Eric J. Beh, Rosaria Lombardo

An Introduction to Correspondence Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

Master the fundamentals of correspondence analysis with this illuminating resource An Introduction to Correspondence Analysis assists researchers in improving their familiarity with the concepts, terminology, and application of several variants of correspondence analysis. The accomplished academics and authors deliver a comprehensive and insightful treatment of the fundamentals of correspondence analysis, including the statistical and visual aspects of the subject. Written in three parts, the book begins by offering readers a description of two variants of correspondence analysis that can be applied to two-way contingency tables for nominal categories of variables. Part Two shifts the discussion to categories of ordinal variables and demonstrates how the ordered structure of these variables can be incorporated into a correspondence analysis. Part Three describes the analysis of multiple nominal categorical variables, including both multiple correspondence analysis and multi-way correspondence analysis. Readers will benefit from explanations of a wide variety of specific topics, for example: * Simple correspondence analysis, including how to reduce multidimensional space, measuring symmetric associations with the Pearson Ratio, constructing low-dimensional displays, and detecting statistically significant points * Non-symmetrical correspondence analysis, including quantifying asymmetric associations * Simple ordinal correspondence analysis, including how to decompose the Pearson Residual for ordinal variables * Multiple correspondence analysis, including crisp coding and the indicator matrix, the Burt Matrix, and stacking * Multi-way correspondence analysis, including symmetric multi-way analysis Perfect for researchers who seek to improve their understanding of key concepts in the graphical analysis of categorical data, An Introduction to Correspondence Analysis will also assist readers already familiar with correspondence analysis who wish to review the theoretical and foundational underpinnings of crucial concepts.

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Produktdetails

• Verlag: Wiley-ISTE
• Erscheinungstermin: 19. März 2021
• Englisch
• ISBN-13: 9781119041962
• Artikelnr.: 61368342

Autorenporträt

Eric J. Beh is Professor of Statistics at the School of Mathematical & Physical Sciences at the University of Newcastle, Australia. He has been actively researching in many areas of categorical data analysis including ecological inference, measures of association and categorical models. For the past 25 years his research has focused primarily on the technical, computational and practical development of correspondence analysis. He has over 100 publications and, with Rosaria Lombardo, has authored Correspondence Analysis: Theory, Methods and New Strategies published by Wiley. Together, they have given short courses and workshops around the world on this topic.

Rosaria Lombardo is Associate Professor of Statistics at the Department of Economics of the University of Campania "L. Vanvitelli", Italy. Her research interests include non-linear multivariate data analysis, quantification theory and, in particular, correspondence analysis and data visualization. Since receiving her PhD in Computational Statistics and Applications at the University of Naples "Federico II", she has authored over 100 publications including those in Statistical Science, Psychometrika, Computational Statistics & Data Analysis, and the Journal of Statistical Planning and Inference.

Inhaltsangabe

Dedication iii

Preface xi

1 Introduction 1

1.1 Data Visualisation 1

1.2 Correspondence Analysis in a "Nutshell" 3

1.3 Data Sets 4

1.3.1 Traditional European Food Data 4

1.3.2 Temperature Data 4

1.3.3 Shoplifting Data 5

1.3.4 Alligator Data 6

1.4 Symmetrical vs Asymmetrical Association 7

1.5 Notation 9

1.5.1 The Two-way Contingency Table 9

1.5.2 The Three-way Contingency Table 10

1.6 Formal Test of Symmetrical Association 11

1.6.1 Test of Independence for Two-way Contingency Tables 11

1.6.2 The Chi-squared Statistic for a Two-way Table 12

1.6.3 Analysis of the Traditional European Food Data 12

1.6.4 The Chi-squared Statistic for a Three-way Table 14

1.6.5 Analysis of the Alligator Data 15

1.7 Formal Test of Asymmetrical Association 15

1.7.1 Test of Predictability for Two-way Contingency Tables 15

1.7.2 The Goodman-Kruskal tau Index 16

1.7.3 Analysis of the Traditional European Food Data 17

1.7.4 Test of Predictability for Three-way Contingency Tables 17

1.7.5 Marcotorchino's Index 18

1.7.6 Analysis of the Alligator Data 19

1.7.7 The Gray-Williams Index & Delta Index 19

1.8 Correspondence Analysis and R 20

1.9 Overview of the Book 24

Part One Classical Analysis of Two Categorical Variables 27

2 Simple Correspondence Analysis 29

2.1 Introduction 29

2.2 Reducing Multidimensional Space 30

2.2.1 Profiles Cloud of Points 30

2.2.2 Profiles for the Traditional European Food Data 31

2.2.3 Weighted Centred Profiles 34

2.3 Measuring Symmetric Association 39

2.3.1 The Pearson Ratio 39

2.3.2 Analysis of the Traditional European Food Data 40

2.4 Decomposing the Pearson Residual for Nominal Variables 42

2.4.1 The Generalised SVD of gammaij . 1 42

2.4.2 SVD of the Pearson Ratio's 44

2.4.3 GSVD and the Traditional European Food Data 45

2.5 Constructing a Low-Dimensional Display 45

2.5.1 Standard Coordinates 45

2.5.2 Principal Coordinates 47

2.6 Practicalities of the Low-Dimensional Plot 51

2.6.1 The Two-Dimensional Correspondence Plot 51

2.6.2 What is NOT Being Shown in a Two-Dimensional Correspondence

Plot? 54

2.6.3 The Three-Dimensional Correspondence Plot 58

2.7 The Biplot Display 58

2.7.1 Definition 58

2.7.2 Isometric Biplots of the Traditional European Food Data 61

2.7.3 What is NOT Being Shown in a Two-Dimensional Biplot? 64

2.8 The Case for No Visual Display 64

2.9 Detecting Statistically Significant Points 65

2.9.1 Confidence Circles and Ellipses 65

2.9.2 Confidence Ellipses for the Traditional European Food Data 66

2.10 Approximate P-values 70

2.10.1 The Hypothesis Test and its P-value 70

2.10.2 P-values and the Traditional European Food Data 71

2.11 Final Comments 71

3 Non-Symmetrical Correspondence Analysis 73

3.1 Introduction 73

3.2 Quantifying Asymmetric Association 74

3.2.1 The Goodman-Kruskal tau Index 74

3.2.2 The tau Index and the Traditional European Food Data 74

3.2.3 Weighted Centred Column Profile 75

3.2.4 Profiles of the Traditional European Food Data 75

3.3 Decomposing pii j

for Nominal Variables 78

3.3.1 The Generalised SVD of pii j 78

3.3.2 GSVD and the Traditional Food Data 7