Correspondence Analysis

Foreword xv Preface xvii Part One Introduction 1 1 Data Visualisation 3 1.1 A Very Brief Introduction to Data Visualisation 3 1.2 Data Visualisation for Contingency Tables 10 1.3 Other Plots 12 1.4 Studying Exposure to Asbestos 13 1.5 Happiness Data 25 1.6 Correspondence Analysis Now 29 1.7 Overview of the Book 34 1.8 R Code 35 References 36 2 Pearson's Chi-Squared Statistic 44 2.1 Introduction 44 2.2 Pearson's Chi-Squared Statistic 44 2.3 The Goodman--Kruskal Tau Index 51 2.4 The 2 × 2 Contingency Table 52 2.5 Early Contingency Tables 54 2.6 R Code 61 References 67 Part Two Correspondence Analysis of Two-Way Contingency Tables 71 3 Methods of Decomposition 73 3.1 Introduction 73 3.2 Reducing Multidimensional Space 73 3.3 Profiles and Cloud of Points 74 3.4 Property of Distributional Equivalence 79 3.5 The Triplet and Classical Reciprocal Averaging 79 3.6 Solving the Triplet Using Eigen-Decomposition 84 3.7 Solving the Triplet Using Singular Value Decomposition 86 3.8 The Generalised Triplet and Reciprocal Averaging 89 3.9 Solving the Generalised Triplet Using Gram--Schmidt Process 91 3.10 Bivariate Moment Decomposition 100 3.11 Hybrid Decomposition 100 3.12 R Code 103 3.13 A Preliminary Graphical Summary 109 3.14 Analysis of Analgesic Drugs 112 References 115 4 Simple Correspondence Analysis 120 4.1 Introduction 120 4.2 Notation 121 4.3 Measuring Departures from Complete Independence 122 4.4 Decomposing the Pearson Ratio 124 4.5 Coordinate Systems 126 4.6 Distances 136 4.7 Transition Formulae 140 4.8 Moments of the Principal Coordinates 141 4.9 How Many Dimensions to Use? 145 4.10 R Code 147 4.11 Other Theoretical Issues 154 4.12 Some Applications of Correspondence Analysis 156 4.13 Analysis of a Mother's Attachment to Her Child 158 References 165 5 Non-Symmetrical Correspondence Analysis 177 5.1 Introduction 177 5.2 The Goodman--Kruskal Tau Index 180 5.3 Non-Symmetrical Correspondence Analysis 186 5.4 The Coordinate Systems 188 5.5 Transition Formulae 197 5.6 Moments of the Principal Coordinates 199 5.7 The Distances 201 5.8 Comparison with Simple Correspondence Analysis 204 5.9 R Code 204 5.10 Analysis of a Mother's Attachment to Her Child 209 References 212 6 Ordered Correspondence Analysis 216 6.1 Introduction 216 6.2 Pearson's Ratio and Bivariate Moment Decomposition 221 6.3 Coordinate Systems 222 6.4 Artificial Data Revisited 233 6.5 Transition Formulae 236 6.6 Distance Measures 238 6.7 Singly Ordered Analysis 239 6.8 R Code 241 References 248 7 Ordered Non-Symmetrical Correspondence Analysis 251 7.1 Introduction 251 7.2 General Considerations 252 7.3 Doubly Ordered Non-Symmetrical Correspondence Analysis 254 7.4 Singly Ordered Non-Symmetrical Correspondence Analysis 257 7.5 Coordinate Systems for Ordered Non-Symmetrical Correspondence Analysis 259 7.6 Tests of Asymmetric Association 265 7.7 Distances in Ordered Non-Symmetrical Correspondence Analysis 266 7.8 Doubly Ordered Non-Symmetrical Correspondence of Asbestos Data 269 7.9 Singly Ordered Non-Symmetrical Correspondence Analysis of Drug Data 277 7.10 R Code for Ordered Non-Symmetrical Correspondence Analysis 283 References 300 8 External Stability and Confidence Regions 302 8.1 Introduction 302 8.2 On the Statistical Significance of a Point 303 8.3 Circular Confidence Regions for Classical Correspondence Analysis 304 8.4 Elliptical Confidence Regions for Classical Correspondence Analysis 306 8.5 Confidence Regions for Non-Symmetrical Correspondence Analysis 311 8.6 Approximate -values and Classical Correspondence Analysis 313 8.7 Approximate -values and Non-Symmetrical Correspondence Analysis 315 8.8 Bootstrap Elliptical Confidence Regions 315 8.9 Ringrose's Bootstrap Confidence Regions 316 8.10 Confidence Regions and Selikoff's Asbestos Data 318 8.11 Confidence Regions and Mother--Child Attachment Data 322 8.12 R Code 325 References 335 9 Variants of Correspondence Analysis 337 9.1 Introduction 337 9.2 Correspondence Analysis Using Adjusted Standardised Residuals 337 9.3 Correspondence Analysis Using the Freeman--Tukey Statistic 340 9.4 Correspondence Analysis of Ranked Data 342 9.5 R Code 343 9.6 The Correspondence Analysis Family 353 9.7 Other Techniques 365 References 366 Part Three Correspondence Analysis of Multi-Way Contingency Tables 373 10 Coding and Multiple Correspondence Analysis 375 10.1 Introduction to Coding 375 10.2 Coding Data 377 10.3 Coding Ordered Categorical Variables by Orthogonal Polynomials 382 10.4 Burt Matrix 384 10.5 An Introduction to Multiple Correspondence Analysis 386 10.6 Multiple Correspondence Analysis 388 10.7 Variants of Multiple Correspondence Analysis 395 10.8 Ordered Multiple Correspondence Analysis 398 10.9 Applications 405 10.10 R Code 417 References 444 11 Symmetrical and Non-Symmetrical Three-Way Correspondence Analysis 451 11.1 Introduction 451 11.2 Notation 453 11.3 Symmetric and Asymmetric Association in Three-Way Contingency Tables 454 11.4 Partitioning Three-Way Measures of Association 455 11.5 Formal Tests of Predictability 463 11.6 Tucker3 Decomposition for Three-Way Tables 466 11.7 Correspondence Analysis of Three-Way Contingency Tables 467 11.8 Modelling of Partial and Marginal Dependence 470 11.9 Graphical Representation 471 11.10 On the Application of Partitions 474 11.11 On the Application of Three-Way Correspondence Analysis 477 11.12 R Code 490 References 511 Part Four The Computation of Correspondence Analysis 517 12 Computing and Correspondence Analysis 519 12.1 Introduction 519 12.2 A Look Through Time 519 12.3 The Impact of R 523 12.4 Some Stand-Alone Programs 533 References 540 Index 545