Foreword
Preface
Acknowledgements
Contents
Part I Joint Graphical Display
1 Personal Reflections
1.1 Early Days
1.2 Internationalization
1.3 Books in French, Japanese and English
1.4 Names for Quantification Theory
1.5 Two Books with Different Orientations
1.6 Joint Graphical Display
1.7 A Promise to J. Douglas Carroll
1.8 From Dismay to Encouragement
References
2 Mathematical Preliminaries
2.1 Graphs with Orthogonal Coordinates
2.1.1 Linear Combination of Variables
2.1.2 Principal Axes
2.2 Correlation and Orthogonal Axes
2.3 Standardized Versus Non-standardized PCA
2.4 Principal Versus Standard Coordinates
References
3 Bi-modal Quantification and Graphs
3.1 Likert Scale
3.1.1 Its Ubiquitous Misuse
3.1.2 Validity Check
3.2 Quantification Theory
3.2.1 Quantification by Reciprocal Averaging
3.2.2 Simultaneous Linear Regressions
3.3 Bi-linear Decomposition
3.3.1 Key Statistic: Singular Values
3.4 Bi-modal Quantification and Space
3.5 Step-by-Step Numerical Illustrations
3.5.1 Basic Quantification Analysis
3.6 Our Focal Points
3.6.1 What Does Total Information Mean?
3.6.2 What is Joint Graphical Display
3.7 Currently Popular Methods for Graphical Display
3.7.1 French Plot or Symmetric Scaling
3.7.2 Non-symmetric Scaling (Asymmetric Scaling)
3.7.3 Comparisons
3.7.4 Rational 2-D Symmetric Plot
3.7.5 CGS Scaling
3.8 Joint Graphs and Contingency Tables
3.8.1 A Theorem on Distance and Dimensionality
References
4 Data Formats and Geometry
4.1 Contingency Table in Different Formats
4.2 Algebraic Differences of Distinct Formats
4.3 CGS Scaling: Incomplete Theory
4.4 More Information on Structure of Data
References
5 Coordinates for Joint Graphs
5.1 Coordinates for Rows and Columns
5.2 One-Component Case
5.3 Theory of Space Partitions
5.4 Two-Component Case
5.5 Three-Component Case
5.6 Wisdom of French Plot
5.7 General Case
5.8 Further Considerations
5.8.1 Graphical Approach and Further Problems
5.8.2 Within-Set Distance in Dual Space
References
6 Clustering as an Alternative
6.1 Decomposition of Input Data
6.1.1 Rorschach Data
6.1.2 Barley Data
6.2 Partitions of Super-Distance Matrix
6.3 Outlines of Cluster Analysis
6.3.1 Universal Transform for Clustering (UTC)
6.4 Clustering of Super-Distance Matrix
6.4.1 Hierarchical Cluster Analysis: Rorschach Data
6.4.2 Hierarchical Cluster Analysis: Barley Data
6.4.3 Partitioning Cluster Analysis: Rorschach Data
6.4.4 Partitioning Cluster Analysis: Barley Data
6.5 Cluster Analysis of Between-Set Relations
6.5.1 Hierarchical Cluster Analysis of Rorschach Data (UTC)
6.5.2 Hierarchical Cluster Analysis of Barley Data (UTC)
6.5.3 Partitioning Cluster Analysis: Rorschach Data and Barley Data (UTC)
6.5.4 Effects of Constant Q for UTC on Cluster Formation
6.6 Overlapping Versus Non-overlapping Clusters
6.7 Discussion and Conclusion
6.8 Final Comments on Part 1
References
Part II Scoring Strategies andย theย Graphical Display
7 Scoring and Profiles
7.1 Introduction
7.2 Profiles
7.3 The Method Reciprocal Averaging
7.3.1 An Overview
7.3.2 Profiles
7.3.3 The Iterative Approach
7.3.4 The Role of Eigendecomposition
7.3.5 The Role of Singular Value Decomposition
7.3.6 Models of Correlation and Association
7.4 Canonical Correlation Analysis
7.4.1 An Overview
7.4.2 The Method
7.5 Example
7.5.1 One-Dimensional Solution via Reciprocal Averaging
7.5.2 K-Dimensional Solution via SVD
7.5.3 On Reconstituting the Cell Frequencies
7.6 Final Remarks
References
8 Some Generalizations of Reciprocal Averaging
8.1 Introduction
8.2 Method of Reciprocal Medians (MRM)
8.3 Reciprocal Geometric Averaging (RGA)
8.3.1 RGA of the First Kind (RGA1)
8.3.2 RGA of the Second Kind (RGA2)
8.3.3 RGA of the Third Kind (RGA3)
8.4 Reciprocal Harmonic Averaging (RHA)
8.5 Final Remarks
References
9 History of the Biplot
9.1 Introduction
9.2 Biplot Construction
9.3 Biplot for Principal Component Analysis
9.4 Final Remarks
References
10 Biplots for Variants of Correspondence Analysis
10.1 Introduction
10.2 Biplots for Simple Correspondence AnalysisโThe Symmetric Case
10.3 Biplots for Simple Correspondence AnalysisโThe Asymmetric Case
10.4 Ordered Simple Correspondence Analysis
10.4.1 An Overview
10.4.2 Biplots for Ordered Simple Correspondence Analysis
10.4.3 The Biplot and a Re-Examination of Table3.1ๆฅๆ ๆธ็ eflinktab3.13.13
10.5 The Biplot for Multi-Way Correspondence Analysis
10.5.1 An Overview
10.5.2 TUCKER3 Decomposition
10.6 The Interactive Biplot
10.6.1 The Biplot and Three-Way Correspondence Analysis
10.6.2 Size and Nature of the Dependence
10.6.3 The Interactive Biplot
10.7 Final Remarks
References
11 On the Analysis of Over-Dispersed Categorical Data
11.1 Introduction
11.2 Generalized Pearson Residual
11.3 Special Cases
11.3.1 Generalized Poisson Distribution
11.3.2 Negative Binomial Distribution
11.3.3 Conway-Maxwell Poisson Distribution
11.4 Over-Dispersion, the Biplot and a Re-Examination of Table3.5ๆฅๆ ๆธ็ eflinktab3.53.53
11.5 Stabilizing the Variance
11.5.1 The Adjusted Standardized Residual
11.5.2 The Freeman-Tukey Residual
11.6 Final Remarks
References