Correspondence Analysis: Theory, Practice and New Strategies -- Contents -- Foreword -- Preface -- Part One: Introduction -- 1 Data Visualisation -- 1.1 A Very Brief Introduction to Data Visualisation -- 1.1.1 A Very Brief History -- 1.1.2 Introduction to Visualisation Tools for Numerical Data -- 1.1.3 Introduction to Visualisation Tools for Univariate Categorical Data -- 1.2 Data Visualisation for Contingency Tables -- 1.2.1 Fourfold Displays -- 1.3 Other Plots -- 1.4 Studying Exposure to Asbestos -- 1.4.1 Asbestos and Irving J. Selikoff -- 1.4.2 Selikoff's Data -- 1.4.3 Numerical Analysis of Selikoff's Data -- 1.4.4 A Graphical Analysis of Selikoff's Data -- 1.4.5 Classical Correspondence Analysis of Selikoff's Data -- 1.4.6 Other Methods of Graphical Analysis -- 1.5 Happiness Data -- 1.6 Correspondence Analysis Now -- 1.6.1 A Bibliographic Taste -- 1.6.2 The Increasing Popularity of Correspondence Analysis -- 1.6.3 The Growth of the Correspondence Analysis Family Tree -- 1.7 Overview of the Book -- 1.8 R Code -- References -- 2 Pearson's Chi-Squared Statistic -- 2.1 Introduction -- 2.2 Pearson's Chi-Squared Statistic -- 2.2.1 Notation -- 2.2.2 Measuring the Departure from Independence -- 2.2.3 Pearson's Chi-Squared Statistic -- 2.2.4 Other χ² Measures of Association -- 2.2.5 The Power Divergence Statistic -- 2.2.6 Dealing with the Sample Size -- 2.3 The Goodman--Kruskal Tau Index -- 2.3.1 Other Measures and Issues -- 2.4 The 2 × 2 Contingency Table -- 2.4.1 Yates' Continuity Correction -- 2.5 Early Contingency Tables -- 2.5.1 The Impact of Adolph Quetelet -- 2.5.2 Gavarret's (1840) Legitimate Children Data -- 2.5.3 Finley's (1884) Tornado Data -- 2.5.4 Galton's (1892) Fingerprint Data -- 2.5.5 Final Comments -- 2.6 R Code -- 2.6.1 Expectation and Variance of the Pearson Chi-Squared Statistic -- 2.6.2 Pearson's Chi-Squared Test of Independence.

2.6.3 The Cressie--Read Statistic -- References -- Part Two: Correspondence Analysis of Two-Way Contingency Tables -- 3 Methods of Decomposition -- 3.1 Introduction -- 3.2 Reducing Multidimensional Space -- 3.3 Profiles and Cloud of Points -- 3.4 Property of Distributional Equivalence -- 3.5 The Triplet and Classical Reciprocal Averaging -- 3.5.1 One-Dimensional Reciprocal Averaging -- 3.5.2 Matrix Form of One-Dimensional Reciprocal Averaging -- 3.5.3 M-Dimensional Reciprocal Averaging -- 3.5.4 Some Historical Comments -- 3.6 Solving the Triplet Using Eigen-Decomposition -- 3.6.1 The Decomposition -- 3.6.2 Example -- 3.7 Solving the Triplet Using Singular Value Decomposition -- 3.7.1 The Standard Decomposition -- 3.7.2 The Generalised Decomposition -- 3.8 The Generalised Triplet and Reciprocal Averaging -- 3.9 Solving the Generalised Triplet Using Gram--Schmidt Process -- 3.9.1 Ordered Categorical Variables and a priori Scores -- 3.9.2 On Finding Orthogonalised Vectors -- 3.9.3 A Recurrence Formulae Approach -- 3.9.4 Changing the Basis Vector -- 3.9.5 Generalised Correlations -- 3.10 Bivariate Moment Decomposition -- 3.11 Hybrid Decomposition -- 3.11.1 An Alternative Singly Ordered Approach -- 3.12 R Code -- 3.12.1 Eigen-Decomposition in R -- 3.12.2 Singular Value Decomposition in R -- 3.12.3 Singular Value Decomposition for Matrix Approximation -- 3.12.4 Generating Emerson's Polynomials -- 3.13 A Preliminary Graphical Summary -- 3.14 Analysis of Analgesic Drugs -- References -- 4 Simple Correspondence Analysis -- 4.1 Introduction -- 4.2 Notation -- 4.3 Measuring Departures from Complete Independence -- 4.3.1 The 'Duplication Constant' -- 4.3.2 Pearson Ratios -- 4.4 Decomposing the Pearson Ratio -- 4.5 Coordinate Systems -- 4.5.1 Standard Coordinates -- 4.5.2 Principal Coordinates -- 4.5.3 Biplot Coordinates -- 4.6 Distances.

4.6.1 Distance from the Origin -- 4.6.2 Intra-Variable Distances and the Lp Metric -- 4.6.3 Inter-Variable Distances -- 4.7 Transition Formulae -- 4.8 Moments of the Principal Coordinates -- 4.8.1 The Mean of fim -- 4.8.2 The Variance of fim -- 4.8.3 The Skewness of fim -- 4.8.4 The Kurtosis of fim -- 4.8.5 Moments of the Asbestos Data -- 4.9 How Many Dimensions to Use? -- 4.10 R Code -- 4.11 Other Theoretical Issues -- 4.12 Some Applications of Correspondence Analysis -- 4.13 Analysis of a Mother's Attachment to Her Child -- References -- 5 Non-Symmetrical Correspondence Analysis -- 5.1 Introduction -- 5.2 The Goodman--Kruskal Tau Index -- 5.2.1 The Tau Index as a Measure of the Increase in Predictability -- 5.2.2 The Tau Index in the Context of ANOVA -- 5.2.3 The Sensitivity of τ -- 5.2.4 A Demonstration: Revisiting Selikoff's Asbestos Data -- 5.3 Non-Symmetrical Correspondence Analysis -- 5.3.1 The Centred Column Profile Matrix -- 5.3.2 Decomposition of τ -- 5.4 The Coordinate Systems -- 5.4.1 Standard Coordinates -- 5.4.2 Principal Coordinates -- 5.4.3 Biplot Coordinates -- 5.5 Transition Formulae -- 5.5.1 Supplementary Points -- 5.5.2 Reconstruction Formulae -- 5.6 Moments of the Principal Coordinates -- 5.6.1 The Mean of fim -- 5.6.2 The Variance of fim -- 5.6.3 The Skewness of fim -- 5.6.4 The Kurtosis of fim -- 5.7 The Distances -- 5.7.1 Column Distances -- 5.7.2 Row Distances -- 5.8 Comparison with Simple Correspondence Analysis -- 5.9 R Code -- 5.10 Analysis of a Mother's Attachment to Her Child -- References -- 6 Ordered Correspondence Analysis -- 6.1 Introduction -- 6.2 Pearson's Ratio and Bivariate Moment Decomposition -- 6.3 Coordinate Systems -- 6.3.1 Standard Coordinates -- 6.3.2 The Generalised Correlations -- 6.3.3 Principal Coordinates -- 6.3.4 Location, Dispersion and Higher Order Components.

6.3.5 The Correspondence Plot and Generalised Correlations -- 6.3.6 Impact on the Choice of Scores -- 6.4 Artificial Data Revisited -- 6.4.1 On the Structure of the Association -- 6.4.2 A Graphical Summary of the Association -- 6.4.3 An Interpretation of the Axes and Components -- 6.4.4 The Impact of the Choice of Scores -- 6.5 Transition Formulae -- 6.6 Distance Measures -- 6.6.1 Distance from the Origin -- 6.6.2 Intra-Variable Distances -- 6.7 Singly Ordered Analysis -- 6.8 R Code -- 6.8.1 Generalised Correlations and Principal Inertias -- 6.8.2 Doubly Ordered Correspondence Analysis -- References -- 7 Ordered Non-Symmetrical Correspondence Analysis -- 7.1 Introduction -- 7.2 General Considerations -- 7.2.1 Orthogonal Polynomials Instead of Singular Vectors -- 7.3 Doubly Ordered Non-Symmetrical Correspondence Analysis -- 7.3.1 Bivariate Moment Decomposition -- 7.3.2 Generalised Correlations in Bivariate Moment Decomposition -- 7.4 Singly Ordered Non-Symmetrical Correspondence Analysis -- 7.4.1 Hybrid Decomposition for an Ordered Predictor Variable -- 7.4.2 Hybrid Decomposition in the Case of Ordered Response Variables -- 7.4.3 Generalised Correlations in Hybrid Decomposition -- 7.5 Coordinate Systems for Ordered Non-Symmetrical Correspondence Analysis -- 7.5.1 Polynomial Plots for Doubly Ordered Non-Symmetrical Correspondence Analysis -- 7.5.2 Polynomial Biplot for Doubly Ordered Non-Symmetrical Correspondence Analysis -- 7.5.3 Polynomial Plot for Singly Ordered Non-Symmetrical Correspondence Analysis with an Ordered Predictor Variable -- 7.5.4 Polynomial Biplot for Singly Ordered Non-Symmetrical Correspondence Analysis with an Ordered Predictor Variable -- 7.5.5 Polynomial Plot for Singly Ordered Non-Symmetrical Correspondence Analysis with an Ordered Response Variable.

7.5.6 Polynomial Biplot for Singly Ordered Non-Symmetrical Correspondence Analysis with an Ordered Response Variable -- 7.6 Tests of Asymmetric Association -- 7.7 Distances in Ordered Non-Symmetrical Correspondence Analysis -- 7.7.1 Distances in Doubly Ordered Non-Symmetrical Correspondence Analysis -- 7.7.2 Distances in Singly Ordered Non-Symmetrical Correspondence Analysis -- 7.8 Doubly Ordered Non-Symmetrical Correspondence of Asbestos Data -- 7.8.1 Trends -- 7.9 Singly Ordered Non-Symmetrical Correspondence Analysis of Drug Data -- 7.9.1 Predictability of Ordered Rows Given Columns -- 7.10 R Code for Ordered Non-Symmetrical Correspondence Analysis -- References -- 8 External Stability and Confidence Regions -- 8.1 Introduction -- 8.2 On the Statistical Significance of a Point -- 8.3 Circular Confidence Regions for Classical Correspondence Analysis -- 8.4 Elliptical Confidence Regions for Classical Correspondence Analysis -- 8.4.1 The Information in the Optimal Correspondence Plot -- 8.4.2 The Information in the First Two Dimensions -- 8.4.3 Eccentricity of Elliptical Regions -- 8.4.4 Comparison of Confidence Regions -- 8.5 Confidence Regions for Non-Symmetrical Correspondence Analysis -- 8.5.1 Circular Regions in Non-Symmetrical Correspondence Analysis -- 8.5.2 Elliptical Regions in Non-Symmetrical Correspondence Analysis -- 8.6 Approximate p-values and Classical Correspondence Analysis -- 8.6.1 Approximate ..-values Based on Confidence Circles -- 8.6.2 Approximate ..-values Based on Confidence Ellipses -- 8.7 Approximate p-values and Non-Symmetrical Correspondence Analysis -- 8.8 Bootstrap Elliptical Confidence Regions -- 8.9 Ringrose's Bootstrap Confidence Regions -- 8.9.1 Confidence Ellipses and Covariance Matrix -- 8.10 Confidence Regions and Selikoff's Asbestos Data -- 8.11 Confidence Regions and Mother--Child Attachment Data -- 8.12 R Code.

8.12.1 Calculating the Path of a Confidence Ellipse.