Correspondence Analysis
Theory, Practice and New Strategies
Wiley Series in Probability and Statistics
1. Auflage Oktober 2014
592 Seiten, Hardcover
Wiley & Sons Ltd
Kurzbeschreibung
A review of the conventional approaches to correspondence analysis as well as new advances that have been made over the last decade, Correspondence Analysis: Theory, Practice and New Strategies discusses the theoretical and practical issues surrounding correspondence analysis. Examining key adaptations for which correspondence analysis can be used, the text provides students and researchers with a comprehensive link between association measures, graphical depiction of association, ordered categorical variables, and ecological inference issues. The authors present a comprehensive theoretical description of non-symmetrical correspondence analysis.
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.
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
School of Mathematics & Physical Sciences, University of Newcastle, Australia
Rosaria Lombardo
Department of Economics, Second University of Naples, Italy
