Multivariate data analysis

Title:

ISBN:

9780138948580

Edition:

4th ed.

Publication Information:

New Jersey : Prentice Hall , 1998.

Physical Description:

730 s. ; 28 sm.

Abstract:

Multıvarıate data analysıs Fıfth edıtıon Haır-anderson-tatham-black Content Preface................................................................. xvii Chapter 1 Introduction ............................................ ı What Is Multivariate Analysis? ........................................ 3 Impact of the Computer Revolution .................................... 5 Multivariate Analysis Defined ......................................... 6 Some Basic Concepts of Multivariate Analysis ........................... 6 The Variate .................................................... 7 Measurement Scales ............................................ 7 Measurement Error and Multivariate Measurement ..................... 9 Statistical Significance versus Statistical Power ........................ 10 Types of Multivariate Techniques ...................................... 13 Principal Components and Common Factor Analysis ................... 14 Multiple Regression ............................................. 14 Multiple Discriminant Analysis ..................................... 14 Multivariate Analysis of Variance and Covariance ...................... 15 Conjoint Analysis ............................................... 15 Canonical Correlation ............................................ 15 Cluster Analysis ................................................ 15 Multidimensional Scaling ......................................... 16 Correspondence Analysis ......................................... 16 Linear Probability Models ......................................... 16 Structural Equation Modeling ...................................... 17 Other Emerging Multivariate Techniques ............................. 17 A Classification of Multivariate Techniques .............................. 18 Guidelines for Multivariate Analyses and Interpretation .................... 22 Establish Practical Significance as Well as Statistical Significance ......... 22 Sample Size Affects All Results .................................... 23 Know Your Data ................................................ 23 Strive for Model Parsimony ....................................... 24 Look at Your Errors .............................................. 24 Validate Your Results ............................................ 24 A Structured Approach to Multivariate Model Building .................... 25 Stage 1: Define the Research Problem, Objectives, and Multivariate Technique to Be Used ......................................... 25 Stage 2: Develop the Analysis Plan ................................. 26 Stage 3: Evaluate the Assumptions Underlying the Multivariate Technique . . 26 Stage 4: Estimate the Multivariate Model and Assess Overall Model Fit .... 26 Stage 5: Interpret the Variate(s) .................................... 27 Stage 6: Validate the Multivariate Model ............................. 27 A Decision Flowchart ............................................ 27 Databases ......................................................... 27 Primary Database ............................................... 28 Other Databases ............................................... 30 Organization of the Remaining Chapters ................................ 30 Summary o Questions o References .................................... 31 Section 1 o Preparing for a Multivariate Analysis ............. 33 Chapter 2 Examining Your Data ................................. 35 Introduction ........................................................ 39 Graphical Examination of the Data ..................................... 40 The Nature of the Variable: Examining the Shape of the Distribution ....... 40 Examining the Relationship between Variables ........................ 42 Examining Group Differences ...................................... 42 Multivariate Profiles ............................................. 44 Summary ..................................................... 46 Missing Data ....................................................... 46 A Simple Example of a Missing Data Analysis ........................ 47 Understanding the Reasons Leading to Missing Data ................... 48 Examining the Patterns of Missing Data ............................. 49 Diagnosing the Randomness of the Missing Data Process ............... 50 Approaches for Dealing with Missing Data .............................. 51 Use of Observations with Complete Data Only ........................ 51 Delete Case(s) and/or Variable(s) .................................. 51 Imputation Methods ............................................. 52 Model-Based Procedures ......................................... 55 An Illustration of Missing Data Diagnosis ............................. 56 A Recap of the Missing Value Analysis .............................. 62 Summary ..................................................... 64 Outliers............................................................ 64 Detecting Outliers ............................................... 65 Outlier Description and Profiling .................................... 66 Retention or Deletion of the Outlier ................................. 66 An Illustrative Example of Analyzing Outliers .......................... 66 Testing the Assumptions of Multivariate Analysis ........................ 70 Assessing Individual Variables versus the Variate ...................... 70 Normality ..................................................... 70 Homoscedasticity ............................................... 73 Linearity ...................................................... 75 Absence of Correlated Errors ...................................... 75 Data Transformations ............................................ 76 An Illustration of Testing the Assumptions Underlying Multivariate Analysis ........................................... 78 Homoscedasticity ............................................... 81 Incorporating Nonmetric Data with Dummy Variables ..................... 83 Summary o Questions o References .................................... 85 Chapter 3 Factor Analysis ........................................ 87 What Is Factor Analysis? ............................................. 90 A Hypothetical Example of Factor Analysis .............................. 92 Factor Analysis Decision Process ..................................... 93 Stage 1: Objectives of Factor Analysis ............................... 95 Stage 2: Designing a Factor Analysis ............................... 97 Stage 3: Assumptions in Factor Analysis ............................. 99 Stage 4: Deriving Factors and Assessing Overall Fit .................... 100 Stage 5: Interpreting the Factors ................................... 106 Stage 6: Validation of Factor Analysis ............................... 114 Stage 7: Additional Uses of Factor Analysis Results .................... 115 An Illustrative Example ............................................... 120 Stage 1: Objectives of Factor Analysis ............................... 120 Stage 2: Designing a Factor Analysis ............................... 121 Stage 3: Assumptions in Factor Analysis ............................. 121 Component Factor Analysis: Stages 4 through 7 ....................... 123 Common Factor Analysis: Stages 4 and 5 ............................ 131 A Managerial Overview of the Results ............................... 134 Summary o Questions o References o Annotated Readings ................. 135 Section 2 o Dependence Techniques ............................

139 Chapter 4 Multiple Regression Analysis ........................ 141 What Is Multiple Regression Analysis? ................................. 148 An Example of Simple and Multiple Regression .......................... 149 Setting a Baseline: Prediction without an Independent Variable ........... 150 Prediction Using a Single Independent Variable-Simple Regression ....... 151 Prediction Using Several Independent Variables-Multiple Regression ...... 156 Summary ..................................................... 158 A Decision Process for Multiple Regression Analysis ..................... 158 Stage 1: Objectives of Multiple Regression .............................. 159 Research Problems Appropriate for Multiple Regression ................ 159 Specifying a Statistical Relationship ................................. 162 Selection of Dependent and Independent Variables .................... 162 Stage 2: Research Design of a Multiple Regression Analysis ............... 164 Sample Size ................................................... 164 Fixed versus Random Effects Predictors ............................. 166 Creating Additional Variables ...................................... 166 Stage 3: Assumptions in Multiple Regression Analysis .................... 172 Assessing Individual Variables versus the Variate ...................... 172 Linearity of the Phenomenon ...................................... 173 Constant Variance of the Error Term ................................ 174 Independence of the Error Terms ................................... 175 Normality of the Error Term Distribution .............................. 175 Summary ..................................................... 176 Stage 4: Estimating the Regression Model and Assessing Overall Model Fit . . 176 General Approaches to Variable Selection ............................ 176 Testing the Regression Variate for Meeting the Regression Assumptions .... 180 Examining the Statistical Significance of Our Model .................... 181 Identifying Influential Observations .................................. 184 Stage 5: Interpreting the Regression Variate ............................. 187 Using the Regression Coefficients .................................. 187 Standardizing the Regression Coefficients: Beta Coefficients ............. 188 Assessing Multicollinearity ........................................ 188 Stage 6: Validation of the Results ..................................... 194 Additional or Split Samples ....................................... 194 Calculating the PRESS Statistic .................................... 194 Comparing Regression Models .................................... 195 Predicting with the Model ......................................... 195 Illustration of a Regression Analysis ................................... 195 Stage 1: Objectives of Multiple Regression ........................... 196 Stage 2: Research Design of a Multiple Regression Analysis ............. 196 Stage 3: Assumptions in Multiple Regression Analysis .................. 196 Stage 4: Estimating the Regression Model and Assessing Overall Model Fit . 197 Stage 5: Interpreting the Regression Variate .......................... 207 Stage 6: Validating the Results .................................... 209 Evaluating Alternative Regression Models ............................ 210 A Managerial Overview of the Results ............................... 213 Summary o Questions o References o Annotated Articles .................. 213 Appendix 4A: Advanced Diagnostics for Multiple Regression Analysis .............................. 217 Assessing Multicollinearity ........................................... 220 A Two-Part Process ............................................. 220 An Illustration of Assessing Multicollinearity ........................... 221 Identifying Influential Observations .................................... 221 Step 1: Examining Residuals ...................................... 222 Step 2: Identifying Leverage Points from the Predictors ................. 223 Step 3: Single-Case Diagnostics Identifying Influential Observations ....... 224 Step 4: Selecting and Accommodating Influential Observations ........... 225 Example from the HATCO Database ................................ 226 Overview ...................................................... 236 Summary o Questions o References .................................... 237 Chapter 5 Multiple Discriminant Analysis ‘ o -o and Logistic Regression .................................... ... 239 What Are Discriminant Analysis and Logistic Regression? ................. 244 Analogy with Regression and MANOVA ................................. 246 Hypothetical Example of Discriminant Analysis .......................... 246 A Two-Group Discriminant Analysis: Purchasers versus Nonpurchasers .... 247 A Geometric Representation of the Two-Group Discriminant Function ...... 250 A Three-Group Example of Discriminant Analysis: Switching Intentions ..... 251 The Decision Process for Discriminant Analysis ......................... 255 Stage 1: Objectives of Discriminant Analysis ............................ 256 Stage 2: Research Design for Discriminant Analysis ...................... 256 Selection of Dependent and Independent Variables .................... 257 Sample Size ................................................... 258 Division of the Sample ........................................... 258 Stage 3: Assumptions of Discriminant Analysis .......................... 259 Stage 4: Estimation of the Discriminant Model and Assessing Overall Fit .... 260 Computational Method ........................................... 260 Statistical Significance ........................................... 262 Assessing Overall Fit ............................................ 263 Casewise Diagnostics ............................................ 270 Summary ..................................................... 271 Stage 5: Interpretation of the Results ................................... 272 Discriminant Weights ............................................ 272 Discriminant Loadings ........................./................. 272 Partial F Values ................................................ 272 Interpretation of Two or More Functions .............................. 273 Which Interpretive Method to Use? ................................. 274 Stage 6: Validation of the Results ...................................... 275 Split-Sample or Cross-Validation Procedures ......................... 275 Profiling Group Differences ....................................... 276 Logistic Regression: Regression with a Binary Dependent Variable ......... 276 Representation of the Binary Dependent Variable ...................... 277 Estimating the Logistic Regression Model ............................ 278 Interpreting the Coefficients ....................................... 278 A Two-Group Illustrative Example ...................................... 281 Stage 1: Objectives of Discriminant Analysis .......................... 281 Stage 2: Research Design for Discriminant Analysis .................... 282 Stage 3: Assumptions of Discriminant Analysis ........................ 282 Stage 4: Estimation of the Discriminant Model and Assessing Overall Fit ... 283 Stage 5: Interpretation of the Results ............................... 293 Stage 6: Validation of the Results .................................. 295 A Managerial Overview .......................................... 295 A Three-Group Illustrative Example ....................................

296 Stage 1: Objectives of Discriminant Analysis .......................... 296 Stage 2: Research Design for Discriminant Analysis .................... 296 Stage 3: Assumptions of Discriminant Analysis ........................ 296 Stage 4: Estimation of the Discriminant Model and Assessing Overall Fit ... 297 Stage 5: Interpretation of Three-Group Discriminant Analysis Results ...... 309 Stage 6: Validation of the Discriminant Results ........................ 313 A Managerial Overview .......................................... 313 An Illustrative Example of Logistic Regression .......................... 314 Stages 1, 2, and 3: Research Objectives, Research Design, and Statistical Assumptions ................................. 314 Stage 4: Estimation of the Logistic Regression Model and Assessing Overall Fit ...................................... 315 Stage 5: Interpretation of the Results ............................ 320 Stage 6: Validation of the Results .................................. 321 A Managerial Overview .......................................... 321 Summary o Questions o References o Annotated Articles .................. 321 Chapter 6 Multivariate Analysis of Variance ................... 326 What Is Multivariate Analysis of Variance? .............................. 331 Univariate Procedures for Assessing Group Differences ................. 331 Multivariate Analysis of Variance ................................... 333 Differences between MANOVA and Discriminant Analysis .................. 336 A Hypothetical Illustration of MANOVA ................................. 336 When Should We Use MANOVA?....................................... 339 Control of Experimentwide Error Rate ............................... 339 Differences among a Combination of Dependent Variables ............... 339 A Decision Process for MANOVA ...................................... 339 Stege 1: Objectives of MANOVA ....................................... 341 Types of Multivariate Questions Suitable for MANOVA .................. 341 Stage 2: Issues in the Research Design of MANOVA ...................... 342 Sample Size Requirements-Overall and by Group .................... 342 Factorial Designs-Two or More Treatments .......................... 342 Using Covariates-ANCOVA and MANCOVA ......................... 346 Stage 3: Assumptions of ANOVA and MANOVA .......................... 347 Independence .................................................. 348 Equality of Variance-Covariance Matrices ............................ 348 Normality ..................................................... 349 Linearity and Multicollinearity among the Dependent Variables ............ 349 Sensitivity to Outliers ............................................ 349 Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit ....... 350 Criteria for Significance Testing .................................... 351 Statistical Power of the Multivariate Tests ............................ 352 Stage 5: Interpretation of the MANOVA Results .......................... 354 Evaluating Covariates ............................................ 354 Assessing the Dependent Variate .................................. 355 Identifying Differences between Individual Groups ..................... 356 Stage 6: Validation of the Results ...................................... 357 Summary ..................................................... 358 Example 1: Difference between Two Independent Groups .................. 358 A Univariate Approach: The t Test .................................. 359 A Multivariate Approach: Hotelling’s T2 .............................. 361 Example 2: Difference between k Independent Groups .................... 366 A Univariate Approach: /(-Groups ANOVA ............................ 366 A Multivariate Approach: /(-Groups MANOVA ......................... 369 Example 3: A Factorial Design for MANOVA with Two Independent Variables . . 374 Stage 1: Objectives of the MANOVA ................................ 374 Stage 2: Research Design of the MANOVA ........................... 375 Stage 3: Assumptions in MANOVA ................................. 375 Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit ...... 375 Stage 5: Interpretation of the Results ............................... 379 A Managerial Overview of the Results .................................. 381 Summary o Questions o References o Annotated Articles .................. 383 Chapter 7 Conjoint Analysis ...................................... 387 What Is Conjoint Analysis? ........................................... 392 A Hypothetical Example of Conjoint Analysis ............................ 393 An Empirical Example ........................................... 394 The Managerial Uses of Conjoint Analysis .............................. 398 Comparing Conjoint Analysis with Other Multivariate Methods ............. 399 Compositional versus Decompositional Techniques ..................... 399 Specifying the Conjoint Variate .................................... 399 Separate Models for Each Individual ................................ 399 Types of Relationships ........................................... 400 Designing a Conjoint Analysis Experiment .............................. 400 Stage 1: The Objectives of Conjoint Analysis ............................ 403 Defining the Total Utility of the Object ............................... 403 Specifying the Determinant Factors ................................. 403 Stage 2: The Design of a Conjoint Analysis .............................. 404 Selecting a Conjoint Analysis Methodology ........................... 404 Designing Stimuli: Selecting and Defining Factors and Levels ............ 405 Specifying the Basic Model Form ................................... 408 Data Collection ................................................. 412 Stage 3: Assumptions of Conjoint Analysis ............................. 418 Stage 4: Estimating the Conjoint Model and Assessing Overall Fit .......... 418 Selecting an Estimation Technique .................................. 419 Evaluating Model Goodness-of-Fit .................................. 420 Stage 5: Interpreting the Results ....................................... 420 Aggregate versus Disaggregate Analysis ............................. 420 Assessing the Relative Importance of Attributes ....................... 421 Stage 6: Validation of the Conjoint Results .............................. 421 Managerial Applications of Conjoint Analysis ............................ 422 Segmentation .................................................. 422 Profitability Analysis ............................................. 422 Conjoint Simulators ............................................. 422 Alternative Conjoint Methodologies .................................... 423 Adaptive Conjoint: Conjoint with a Large Number of Factors ............. 424 Overview of the Three Conjoint Methodologies ........................ 429 An Illustration of Conjoint Analysis .................................... 429 Stage 1: Objectives of the Conjoint Analysis .......................... 430 Stage 2: Design of the Conjoint Analysis ............................. 430 Stage 3: Assumptions in Conjoint Analysis ........................... 432 Stage 4: Estimating the Conjoint Model and Assessing Overall Model Fit . . . 432 Stage 5: Interpreting the Results ................................... 432 Stage 6: Validation of the Results .................................. 434 A Managerial Application: Use of a Choice Simulator ...................

435 Summary o Questions o References o Annotated Articles .................. 436 Chapter 8 Canonical Correlation Analysis ...................... 442 What Is Canonical Correlation? ........................................ 444 Hypothetical Example of Canonical Correlation .......................... 444 Analyzing Relationships with Canonical Correlation ...................... 445 Stage 1: Objectives of Canonical Correlation Analysis .................... 447 Stage 2: Designing a Canonical Correlation Analysis ..................... 447 Stage 3: Assumptions in Canonical Correlation .......................... 448 Stage 4: Deriving the Canonical Functions and Assessing Overall Fit ....... 448 Deriving Canonical Functions ...................................... 449 Which Canonical Functions Should Be Interpreted? .................... 450 Stage 5: Interpreting the Canonical Variate .............................. 453 Canonical Weights .............................................. 453 Canonical Loadings ............................................. 453 Canonical Cross-Loadings ........................................ 454 Which Interpretation Approach to Use ............................... 454 Stage 6: Validation and Diagnosis ...................................... 454 An Illustrative Example ............................................... 455 Stage 1: Objectives of Canonical Correlation Analysis .................. 455 Stages 2 and 3: Designing a Canonical Correlation Analysis and Testing the Assumptions ................................................ 455 Stage 4: Deriving the Canonical Functions and Assessing Overall Fit ...... 456 Stage 5: Interpreting the Canonical Variates .......................... 457 Stage 6: Validation and Diagnosis .................................. 460 A Managerial Overview ............................................... 461 Summary o Questions o References o Annotated Articles .................. 462 .^ o " .... Section 3 o Interdependence Techniques ....................... 467 Chapter 9 Cluster Analysis ....................................... 469 What Is Cluster Analysis? ............................................ 473 How Does Cluster Analysis Work? ..................................... 474 Measuring Similarity ............................................. 476 Forming Clusters ............................................... 476 Determining the Number of Clusters in the Final Solution ................ 477 Cluster Analysis Decision Process ..................................... 479 Stage 1: Objectives of Cluster Analysis ................................. 481 Selection of Clustering Variables ................................... 481 Stage 2: Research Design in Cluster Analysis ........................... 482 Detecting Outliers ............................................... 482 Similarity Measures ............................................. 483 Standardizing the Data ........................................... 489 Stage 3: Assumptions in Cluster Analysis ............................... 490 Representativeness of the Sample ................................. 490 Impact of Multicollinearity ......................................... 491 Stage 4: Deriving Clusters and Assessing Overall Fit ..................... 491 Clustering Algorithms ............................................ 491 How Many Clusters Should Be Formed? ............................. 499 Should the Cluster Analysis Be Respecified? ......................... 499 Stage 5: Interpretation of the Clusters .................................. 500 Stage 6: Validation and Profiling of the Clusters .......................... 500 Validating the Cluster Solution ..................................... 501 Profiling the Cluster Solution ...................................... 501 Summary of the Decision Process ..................................... 502 An Illustrative Example ............................................... 502 Stage 1: Objectives of the Cluster Analysis ........................... 502 Stage 2: Research Design of the Cluster Analysis ..................... 502 Stage 3: Assumptions in Cluster Analysis ............................ 503 Stage 4: Deriving Clusters and Assessing Overall Fit ................... 503 Stage 5: Interpretation of the Clusters ............................... 509 Stage 6: Validation and Profiling of the Clusters ....................... 512 A Managerial Overview .......................................... 515 Summary o Questions o References o Annotated Articles .................. 515 Chapter 10 Multidimensional Scaling ........................... 519 What Is Multidimensional Scaling? ..................................... 522 A Simplified Look at How MDS Works .................................. 524 Comparing MDS to Other Interdependence Techniques .................... 526 Individual as the Unit of Analysis ................................... 527 Lack of a Variate ............................................... 527 A Decision Framework for Perceptual Mapping .......................... 527 Stage 1: Objectives of MDS ........................................... 527 Key Decisions in Setting Objectives ................................. 529 Stage 2: Research Design of MDS ..................................... 531 Selection of Either a Decompositional (Attribute-Free) or Compositional (Attribute-Based) Approach ..................................... 531 Objects: Their Number and Selection ................................ 533 Nonmetric versus Metric Methods .................................. 534 Collection of Similarity or Preference Data ........................... 534 Stage 3: Assumptions of MDS Analysis ................................. 536 Stage 4: Deriving the MDS Solution and Assessing Overall Fit ............. 537 Determining an Object’s Position in the Perceptual Map ................. 537 Selecting the Dimensionality of the Perceptual Map .................... 539 Incorporating Preferences into MDS ................................ 541 Stage 5: Interpreting the MDS Results .................................. 545 Identifying the Dimensions ........................................ 546 Stage 6: Validating the MDS Results .................................... 547 Correspondence Analysis ............................................ 548 A Simple Example of CA ......................................... 548 Stage 1: Objectives of CA ........................................ 552 Stage 2: Research Design of CA ................................... 552 Stage 3: Assumptions in CA ...................................... 553 Stage 4: Deriving CA Results and Assessing Overall Fit ................ 553 Stage 5: Interpretation of the Results ............................... 553 Stage 6: Validation of the Results .................................. 554 Overview of Correspondence Analysis ............................... 554 Illustration of MDS and CA ........................................... 555 Stage 1: Objectives of Perceptual Mapping ........................... 555 Stage 2: Research Design of the Perceptual Mapping Study ............. 555 Stage 3: Assumptions in Perceptual Mapping ......................... 556 Multidimensional Scaling: Stages 4 and 5 ............................ 556 Overview of the Decompositional Results ............................ 564 Correspondence Analysis: Stages 4 and 5 ........................... 565 Stage 6: Validation of the Results .................................. 569 A Managerial Overview of MDS Results .............................

570 Summary o Questions o References o Annotated Articles .................. 570 Section 4 Advanced and Emerging Techniques ................ 575 Chapter 11 Structural Equation Modeling ...................... 577 What Is Structural Equation Modeling? ................................. 584 Accommodating Multiple Interrelated Dependence Relationships .......... 584 Incorporating Variables that We Do Not Measure Directly ................ 585 A Simple Example of SEM ............................................ 586 The Research Question .......................................... 587 Setting Up the Structural Equation Model for Path Analysis .............. 587 An Application of Path Analysis .................................... 588 Summary ..................................................... 589 The Role of Theory in Structural Equation Modeling ...................... 589 Developing a Modeling Strategy ....................................... 590 Confirmatory Modeling Strategy .................................... 590 Competing Models Strategy ....................................... 591 Model Development Strategy ...................................... 592 Stages in Structural Equation Modeling ................................. 592 Stage 1: Developing a Theoretically Based Model ...................... 592 Stage 2: Constructing a Path Diagram of Causal Relationships ........... 594 Stage 3: Converting the Path Diagram into a Set of Structural and Measurement Models ...................................... 596 Stage 4: Choosing the Input Matrix Type and Estimating the Proposed Model .............................................. 601 Stage 5: Assessing the Identification of the Structural Model ............. 608 Stage 6: Evaluating Goodness-of-Fit Criteria .......................... 610 Stage 7: Interpreting and Modifying the Model ........................ 614 A Recap of the Seven-Stage Process ............................... 616 Two Illustrations of Structural Equation Modeling ........................ 616 Confirmatory Factor Analysis ......................................... 616 Stage 1: Developing a Theoretically Based Model ...................... 617 Stage 2: Constructing a Path Diagram of Causal Relationships ........... 617 Stage 3: Converting the Path Diagram into a Set of Structural and Measurement Models .......................................... 618 Stage 4: Choosing Input Matrix Type and Estimating the Proposed Model .. . 619 Stage 5: Assessing the Identification of the Structural Model ............. 619 Stage 6: Evaluating Goodness-of-Fit Criteria .......................... 620 Stage 7: Interpreting and Modifying the Model ........................ 624 Higher-Order Factor Analysis Models ............................... 625 Summary ..................................................... 627 Estimating a Path Model with Structural Equation Modeling ................ 627 Stage 1: Developing a Theoretically Based Model ...................... 628 Stage 2: Constructing a Path Diagram of Causal Relationships ........... 629 Stage 3: Converting the Path Diagram into a Set of Structural and Measurement Models .......................................... 629 Stage 4: Choosing Input Matrix Type and Estimating the Proposed Model .. . 631 Stage 5: Assessing the Identification of the Structural Model ............. 631 Stage 6: Evaluating Goodness-of-Fit Criteria .......................... 633 Stage 7: Interpreting and Modifying the Model ........................ 639 Overview of the Seven-Stage Process ............................... 641 Summary o Questions ................................................ 644 Appendix 11A: A Mathematical Representation in LISREL Notation ........................... 645 LISREL Notation .................................................... 645 From a Path Diagram to LISREL Notation ............................... 648 Constructing Structural Equations from the Path Diagram ............... 648 Summary .......................................................... 652 Appendix 11B: Overall Goodness-of-Fit Measures for Structural Equation Modeling .................. 653 Measures of Absolute Fit ............................................. 654 Likelihood-Ratio Chi-Square Statistic ................................ 654 Noncentrality and Scaled Noncentrality Parameters .................... 655 Goodness-of-Fit Index ........................................... 655 Root Mean Square Residual ...................................... 656 Root Mean Square Error of Approximation ........................ 656 Expected Cross-Validation Index ................................... 656 Cross-Validation Index ........................................... 656 Incremental Fit Measures ............................................. 657 Adjusted Goodness-of-Fit Index .................................... 657 Tucker-Lewis Index ............................................. 657 Normed Fit Index ............................................... 657 Other Incremental Fit Measures .................................... 657 Parsimonious Fit Measures ........................................... 658 Parsimonious Normed Fit Index .................................... 658 Parsimonious Goodness-of-Fit Index ................................ 658 Normed Chi-Square ........................................ 658 Akaike Information Criterion ....................................... 659 A Review of the Structural Model Goodness-of-Fit Measures ............... 659 Summary o References o Annotated Articles ............................. 659 Chapter 12 Emerging Techniques in Multivariate Analysis ... 667 Introduction ........................................................ 671 The Information Avalanche ........................................ 671 Analysis without Statistical Inference ................................ o" 672 Topics Covered in this Chapter .................................... 672 Data Warehousing and Data Mining .................................... 673 What Are Data Warehousing and Data Mining? ....................... 674 Fundamental Concepts in Data Warehousing ......................... 675 Fundamental Issues in Data Mining ............................. 677 Neural Networks .................................................... 684 Basic Concepts of Neural Networks ................................. 685 Estimating a Neural Network Model ................................. 688 Using a Neural Network for Classification ............................ 691 Summary ..................................................... 692 Resampling ........................................................ 692 A Brief Review of Parametric Inference .............................. 693 Basic Concepts in Resampling ..................................... 693 An Example of Resampling and Multiple Regression ................... 694 Summary ..................................................... 696 Summary o Questions o References .................................... 697 Appendix A: Applications of Multivariate Data Analysis ...... 700 Index ................................................................ i-i

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Multivaryete çözümleme

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