Eric J. Beh, Rosaria Lombardo

Correspondence Analysis

Theory, Practice and New Strategies

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 592
• Erscheinungstermin: 17. November 2014
• Englisch
• Abmessung: 250mm x 175mm x 36mm
• Gewicht: 1189g
• ISBN-13: 9781119953241
• ISBN-10: 1119953243
• Artikelnr.: 39043654

Autorenporträt

Eric J. Beh School of Mathematics & Physical Sciences, University of Newcastle, Australia Rosaria Lombardo Department of Economics, Second University of Naples, Italy

Inhaltsangabe

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