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Correspondence Analysis: Theory, Practice and New Strategies

Book Description

A comprehensive overview of the internationalisation of correspondence analysis

Correspondence Analysis: Theory, Practice and New Strategies examines the key issues of correspondence analysis, and discusses the new advances that have been made over the last 20 years.

The main focus of this book is to provide a comprehensive discussion of some of the key technical and practical aspects of correspondence analysis, and to demonstrate how they may be put to use. Particular attention is given to the history and mathematical links of the developments made. These links include not just those major contributions made by researchers in Europe (which is where much of the attention surrounding correspondence analysis has focused) but also the important contributions made by researchers in other parts of the world.

Key features include:

  • A comprehensive international perspective on the key developments of correspondence analysis.

  • Discussion of correspondence analysis for nominal and ordinal categorical data.

  • Discussion of correspondence analysis of contingency tables with varying association structures (symmetric and non-symmetric relationship between two or more categorical variables).

  • Extensive treatment of many of the members of the correspondence analysis family for two-way, three-way and multiple contingency tables.

  • Correspondence Analysis offers a comprehensive and detailed overview of this topic which will be of value to academics, postgraduate students and researchers wanting a better understanding of correspondence analysis. Readers interested in the historical development, internationalisation and diverse applicability of correspondence analysis will also find much to enjoy in this book.

    Table of Contents

    1. Cover
    2. Wiley Series in Probability and Statistics
    3. Title Page
    4. Copyright
    5. Dedication
    6. Foreword
    7. Preface
    8. Part One: Introduction
      1. Chapter 1: Data Visualisation
        1. 1.1 A Very Brief Introduction to Data Visualisation
        2. 1.2 Data Visualisation for Contingency Tables
        3. 1.3 Other Plots
        4. 1.4 Studying Exposure to Asbestos
        5. 1.5 Happiness Data
        6. 1.6 Correspondence Analysis Now
        7. 1.7 Overview of the Book
        8. 1.8 R Code
        9. References
      2. Chapter 2: Pearson's Chi-Squared Statistic
        1. 2.1 Introduction
        2. 2.2 Pearson's Chi-Squared Statistic
        3. 2.3 The Goodman–-Kruskal Tau Index
        4. 2.4 The 2 × 2 Contingency Table
        5. 2.5 Early Contingency Tables
        6. 2.6 R Code
        7. References
    9. Part Two: Correspondence Analysis of Two-Way Contingency Tables
      1. Chapter 3: Methods of Decomposition
        1. 3.1 Introduction
        2. 3.2 Reducing Multidimensional Space
        3. 3.3 Profiles and Cloud of Points
        4. 3.4 Property of Distributional Equivalence
        5. 3.5 The Triplet and Classical Reciprocal Averaging
        6. 3.6 Solving the Triplet Using Eigen-Decomposition
        7. 3.7 Solving the Triplet Using Singular Value Decomposition
        8. 3.8 The Generalised Triplet and Reciprocal Averaging
        9. 3.9 Solving the Generalised Triplet Using Gram–Schmidt Process
        10. 3.10 Bivariate Moment Decomposition
        11. 3.11 Hybrid Decomposition
        12. 3.12 R Code
        13. 3.13 A Preliminary Graphical Summary
        14. 3.14 Analysis of Analgesic Drugs
        15. References
      2. Chapter 4: Simple Correspondence Analysis
        1. 4.1 Introduction
        2. 4.2 Notation
        3. 4.3 Measuring Departures from Complete Independence
        4. 4.4 Decomposing the Pearson Ratio
        5. 4.5 Coordinate Systems
        6. 4.6 Distances
        7. 4.7 Transition Formulae
        8. 4.8 Moments of the Principal Coordinates
        9. 4.9 How Many Dimensions to Use?
        10. 4.10 R Code
        11. 4.11 Other Theoretical Issues
        12. 4.12 Some Applications of Correspondence Analysis
        13. 4.13 Analysis of a Mother's Attachment to Her Child
        14. References
      3. Chapter 5: Non-Symmetrical Correspondence Analysis
        1. 5.1 Introduction
        2. 5.2 The Goodman–Kruskal Tau Index
        3. 5.3 Non-Symmetrical Correspondence Analysis
        4. 5.4 The Coordinate Systems
        5. 5.5 Transition Formulae
        6. 5.6 Moments of the Principal Coordinates
        7. 5.7 The Distances
        8. 5.8 Comparison with Simple Correspondence Analysis
        9. 5.9 R Code
        10. 5.10 Analysis of a Mother's Attachment to Her Child
        11. References
      4. Chapter 6: Ordered Correspondence Analysis
        1. 6.1 Introduction
        2. 6.2 Pearson's Ratio and Bivariate Moment Decomposition
        3. 6.3 Coordinate Systems
        4. 6.4 Artificial Data Revisited
        5. 6.5 Transition Formulae
        6. 6.6 Distance Measures
        7. 6.7 Singly Ordered Analysis
        8. 6.8 R Code
        9. References
      5. Chapter 7: Ordered Non-Symmetrical Correspondence Analysis
        1. 7.1 Introduction
        2. 7.2 General Considerations
        3. 7.3 Doubly Ordered Non-Symmetrical Correspondence Analysis
        4. 7.4 Singly Ordered Non-Symmetrical Correspondence Analysis
        5. 7.5 Coordinate Systems for Ordered Non-Symmetrical Correspondence Analysis
        6. 7.6 Tests of Asymmetric Association
        7. 7.7 Distances in Ordered Non-Symmetrical Correspondence Analysis
        8. 7.8 Doubly Ordered Non-Symmetrical Correspondence of Asbestos Data
        9. 7.9 Singly Ordered Non-Symmetrical Correspondence Analysis of Drug Data
        10. 7.10 R Code for Ordered Non-Symmetrical Correspondence Analysis
        11. References
      6. Chapter 8: External Stability and Confidence Regions
        1. 8.1 Introduction
        2. 8.2 On the Statistical Significance of a Point
        3. 8.3 Circular Confidence Regions for Classical Correspondence Analysis
        4. 8.4 Elliptical Confidence Regions for Classical Correspondence Analysis
        5. 8.5 Confidence Regions for Non-Symmetrical Correspondence Analysis
        6. 8.6 Approximate p-Values and Classical Correspondence Analysis
        7. 8.7 Approximate p-Values and Non-Symmetrical Correspondence Analysis
        8. 8.8 Bootstrap Elliptical Confidence Regions
        9. 8.9 Ringrose's Bootstrap Confidence Regions
        10. 8.10 Confidence Regions and Selikoff's Asbestos Data
        11. 8.11 Confidence Regions and Mother–Child Attachment Data
        12. 8.12 R Code
        13. References
      7. Chapter 9: Variants of Correspondence Analysis
        1. 9.1 Introduction
        2. 9.2 Correspondence Analysis Using Adjusted Standardised Residuals
        3. 9.3 Correspondence Analysis Using the Freeman–Tukey Statistic
        4. 9.4 Correspondence Analysis of Ranked Data
        5. 9.5 R Code
        6. 9.6 The Correspondence Analysis Family
        7. 9.7 Other Techniques
        8. References
    10. Part Three: Correspondence Analysis of Multi-Way Contingency Tables
      1. Chapter 10: Coding and Multiple Correspondence Analysis
        1. 10.1 Introduction to Coding
        2. 10.2 Coding Data
        3. 10.3 Coding Ordered Categorical Variables by Orthogonal Polynomials
        4. 10.4 Burt Matrix
        5. 10.5 An Introduction to Multiple Correspondence Analysis
        6. 10.6 Multiple Correspondence Analysis
        7. 10.7 Variants of Multiple Correspondence Analysis
        8. 10.8 Ordered Multiple Correspondence Analysis
        9. 10.9 Applications
        10. 10.10 R Code
        11. References
      2. Chapter 11: Symmetrical and Non-Symmetrical Three-Way Correspondence Analysis
        1. 11.1 Introduction
        2. 11.2 Notation
        3. 11.3 Symmetric and Asymmetric Association in Three-Way Contingency Tables
        4. 11.4 Partitioning Three-Way Measures of Association
        5. 11.5 Formal Tests of Predictability
        6. 11.6 Tucker3 Decomposition for Three-Way Tables
        7. 11.7 Correspondence Analysis of Three-Way Contingency Tables
        8. 11.8 Modelling of Partial and Marginal Dependence
        9. 11.9 Graphical Representation
        10. 11.10 On the Application of Partitions
        11. 11.11 On the Application of Three-Way Correspondence Analysis
        12. 11.12 R Code
        13. References
    11. Part Four: The Computation of Correspondence Analysis
      1. Chapter 12: Computing and Correspondence Analysis
        1. 12.1 Introduction
        2. 12.2 A Look Through Time
        3. 12.3 The Impact of R
        4. 12.4 Some Stand-Alone Programs
        5. References
    12. Index
    13. End User License Agreement