Handbook of Applied Multivariate Statistics and Mathematical Modeling

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HANDBOOK OF APPLIED MULTIVARIATE STATISTICS AND MATHEMATICAL MODELING

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CONTENTS

CONTRIBUTORS

PREFACE

PART I: INTRODUCTION

Chapter 1. Multivariate Statistics and Mathematical Modeling

I. Data Preparation

II. Study Your Data

III. Selecting a Statistical Technique

IV. Data Requirements

V. Interpreting Results

VI. Statistical versus Practical Significance

VII. Overview

References

Chapter 2. Role of Theory and Experimental Design in Multivariate Analysis and Mathematical Modeling

I. The Importance of Theory in Scientific Methodology

II. The Evolution of Postpositivist Scientific Method

III. Criticisms of Modern Inductive–Hypothetico-deductive Method

IV. Critical Multiplism (Postpositivist Inductive-Hypothetico–deductive Method)

V. Conclusion

References

Chapter 3. Scale Construction and Psychometric Considerations

I. Introduction

II. Scale Definition

III. Scale Construction

IV. Scaling Methods

V. Psychometric Considerations

VI. A Final Word

References

Chapter 4. Interrater Reliability and Agreement

I. Agreement versus Reliability

II. Level of Measurement

III. Type of Replication

IV. Interrater Reliability

V. Interrater Agreement

VI. Summary of Recommendations

References

Chapter 5. Interpreting and Reporting Results

I. Introduction

II. Graphical Displays and Exploratory Data Analysis

III. Contrasts

IV. Interpreting Significance Levels

V. Interpreting the Size of Effects

VI. Understanding Assumptions

VII. Process

VIII. Conclusion

References

PART II: MULTIVARIATE ANALYSIS

Chapter 6. Issues in the Use and Application of Multiple Regression Analysis

I. Overview of Multiple Regression

II. Assumptions and Robustness

III. Regression Diagnostics and Transformations

IV. Interactions and Moderator Effects

V. Sample Size Requirements for Multiple Regression Analyses

VI. Handling Missing Data

VII. Conclusion

References

Chapter 7. Multivariate Analysis of Variance and Covariance

I. Overview

II. Purpose of Multivariate Analysis of Variance

III. Design

IV. Analysis Guidelines

V. Recommended Practices

References

Chapter 8. Discriminant Analysis

I. Introduction

II. Illustrative Example

III. Descriptive Discriminant Analysis

IV. Predictive Discriminant Analysis

V. Other Issues and Concerns

VI. Conclusion

References

Chapter 9. Canonical Correlation Analysis

I. Appropriate Research Settings

II. General Taxonomy of Relationship Statistics

III. How Relations Are Expressed

IV. Tests of Significance

V. Variance Accounted for—Redundancy

VI. Interpreting the Components or Variates

VII. Methodological Issues in Canonical Analysis

VIII. Concluding Remarks

References

Chapter 10. Exploratory Factor Analysis

I. Exploratory Factor Analysis

II. Factor Analysis and Principal Components

III. Estimating the Parameters

IV. Standard Errors for Parameter Estimates

V. Target Rotation

VI. Case Study

VII. Summary

References

Chapter 11. Cluster Analysis

I. General Overview

II. Uses for Cluster Analysis

III. Cluster Analysis Methods

IV. Conclusion

References

Chapter 12. Multidimensional Scaling

I. Proximity Data

II. Model and Analysis

III. Conducting a Multidimensional Scaling

IV. Examples

V. Multidimensional Scaling and Other Multivariate Techniques

VI. Concluding Remarks

References

Chapter 13. Time-Series Designs and Analyses

I. Alternative Purposes of Time-Series Studies

II. The Regression Approach to Fitting Trends

III. The Problem of Autocorrelation

IV. The Autoregressive Integrated Moving Average Approach to Modeling Autocorrelation

V. Multiple Cases

VI. Threats to Internal Validity in the Simple Interrupted Time-Series Design: Old and New Considerations

VII. More Elaborate Interrupted Time-Series Designs

VIII. Elaboration in Time-Series Studies of Covariation

IX. Design and Implementation Issues

X. Summary and Conclusions

References

Chapter 14. Poisson Regression, Logistic Regression, and Loglinear Models for Random Counts

I. Preliminaries

II. Measuring Association for Counts and Rates

III. Generalized Linear Models

IV. Poisson Regression Models

V. Logistic Regression Analysis

VI. Loglinear Models for Nominal Variables

VII. Exceptions

References

PART III: EVALUATION OF MATHEMATICAL MODELS

Chapter 15. Structural Equation Modeling: Uses and Issues

I. Defining Structural Equation Modeling

II. Common Uses of Structural Equation Modeling

III. Planning a Structural Equation Modeling Analysis

IV. Data Requirements

V. Preparing Data for Analysis

VI. Multiple Groups

VII. Assessing Model Fit

VIII. Checking the Output for Problems

IX. Interpreting Results

X. Conclusion

References

Chapter 16. Confirmatory Factor Analysis

I. Overview

II. Applications of Confirmatory Factor Analysis

III. Data Requirements

IV. Elements of a Confirmatory Factor Analysis

V. Additional Considerations

VI. Conclusions and Recommendations

References

Chapter 17. Multivariate Meta-analysis

I. What Is Meta-analysis?

II. How Multivariate Data Arise in Meta-analysis

III. Approaches to Multivariate Data

IV. Specific Distributional Results for Common Outcomes

V. Approaches to Multivariate Analysis

VI. Examples of Analysis

VII. Summary

References

Chapter 18. Generalizability Theory

I. Introduction

II. Fundamentals of Generalizabilitity Theory

III. Generalizability Theory Extended to Multifaceted Designs

IV. Generalizability Theory Extended to Multivariate Designs

V. Generalizability Theory as a Latent Trait Theory Model

VI. Computer Programs

VII. Conclusion

References

Chapter 19. Item Response Models for the Analysis of Educational and Psychological Test Data

I. Introduction

II. Shortcomings of Classical Test Models

III. Introduction to Item Response Theory Models

IV. Item Response Theory Parameter Estimation and Model Fit

V. Special Features of Item Response Theory Models

VI. Applications

VII. Future Directions and Conclusions

References

Chapter 20. Multitrait–Multimethod Analysis

I. Random Analysis of Variance Model

II. Confirmatory Factor Analytic Model

III. Covariance Component Analysis

IV. Composite Direct Product Model

V. Conclusion

References

Chapter 21. Using Random Coefficient Linear Models for the Analysis of Hierarchically Nested Data

I. Multilevel Models for Multilevel Data

II. Fields of Study Where Multilevel Data Analyses Can Be Applied

III. Random Coefficient Models Compared with Fixed Linear Models

IV. Illustration of the Random Coefficient Model

V. Complex Random Coefficient Models

VI. Summary

VII. Software

References

Chapter 22. Analysis of Circumplex Models

I. Exploratory Approaches to the Evaluation of Circumplexes

II. Confirmatory Approaches to the Evaluation of Circumplexes

III. Variations on Examining Circumplexes

IV. Conclusions

References

Chapter 23. Using Covariance Structure Analysis to Model Change over Time

I. Latent Growth Modeling: The Basic Approach

II. Introducing a Time-Invariant Predictor of Change into the Analysis

III. Including a Time-Varying Predictor of Change in the Analyses

IV. Discussion

References

AUTHOR INDEX

SUBJECT INDEX