multivariate data analysis

5/19/2018 Multivariate Data Analysis

1/17

SEVENTH E ITION

M U L T I V A R I A T E D A T A A N A L Y S I S

. - * . . . -

4

Global Perspective

JosephF. Hair Jr.

Kennesaw State University

W illiam C. Black

Louisiana State University

Barry J. Babin

Un iversity of Southern Mississippi

Rolph E . Anderson

rexel University


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CONTENTS

Preface xxv

About the Authors xxvii

Chapter 1 Int roduct ion: Me thod s and Mo de l Bui ld ing 1

W ha t Is Mu ltivariate Analysis? 3

M ultiv aria te Analysis in Statistical Terms 4

Some Basic Concepts of Mu ltiva riate Analysis 4

The Variate 4

Mea surem ent Scales 5

Measurement Error and Multivariate Measurement 7

Statistical Significance Versus Statistical Power 8

Types of Statistical Error and Statistical Power 9

Impacts on Statistical Pow er 9

Using Power w ith Mu ltivaria te Techniques 11

A Classification of Mu ltiva riate Techniques 11

Dependence Techniques 14

Interdependence Techniques 14

Types of Mu ltiva riate Techniques 15

Principal Com ponents and Comm on Factor Analysis 16

Mu ltiple Regression 16

M ultip le Discriminant Analysis and Logistic Regression 16

Canonical Correlation 17

Mu ltivaria te Analysis of Variance and Covariance 17

Conjoint Analysis 18

Cluster Analysis 18

Perceptual Ma ppin g 19

Correspondence Analysis 19

Structural Equation Modeling and Confirmatory Factor

Analysis 19

Guidelines for Mu ltivariate Analyses and Interpre tation 20

Establish Practical Significance as Well as Statistical

Significance 20

Recognize Tha t Sample Size Affects All Results 21

Know Your Data 21

Strive for Mo del Parsimony 21

Look at Your Errors 22

Validate Your Results 22

A Structured Approach to Mu ltivaria te Mo del Building 22


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Stage 1 : De fine the Research Problem , Ob jectives,

and M ult iva r iate Technique to Be Used 23

Stage 2: Dev elop the Ana lysis Plan 23

Stage 3: Evaluate the Assumptions Underly ing the Mult ivar iate

Technique 23

Stage 4: Estimate the M ult iva r iate Mo del an d Assess Overal l

M od el Fit 23

Stage 5: Inte rpre t th e Variate(s) 24

Stage 6: Val idate the M ult iva r iate M ode l 24

A Decision Flow cha rt 24

Databases 24

Primary Database 25

Oth er Databases 27

Org aniza t ion of the Rema ining Chapters 28

Section I: Understanding and Preparing For Multivariate Analysis

Section

II :

Ana lysis Using Depend ence Techniques 28

Section III: Interdep end ence Techniques 28

Sect ion IV: Structural Equat ions Mo del in g 28

Summary 28 Questions 3 Suggested Readings 3

References 3

S E C TIO N I U n d e r s t a n d i n g a n d P r e p a r i n g F o r M u l t i v a r i a t e

A n a l y s i s 3 1

Chap t e r 2 C l ean i ng an d T r an s f o r m i n g Da ta 33

Introduct ion 36

Graphical Exam inat ion of the Data 37

Univar iate Prof i l ing: Examining the Shape of the

Distr ibut ion 38

Bivar iate Prof i l ing: Examining the Relat ionship Between

Variables 39

Bivar iate Prof i l ing: Exam ining Group Dif ferences 40

Mu lt ivar ia te Profi les 41

Missing Data 42

The Impac t of Missing Data 42

A Simple Example of a Missing Data Analysis 43

A Four-Step Process for Iden t i fy ing Missing Data and A pp lyin g

Remedies 44

An I l lustrat ion of Missing Data Diagnosis with

th e Four-Step Process 54

Outl iers 64

Detect ing and Hand l ing Out l iers 65

An I l lustrat ive Example of An alyzin g Out l iers 68

Testing the Assum ptions of M ult iva r iate Analysis 70


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Contents

Assessing Indiv idua l Variables Versus th e Variate 70

Four Im port ant Stat ist ical Assu mptions 71

Data Tran sform ations 77

An I l lustrat ion of Test ing the Assumptions Underlying

M ult iva riate Analysis 79

Incorp orat ing Nonm etr ic Data w it h Dum my Variables 86


References 9

Ch ap te r 3 Facto r An a lys is 91

W ha t Is Factor Analysis? 94

A Hy poth etica l Example of Factor Analys is 95

Factor Ana lysis Decision Process 96

Stage 1: Objectives of Factor Analysis 96

Spec ifying th e Un it of Analysis 98

Ac hiev ing Data Sum ma rization Versus Data Reduc tion 98

Variable Selection 99

Using Factor Analysis w it h Othe r M ult iva ria te Techniques 10

Stage 2: Design ing a Factor Analysis 100

Correlations Am on g Variables or Respondents 100

Variable Selection and Me asure me nt Issues 101

Sam ple Size 102

Summary 102

Stage 3: As sum ptions in Factor Analysis 103

Co nce ptua l Issues 103

Statis tical Issues 103

Summary 104

Stage 4: Der iving Factors and Assessing Ove rall Fit 105

Selecting the Factor Extrac tion M et ho d 105

Criteria fo r th e Num ber of Factors to Extract 108

Stage 5: Inte rpr etin g the Factors 112

The Three Processes of Factor Inte rpr eta tion 112

Ro tatio n of Factors 113

Jud ging th e Significance of Factor Loadings 116

Interp ret ing a Factor Ma tr ix 118

Stage 6: Va lidatio n of Factor Analysis 122

Use of a Co nfirm ato ry Perspective 122

Assessing Factor Structure Sta bil i ty 122

Detect ing Inf lue ntia l Observat ions 123

Stage 7: A dd itio na l Uses of Factor Analys is Results 123

Selecting Surroga te Variables fo r Subse quent Analysis 123

Creating Sum ma ted Scales 124


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Co m pu tin g Factor Scores 127

Selecting Am on g the Three Me thods 128

A n I l lustrat ive Example 129

Stage 1: Ob jectives of Factor Ana lysis 129

Stage 2: Des igning a Factor Analysis 129

Stage 3: Ass um ptions in Factor Analysis 129

Co mp one nt Factor Analys is: Stages 4 Thr oug h 7 132

Com mo n Factor Analys is: Stages 4 and 5 144

A Man ageria l Ov erview of the Results 146


References 15

S E C T IO N I I A n a l y s i s U s i n g D e p e n d e n c e T e c h n i q u e s 1 5 3

Chapter 4 Simple and M ult iple Regression 155

W ha t Is M ult ipl e Regression Analysis? 161

An Example of Simple and M ult ipl e Regression 162

Prediction Using a Single Independent Variable:

Simp le Regression 162

Prediction Using Several Independent Variables:

M ult ipl e Regression 165

Summary 167

A Decision Process for M ult ipl e Regression Analysis 167

Stage 1: Objectives of M ult ipl e Regression 169

Research Problems Ap pro pria te fo r M ult iple Regression 169

Spec ifying a Statistical Relations hip 171

Selection of Dep ende nt and Inde pen den t Variables 171

Stage 2: Research Design of a M ul tip le Regression Ana lysis 173

Sam ple Size 174

Creating Ad dit ion al Variables 176

Stage 3: Ass um ptions in M ult iple Regression Analysis 181

Assessing Indiv idua l Variables Versus th e Variate 182

Me thod s of Diagnosis 183

Linearity of the Pheno men on 183

Co nstan t Variance of th e Error Term 185

Independence of th e Error Terms 185

No rma li ty of the Error Term Dis tr ibut ion 185

Summary 186

Stage 4: Estimating the Regression Model and Assessing Overall

M od el Fit 186

Selecting an Estim ation Technique 186

Testing the Regression Variate for Meeting the Regression

Assumptions 191


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Contents

Examining the Statistical Significance of Our Mo de l 192

Identifying Influen tial Observations 194

Stage 5: Interpreting the Regression Variate 197

Using the Regression Coefficients 197

Assessing Mu lticollinear ity 200

Stage 6: Validation of the Results 206

Add itional or Split Samples 206

Calcu lating th e PRESS Statistic 206

Comparing Regression Models 206

Forecasting w ith the Mo del 207

Illustration of a Regression Analysis 207

Stage 1: Objectives of Mu ltiple Regression 207

Stage 2: Research Design of a M ultip le Regression Analysis 2

Stage 3: Assum ptions in M ultip le Regression Analysis 208

Stage 4: Estimating the Regression Model and Assessing

Overall Mo del Fit 208

Stage 5: Interpreting the Regression Variate 223

Stage 6: Validating the Results 226

Evaluating Altern ative Regression Mode ls 227

A Manag erial Overview of the Results 231


References 234

Cha pter 5 Can onical Correlat ion 235

W ha t Is Canonical Correlation? 237

Hypothe tical Example of Canonical Correlation 238

Developing a Variate of Dep ende nt Variables 238

Estimating the First Canonical Function 238

Estimating a Second Canonical Function 240

Relationships of Canonical Correlation Analysis to Other

Mu ltivaria te Techniques 241

Stage 1: Objectives of Canonical Corre lation Analysis 242

Selection of Variable Sets 242

Evalua ting Research Objectives 242

Stage 2: Designing a Canonical Correlation Analysis 243

Sample Size 243

Variables and Their Conceptual Linkage 243

Missing Data and Outliers 244

Stage 3: Assumptions in Canonical Correlation 244

Linearity 244

Normality 244

Homoscedasticity and Mu lticollinearity 244


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xiv Contents

Stage 4: Deriving the Canonical Functions and Assessing

Ov era ll Fit 245

De riving Canonical Functions 246

W hich Canonical Functions Should Be Interp reted ? 246

Stage 5: Inte rpr etin g the Canonical Variate 250

Canonical W eigh ts 250

Canon ical Loadings 250

Canon ical Cross-Loadings 250

Wh ich Interp retat io n Approac h to Use 251

Stage 6: Va lidatio n and Diagnosis 251

An I l lustrat ive Example 252

Stage 1: Objectives of Canonical Cor relation Analysis 253

Stages 2 and 3: Designing a Canonical Correlation Analysis

and Testing the Assum ptions 253

Stage 4: Deriving the Canonical Functions and Assessing

Ov era ll Fit 253

Stage 5: Inte rpre ting th e Canonical Variates 254

Stage 6: Va lidatio n and Diagnosis 257


Summary 258 Questions 259 References 26

C h a p te r 6 C o n jo i n t A n a l ys i s 2 6 1

W ha t Is Co njoint Analysis? 266

Hyp othetical Example of Con joint Analysis 267

Specifying Util i ty , Factors, Levels, and Profi les 267

Ga therin g Preferences fr om Respondents 268

Estim ating Part-W orths 269

Determin ing At t r ibu t e Importance 270

Assessing Predic tive Accuracy 270

The Ma nage rial Uses of Co njoint Analysis 271

Compar ing Con jo in t Analysis w i th Other Mu l t ivar ia te

Methods 272

Com pos itional Versus Dec om positiona l Techniques 272

Specifying th e Co njoint Variate 272

Separate Mod els fo r Each Indiv idua l 272

Flex ibil i ty in Types of Relationships 273

Designing a Con joint Analysis Experiment 273

Stage 1: The Objectives of Co njoin t Analysis 276

Defin in g the Total Uti l i ty of the Object 276

Specifying th e De term inan t Factors 276

Stage 2: The Design of a Co njoint Analysis 277

Selecting a Con joint Analysis Me thod olog y 278


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Contents

Designing Profi les: Selecting and Defining Factors

and Levels 278

Spec ifying th e Basic Mo del Form 283

Data Collection 286

Stage 3: Assum ptions of Con joint Analysis 293

Stage 4: Estimating the Con joint Mod el and Assessing Overall Fit

Selecting an Estim ation Technique 294

Estimated Part-W orths 297

Eva luating M ode l Goodne ss-of-Fit 298

Stage 5: Inte rpr etin g th e Results 299

Exam ining the Estimated Part-Worths 300

Assessing the Relative Importance of Attr ibut es 302

Stage 6: Va lidatio n of th e Co njoint Results 303

Man ageria l Appl icat ions of Con joint Analysis 303

Segmentat ion 304

Pro f i tabi l i ty Analysis 304

Co njoin t Sim ulators 305

Al terna t ive Con jo in t Metho do log ies 306

Adaptive/Self-Expl icated Conjoint: Conjoint with

a Large Nu mb er of Factors 306

Choice-Based Co njoin t: Ad din g An oth er Touch of Realism 30

Ov ervie w of the Three Conjoint Me thod ologie s 312

An I l lustrat ion of Con joint Analysis 312

Stage 1: Objectives of th e Co njoin t Analys is 313

Stage 2: Design of th e Co njoin t Analysis 313

Stage 3: As sum ptions in Co njoin t Analysis 316

Stage 4: Est imating the Con joint M ode l and Assessing O veral l

Mo del Fit 316

Stage 5: Inte rpr etin g th e Results 320

Stage 6: Va lidatio n of th e Results 324

A Man ageria l Ap pl ica t ion: Use of a Choice Simulator 325


References 33

C h a p te r 7 M u l t i p l e D i sc r im in a n t A n a l ys i s a n d L o g i s ti c R e g re ss io n 3 3

W ha t Are Disc riminan t Analysis and Logistic Regression? 339

Disc riminan t Analys is 340

Logistic Regression 341

Ana logy w it h Regression and MANO VA 341

Hyp othetical Example of Discriminant Analysis 342

A Two-Group Discriminant Analysis: Purchasers Versus

Nonpurchasers 342


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A Geometric Representat ion of the Two-Group Discriminant

Function 345

A Three-Group Example of D iscriminant Analysis: Switching

Intentions 346

The Decision Process fo r Discrim inant Analys is 348

Stage 1: Objectives of Discrim inant Analysis 350

Stage 2: Research Design fo r Discrimina nt Analysis 351

Selecting Dep ende nt and Inde pen den t Variables 351

Sam ple Size 353

Division of the Sample 353

Stage 3: Ass um ptions of Discrim inant Analys is 354

Impacts on Estim ation and Classification 354

Impacts on Interp retat io n 355

Stage 4: Est imation of t he Discriminant Mo del and Assessing

Ov era ll Fit 356

Selecting an Estimation M eth od 356

Statistical Significance 358

Assessing Ove rall M ode l Fit 359

Casewise Diagn ostics 368

Stage 5: Inte rpr eta tion of th e Results 369

Discriminant W eights 369

Disc riminan t Loadings 370

PartialFValues 370

Interp retat io n of Two or More Functions 370

Wh ich Interpre t ive Me tho d to Use? 373

Stage 6: Va lidatio n of the Results 373

Va lidatio n Procedures 373

Pro fi l ing Group Differences 374

A Two-G roup Il lustra tive Example 375


Stage 2: Research Design fo r Discrimina nt Analysis 375

Stage 3: Ass um ptions of Discrim inant Analysis 376

Stage 4: Est imation of the Discriminant Mo del

and Assessing Ov era ll Fit 376

Stage 5: Inte rpr eta tion of the Results 387


A Man ageria l Ov ervie w 391

A Three-Grou p Il lustra tive Example 391


Stage 2: Research Design fo r Discriminant Analysis 392

Stage 3: Ass um ptions of Discrim inant Analysis 392


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Contents

Stage 4: Estimation of the Discriminant Model and Assessing

Ov era ll Fit 392

Stage 5: Interpretation of Three-Group Discriminant Analysis

Results 404

Stage 6: Va lidatio n of the Discrim inant Results 410

A Manag eria l Ov erview 412

Logistic Regression: Regression with a Binary Dependent

Variable 413

Repres entation of the Binary Dep enden t Variable 414

Sam ple Size 415

Estim ating the Logistic Regression Mo del 416

Assessing th e Goodne ss-of-Fit of th e Estim ation Mo de l 419

Testing for Significance of the Coefficients 421

Interpre t ing the Coeff icients 422

Calculating Probabil it ies for a Specific Value of the Independen

Variable 425

Ov erview of Interpre t ing Coeff icients 425

Summary 425

An Il lustra tive Example of Logistic Regression 426

Stages 1 , 2, and 3: Research Ob jectiv es, Research De sign,

and Statistical Ass um ptions 426

Stage 4: Estimation of the Logistic Regression Model

and Assessing Ov erall Fit 426

Stage 5: Inte rpre tatio n of the Results 432


A Mana geria l Ov erview 434


References 437

C h a p te r 8 A N O V A a n d M A N O V A 4 3 9

MANOVA: Extending Univariate Methods for Assessing Group

Differences 443

M ultiv aria te Procedures fo r Assessing Group Differences 444

A Hypo thetical I l lustrat ion of MANOVA 447

Analysis Design 447

Differences fro m Discrim inant Analysis 448

Form ing the Variate and Assessing Differences 448

A Decision Process fo r MA NO VA 449

Stage 1: Objectives of MANO VA 450

W hen Should We Use MANOVA? 450

Types of Mu lt ivaria te Questions Suitable for MANOVA 451

Selecting th e Dep enden t Measures 452


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xviii ontents

Stage 2: Issues in th e Research Design of MA NO VA 453

Sample Size Requirements Overal l and by Group 453

Factorial DesignsTw o or Mo re Treatm ents 453

Using CovariatesANC OVA and MANCOVA 455

MANOV A Cou nterparts of Othe r ANOVA Designs 457

A Special Case of MAN OVA : Repeated Measures 457

Stage 3: Assum ptions of ANOVA and MANO VA 458

Independence 458

Equa l i ty of Variance Covariance Matr ices 459

Normal i ty 460

Linearity and Mu lticoll inearity Am on g the Dependent Variables 460

Sens it iv i ty to Out l iers 460

Stage 4: Est imat ion of th e M ANOVA Mo del and Assessing

Ov erall Fit 460

Est imat ion w it h the General Linear Mo del 462

Criteria fo r Signif icance Testing 463

Statistical Pow er of the M ultiv ari ate Tests 463

Stage 5: Inter pre tat ion of the MANOVA Results 468

Evaluat ing Covariates 468

Assessing Effects on the De pen den t Variate 468

Ide nt i fy in g Dif ferences Betwe en Individu al Groups 472

Assessing Signif icance for Ind ividu al De pen den t Variables 474

Stage 6: Va lidat ion of the Results 475

Summary 476

I l lustrat ion of a MANO VA Analysis 476

Example 1: Di f ference Between Two Indepe nden t Groups 477

Stage 1: Objectives of th e Analysis 478

Stage 2: Research Design of th e MAN OVA 478

Stage 3: Assum ptions in MANO VA 479

Stage 4: Est imat ion of the MANOVA Model and Assessing

th e Ov erall Fit 480

Stage 5: Int erp ret atio n of th e Results 482

Example 2: Difference Between

Indepe nden t Groups 482

Stage 1: Object ives of the MANOVA 483

Stage 2: Research Design of MANO VA 483

Stage 3: Assum ptions in MANO VA 484

Stage 4: Est imat ion of th e M ANOVA Mo del and Assessing

Ov erall Fit 485

Stage 5: Inte rpre tat ion of the Results 485

Example 3: A Factor ial Design for MANO VA w it h Two Indep ende nt

Variables 488


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Contents

Stage 1: Objectives of the MAN OVA 489

Stage 2: Research Design of the MAN OVA 489

Stage 3: Assu mptions in MANOVA 491

Stage 4: Estimation of the MANOVA Model and Assessing

Ov era ll Fit 492


Summary 496



References 5

SECTION I I I Ana lysis Using Inte rde pe nd en ce Techniques 50

Chapter 9 Grouping Data with Cluster Analysis 505

W ha t Is Cluster Analysis? 508

Cluster Analys is as a M ult iva ria te Technique 508

Conceptual Deve lopme nt w it h Cluster Analysis 508

Necessity of Conce ptual Sup port in Cluster Analysis 509

Ho w Does Cluster Analysis W ork? 510

A Simple Example 510

Objec tive Versus Subjective Cons iderations 515

Cluster Ana lysis Decision Process 515

Stage 1: Objec tives of Cluster Analy sis 517

Stage 2: Research Des ign in Cluster Ana lysis 518

Stage 3: As sum ptions in Cluster Analysis 526

Stage 4: Der iving Clusters and Assessing Ov erall Fit 527

Stage 5: Inte rpr eta tion of th e Clusters 538

Stage 6: Va lidatio n and Pro fi l ing of th e Clusters 539

An Il lustr ative Example 541

Stage 1: Objectives of the Cluster Analysis 541

Stage 2: Research Design of th e Cluster An alys is 542

Stage 3: Ass um ptions in Cluster Analys is 545

Em ploying Hierarchical and Nonh ierarchical Me tho ds 546

Step 1: Hierarch ical Cluster Ana lysis (Stage 4) 546

Step 2: Nonh ierarchical Cluster Analysis (Stages 4, 5, and 6) 5

Summ ary 561 Questions 563 Suggested Readings 563

References 563

C h a p te r 1 0 M D S a n d C o r re sp o n d e n ce A n a l ys i s 5 65

W ha t Is Mu lt id ime nsion al Scaling? 568

Com paring Objects 568

Dimens ions: The Basis fo r Com parison 569


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A Simp l i f ied Look at How MDS Works 570

Gathe ring Similar i ty Judgments 570

Creating a Perceptual Ma p 570

Interp ret ing the Axes 571

Com paring MDS to Oth er Interdepen dence Techniques 572

Indiv idua l as th e Un it of Analysis 573

Lack of a Varia te 573

A Decision Fram ewo rk fo r Perceptual M ap pin g 573

Stage 1: Ob jective s of MDS 573

Key Decisions in Settin g Objectives 573

Stage 2: Research Design of MDS 578

Selection of Either a Decompositional (Attribute-Free)

or Com posit ional (Attr ibute-Based) Approach 578

Objects: Their Num ber and Selection 580

Nonm etric Versus Metr ic Me thods 581

Collection of Sim ilarity or Preference Data 581

Stage 3: Ass um ptions of MDS Analysis 584

Stage 4: Deriving the MDS Solution and Assessing

Ov era ll Fit 584

De term ining an Object s Position in the Perceptual Ma p 584

Selecting th e Dim ens ionality of th e Perceptual Ma p 586

Inc orp ora ting Preferences int o MDS 587

Stage 5: Inte rpr etin g the MDS Results 592

Iden ti fying the Dimensions 593

Stage 6: Va lidatin g th e MDS Results 594

Issues in Va lida tion 594

Approaches to Val idat ion 594

Ov erview of Mu lt id imen siona l Scaling 595

Correspondence Analysis 595

Dis tinguis hing Characteristics 595

Differences fro m Other Mu lt ivar iate Techniques 596

A Simple Exam ple of CA 596

A Decision Fram ewo rk fo r Correspondence Analysis 600

Stage 1: Objectives of CA 601

Stage 2: Research Design of CA 601

Stage 3: Ass um ptions in CA 602

Stage 4: De rivin g CA Results and Assessing Ov era ll Fit 602


Stage 6: Valid ation of the Results 604

Ov erv iew of Correspondence Analysis 604

Il lustra tions of MDS and Correspondence Analysis 605


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Contents

Stage 1: Objectives of Perceptual M ap pin g 606

Ide ntif yin g Objects for Inclusion 606

Basing the Analysis on Similarity or Preference Data 607

Using a Disaggreg ate or Ag gre gate Analysis 607

Stage 2: Research Design of th e Perceptual M app ing Study 607

Selecting Decom posit ional or Com posit ional Me thods 607

Selecting Firms fo r Analysis 608

Nonm etric Versus Metr ic Me thods 608

Collecting Data fo r MDS 608

Collecting Data fo r Correspondence Analysis 609

Stage 3: Ass um ptions in Perceptual M ap pin g 610

M ultid im ens iona l Scaling: Stages 4 and 5 610

Stage 4: De riving MDS Results and Assessing Ov erall Fit 610


Ov erview of the Decom posit ional Results 616

Correspondence Analys is: Stages 4 and 5 617

Stage 4: Estim ating a Correspondence Analysis 617

Stage 5: Inte rpre ting CA Results 619

Ov erview of CA 621

Stage 6: Va lidatio n of th e Results 622

A Man ageria l Ov erview of MDS Results 622


References 625

S E C TIO N I V S t r u c t u r a l E q u a t i o n s M o d e l i n g 6 2 7

Chap te r 11 SEM: A n In t ro duc t ion 629

W ha t Is Structural Equation Mo del ing? 634

Estimation of Mult ip le Interre lated Dependence

Relationships 635

Inc orp orat ing Latent Variables Not Meas ured Directly 635

De fin ing a Mo del 637

SEM and Other Mu lt ivaria te Techniques 641

Sim ilarity to Dependence Techniques 641

Sim ilarity to Interdepen dence Techniques 641

The Emergence of SEM 642

The Role of Theory in Structural Equation M ode l ing 642

Spec ifying Relationships 642

Establishing Causation 643

Deve loping a Mo del ing Strategy 646

A Simp le Exam ple of SEM 647

The Research Qu es tion 647


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xxii Contents

Sett ing Up the Structural Equation Mod el

fo r Path Analysis 648

The Basics of SEM Es tima tion and Assess ment 649

Six Stages in Struc tural Equa tion M od elin g 653

Stage 1: De finin g Indiv idua l Constructs 655

Op erat ional izing the Construct 655

Pretesting 655

Stage 2: Deve loping and Specifying the Measurem ent

Model 656

SEM No tatio n 656

Creating the Measurem ent Mo del 657

Stage 3: De sign ing a Stud y to Produce Em pirical Results 657

Issues in Research Des ign 658

Issues in M od el Estim ation 662

Stage 4: Assessing Me asurem ent M ode l Va lidity 664

The Basics of Go odne ss-of-F it 665

Ab solu te Fit Indices 666

Incr em enta l Fit Indices 668

Parsim ony Fit Indices 669

Problems Associated w it h Using Fit Indices 669

Unacceptable M ode l Spec ification to Achiev e Fit 671

Guidelines fo r Establishing Acce ptable and Unacceptable Fit 672

Stage 5: Specifying th e Struc tural Mo del 673

Stage 6: Assessing the Structural M ode l Va lidity 675

Structural Mo del GOF 675

Co mp etit ive Fit 676

Comparison to the Measu rement Mo del 676

Testing Structu ral Relationships 677


Appendix 11A: Estimating Relationships Using Path Analysis 681

Appendix IB :S MAbbreviations 683

Appendix C: Detail on Selected

GOF

Indices 684

References 685

Cha p te r 12 A pp l i ca t ion s o f SEM 687

Part 1: Co nfirm ato ry Factor Analysis 693

CFA and Exp loratory Factor Analysis 693

A Simple Exam ple of CFA and SEM 694

A Visual Diagram 694

SEM Stages for Testing Measurement Theory Validation

w it h CFA 695

Stage 1: De fining Indiv idua l Constructs 696


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Contents X

Stage 2: Deve loping the Overal l Meas uremen t Mo del 696

Unidimensional i ty 696

Congeneric Measu rement Mo del 698

Items per Construct 698

Reflective Versus Form ative Constructs 701

Stage 3: De sign ing a Stud y to Produce Em pirical Results 702

M eas ure me nt Scales in CFA 702

SEM and Sam pling 703

Specifying the M ode l 703

Issues in Ide ntif ic atio n 704

Av oidin g Identi f ica t ion Problems 704

Problems in Estim ation 706

Stage 4: Assessing Me asure me nt M ode l Va lidity 707

Assessing Fit 707

Path Estimates 707

Cons truct Va lidity 708

M ode l Diagnostics 711

Sum mary Example 713

CFA Il lus trat ion 715

Stage 1: De finin g Indiv idua l Constructs 716

Stage 2: Deve loping the Overal l Measu rement Mode l 716

Stage 3: Des igning a Study to Produce Empirical Results 718

Stage 4: Assessing Meas urement Mod el Val id i ty 719

HBAT CFA Sum ma ry 727

Part 2: W ha t Is a Struc tural Mode l? 727

A Simple Example of a Struc tural M ode l 728

An Ov ervie w of Theory Testing w it h SEM 729

Stages in Testing Struc tural The ory 730

One-Step Versus Two-Step Approac hes 730

Stage 5: Spec ifying th e Struc tural M od el 731

Un it of Analysis 731

M ode l Spec ification Using a Path Diagram 731

Designing the Study 735

Stage 6: Assessing the Structural Mod el Va lidity 737

Un ders tand ing Struc tural M ode l Fit fro m CFA Fit 737

Examine th e M od el Diagnostics 739

SEM Il lus tratio n 740

Stage 5: Spec ifying the Struc tural M od el 740

Stage 6: Assessing the Struc tural M od el Va lidity 742

Part 3: Extensions and Ap plica tions of SEM 749


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xxiv Contents

Reflective Versus Form ative Measures 749

Reflective Versus Form ative Me asure me nt Theo ry 749

Op erat iona l izing a Formative Construct 750

Dist inguishing Reflective fro m Formative Constructs 751

W hich to Use Reflective or Form ative? 753

Higher-Orde r Factor Analysis 754

Em pirical Concerns 754

Theo retical Concerns 756

Using Second-Order Me asure me nt Theories 756

W hen to Use Higher-Orde r Factor Analysis 757

M ult ip le Groups Analysis 758

Meas urement Mo del Comparisons 758

Struc tural M ode l Com parisons 763

Me asure me nt Bias 764

M ode l Spec ification 764

Mo del Interp retat io n 765

Relat ionship Types: Me diat ion and Mo dera t ion 766

Mediat ion 766

Moderat ion 770

Long itudinal Data 773

Ad dit ion al Covariance Sources: Tim ing 773

Using Error Covariances to Represent Ad de d Covariance 774

Partial Least Squares 775

Charac teristics of PLS 775

Adv antag es and Disadvantages of PLS 776

Ch oo sin g PLS Versus SEM 777


References 782

Index 785

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