Handbook of Applied Multivariate Statistics and Mathematical Modeling (eBook)

Front Cover 1
HANDBOOK OF APPLIED MULTIVARIATE STATISTICS AND MATHEMATICAL MODELING 4
Copyright Page 5
CONTENTS 6
CONTRIBUTORS 22
PREFACE 26
PART I: INTRODUCTION 30
Chapter 1. Multivariate Statistics and Mathematical Modeling 32
I. Data Preparation 37
II. Study Your Data 43
III. Selecting a Statistical Technique 44
IV. Data Requirements 46
V. Interpreting Results 51
VI. Statistical versus Practical Significance 54
VII. Overview 56
References 63
Chapter 2. Role of Theory and Experimental Design in Multivariate Analysis and Mathematical Modeling 66
I. The Importance of Theory in Scientific Methodology 66
II. The Evolution of Postpositivist Scientific Method 77
III. Criticisms of Modern Inductive–Hypothetico-deductive Method 82
IV. Critical Multiplism (Postpositivist Inductive-Hypothetico–deductive Method) 86
V. Conclusion 88
References 89
Chapter 3. Scale Construction and Psychometric Considerations 94
I. Introduction 94
II. Scale Definition 97
III. Scale Construction 100
IV. Scaling Methods 108
V. Psychometric Considerations 115
VI. A Final Word 121
References 121
Chapter 4. Interrater Reliability and Agreement 124
I. Agreement versus Reliability 125
II. Level of Measurement 130
III. Type of Replication 131
IV. Interrater Reliability 132
V. Interrater Agreement 140
VI. Summary of Recommendations 146
References 147
Chapter 5. Interpreting and Reporting Results 154
I. Introduction 154
II. Graphical Displays and Exploratory Data Analysis 155
III. Contrasts 161
IV. Interpreting Significance Levels 162
V. Interpreting the Size of Effects 167
VI. Understanding Assumptions 169
VII. Process 172
VIII. Conclusion 175
References 176
PART II: MULTIVARIATE ANALYSIS 179
Chapter 6. Issues in the Use and Application of Multiple Regression Analysis 180
I. Overview of Multiple Regression 181
II. Assumptions and Robustness 185
III. Regression Diagnostics and Transformations 189
IV. Interactions and Moderator Effects 200
V. Sample Size Requirements for Multiple Regression Analyses 204
VI. Handling Missing Data 206
VII. Conclusion 209
References 210
Chapter 7. Multivariate Analysis of Variance and Covariance 212
I. Overview 212
II. Purpose of Multivariate Analysis of Variance 214
III. Design 214
IV. Analysis Guidelines 218
V. Recommended Practices 233
References 236
Chapter 8. Discriminant Analysis 238
I. Introduction 238
II. Illustrative Example 239
III. Descriptive Discriminant Analysis 240
IV. Predictive Discriminant Analysis 259
V. Other Issues and Concerns 261
VI. Conclusion 263
References 263
Chapter 9. Canonical Correlation Analysis 266
I. Appropriate Research Settings 266
II. General Taxonomy of Relationship Statistics 267
III. How Relations Are Expressed 270
IV. Tests of Significance 272
V. Variance Accounted for—Redundancy 273
VI. Interpreting the Components or Variates 280
VII. Methodological Issues in Canonical Analysis 285
VIII. Concluding Remarks 289
References 290
Chapter 10. Exploratory Factor Analysis 294
I. Exploratory Factor Analysis 294
II. Factor Analysis and Principal Components 303
III. Estimating the Parameters 304
IV. Standard Errors for Parameter Estimates 315
V. Target Rotation 317
VI. Case Study 319
VII. Summary 322
References 324
Chapter 11. Cluster Analysis 326
I. General Overview 327
II. Uses for Cluster Analysis 329
III. Cluster Analysis Methods 330
IV. Conclusion 347
References 347
Chapter 12. Multidimensional Scaling 352
I. Proximity Data 354
II. Model and Analysis 355
III. Conducting a Multidimensional Scaling 358
IV. Examples 370
V. Multidimensional Scaling and Other Multivariate Techniques 373
VI. Concluding Remarks 376
References 378
Chapter 13. Time-Series Designs and Analyses 382
I. Alternative Purposes of Time-Series Studies 383
II. The Regression Approach to Fitting Trends 385
III. The Problem of Autocorrelation 388
IV. The Autoregressive Integrated Moving Average Approach to Modeling Autocorrelation 389
V. Multiple Cases 405
VI. Threats to Internal Validity in the Simple Interrupted Time-Series Design: Old and New Considerations 408
VII. More Elaborate Interrupted Time-Series Designs 409
VIII. Elaboration in Time-Series Studies of Covariation 410
IX. Design and Implementation Issues 411
X. Summary and Conclusions 414
References 415
Chapter 14. Poisson Regression, Logistic Regression, and Loglinear Models for Random Counts 420
I. Preliminaries 420
II. Measuring Association for Counts and Rates 426
III. Generalized Linear Models 430
IV. Poisson Regression Models 434
V. Logistic Regression Analysis 444
VI. Loglinear Models for Nominal Variables 453
VII. Exceptions 463
References 465
PART III: EVALUATION OF MATHEMATICAL MODELS 467
Chapter 15. Structural Equation Modeling: Uses and Issues 468
I. Defining Structural Equation Modeling 469
II. Common Uses of Structural Equation Modeling 470
III. Planning a Structural Equation Modeling Analysis 473
IV. Data Requirements 474
V. Preparing Data for Analysis 476
VI. Multiple Groups 479
VII. Assessing Model Fit 480
VIII. Checking the Output for Problems 483
IX. Interpreting Results 487
X. Conclusion 491
References 491
Chapter 16. Confirmatory Factor Analysis 494
I. Overview 495
II. Applications of Confirmatory Factor Analysis 498
III. Data Requirements 500
IV. Elements of a Confirmatory Factor Analysis 503
V. Additional Considerations 518
VI. Conclusions and Recommendations 520
References 521
Chapter 17. Multivariate Meta-analysis 528
I. What Is Meta-analysis? 528
II. How Multivariate Data Arise in Meta-analysis 530
III. Approaches to Multivariate Data 531
IV. Specific Distributional Results for Common Outcomes 535
V. Approaches to Multivariate Analysis 541
VI. Examples of Analysis 545
VII. Summary 552
References 553
Chapter 18. Generalizability Theory 556
I. Introduction 556
II. Fundamentals of Generalizabilitity Theory 558
III. Generalizability Theory Extended to Multifaceted Designs 567
IV. Generalizability Theory Extended to Multivariate Designs 571
V. Generalizability Theory as a Latent Trait Theory Model 571
VI. Computer Programs 574
VII. Conclusion 575
References 575
Chapter 19. Item Response Models for the Analysis of Educational and Psychological Test Data 582
I. Introduction 582
II. Shortcomings of Classical Test Models 585
III. Introduction to Item Response Theory Models 586
IV. Item Response Theory Parameter Estimation and Model Fit 594
V. Special Features of Item Response Theory Models 600
VI. Applications 602
VII. Future Directions and Conclusions 607
References 608
Chapter 20. Multitrait–Multimethod Analysis 612
I. Random Analysis of Variance Model 615
II. Confirmatory Factor Analytic Model 622
III. Covariance Component Analysis 626
IV. Composite Direct Product Model 630
V. Conclusion 636
References 638
Chapter 21. Using Random Coefficient Linear Models for the Analysis of Hierarchically Nested Data 642
I. Multilevel Models for Multilevel Data 642
II. Fields of Study Where Multilevel Data Analyses Can Be Applied 643
III. Random Coefficient Models Compared with Fixed Linear Models 647
IV. Illustration of the Random Coefficient Model 648
V. Complex Random Coefficient Models 656
VI. Summary 666
VII. Software 666
References 667
Chapter 22. Analysis of Circumplex Models 670
I. Exploratory Approaches to the Evaluation of Circumplexes 673
II. Confirmatory Approaches to the Evaluation of Circumplexes 677
III. Variations on Examining Circumplexes 687
IV. Conclusions 688
References 689
Chapter 23. Using Covariance Structure Analysis to Model Change over Time 694
I. Latent Growth Modeling: The Basic Approach 695
II. Introducing a Time-Invariant Predictor of Change into the Analysis 706
III. Including a Time-Varying Predictor of Change in the Analyses 712
IV. Discussion 720
References 721
AUTHOR INDEX 724
SUBJECT INDEX 738