CONTENTS Preface iii About the Authors v Chapter 1 Introduction: Methods and Model Building 1 What Is Multivariate Analysis? 3 Multivariate Analysis in Statistical Terms 4 Some Basic Concepts of Multivariate Analysis 4 The Variate 4 Measurement 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 Power 9 Using Power with Multivariate Techniques 11 A Classification of Multivariate Techniques 11 Dependence Techniques 14 Interdependence Techniques 14 Types of Multivariate Techniques 15 Principal Components and Common Factor Analysis 16 Multiple Regression 16 Multiple Discriminant Analysis and Logistic Regression 16 Canonical Correlation 17 Multivariate Analysis of Variance and Covariance 17 Conjoint Analysis 18 Cluster Analysis 18 Perceptual Mapping 19 Correspondence Analysis 19 Structural Equation Modeling and Confirmatory Factor Analysis 19 Guidelines for Multivariate Analyses and Interpretation 20 Establish Practical Significance as Well as Statistical Significance 20 Recognize That Sample Size Affects All Results 21 Know Your Data 21 Strive for Model Parsimony 21 Look at Your Errors 22 Validate Your Results 22 A Structured Approach to Multivariate Model Building 22 Stage 1: Define the Research Problem, Objectives, and Multivariate Technique to Be Used 23 Stage 2: Develop the Analysis Plan 23 Stage 3: Evaluate the Assumptions Underlying the Multivariate Technique 23 Stage 4: Estimate the Multivariate Model and Assess Overall Model Fit 23 Stage 5: Interpret the Variate(s) 24 Stage 6: Validate the Multivariate Model 24 A Decision Flowchart 24 Databases 24 Primary Database 25 Other Databases 27 Organization of the Remaining Chapters 28 Section I: Understanding and Preparing For Multivariate Analysis 28 Section II: Analysis Using Dependence Techniques 28 Section III: Interdependence Techniques 28 Section IV: Structural Equations Modeling 28 Summary 28 . Questions 30 . Suggested Readings 30 References 30 SECTION I Understanding and Preparing For Multivariate Analysis 31 Chapter 2 Cleaning and Transforming Data 33 Introduction 36 Graphical Examination of the Data 37 Univariate Profiling: Examining the Shape of the Distribution 38 Bivariate Profiling: Examining the Relationship Between Variables 39 Bivariate Profiling: Examining Group Differences 40 Multivariate Profiles 41 Missing Data 42 The Impact of Missing Data 42 A Simple Example of a Missing Data Analysis 43 A Four-Step Process for Identifying Missing Data and Applying Remedies 44 An Illustration of Missing Data Diagnosis with the Four-Step Process 54 Outliers 64 Detecting and Handling Outliers 65 An Illustrative Example of Analyzing Outliers 68 Testing the Assumptions of Multivariate Analysis 70 Assessing Individual Variables Versus the Variate 70 Four Important Statistical Assumptions 71 Data Transformations 77 An Illustration of Testing the Assumptions Underlying Multivariate Analysis 79 Incorporating Nonmetric Data with Dummy Variables 86 Summary 88 . Questions 89 . Suggested Readings 89 References 90 Chapter 3 Factor Analysis 91 What Is Factor Analysis? 94 A Hypothetical Example of Factor Analysis 95 Factor Analysis Decision Process 96 Stage 1: Objectives of Factor Analysis 96 Specifying the Unit of Analysis 98 Achieving Data Summarization Versus Data Reduction 98 Variable Selection 99 Using Factor Analysis with Other Multivariate Techniques 100 Stage 2: Designing a Factor Analysis 100 Correlations Among Variables or Respondents 100 Variable Selection and Measurement Issues 101 Sample Size 102 Summary 102 Stage 3: Assumptions in Factor Analysis 103 Conceptual Issues 103 Statistical Issues 103 Summary 104 Stage 4: Deriving Factors and Assessing Overall Fit 105 Selecting the Factor Extraction Method 105 Criteria for the Number of Factors to Extract 108 Stage 5: Interpreting the Factors 112 The Three Processes of Factor Interpretation 112 Rotation of Factors 113 Judging the Significance of Factor Loadings 116 Interpreting a Factor Matrix 118 Stage 6: Validation of Factor Analysis 122 Use of a Confirmatory Perspective 122 Assessing Factor Structure Stability 122 Detecting Influential Observations 123 Stage 7: Additional Uses of Factor Analysis Results 123 Selecting Surrogate Variables for Subsequent Analysis 123 Creating Summated Scales 124 Computing Factor Scores 127 Selecting Among the Three Methods 128 An Illustrative Example 129 Stage 1: Objectives of Factor Analysis 129 Stage 2: Designing a Factor Analysis 129 Stage 3: Assumptions in Factor Analysis 129 Component Factor Analysis: Stages 4 Through 7 132 Common Factor Analysis: Stages 4 and 5 144 A Managerial Overview of the Results 146 Summary 148 . Questions 150 . Suggested Readings 150 References 150 SECTION II Analysis Using Dependence Techniques 153 Chapter 4 Simple and Multiple Regression 155 What Is Multiple Regression Analysis? 161 An Example of Simple and Multiple Regression 162 Prediction Using a Single Independent Variable: Simple Regression 162 Prediction Using Several Independent Variables: Multiple Regression 165 Summary 167 A Decision Process for Multiple Regression Analysis 167 Stage 1: Objectives of Multiple Regression 169 Research Problems Appropriate for Multiple Regression 169 Specifying a Statistical Relationship 171 Selection of Dependent and Independent Variables 171 Stage 2: Research Design of a Multiple Regression Analysis 173 Sample Size 174 Creating Additional Variables 176 Stage 3: Assumptions in Multiple Regression Analysis 181 Assessing Individual Variables Versus the Variate 182 Methods of Diagnosis 183 Linearity of the Phenomenon 183 Constant Variance of the Error Term 185 Independence of the Error Terms 185 Normality of the Error Term Distribution 185 Summary 186 Stage 4: Estimating the Regression Model and Assessing Overall Model Fit 186 Selecting an Estimation Technique 186 Testing the Regression Variate for Meeting the Regression Assumptions 191 Examining the Statistical Significance of Our Model 192 Identifying Influential Observations 194 Stage 5: Interpreting the Regression Variate 197 Using the Regression Coefficients 197 Assessing Multicollinearity 200 Stage 6: Validation of the Results 206 Additional or Split Samples 206 Calculating the PRESS Statistic 206 Comparing Regression Models 206 Forecasting with the Model 207 Illustration of a Regression Analysis 207 Stage 1: Objectives of Multiple Regression 207 Stage 2: Research Design of a Multiple Regression Analysis 208 Stage 3: Assumptions in Multiple Regression Analysis 208 Stage 4: Estimating the Regression Model and Assessing Overall Model Fit 208 Stage 5: Interpreting the Regression Variate 223 Stage 6: Validating the Results 226 Evaluating Alternative Regression Models 227 A Managerial Overview of the Results 231 Summary 231 . Questions 234 . Suggested Readings 234 References 234 Chapter 5 Canonical Correlation 235 What Is Canonical Correlation? 237 Hypothetical Example of Canonical Correlation 238 Developing a Variate of Dependent Variables 238 Estimating the First Canonical Function 238 Estimating a Second Canonical Function 240 Relationships of Canonical Correlation Analysis to Other Multivariate Techniques 241 Stage 1: Objectives of Canonical Correlation Analysis 242 Selection of Variable Sets 242 Evaluating 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 Multicollinearity 244 Stage 4: Deriving the Canonical Functions and Assessing Overall Fit 245 Deriving Canonical Functions 246 Which Canonical Functions Should Be Interpreted? 246 Stage 5: Interpreting the Canonical Variate 250 Canonical Weights 250 Canonical Loadings 250 Canonical Cross-Loadings 250 Which Interpretation Approach to Use 251 Stage 6: Validation and Diagnosis 251 An Illustrative Example 252 Stage 1: Objectives of Canonical Correlation Analysis 253 Stages 2 and 3: Designing a Canonical Correlation Analysis and Testing the Assumptions 253 Stage 4: Deriving the Canonical Functions and Assessing Overall Fit 253 Stage 5: Interpreting the Canonical Variates 254 Stage 6: Validation and Diagnosis 257 A Managerial Overview of the Results 258 Summary 258 . Questions 259 . References 260 Chapter 6 Conjoint Analysis 261 What Is Conjoint Analysis? 266 Hypothetical Example of Conjoint Analysis 267 Specifying Utility, Factors, Levels, and Profiles 267 Gathering Preferences from Respondents 268 Estimating Part-Worths 269 Determining Attribute Importance 270 Assessing Predictive Accuracy 270 The Managerial Uses of Conjoint Analysis 271 Comparing Conjoint Analysis with Other Multivariate Methods 272 Compositional Versus Decompositional Techniques 272 Specifying the Conjoint Variate 272 Separate Models for Each Individual 272 Flexibility in Types of Relationships 273 Designing a Conjoint Analysis Experiment 273 Stage 1: The Objectives of Conjoint Analysis 276 Defining the Total Utility of the Object 276 Specifying the Determinant Factors 276 Stage 2: The Design of a Conjoint Analysis 277 Selecting a Conjoint Analysis Methodology 278 Designing Profiles: Selecting and Defining Factors and Levels 278 Specifying the Basic Model Form 283 Data Collection 286 Stage 3: Assumptions of Conjoint Analysis 293 Stage 4: Estimating the Conjoint Model and Assessing Overall Fit 294 Selecting an Estimation Technique 294 Estimated Part-Worths 297 Evaluating Model Goodness-of-Fit 298 Stage 5: Interpreting the Results 299 Examining the Estimated Part-Worths 300 Assessing the Relative Importance of Attributes 302 Stage 6: Validation of the Conjoint Results 303 Managerial Applications of Conjoint Analysis 303 Segmentation 304 Profitability Analysis 304 Conjoint Simulators 305 Alternative Conjoint Methodologies 306 Adaptive/Self-Explicated Conjoint: Conjoint with a Large Number of Factors 306 Choice-Based Conjoint: Adding Another Touch of Realism 308 Overview of the Three Conjoint Methodologies 312 An Illustration of Conjoint Analysis 312 Stage 1: Objectives of the Conjoint Analysis 313 Stage 2: Design of the Conjoint Analysis 313 Stage 3: Assumptions in Conjoint Analysis 316 Stage 4: Estimating the Conjoint Model and Assessing Overall Model Fit 316 Stage 5: Interpreting the Results 320 Stage 6: Validation of the Results 324 A Managerial Application: Use of a Choice Simulator 325 Summary 327 . Questions 330 . Suggested Readings 330 References 330 Chapter 7 Multiple Discriminant Analysis and Logistic Regression 335 What Are Discriminant Analysis and Logistic Regression? 339 Discriminant Analysis 340 Logistic Regression 341 Analogy with Regression and MANOVA 341 Hypothetical Example of Discriminant Analysis 342 A Two-Group Discriminant Analysis: Purchasers Versus Nonpurchasers 342 A Geometric Representation of the Two-Group Discriminant Function 345 A Three-Group Example of Discriminant Analysis: Switching Intentions 346 The Decision Process for Discriminant Analysis 348 Stage 1: Objectives of Discriminant Analysis 350 Stage 2: Research Design for Discriminant Analysis 351 Selecting Dependent and Independent Variables 351 Sample Size 353 Division of the Sample 353 Stage 3: Assumptions of Discriminant Analysis 354 Impacts on Estimation and Classification 354 Impacts on Interpretation 355 Stage 4: Estimation of the Discriminant Model and Assessing Overall Fit 356 Selecting an Estimation Method 356 Statistical Significance 358 Assessing Overall Model Fit 359 Casewise Diagnostics 368 Stage 5: Interpretation of the Results 369 Discriminant Weights 369 Discriminant Loadings 370 Partial F Values 370 Interpretation of Two or More Functions 370 Which Interpretive Method to Use? 373 Stage 6: Validation of the Results 373 Validation Procedures 373 Profiling Group Differences 374 A Two-Group Illustrative Example 375 Stage 1: Objectives of Discriminant Analysis 375 Stage 2: Research Design for Discriminant Analysis 375 Stage 3: Assumptions of Discriminant Analysis 376 Stage 4: Estimation of the Discriminant Model and Assessing Overall Fit 376 Stage 5: Interpretation of the Results 387 Stage 6: Validation of the Results 390 A Managerial Overview 391 A Three-Group Illustrative Example 391 Stage 1: Objectives of Discriminant Analysis 391 Stage 2: Research Design for Discriminant Analysis 392 Stage 3: Assumptions of Discriminant Analysis 392 Stage 4: Estimation of the Discriminant Model and Assessing Overall Fit 392 Stage 5: Interpretation of Three-Group Discriminant Analysis Results 404 Stage 6: Validation of the Discriminant Results 410 A Managerial Overview 412 Logistic Regression: Regression with a Binary Dependent Variable 413 Representation of the Binary Dependent Variable 414 Sample Size 415 Estimating the Logistic Regression Model 416 Assessing the Goodness-of-Fit of the Estimation Model 419 Testing for Significance of the Coefficients 421 Interpreting the Coefficients 422 Calculating Probabilities for a Specific Value of the Independent Variable 425 Overview of Interpreting Coefficients 425 Summary 425 An Illustrative Example of Logistic Regression 426 Stages 1, 2, and 3: Research Objectives, Research Design, and Statistical Assumptions 426 Stage 4: Estimation of the Logistic Regression Model and Assessing Overall Fit 426 Stage 5: Interpretation of the Results 432 Stage 6: Validation of the Results 433 A Managerial Overview 434 Summary 434 . Questions 437 . Suggested Readings 437 References 437 Chapter 8 ANOVA and MANOVA 439 MANOVA: Extending Univariate Methods for Assessing Group Differences 443 Multivariate Procedures for Assessing Group Differences 444 A Hypothetical Illustration of MANOVA 447 Analysis Design 447 Differences from Discriminant Analysis 448 Forming the Variate and Assessing Differences 448 A Decision Process for MANOVA 449 Stage 1: Objectives of MANOVA 450 When Should We Use MANOVA? 450 Types of Multivariate Questions Suitable for MANOVA 451 Selecting the Dependent Measures 452 Stage 2: Issues in the Research Design of MANOVA 453 Sample Size Requirements—Overall and by Group 453 Factorial Designs—Two or More Treatments 453 Using Covariates—ANCOVA and MANCOVA 455 MANOVA Counterparts of Other ANOVA Designs 457 A Special Case of MANOVA: Repeated Measures 457 Stage 3: Assumptions of ANOVA and MANOVA 458 Independence 458 Equality of Variance–Covariance Matrices 459 Normality 460 Linearity and Multicollinearity Among the Dependent Variables 460 Sensitivity to Outliers 460 Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit 460 Estimation with the General Linear Model 462 Criteria for Significance Testing 463 Statistical Power of the Multivariate Tests 463 Stage 5: Interpretation of the MANOVA Results 468 Evaluating Covariates 468 Assessing Effects on the Dependent Variate 468 Identifying Differences Between Individual Groups 472 Assessing Significance for Individual Dependent Variables 474 Stage 6: Validation of the Results 475 Summary 476 Illustration of a MANOVA Analysis 476 Example 1: Difference Between Two Independent Groups 477 Stage 1: Objectives of the Analysis 478 Stage 2: Research Design of the MANOVA 478 Stage 3: Assumptions in MANOVA 479 Stage 4: Estimation of the MANOVA Model and Assessing the Overall Fit 480 Stage 5: Interpretation of the Results 482 Example 2: Difference Between K Independent Groups 482 Stage 1: Objectives of the MANOVA 483 Stage 2: Research Design of MANOVA 483 Stage 3: Assumptions in MANOVA 484 Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit 485 Stage 5: Interpretation of the Results 485 Example 3: A Factorial Design for MANOVA with Two Independent Variables 488 Stage 1: Objectives of the MANOVA 489 Stage 2: Research Design of the MANOVA 489 Stage 3: Assumptions in MANOVA 491 Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit 492 Stage 5: Interpretation of the Results 495 Summary 496 A Managerial Overview of the Results 496 Summary 498 . Questions 500 . Suggested Readings 500 References 500 SECTION III Analysis Using Interdependence Techniques 503 Chapter 9 Grouping Data with Cluster Analysis 505 What Is Cluster Analysis? 508 Cluster Analysis as a Multivariate Technique 508 Conceptual Development with Cluster Analysis 508 Necessity of Conceptual Support in Cluster Analysis 509 How Does Cluster Analysis Work? 510 A Simple Example 510 Objective Versus Subjective Considerations 515 Cluster Analysis Decision Process 515 Stage 1: Objectives of Cluster Analysis 517 Stage 2: Research Design in Cluster Analysis 518 Stage 3: Assumptions in Cluster Analysis 526 Stage 4: Deriving Clusters and Assessing Overall Fit 527 Stage 5: Interpretation of the Clusters 538 Stage 6: Validation and Profiling of the Clusters 539 An Illustrative Example 541 Stage 1: Objectives of the Cluster Analysis 541 Stage 2: Research Design of the Cluster Analysis 542 Stage 3: Assumptions in Cluster Analysis 545 Employing Hierarchical and Nonhierarchical Methods 546 Step 1: Hierarchical Cluster Analysis (Stage 4) 546 Step 2: Nonhierarchical Cluster Analysis (Stages 4, 5, and 6) 552 Summary 561 . Questions 563 . Suggested Readings 563 References 563 Chapter 10 MDS and Correspondence Analysis 565 What Is Multidimensional Scaling? 568 Comparing Objects 568 Dimensions: The Basis for Comparison 569 A Simplified Look at How MDS Works 570 Gathering Similarity Judgments 570 Creating a Perceptual Map 570 Interpreting the Axes 571 Comparing MDS to Other Interdependence Techniques 572 Individual as the Unit of Analysis 573 Lack of a Variate 573 A Decision Framework for Perceptual Mapping 573 Stage 1: Objectives of MDS 573 Key Decisions in Setting Objectives 573 Stage 2: Research Design of MDS 578 Selection of Either a Decompositional (Attribute-Free) or Compositional (Attribute-Based) Approach 578 Objects: Their Number and Selection 580 Nonmetric Versus Metric Methods 581 Collection of Similarity or Preference Data 581 Stage 3: Assumptions of MDS Analysis 584 Stage 4: Deriving the MDS Solution and Assessing Overall Fit 584 Determining an Object’s Position in the Perceptual Map 584 Selecting the Dimensionality of the Perceptual Map 586 Incorporating Preferences into MDS 587 Stage 5: Interpreting the MDS Results 592 Identifying the Dimensions 593 Stage 6: Validating the MDS Results 594 Issues in Validation 594 Approaches to Validation 594 Overview of Multidimensional Scaling 595 Correspondence Analysis 595 Distinguishing Characteristics 595 Differences from Other Multivariate Techniques 596 A Simple Example of CA 596 A Decision Framework for Correspondence Analysis 600 Stage 1: Objectives of CA 601 Stage 2: Research Design of CA 601 Stage 3: Assumptions in CA 602 Stage 4: Deriving CA Results and Assessing Overall Fit 602 Stage 5: Interpretation of the Results 603 Stage 6: Validation of the Results 604 Overview of Correspondence Analysis 604 Illustrations of MDS and Correspondence Analysis 605 Stage 1: Objectives of Perceptual Mapping 606 Identifying Objects for Inclusion 606 Basing the Analysis on Similarity or Preference Data 607 Using a Disaggregate or Aggregate Analysis 607 Stage 2: Research Design of the Perceptual Mapping Study 607 Selecting Decompositional or Compositional Methods 607 Selecting Firms for Analysis 608 Nonmetric Versus Metric Methods 608 Collecting Data for MDS 608 Collecting Data for Correspondence Analysis 609 Stage 3: Assumptions in Perceptual Mapping 610 Multidimensional Scaling: Stages 4 and 5 610 Stage 4: Deriving MDS Results and Assessing Overall Fit 610 Stage 5: Interpretation of the Results 615 Overview of the Decompositional Results 616 Correspondence Analysis: Stages 4 and 5 617 Stage 4: Estimating a Correspondence Analysis 617 Stage 5: Interpreting CA Results 619 Overview of CA 621 Stage 6: Validation of the Results 622 A Managerial Overview of MDS Results 622 Summary 623 . Questions 625 . Suggested Readings 625 References 625 SECTION IV Structural Equations Modeling 627 Chapter 11 SEM: An Introduction 629 What Is Structural Equation Modeling? 634 Estimation of Multiple Interrelated Dependence Relationships 635 Incorporating Latent Variables Not Measured Directly 635 Defining a Model 637 SEM and Other Multivariate Techniques 641 Similarity to Dependence Techniques 641 Similarity to Interdependence Techniques 641 The Emergence of SEM 642 The Role of Theory in Structural Equation Modeling 642 Specifying Relationships 642 Establishing Causation 643 Developing a Modeling Strategy 646 A Simple Example of SEM 647 The Research Question 647 Setting Up the Structural Equation Model for Path Analysis 648 The Basics of SEM Estimation and Assessment 649 Six Stages in Structural Equation Modeling 653 Stage 1: Defining Individual Constructs 655 Operationalizing the Construct 655 Pretesting 655 Stage 2: Developing and Specifying the Measurement Model 656 SEM Notation 656 Creating the Measurement Model 657 Stage 3: Designing a Study to Produce Empirical Results 657 Issues in Research Design 658 Issues in Model Estimation 662 Stage 4: Assessing Measurement Model Validity 664 The Basics of Goodness-of-Fit 665 Absolute Fit Indices 666 Incremental Fit Indices 668 Parsimony Fit Indices 669 Problems Associated with Using Fit Indices 669 Unacceptable Model Specification to Achieve Fit 671 Guidelines for Establishing Acceptable and Unacceptable Fit 672 Stage 5: Specifying the Structural Model 673 Stage 6: Assessing the Structural Model Validity 675 Structural Model GOF 675 Competitive Fit 676 Comparison to the Measurement Model 676 Testing Structural Relationships 677 Summary 678 . Questions 680 . Suggested Readings 680 Appendix 11A: Estimating Relationships Using Path Analysis 681 Appendix 11B: SEM Abbreviations 683 Appendix 11C: Detail on Selected GOF Indices 684 References 685 Chapter 12 Applications of SEM 687 Part 1: Confirmatory Factor Analysis 693 CFA and Exploratory Factor Analysis 693 A Simple Example of CFA and SEM 694 A Visual Diagram 694 SEM Stages for Testing Measurement Theory Validation with CFA 695 Stage 1: Defining Individual Constructs 696 Stage 2: Developing the Overall Measurement Model 696 Unidimensionality 696 Congeneric Measurement Model 698 Items per Construct 698 Reflective Versus Formative Constructs 701 Stage 3: Designing a Study to Produce Empirical Results 702 Measurement Scales in CFA 702 SEM and Sampling 703 Specifying the Model 703 Issues in Identification 704 Avoiding Identification Problems 704 Problems in Estimation 706 Stage 4: Assessing Measurement Model Validity 707 Assessing Fit 707 Path Estimates 707 Construct Validity 708 Model Diagnostics 711 Summary Example 713 CFA Illustration 715 Stage 1: Defining Individual Constructs 716 Stage 2: Developing the Overall Measurement Model 716 Stage 3: Designing a Study to Produce Empirical Results 718 Stage 4: Assessing Measurement Model Validity 719 HBAT CFA Summary 727 Part 2: What Is a Structural Model? 727 A Simple Example of a Structural Model 728 An Overview of Theory Testing with SEM 729 Stages in Testing Structural Theory 730 One-Step Versus Two-Step Approaches 730 Stage 5: Specifying the Structural Model 731 Unit of Analysis 731 Model Specification Using a Path Diagram 731 Designing the Study 735 Stage 6: Assessing the Structural Model Validity 737 Understanding Structural Model Fit from CFA Fit 737 Examine the Model Diagnostics 739 SEM Illustration 740 Stage 5: Specifying the Structural Model 740 Stage 6: Assessing the Structural Model Validity 742 Part 3: Extensions and Applications of SEM 749 Reflective Versus Formative Measures 749 Reflective Versus Formative Measurement Theory 749 Operationalizing a Formative Construct 750 Distinguishing Reflective from Formative Constructs 751 Which to Use—Reflective or Formative? 753 Higher-Order Factor Analysis 754 Empirical Concerns 754 Theoretical Concerns 756 Using Second-Order Measurement Theories 756 When to Use Higher-Order Factor Analysis 757 Multiple Groups Analysis 758 Measurement Model Comparisons 758 Structural Model Comparisons 763 Measurement Bias 764 Model Specification 764 Model Interpretation 765 Relationship Types: Mediation and Moderation 766 Mediation 766 Moderation 770 Longitudinal Data 773 Additional Covariance Sources: Timing 773 Using Error Covariances to Represent Added Covariance 774 Partial Least Squares 775 Characteristics of PLS 775 Advantages and Disadvantages of PLS 776 Choosing PLS Versus SEM 777 Summary 778 . Questions 781 . Suggested Readings 781 References 782 Index 785