Handbook of Applied Multivariate Statistics and Mathematical Modeling
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Table of contents
- Cover
- CONTENTSv
- CONTRIBUTORSxxi
- PREFACExxv
- PART I: INTRODUCTION1
- Chapter 1. Multivariate Statistics and Mathematical Modeling3
- I. Data Preparation8
- II. Study Your Data14
- III. Selecting a Statistical Technique15
- IV. Data Requirements17
- V. Interpreting Results22
- VI. Statistical versus Practical Significance25
- VII. Overview27
- References34
- Chapter 2. Role of Theory and Experimental Design in Multivariate Analysis and Mathematical Modeling37
- I. The Importance of Theory in Scientific Methodology37
- II. The Evolution of Postpositivist Scientific Method48
- III. Criticisms of Modern Inductive–Hypothetico-deductive Method53
- IV. Critical Multiplism (Postpositivist Inductive-Hypothetico–deductive Method)57
- V. Conclusion59
- References60
- Chapter 3. Scale Construction and Psychometric Considerations65
- I. Introduction65
- II. Scale Definition68
- III. Scale Construction71
- IV. Scaling Methods79
- V. Psychometric Considerations86
- VI. A Final Word92
- References92
- Chapter 4. Interrater Reliability and Agreement95
- I. Agreement versus Reliability96
- II. Level of Measurement101
- III. Type of Replication102
- IV. Interrater Reliability103
- V. Interrater Agreement111
- VI. Summary of Recommendations117
- References118
- Chapter 5. Interpreting and Reporting Results125
- I. Introduction125
- II. Graphical Displays and Exploratory Data Analysis126
- III. Contrasts132
- IV. Interpreting Significance Levels133
- V. Interpreting the Size of Effects138
- VI. Understanding Assumptions140
- VII. Process143
- VIII. Conclusion146
- References147
- PART II: MULTIVARIATE ANALYSIS150
- Chapter 6. Issues in the Use and Application of Multiple Regression Analysis151
- I. Overview of Multiple Regression152
- II. Assumptions and Robustness156
- III. Regression Diagnostics and Transformations160
- IV. Interactions and Moderator Effects171
- V. Sample Size Requirements for Multiple Regression Analyses175
- VI. Handling Missing Data177
- VII. Conclusion180
- References181
- Chapter 7. Multivariate Analysis of Variance and Covariance183
- I. Overview183
- II. Purpose of Multivariate Analysis of Variance185
- III. Design185
- IV. Analysis Guidelines189
- V. Recommended Practices204
- References207
- Chapter 8. Discriminant Analysis209
- I. Introduction209
- II. Illustrative Example210
- III. Descriptive Discriminant Analysis211
- IV. Predictive Discriminant Analysis230
- V. Other Issues and Concerns232
- VI. Conclusion234
- References234
- Chapter 9. Canonical Correlation Analysis237
- I. Appropriate Research Settings237
- II. General Taxonomy of Relationship Statistics238
- III. How Relations Are Expressed241
- IV. Tests of Significance243
- V. Variance Accounted for„Redundancy244
- VI. Interpreting the Components or Variates251
- VII. Methodological Issues in Canonical Analysis256
- VIII. Concluding Remarks260
- References261
- Chapter 10. Exploratory Factor Analysis265
- I. Exploratory Factor Analysis265
- II. Factor Analysis and Principal Components274
- III. Estimating the Parameters275
- IV. Standard Errors for Parameter Estimates286
- V. Target Rotation288
- VI. Case Study290
- VII. Summary293
- References295
- Chapter 11. Cluster Analysis297
- I. General Overview298
- II. Uses for Cluster Analysis300
- III. Cluster Analysis Methods301
- IV. Conclusion318
- References318
- Chapter 12. Multidimensional Scaling323
- I. Proximity Data325
- II. Model and Analysis326
- III. Conducting a Multidimensional Scaling329
- IV. Examples341
- V. Multidimensional Scaling and Other Multivariate Techniques344
- VI. Concluding Remarks347
- References349
- Chapter 13. Time-Series Designs and Analyses353
- I. Alternative Purposes of Time-Series Studies354
- II. The Regression Approach to Fitting Trends356
- III. The Problem of Autocorrelation359
- IV. The Autoregressive Integrated Moving Average Approach to Modeling Autocorrelation360
- V. Multiple Cases376
- VI. Threats to Internal Validity in the Simple Interrupted Time-Series Design: Old and New Considera379
- VII. More Elaborate Interrupted Time-Series Designs380
- VIII. Elaboration in Time-Series Studies of Covariation381
- IX. Design and Implementation Issues382
- X. Summary and Conclusions385
- References386
- Chapter 14. Poisson Regression, Logistic Regression, and Loglinear Models for Random Counts391
- I. Preliminaries391
- II. Measuring Association for Counts and Rates397
- III. Generalized Linear Models401
- IV. Poisson Regression Models405
- V. Logistic Regression Analysis415
- VI. Loglinear Models for Nominal Variables424
- VII. Exceptions434
- References436
- PART III: EVALUATION OF MATHEMATICAL MODELS438
- Chapter 15. Structural Equation Modeling: Uses and Issues439
- I. Defining Structural Equation Modeling440
- II. Common Uses of Structural Equation Modeling441
- III. Planning a Structural Equation Modeling Analysis444
- IV. Data Requirements445
- V. Preparing Data for Analysis447
- VI. Multiple Groups450
- VII. Assessing Model Fit451
- VIII. Checking the Output for Problems454
- IX. Interpreting Results458
- X. Conclusion462
- References462
- Chapter 16. Confirmatory Factor Analysis465
- I. Overview466
- II. Applications of Confirmatory Factor Analysis469
- III. Data Requirements471
- IV. Elements of a Confirmatory Factor Analysis474
- V. Additional Considerations489
- VI. Conclusions and Recommendations491
- References492
- Chapter 17. Multivariate Meta-analysis499
- I. What Is Meta-analysis?499
- II. How Multivariate Data Arise in Meta-analysis501
- III. Approaches to Multivariate Data502
- IV. Specific Distributional Results for Common Outcomes506
- V. Approaches to Multivariate Analysis512
- VI. Examples of Analysis516
- VII. Summary523
- References524
- Chapter 18. Generalizability Theory527
- I. Introduction527
- II. Fundamentals of Generalizabilitity Theory529
- III. Generalizability Theory Extended to Multifaceted Designs538
- IV. Generalizability Theory Extended to Multivariate Designs542
- V. Generalizability Theory as a Latent Trait Theory Model542
- VI. Computer Programs545
- VII. Conclusion546
- References546
- Chapter 19. Item Response Models for the Analysis of Educational and Psychological Test Data553
- I. Introduction553
- II. Shortcomings of Classical Test Models556
- III. Introduction to Item Response Theory Models557
- IV. Item Response Theory Parameter Estimation and Model Fit565
- V. Special Features of Item Response Theory Models571
- VI. Applications573
- VII. Future Directions and Conclusions578
- References579
- Chapter 20. Multitrait–Multimethod Analysis583
- I. Random Analysis of Variance Model586
- II. Confirmatory Factor Analytic Model593
- III. Covariance Component Analysis597
- IV. Composite Direct Product Model601
- V. Conclusion607
- References609
- Chapter 21. Using Random Coefficient Linear Models for the Analysis of Hierarchically Nested Data613
- I. Multilevel Models for Multilevel Data613
- II. Fields of Study Where Multilevel Data Analyses Can Be Applied614
- III. Random Coefficient Models Compared with Fixed Linear Models618
- IV. Illustration of the Random Coefficient Model619
- V. Complex Random Coefficient Models627
- VI. Summary637
- VII. Software637
- References638
- Chapter 22. Analysis of Circumplex Models641
- I. Exploratory Approaches to the Evaluation of Circumplexes644
- II. Confirmatory Approaches to the Evaluation of Circumplexes648
- III. Variations on Examining Circumplexes658
- IV. Conclusions659
- References660
- Chapter 23. Using Covariance Structure Analysis to Model Change over Time665
- I. Latent Growth Modeling: The Basic Approach666
- II. Introducing a Time-Invariant Predictor of Change into the Analysis677
- III. Including a Time-Varying Predictor of Change in the Analyses683
- IV. Discussion691
- References692
- AUTHOR INDEX695
- SUBJECT INDEX709
Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments. The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools. The objective of the book is to inform readers about which tool to use to accomplish which task. Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer. As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities.