**Multivariate Data Analysis, 8th Edition**

By Joseph F. Hair Jr., William C. Black, Barr y J. Babin, Rolph E. Anderson

Preface xiv

Acknowledgments xvii

1 overview of Multivariate Methods 1

What is Multivariate Analysis? 3

three converging trends 4

Topic 1: Rise of Big Data 4

Topic 2: Statistical Versus Data Mining Models 7

Topic 3: Causal Inference 9

Summary 9

Multivariate Analysis in Statistical terms 9

Some Basic concepts of Multivariate Analysis 10

The Variate 10

Measurement Scales 11

Measurement Error and Multivariate Measurement 13

Managing the Multivariate Model 14

Managing the Variate 14

Managing the Dependence Model 17

Statistical Significance Versus Statistical Power 18

Review 20

A classification of Multivariate techniques 21

Dependence Techniques 21

Interdependence Techniques 25

types of Multivariate techniques 25

Exploratory Factor Analysis: Principal Components

and Common Factor Analysis 25

Cluster Analysis 26

Multiple Regression 26

Multivariate Analysis of Variance and Covariance 26

Multiple Discriminant Analysis 26

Logistic Regression 27

Structural Equation Modeling and Confirmatory Factor

Analysis 27

Partial Least Squares Structural Equation Modeling 28

Canonical Correlation 28

Conjoint Analysis 28

Perceptual Mapping 29

Correspondence Analysis 29

Guidelines for Multivariate Analyses and

interpretation 29

Establish Practical Significance as Well as Statistical

Significance 30

Recognize That Sample Size Affects All Results 30

Know Your Data 30

Strive for Model Parsimony 31

Look at Your Errors 31

Simplify Your Models By Separation 31

Validate Your Results 32

A Structured Approach to Multivariate Model

Building 32

Stage 1: Define the Research Problem, Objectives,

and Multivariate Technique to Be Used 33

Stage 2: Develop the Analysis Plan 33

Stage 3: Evaluate the Assumptions Underlying the

Multivariate Technique 33

Stage 4: Estimate the Multivariate Model and Assess

Overall Model Fit 34

Stage 5: Interpret the Variate(s) 34

Stage 6: Validate the Multivariate Model 34

A Decision Flowchart 34

Databases 34

Primary Database 35

Other Databases 37

organization of the Remaining chapters 37

Section I: Preparing for a Multivariate Analysis 37

Section II: Interdependence Techniques 38

Sections III and IV: Dependence Techniques 38

Section V: Moving Beyond the Basics 38

Online Resources: Additional Chapters 38

Summary 39

Questions 41

Suggested Readings and online Resources 41

References 41

Section i

Preparing for Multivariate

Analysis 43

2 examining Your Data 45

introduction 49

the challenge of Big Data Research efforts 49

Data Management 50

Data Quality 50

Summary 51

Preliminary examination of the Data 51

Univariate Profiling: Examining the Shape of the

Distribution 51

Bivariate Profiling: Examining the Relationship Between

Variables 52

Bivariate Profiling: Examining Group Differences 53

Multivariate Profiles 54

New Measures of Association 55

Summary 55

Missing Data 56

The Impact of Missing Data 56

Recent Developments in Missing Data Analysis 57

A Simple Example of a Missing Data Analysis 57

A Four-Step Process for Identifying Missing Data

and Applying Remedies 58

An Illustration of Missing Data Diagnosis with the

Four-Step Process 72

outliers 85

Two Different Contexts for Defining Outliers 85

Impacts of Outliers 86

Classifying Outliers 87

Detecting and Handling Outliers 88

An Illustrative Example of Analyzing Outliers 91

testing the Assumptions of Multivariate

Analysis 93

Assessing Individual Variables Versus the Variate 93

Four Important Statistical Assumptions 94

Data transformations 100

Transformations Related to Statistical Properties 101

Transformations Related to Interpretation 101

Transformations Related to Specific Relationship

Types 102

Transformations Related to Simplification 103

General Guidelines for Transformations 104

An illustration of testing the Assumptions

Underlying Multivariate Analysis 105

Normality 105

Homoscedasticity 108

Linearity 108

Summary 112

incorporating nonmetric Data with Dummy

Variables 112

Concept of Dummy Variables 112

Dummy Variable Coding 113

Using Dummy Variables 113

Summary 114

Questions 115

Suggested Readings and online Resources 116

References 116

Section ii

interdependence techniques 119

3 exploratory Factor Analysis 121

What is exploratory Factor Analysis? 124

A Hypothetical example of exploratory Factor

Analysis 126

Factor Analysis Decision Process 127

Stage 1: objectives of Factor Analysis 127

Specifying the Unit of Analysis 127

Achieving Data Summarization Versus Data

Reduction 129

Variable Selection 131

Using Factor Analysis with Other Multivariate

Techniques 131

Stage 2: Designing an exploratory Factor

Analysis 132

Variable Selection and Measurement Issues 132

Sample Size 132

Correlations among Variables or Respondents 133

Stage 3: Assumptions in exploratory Factor

Analysis 135

Conceptual Issues 135

Statistical Issues 135

Summary 136

Stage 4: Deriving Factors and Assessing overall

Fit 136

Selecting the Factor Extraction Method 138

Stopping Rules: Criteria for the Number of Factors to

Extract 140

Alternatives to Principal Components and Common Factor

Analysis 144

Stage 5: interpreting the Factors 146

The Three Processes of Factor Interpretation 146

Factor Extraction 147

Rotation of Factors 147

Judging the Significance of Factor Loadings 151

Interpreting a Factor Matrix 153

Stage 6: Validation of exploratory Factor

Analysis 158

Use of Replication or a Confirmatory Perspective 158

Assessing Factor Structure Stability 159

Detecting Influential Observations 159

Stage 7: Data Reduction—Additional Uses of

exploratory Factor Analysis Results 159

Selecting Surrogate Variables for Subsequent

Analysis 160

Creating Summated Scales 160

Computing Factor Scores 163

Selecting among the Three Methods 164

An illustrative example 165

Stage 1: Objectives of Factor Analysis 165

Stage 2: Designing a Factor Analysis 165

Stage 3: Assumptions in Factor Analysis 165

Principal Component Factor Analysis: Stages 4–7 168

Common Factor Analysis: Stages 4 and 5 181

A Managerial Overview of the Results 183

Summary 184

Questions 187

Suggested Readings and online Resources 187

References 187

4 cluster Analysis 189

What is cluster Analysis? 192

Cluster Analysis as a Multivariate Technique 192

Conceptual Development with Cluster Analysis 192

Necessity of Conceptual Support in Cluster Analysis 193

How Does cluster Analysis Work? 193

A Simple Example 194

Objective Versus Subjective Considerations 199

cluster Analysis Decision Process 199

Stage 1: Objectives of Cluster Analysis 199

Stage 2: Research Design in Cluster Analysis 202

Stage 3: Assumptions in Cluster Analysis 211

Stage 4: Deriving Clusters and Assessing Overall Fit 212

Stage 5: Interpretation of the Clusters 227

Stage 6: Validation and Profiling of the Clusters 228

implication of Big Data Analytics 230

Challenges 230

An illustrative example 230

Stage 1: Objectives of the Cluster Analysis 231

Stage 2: Research Design of the Cluster Analysis 232

Stage 3: Assumptions in Cluster Analysis 235

Stages 4–6: Employing Hierarchical and Nonhierarchical

Methods 235

Part 1: Hierarchical Cluster Analysis (Stage 4) 235

Part 2: Nonhierarchical Cluster Analysis

(Stages 4–6) 245

Examining an Alternative Cluster Solution:

Stages 4–6 251

A Managerial Overview of the Clustering Process 252

Summary 253

Questions 254

Suggested Readings and online Resources 255

References 255

Section iii

Dependence techniques – Metric

outcomes 257

5 Multiple Regression Analysis 259

What is Multiple Regression Analysis? 265

Multiple Regression in the era of Big Data 265

An example of Simple and Multiple

Regression 266

Prediction Using a Single Independent Variable:

Simple Regression 267

Prediction Using Several Independent Variables:

Multiple Regression 269

Summary 271

A Decision Process for Multiple Regression

Analysis 272

Stage 1: objectives of Multiple Regression 273

Research Problems Appropriate for Multiple

Regression 273

Specifying a Statistical Relationship 274

Selection of Dependent and Independent Variables 275

Stage 2: Research Design of a Multiple Regression

Analysis 278

Sample Size 278

Creating Additional Variables 281

Overview 286

Stage 3: Assumptions in Multiple Regression

Analysis 287

Assessing Individual Variables Versus the Variate 287

Methods of Diagnosis 288

Linearity of the Phenomenon 288

Constant Variance of the Error Term 290

Normality of the Error Term Distribution 291

Independence of the Error Terms 291

Summary 292

Stage 4: estimating the Regression Model

and Assessing overall Model Fit 292

Managing the Variate 292

Variable Specification 294

Variable Selection 295

Testing the Regression Variate for Meeting the Regression

Assumptions 298

Examining the Statistical Significance of Our Model 299

Understanding Influential Observations 302

Stage 5: interpreting the Regression Variate 308

Using the Regression Coefficients 308

Assessing Multicollinearity 311

Relative Importance of Independent Variables 317

Summary 320

Stage 6: Validation of the Results 321

Additional or Split Samples 321

Calculating the PRESS Statistic 321

Comparing Regression Models 322

Forecasting with the Model 322

extending Multiple Regression 322

Multilevel Models 323

Panel Models 328

illustration of a Regression Analysis 331

Stage 1: Objectives of Multiple Regression 331

Stage 2: Research Design of a Multiple Regression

Analysis 331

Stage 3: Assumptions in Multiple Regression

Analysis 332

Stage 4: Estimating the Regression Model and Assessing

Overall Model Fit 332

Stage 5: Interpreting the Regression Variate 348

Stage 6: Validating the Results 353

evaluating Alternative Regression Models 355

Confirmatory Regression Model 355

Use of Summated Scales as Remedies for

Multicollinearity 357

Including a Nonmetric Independent Variable 361

A Managerial Overview of the Results 361

Summary 363

Questions 366

Suggested Readings and online Resources 367

References 367

6 MAnoVA: extending AnoVA 371

Re-emergence of experimentation 376

experimental Approaches Versus other Multivariate

Methods 376

MAnoVA: extending Univariate Methods for

Assessing Group Differences 377

Multivariate Procedures for Assessing Group

Differences 377

A Hypothetical illustration of MAnoVA 381

Analysis Design 381

Differences from Discriminant Analysis 381

Forming the Variate and Assessing Differences 382

A Decision Process for MAnoVA 383

Stage 1: objectives of MAnoVA 385

When Should We Use MANOVA? 385

Types of Multivariate Questions Suitable for

MANOVA 385

Selecting the Dependent Measures 386

Stage 2: issues in the Research Design of

MAnoVA 387

Types of Research Approaches 387

Types of Variables in Experimental Research 389

Sample Size Requirements—Overall and by

Group 391

Factorial Designs—Two or More Treatments 391

Using Covariates—ANCOVA and MANCOVA 394

Modeling Other Relationships Between Treatment and

Outcome 396

MANOVA Counterparts of Other ANOVA Designs 397

A Special Case of MANOVA: Repeated Measures 397

Stage 3: Assumptions of AnoVA and

MAnoVA 398

Independence 399

Equality of Variance–Covariance Matrices 399

Normality 400

Linearity and Multicollinearity among the Dependent

Variables 401

Sensitivity to Outliers 401

Stage 4: estimation of the MAnoVA Model

and Assessing overall Fit 401

Estimation with the General Linear Model 403

Measures for Significance Testing 403

Statistical Power of the Multivariate Tests 403

Estimating Additional Relationships: Mediation and

Moderation 407

Stage 5: interpretation of the MAnoVA Results 410

Evaluating Covariates 410

Assessing Effects on the Dependent Variate 411

Identifying Differences Between Individual Groups 415

Assessing Significance for Individual Outcome

Variables 417

Interpreting Mediation and Moderation 419

Stage 6: Validation of the Results 421

Advanced issues: causal inference in

nonrandomized Situations 421

Causality in the Social and Behavioral Sciences 422

The Potential Outcomes Approach 423

Counterfactuals in Non-experimental Research

Designs 423

Propensity Score Models 424

Overview 428

Summary 430

illustration of a MAnoVA Analysis 430

Research Setting 430

example 1: Difference Between two independent

Groups 432

Stage 1: Objectives of the Analysis 432

Stage 2: Research Design of the MANOVA 433

Stage 3: Assumptions in MANOVA 433

Stage 4: Estimation of the MANOVA Model and Assessing

Overall Fit 434

Stage 5: Interpretation of the Results 437

Summary 438

example 2: Difference Between K independent

Groups 438

Stage 1: Objectives of the MANOVA 438

Stage 2: Research Design of MANOVA 439

Stage 3: Assumptions IN MANOVA 439

Stage 4: Estimation of the MANOVA Model and Assessing

Overall Fit 440

Stage 5: Interpretation of the Results 443

Summary 444

example 3: A Factorial Design for MAnoVA with

two independent Variables 444

Stage 1: Objectives of the MANOVA 445

Stage 2: Research Design of the MANOVA 445

Stage 3: Assumptions in MANOVA 447

Stage 4: Estimation of the MANOVA Model and Assessing

Overall Fit 448

Stage 5: Interpretation of the Results 451

Summary 452

example 4: Moderation and Mediation 452

Moderation of Distribution System (X5) by Firm

Size (X3) 453

Summary 456

Mediation of Distribution System (X5) By Purchase

Level (X22) 457

Summary 459

A Managerial overview of the Results 459

Summary 460

Questions 463

Suggested Readings and online Resources 464

References 464

Section iV

Dependence techniques –

non-metric outcomes 469

7 Multiple Discriminant Analysis 471

What is Discriminant Analysis? 474

The Variate 474

Testing Hypotheses 475

Similarities to other Multivariate techniques 476

Hypothetical example of Discriminant Analysis 476

A Two-Group Discriminant Analysis: Purchasers Versus

Non-purchasers 476

A Three-Group Example of Discriminant Analysis:

Switching Intentions 481

the Decision Process for Discriminant Analysis 484

Stage 1: objectives of Discriminant Analysis 484

Descriptive Profile Analysis 485

Classification Purposes 485

Stage 2: Research Design for Discriminant

Analysis 485

Selecting Dependent and Independent Variables 485

Sample Size 487

Division of the Sample 488

Stage 3: Assumptions of Discriminant Analysis 488

Impacts on Estimation and Classification 489

Impacts on Interpretation 489

Stage 4: estimation of the Discriminant Model

and Assessing overall Fit 490

Selecting an Estimation Method 491

Statistical Significance 492

Assessing Overall Model Fit 493

Casewise Diagnostics 501

Stage 5: interpretation of the Results 503

Discriminant Weights 503

Discriminant Loadings 503

Partial F Values 504

Interpretation of Two or More Functions 504

Which Interpretive Method to Use? 506

Stage 6: Validation of the Results 506

Validation Procedures 506

Profiling Group Differences 507

A two-Group illustrative example 508

Stage 1: Objectives of Discriminant Analysis 508

Stage 2: Research Design for Discriminant Analysis 508

Stage 3: Assumptions of Discriminant Analysis 509

Stage 4: Estimation of the Discriminant Model and

Assessing Overall Fit 509

Stage 5: Interpretation of the Results 520

Stage 6: Validation of the Results 522

A Managerial Overview 523

A three-Group illustrative example 523

Stage 1: Objectives of Discriminant Analysis 524

Stage 2: Research Design for Discriminant

Analysis 524

Stage 3: Assumptions of Discriminant Analysis 524

Stage 4: Estimation of the Discriminant Model and

Assessing Overall Fit 525

Stage 5: Interpretation of Three-Group Discriminant

Analysis Results 537

Stage 6: Validation of the Discriminant Results 542

A Managerial Overview 543

Summary 544

Questions 546

Suggested Readings and online Resources 547

References 547

8 Logistic Regression: Regression

with a Binary Dependent

Variable 548

What is Logistic Regression? 551

the Decision Process for Logistic Regression 552

Stage 1: objectives of Logistic Regression 552

Explanation 552

Classification 553

Stage 2: Research Design for Logistic

Regression 553

Representation of the Binary Dependent Variable 553

Sample Size 555

Use of Aggregated Data 556

Stage 3: Assumptions of Logistic Regression 556

Stage 4: estimation of the Logistic Regression

Model and Assessing overall Fit 557

Estimating the Logistic Regression Model 558

Assessing the Goodness-of-Fit of the Estimated

Model 563

Overview of Assessing Model Fit 571

Casewise Diagnostics 571

Summary 572

Stage 5: interpretation of the Results 572

Testing for Significance of the Coefficients 573

Interpreting the Coefficients 574

Calculating Probabilities for a Specific Value of

the Independent Variable 578

Overview of Interpreting Coefficients 579

Stage 6: Validation of the Results 579

An illustrative example of Logistic Regression 580

Stage 1: Objectives of Logistic Regression 580

Stage 2: Research Design for Logistic Regression 580

Stage 3: Assumptions of Logistic Regression 581

Stage 4: Estimation of the Logistic Regression Model and

Assessing Overall Fit 581

Stage 5: Interpretation of Results 592

Stage 6: Validation of the Results 596

A Managerial Overview 596

Summary 596

Questions 598

Suggested Readings and online Resources 598

References 598

Section V

Moving Beyond the Basics 601

9 Structural equation Modeling:

An introduction 603

What is Structural equation Modeling? 607

Estimation of Multiple Interrelated Dependence

Relationships 607

Incorporating Latent Variables Not Measured

Directly 608

Defining a Model 610

SeM and other Multivariate techniques 613

Similarity to Dependence Techniques 613

Similarity to Interdependence Techniques 613

The Emergence of SEM 614

the Role of theory in Structural equation

Modeling 614

Specifying Relationships 614

Establishing Causation 615

Developing a Modeling Strategy 618

A Simple example of SeM 619

Theory 619

Setting Up the Structural Equation Model for Path

Analysis 620

The Basics of SEM Estimation and Assessment 621

Six Stages in Structural equation Modeling 625

Stage 1: Defining individual constructs 627

Operationalizing the Construct 627

Pretesting 627

Stage 2: Developing and Specifying the

Measurement Model 627

SEM Notation 628

Creating the Measurement Model 629

Stage 3: Designing a Study to Produce empirical

Results 629

Issues in Research Design 629

Issues in Model Estimation 633

Stage 4: Assessing Measurement Model

Validity 635

The Basics of Goodness-of-Fit 635

Absolute Fit Indices 636

Incremental Fit Indices 638

Parsimony Fit Indices 639

Problems Associated with Using Fit Indices 639

Unacceptable Model Specification to Achieve Fit 641

Guidelines for Establishing Acceptable

and Unacceptable Fit 641

Stage 5: Specifying the Structural Model 643

Stage 6: Assessing the Structural Model

Validity 644

Competitive Fit 645

Testing Structural Relationships 647

Summary 648

Questions 649

Suggested Readings and online Resources 649

Appendix 9A: estimating Relationships Using Path

Analysis 650

Appendix 9B: SeM Abbreviations 653

Appendix 9c: Detail on Selected GoF indices 654

References 656

10 SeM: confirmatory Factor

Analysis 658

What is confirmatory Factor Analysis? 660

CFA and Exploratory Factor Analysis 660

Measurement Theory and Psychometrics 661

A Simple Example of CFA and SEM 661

A Visual Diagram 661

SeM Stages for testing Measurement theory

Validation with cFA 663

Stage 1: Defining individual constructs 663

Stage 2: Developing the overall Measurement

Model 663

Unidimensionality 664

Congeneric Measurement Model 665

Items per Construct 665

Reflective Versus Formative Measurement 668

Stage 3: Designing a Study to Produce empirical

Results 670

Measurement Scales in CFA 670

SEM and Sampling 670

Specifying the Model 670

Issues in Identification 671

Problems in Estimation 673

Stage 4: Assessing Measurement Model

Validity 673

Assessing Fit 674

Path Estimates 674

Construct Validity 675

Model Diagnostics 677

Summary Example 681

cFA illustration 681

Stage 1: Defining Individual Constructs 682

Stage 2: Developing the Overall Measurement

Model 682

Stage 3: Designing a Study to Produce Empirical

Results 684

Stage 4: Assessing Measurement Model Validity 685

HBAT CFA Summary 692

CFA Results Detect Problems 693

Summary 696

Questions 697

Suggested Readings and online Resources 697

References 697

11 testing Structural

equation Models 699

What is a Structural Model? 700

A Simple example of a Structural Model 701

An overview of theory testing with SeM 702

Stages in testing Structural theory 703

One-Step Versus Two-Step Approaches 703

Stage 5: Specifying the Structural Model 703

Unit of Analysis 704

Model Specification Using a Path Diagram 704

Designing the Study 708

Stage 6: Assessing the Structural Model Validity 710

Understanding Structural Model Fit from CFA Fit 710

Examine the Model Diagnostics 712

SeM illustration 713

Stage 5: Specifying the Structural Model 713

Stage 6: Assessing the Structural Model Validity 715

Summary 722

Questions 723

Suggested Readings and online Resources 723

Appendix 11A 724

References 725

12 Advanced SeM topics 726

Reflective Versus Formative Scales 728

Reflective Versus Formative Measurement Theory 728

Operationalizing a Formative Measure 729

Differences Between Reflective and Formative

Measures 730

Which to Use—Reflective or Formative? 732

Higher-order Factor Models 732

Empirical Concerns 733

Theoretical Concerns 734

Using Second-Order Measurement Theories 735

When to Use Higher-Order Factor Analysis 736

Multiple Groups Analysis 736

Measurement Model Comparisons 737

Structural Model Comparisons 741

Measurement type Bias 742

Model Specification 742

Model Interpretation 744

Relationship types: Mediation and Moderation 744

Mediation 745

Moderation 748

Developments in Advanced SeM Approaches 752

Longitudinal Data 752

Latent Growth Models 752

Bayesian SEM 753

Summary 755

Questions 756

Suggested Readings and online Resources 757

References 757

13 Partial Least Squares Structural

equation Modeling (PLS-SeM) 759

What is PLS-SeM? 764

Structural Model 764

Measurement Model 764

Theory and Path Models in PLS-SEM 765

The Emergence of SEM 765

Role of PLS-SEM Versus CB-SEM 766

estimation of Path Models with PLS-SeM 766

Measurement Model Estimation 766

Structural Model Estimation 767

Estimating the Path Model Using the PLS-SEM

Algorithm 767

PLS-SeM Decision Process 768

Stage 1: Defining Research objectives and

Selecting constructs 768

Stage 2: Designing a Study to Produce empirical

Results 769

Metric Versus Nonmetric Data and Multivariate

Normality 769

Missing Data 770

Statistical Power 770

Model Complexity and Sample Size 770

Stage 3: Specifying the Measurement and

Structural Models 771

Measurement Theory and Models 773

Structural Theory and Path Models 774

Stage 4: Assessing Measurement Model

Validity 774

Assessing Reflective Measurement Models 775

Assessing Formative Measurement Models 776

Summary 779

Stage 5: Assessing the Structural Model 779

Collinearity among Predictor Constructs 779

Examining the Coefficient of Determination 780

Effect Size 780

Blindfolding 780

Size and Significance of Path Coefficients 780

Summary 781

Stage 6: Advanced Analyses Using PLS-SeM 782

Multi-Group Analysis of Observed Heterogeneity 782

Detecting Unobserved Heterogeneity 782

Confirmatory Tetrad Analysis 782

Mediation Effects 782

Moderation 783

Higher-Order Measurement Models 783

Summary 783

PLS-SeM illustration 783

Theoretical PLS-SEM Path Model 784

Stage 4: Assessing Measurement Model Reliability

and Validity 785

Path Coefficients 785

Construct Reliability 786

Construct Validity 787

HBAT CCA Summary 790

Stage 5: Assessing the Structural Model 790

HBAT PLS-SEM Summary 791

Summary 792

Questions 793

Suggested Readings and online Resources 793

References 793

Index 800

Acknowledgments xvii

1 overview of Multivariate Methods 1

What is Multivariate Analysis? 3

three converging trends 4

Topic 1: Rise of Big Data 4

Topic 2: Statistical Versus Data Mining Models 7

Topic 3: Causal Inference 9

Summary 9

Multivariate Analysis in Statistical terms 9

Some Basic concepts of Multivariate Analysis 10

The Variate 10

Measurement Scales 11

Measurement Error and Multivariate Measurement 13

Managing the Multivariate Model 14

Managing the Variate 14

Managing the Dependence Model 17

Statistical Significance Versus Statistical Power 18

Review 20

A classification of Multivariate techniques 21

Dependence Techniques 21

Interdependence Techniques 25

types of Multivariate techniques 25

Exploratory Factor Analysis: Principal Components

and Common Factor Analysis 25

Cluster Analysis 26

Multiple Regression 26

Multivariate Analysis of Variance and Covariance 26

Multiple Discriminant Analysis 26

Logistic Regression 27

Structural Equation Modeling and Confirmatory Factor

Analysis 27

Partial Least Squares Structural Equation Modeling 28

Canonical Correlation 28

Conjoint Analysis 28

Perceptual Mapping 29

Correspondence Analysis 29

Guidelines for Multivariate Analyses and

interpretation 29

Establish Practical Significance as Well as Statistical

Significance 30

Recognize That Sample Size Affects All Results 30

Know Your Data 30

Strive for Model Parsimony 31

Look at Your Errors 31

Simplify Your Models By Separation 31

Validate Your Results 32

A Structured Approach to Multivariate Model

Building 32

Stage 1: Define the Research Problem, Objectives,

and Multivariate Technique to Be Used 33

Stage 2: Develop the Analysis Plan 33

Stage 3: Evaluate the Assumptions Underlying the

Multivariate Technique 33

Stage 4: Estimate the Multivariate Model and Assess

Overall Model Fit 34

Stage 5: Interpret the Variate(s) 34

Stage 6: Validate the Multivariate Model 34

A Decision Flowchart 34

Databases 34

Primary Database 35

Other Databases 37

organization of the Remaining chapters 37

Section I: Preparing for a Multivariate Analysis 37

Section II: Interdependence Techniques 38

Sections III and IV: Dependence Techniques 38

Section V: Moving Beyond the Basics 38

Online Resources: Additional Chapters 38

Summary 39

Questions 41

Suggested Readings and online Resources 41

References 41

Section i

Preparing for Multivariate

Analysis 43

2 examining Your Data 45

introduction 49

the challenge of Big Data Research efforts 49

Data Management 50

Data Quality 50

Summary 51

Preliminary examination of the Data 51

Univariate Profiling: Examining the Shape of the

Distribution 51

Bivariate Profiling: Examining the Relationship Between

Variables 52

Bivariate Profiling: Examining Group Differences 53

Multivariate Profiles 54

New Measures of Association 55

Summary 55

Missing Data 56

The Impact of Missing Data 56

Recent Developments in Missing Data Analysis 57

A Simple Example of a Missing Data Analysis 57

A Four-Step Process for Identifying Missing Data

and Applying Remedies 58

An Illustration of Missing Data Diagnosis with the

Four-Step Process 72

outliers 85

Two Different Contexts for Defining Outliers 85

Impacts of Outliers 86

Classifying Outliers 87

Detecting and Handling Outliers 88

An Illustrative Example of Analyzing Outliers 91

testing the Assumptions of Multivariate

Analysis 93

Assessing Individual Variables Versus the Variate 93

Four Important Statistical Assumptions 94

Data transformations 100

Transformations Related to Statistical Properties 101

Transformations Related to Interpretation 101

Transformations Related to Specific Relationship

Types 102

Transformations Related to Simplification 103

General Guidelines for Transformations 104

An illustration of testing the Assumptions

Underlying Multivariate Analysis 105

Normality 105

Homoscedasticity 108

Linearity 108

Summary 112

incorporating nonmetric Data with Dummy

Variables 112

Concept of Dummy Variables 112

Dummy Variable Coding 113

Using Dummy Variables 113

Summary 114

Questions 115

Suggested Readings and online Resources 116

References 116

Section ii

interdependence techniques 119

3 exploratory Factor Analysis 121

What is exploratory Factor Analysis? 124

A Hypothetical example of exploratory Factor

Analysis 126

Factor Analysis Decision Process 127

Stage 1: objectives of Factor Analysis 127

Specifying the Unit of Analysis 127

Achieving Data Summarization Versus Data

Reduction 129

Variable Selection 131

Using Factor Analysis with Other Multivariate

Techniques 131

Stage 2: Designing an exploratory Factor

Analysis 132

Variable Selection and Measurement Issues 132

Sample Size 132

Correlations among Variables or Respondents 133

Stage 3: Assumptions in exploratory Factor

Analysis 135

Conceptual Issues 135

Statistical Issues 135

Summary 136

Stage 4: Deriving Factors and Assessing overall

Fit 136

Selecting the Factor Extraction Method 138

Stopping Rules: Criteria for the Number of Factors to

Extract 140

Alternatives to Principal Components and Common Factor

Analysis 144

Stage 5: interpreting the Factors 146

The Three Processes of Factor Interpretation 146

Factor Extraction 147

Rotation of Factors 147

Judging the Significance of Factor Loadings 151

Interpreting a Factor Matrix 153

Stage 6: Validation of exploratory Factor

Analysis 158

Use of Replication or a Confirmatory Perspective 158

Assessing Factor Structure Stability 159

Detecting Influential Observations 159

Stage 7: Data Reduction—Additional Uses of

exploratory Factor Analysis Results 159

Selecting Surrogate Variables for Subsequent

Analysis 160

Creating Summated Scales 160

Computing Factor Scores 163

Selecting among the Three Methods 164

An illustrative example 165

Stage 1: Objectives of Factor Analysis 165

Stage 2: Designing a Factor Analysis 165

Stage 3: Assumptions in Factor Analysis 165

Principal Component Factor Analysis: Stages 4–7 168

Common Factor Analysis: Stages 4 and 5 181

A Managerial Overview of the Results 183

Summary 184

Questions 187

Suggested Readings and online Resources 187

References 187

4 cluster Analysis 189

What is cluster Analysis? 192

Cluster Analysis as a Multivariate Technique 192

Conceptual Development with Cluster Analysis 192

Necessity of Conceptual Support in Cluster Analysis 193

How Does cluster Analysis Work? 193

A Simple Example 194

Objective Versus Subjective Considerations 199

cluster Analysis Decision Process 199

Stage 1: Objectives of Cluster Analysis 199

Stage 2: Research Design in Cluster Analysis 202

Stage 3: Assumptions in Cluster Analysis 211

Stage 4: Deriving Clusters and Assessing Overall Fit 212

Stage 5: Interpretation of the Clusters 227

Stage 6: Validation and Profiling of the Clusters 228

implication of Big Data Analytics 230

Challenges 230

An illustrative example 230

Stage 1: Objectives of the Cluster Analysis 231

Stage 2: Research Design of the Cluster Analysis 232

Stage 3: Assumptions in Cluster Analysis 235

Stages 4–6: Employing Hierarchical and Nonhierarchical

Methods 235

Part 1: Hierarchical Cluster Analysis (Stage 4) 235

Part 2: Nonhierarchical Cluster Analysis

(Stages 4–6) 245

Examining an Alternative Cluster Solution:

Stages 4–6 251

A Managerial Overview of the Clustering Process 252

Summary 253

Questions 254

Suggested Readings and online Resources 255

References 255

Section iii

Dependence techniques – Metric

outcomes 257

5 Multiple Regression Analysis 259

What is Multiple Regression Analysis? 265

Multiple Regression in the era of Big Data 265

An example of Simple and Multiple

Regression 266

Prediction Using a Single Independent Variable:

Simple Regression 267

Prediction Using Several Independent Variables:

Multiple Regression 269

Summary 271

A Decision Process for Multiple Regression

Analysis 272

Stage 1: objectives of Multiple Regression 273

Research Problems Appropriate for Multiple

Regression 273

Specifying a Statistical Relationship 274

Selection of Dependent and Independent Variables 275

Stage 2: Research Design of a Multiple Regression

Analysis 278

Sample Size 278

Creating Additional Variables 281

Overview 286

Stage 3: Assumptions in Multiple Regression

Analysis 287

Assessing Individual Variables Versus the Variate 287

Methods of Diagnosis 288

Linearity of the Phenomenon 288

Constant Variance of the Error Term 290

Normality of the Error Term Distribution 291

Independence of the Error Terms 291

Summary 292

Stage 4: estimating the Regression Model

and Assessing overall Model Fit 292

Managing the Variate 292

Variable Specification 294

Variable Selection 295

Testing the Regression Variate for Meeting the Regression

Assumptions 298

Examining the Statistical Significance of Our Model 299

Understanding Influential Observations 302

Stage 5: interpreting the Regression Variate 308

Using the Regression Coefficients 308

Assessing Multicollinearity 311

Relative Importance of Independent Variables 317

Summary 320

Stage 6: Validation of the Results 321

Additional or Split Samples 321

Calculating the PRESS Statistic 321

Comparing Regression Models 322

Forecasting with the Model 322

extending Multiple Regression 322

Multilevel Models 323

Panel Models 328

illustration of a Regression Analysis 331

Stage 1: Objectives of Multiple Regression 331

Stage 2: Research Design of a Multiple Regression

Analysis 331

Stage 3: Assumptions in Multiple Regression

Analysis 332

Stage 4: Estimating the Regression Model and Assessing

Overall Model Fit 332

Stage 5: Interpreting the Regression Variate 348

Stage 6: Validating the Results 353

evaluating Alternative Regression Models 355

Confirmatory Regression Model 355

Use of Summated Scales as Remedies for

Multicollinearity 357

Including a Nonmetric Independent Variable 361

A Managerial Overview of the Results 361

Summary 363

Questions 366

Suggested Readings and online Resources 367

References 367

6 MAnoVA: extending AnoVA 371

Re-emergence of experimentation 376

experimental Approaches Versus other Multivariate

Methods 376

MAnoVA: extending Univariate Methods for

Assessing Group Differences 377

Multivariate Procedures for Assessing Group

Differences 377

A Hypothetical illustration of MAnoVA 381

Analysis Design 381

Differences from Discriminant Analysis 381

Forming the Variate and Assessing Differences 382

A Decision Process for MAnoVA 383

Stage 1: objectives of MAnoVA 385

When Should We Use MANOVA? 385

Types of Multivariate Questions Suitable for

MANOVA 385

Selecting the Dependent Measures 386

Stage 2: issues in the Research Design of

MAnoVA 387

Types of Research Approaches 387

Types of Variables in Experimental Research 389

Sample Size Requirements—Overall and by

Group 391

Factorial Designs—Two or More Treatments 391

Using Covariates—ANCOVA and MANCOVA 394

Modeling Other Relationships Between Treatment and

Outcome 396

MANOVA Counterparts of Other ANOVA Designs 397

A Special Case of MANOVA: Repeated Measures 397

Stage 3: Assumptions of AnoVA and

MAnoVA 398

Independence 399

Equality of Variance–Covariance Matrices 399

Normality 400

Linearity and Multicollinearity among the Dependent

Variables 401

Sensitivity to Outliers 401

Stage 4: estimation of the MAnoVA Model

and Assessing overall Fit 401

Estimation with the General Linear Model 403

Measures for Significance Testing 403

Statistical Power of the Multivariate Tests 403

Estimating Additional Relationships: Mediation and

Moderation 407

Stage 5: interpretation of the MAnoVA Results 410

Evaluating Covariates 410

Assessing Effects on the Dependent Variate 411

Identifying Differences Between Individual Groups 415

Assessing Significance for Individual Outcome

Variables 417

Interpreting Mediation and Moderation 419

Stage 6: Validation of the Results 421

Advanced issues: causal inference in

nonrandomized Situations 421

Causality in the Social and Behavioral Sciences 422

The Potential Outcomes Approach 423

Counterfactuals in Non-experimental Research

Designs 423

Propensity Score Models 424

Overview 428

Summary 430

illustration of a MAnoVA Analysis 430

Research Setting 430

example 1: Difference Between two independent

Groups 432

Stage 1: Objectives of the Analysis 432

Stage 2: Research Design of the MANOVA 433

Stage 3: Assumptions in MANOVA 433

Stage 4: Estimation of the MANOVA Model and Assessing

Overall Fit 434

Stage 5: Interpretation of the Results 437

Summary 438

example 2: Difference Between K independent

Groups 438

Stage 1: Objectives of the MANOVA 438

Stage 2: Research Design of MANOVA 439

Stage 3: Assumptions IN MANOVA 439

Stage 4: Estimation of the MANOVA Model and Assessing

Overall Fit 440

Stage 5: Interpretation of the Results 443

Summary 444

example 3: A Factorial Design for MAnoVA with

two independent Variables 444

Stage 1: Objectives of the MANOVA 445

Stage 2: Research Design of the MANOVA 445

Stage 3: Assumptions in MANOVA 447

Stage 4: Estimation of the MANOVA Model and Assessing

Overall Fit 448

Stage 5: Interpretation of the Results 451

Summary 452

example 4: Moderation and Mediation 452

Moderation of Distribution System (X5) by Firm

Size (X3) 453

Summary 456

Mediation of Distribution System (X5) By Purchase

Level (X22) 457

Summary 459

A Managerial overview of the Results 459

Summary 460

Questions 463

Suggested Readings and online Resources 464

References 464

Section iV

Dependence techniques –

non-metric outcomes 469

7 Multiple Discriminant Analysis 471

What is Discriminant Analysis? 474

The Variate 474

Testing Hypotheses 475

Similarities to other Multivariate techniques 476

Hypothetical example of Discriminant Analysis 476

A Two-Group Discriminant Analysis: Purchasers Versus

Non-purchasers 476

A Three-Group Example of Discriminant Analysis:

Switching Intentions 481

the Decision Process for Discriminant Analysis 484

Stage 1: objectives of Discriminant Analysis 484

Descriptive Profile Analysis 485

Classification Purposes 485

Stage 2: Research Design for Discriminant

Analysis 485

Selecting Dependent and Independent Variables 485

Sample Size 487

Division of the Sample 488

Stage 3: Assumptions of Discriminant Analysis 488

Impacts on Estimation and Classification 489

Impacts on Interpretation 489

Stage 4: estimation of the Discriminant Model

and Assessing overall Fit 490

Selecting an Estimation Method 491

Statistical Significance 492

Assessing Overall Model Fit 493

Casewise Diagnostics 501

Stage 5: interpretation of the Results 503

Discriminant Weights 503

Discriminant Loadings 503

Partial F Values 504

Interpretation of Two or More Functions 504

Which Interpretive Method to Use? 506

Stage 6: Validation of the Results 506

Validation Procedures 506

Profiling Group Differences 507

A two-Group illustrative example 508

Stage 1: Objectives of Discriminant Analysis 508

Stage 2: Research Design for Discriminant Analysis 508

Stage 3: Assumptions of Discriminant Analysis 509

Stage 4: Estimation of the Discriminant Model and

Assessing Overall Fit 509

Stage 5: Interpretation of the Results 520

Stage 6: Validation of the Results 522

A Managerial Overview 523

A three-Group illustrative example 523

Stage 1: Objectives of Discriminant Analysis 524

Stage 2: Research Design for Discriminant

Analysis 524

Stage 3: Assumptions of Discriminant Analysis 524

Stage 4: Estimation of the Discriminant Model and

Assessing Overall Fit 525

Stage 5: Interpretation of Three-Group Discriminant

Analysis Results 537

Stage 6: Validation of the Discriminant Results 542

A Managerial Overview 543

Summary 544

Questions 546

Suggested Readings and online Resources 547

References 547

8 Logistic Regression: Regression

with a Binary Dependent

Variable 548

What is Logistic Regression? 551

the Decision Process for Logistic Regression 552

Stage 1: objectives of Logistic Regression 552

Explanation 552

Classification 553

Stage 2: Research Design for Logistic

Regression 553

Representation of the Binary Dependent Variable 553

Sample Size 555

Use of Aggregated Data 556

Stage 3: Assumptions of Logistic Regression 556

Stage 4: estimation of the Logistic Regression

Model and Assessing overall Fit 557

Estimating the Logistic Regression Model 558

Assessing the Goodness-of-Fit of the Estimated

Model 563

Overview of Assessing Model Fit 571

Casewise Diagnostics 571

Summary 572

Stage 5: interpretation of the Results 572

Testing for Significance of the Coefficients 573

Interpreting the Coefficients 574

Calculating Probabilities for a Specific Value of

the Independent Variable 578

Overview of Interpreting Coefficients 579

Stage 6: Validation of the Results 579

An illustrative example of Logistic Regression 580

Stage 1: Objectives of Logistic Regression 580

Stage 2: Research Design for Logistic Regression 580

Stage 3: Assumptions of Logistic Regression 581

Stage 4: Estimation of the Logistic Regression Model and

Assessing Overall Fit 581

Stage 5: Interpretation of Results 592

Stage 6: Validation of the Results 596

A Managerial Overview 596

Summary 596

Questions 598

Suggested Readings and online Resources 598

References 598

Section V

Moving Beyond the Basics 601

9 Structural equation Modeling:

An introduction 603

What is Structural equation Modeling? 607

Estimation of Multiple Interrelated Dependence

Relationships 607

Incorporating Latent Variables Not Measured

Directly 608

Defining a Model 610

SeM and other Multivariate techniques 613

Similarity to Dependence Techniques 613

Similarity to Interdependence Techniques 613

The Emergence of SEM 614

the Role of theory in Structural equation

Modeling 614

Specifying Relationships 614

Establishing Causation 615

Developing a Modeling Strategy 618

A Simple example of SeM 619

Theory 619

Setting Up the Structural Equation Model for Path

Analysis 620

The Basics of SEM Estimation and Assessment 621

Six Stages in Structural equation Modeling 625

Stage 1: Defining individual constructs 627

Operationalizing the Construct 627

Pretesting 627

Stage 2: Developing and Specifying the

Measurement Model 627

SEM Notation 628

Creating the Measurement Model 629

Stage 3: Designing a Study to Produce empirical

Results 629

Issues in Research Design 629

Issues in Model Estimation 633

Stage 4: Assessing Measurement Model

Validity 635

The Basics of Goodness-of-Fit 635

Absolute Fit Indices 636

Incremental Fit Indices 638

Parsimony Fit Indices 639

Problems Associated with Using Fit Indices 639

Unacceptable Model Specification to Achieve Fit 641

Guidelines for Establishing Acceptable

and Unacceptable Fit 641

Stage 5: Specifying the Structural Model 643

Stage 6: Assessing the Structural Model

Validity 644

Competitive Fit 645

Testing Structural Relationships 647

Summary 648

Questions 649

Suggested Readings and online Resources 649

Appendix 9A: estimating Relationships Using Path

Analysis 650

Appendix 9B: SeM Abbreviations 653

Appendix 9c: Detail on Selected GoF indices 654

References 656

10 SeM: confirmatory Factor

Analysis 658

What is confirmatory Factor Analysis? 660

CFA and Exploratory Factor Analysis 660

Measurement Theory and Psychometrics 661

A Simple Example of CFA and SEM 661

A Visual Diagram 661

SeM Stages for testing Measurement theory

Validation with cFA 663

Stage 1: Defining individual constructs 663

Stage 2: Developing the overall Measurement

Model 663

Unidimensionality 664

Congeneric Measurement Model 665

Items per Construct 665

Reflective Versus Formative Measurement 668

Stage 3: Designing a Study to Produce empirical

Results 670

Measurement Scales in CFA 670

SEM and Sampling 670

Specifying the Model 670

Issues in Identification 671

Problems in Estimation 673

Stage 4: Assessing Measurement Model

Validity 673

Assessing Fit 674

Path Estimates 674

Construct Validity 675

Model Diagnostics 677

Summary Example 681

cFA illustration 681

Stage 1: Defining Individual Constructs 682

Stage 2: Developing the Overall Measurement

Model 682

Stage 3: Designing a Study to Produce Empirical

Results 684

Stage 4: Assessing Measurement Model Validity 685

HBAT CFA Summary 692

CFA Results Detect Problems 693

Summary 696

Questions 697

Suggested Readings and online Resources 697

References 697

11 testing Structural

equation Models 699

What is a Structural Model? 700

A Simple example of a Structural Model 701

An overview of theory testing with SeM 702

Stages in testing Structural theory 703

One-Step Versus Two-Step Approaches 703

Stage 5: Specifying the Structural Model 703

Unit of Analysis 704

Model Specification Using a Path Diagram 704

Designing the Study 708

Stage 6: Assessing the Structural Model Validity 710

Understanding Structural Model Fit from CFA Fit 710

Examine the Model Diagnostics 712

SeM illustration 713

Stage 5: Specifying the Structural Model 713

Stage 6: Assessing the Structural Model Validity 715

Summary 722

Questions 723

Suggested Readings and online Resources 723

Appendix 11A 724

References 725

12 Advanced SeM topics 726

Reflective Versus Formative Scales 728

Reflective Versus Formative Measurement Theory 728

Operationalizing a Formative Measure 729

Differences Between Reflective and Formative

Measures 730

Which to Use—Reflective or Formative? 732

Higher-order Factor Models 732

Empirical Concerns 733

Theoretical Concerns 734

Using Second-Order Measurement Theories 735

When to Use Higher-Order Factor Analysis 736

Multiple Groups Analysis 736

Measurement Model Comparisons 737

Structural Model Comparisons 741

Measurement type Bias 742

Model Specification 742

Model Interpretation 744

Relationship types: Mediation and Moderation 744

Mediation 745

Moderation 748

Developments in Advanced SeM Approaches 752

Longitudinal Data 752

Latent Growth Models 752

Bayesian SEM 753

Summary 755

Questions 756

Suggested Readings and online Resources 757

References 757

13 Partial Least Squares Structural

equation Modeling (PLS-SeM) 759

What is PLS-SeM? 764

Structural Model 764

Measurement Model 764

Theory and Path Models in PLS-SEM 765

The Emergence of SEM 765

Role of PLS-SEM Versus CB-SEM 766

estimation of Path Models with PLS-SeM 766

Measurement Model Estimation 766

Structural Model Estimation 767

Estimating the Path Model Using the PLS-SEM

Algorithm 767

PLS-SeM Decision Process 768

Stage 1: Defining Research objectives and

Selecting constructs 768

Stage 2: Designing a Study to Produce empirical

Results 769

Metric Versus Nonmetric Data and Multivariate

Normality 769

Missing Data 770

Statistical Power 770

Model Complexity and Sample Size 770

Stage 3: Specifying the Measurement and

Structural Models 771

Measurement Theory and Models 773

Structural Theory and Path Models 774

Stage 4: Assessing Measurement Model

Validity 774

Assessing Reflective Measurement Models 775

Assessing Formative Measurement Models 776

Summary 779

Stage 5: Assessing the Structural Model 779

Collinearity among Predictor Constructs 779

Examining the Coefficient of Determination 780

Effect Size 780

Blindfolding 780

Size and Significance of Path Coefficients 780

Summary 781

Stage 6: Advanced Analyses Using PLS-SeM 782

Multi-Group Analysis of Observed Heterogeneity 782

Detecting Unobserved Heterogeneity 782

Confirmatory Tetrad Analysis 782

Mediation Effects 782

Moderation 783

Higher-Order Measurement Models 783

Summary 783

PLS-SeM illustration 783

Theoretical PLS-SEM Path Model 784

Stage 4: Assessing Measurement Model Reliability

and Validity 785

Path Coefficients 785

Construct Reliability 786

Construct Validity 787

HBAT CCA Summary 790

Stage 5: Assessing the Structural Model 790

HBAT PLS-SEM Summary 791

Summary 792

Questions 793

Suggested Readings and online Resources 793

References 793

Index 800