

Comparison betweenthe LVs coming from the 3 methodsB + CentroidB + FactorialGSCAWhen all blocks are good, all the methodsgive almost the same results.

IMAGE

CUSTOMER EXPECTATION

PERCEIVED QUALITY

PERCEIVED VALUE

CUSTOMER SATISFACTION

LOYALTY

Economic inequality and political instability (Russet)GINIFARMRENTGNPRLABOAgricultural inequality (X1)Industrialdevelopment (X2)ECKSDEATD-STBD-INSINSTDICTPoliticalinstability (X3)123++++-+++-+++-

Use of XLSTAT-PLSPMMode B + Centroid schemeY1 = X1w1Y2 = X2w2Y3 = X3w3

Use of XLSTAT-PLSPMMode B + Factorial schemeY1 = X1w1Y2 = X2w2Y3 = X3w3

Use of GSCA (All formative)When there is only one structural equation andwhen all blocks are formative,GSCA is equivalentto a canonical correlation analysis.

Use of XLSTAT-PLSPM for two blocksMode B Canonical Correlation Analysis

Comparison between methods****Practice supports theory

Mode B + Centroid scheme

Mode B + Factorial scheme

GSCA (( CCA)

1.386

1.384

1.235

.966116

.966178

.848

16.138

15.939

15.568

R2(Y3; Y1,Y2)

0.657

0.661

0.669

_1274247499.unknown

_1275801235.unknown

_1274247279.unknown

ConclusionWhen 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.

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