Eric J. Beh - An Introduction to Correspondence Analysis

1 Cover

2 Title Page An Introduction to Correspondence Analysis Eric J. Beh School of Mathematical & Physical Sciences, University of Newcastle, Australia Rosaria Lombardo Department of Economics, University of Campania “Luigi Vanvitelli,” Italy

3 Copyright

4 Dedication

5 Preface

6 1 Introduction1.1 Data Visualisation 1.2 Correspondence Analysis in a “Nutshell” 1.3 Data Sets 1.4 Symmetrical Versus Asymmetrical Association 1.5 Notation 1.6 Formal Test of Symmetrical Association 1.7 Formal Test of Asymmetrical Association 1.8 Correspondence Analysis and R 1.9 Overview of the Book

7 Part I: Classical Analysis of Two Categorical Variables 2 Simple Correspondence Analysis2.1 Introduction 2.2 Reducing Multi-dimensional Space 2.3 Measuring Symmetric Association 2.4 Decomposing the Pearson Residual for Nominal Variables 2.5 Constructing a Low-Dimensional Display 2.6 Practicalities of the Low-Dimensional Plot 2.7 The Biplot Display 2.8 The Case for No Visual Display 2.9 Detecting Statistically Significant Points 2.10 Approximate p-values 2.11 Final Comments 3 Non-Symmetrical Correspondence Analysis3.1 Introduction 3.2 Quantifying Asymmetric Association 3.3 Decomposing for Nominal Variables 3.4 Constructing a Low-Dimensional Display 3.5 Practicalities of the Low-Dimensional Plot 3.6 The Biplot Display 3.7 Detecting Statistically Significant Points 3.8 Final Comments

8 Part II: Ordinal Analysis of Two Categorical Variables 4 Simple Ordinal Correspondence Analysis 4.1 Introduction 4.2 A Simple Correspondence Analysis of the Temperature Data 4.3 On the Mean and Variation of Profiles with Ordered Categories 4.4 Decomposing the Pearson Residual for Ordinal Variables 4.5 Constructing a Low-Dimensional Display 4.6 The Biplot Display 4.7 Final Comments 5 Ordered Non-symmetrical Correspondence Analysis5.1 Introduction 5.2 The Goodman–Kruskal tau Index Revisited 5.3 Decomposing for Ordinal and Nominal Variables 5.4 Constructing a Low-Dimensional Display 5.5 The Biplot 5.6 Some Final Words

9 Part III: Analysis of Multiple Categorical Variables 6 Multiple Correspondence Analysis6.1 Introduction 6.2 Crisp Coding and the Indicator Matrix 6.3 The Burt Matrix 6.4 Stacking 6.5 Final Comments 7 Multi-way Correspondence Analysis7.1 An Introduction 7.2 Pearson’s Residual and the Partition of 7.3 Symmetric Multi-way Correspondence Analysis 7.4 Constructing a Low-Dimensional Display 7.5 The Marcotorchino Residual and the Partition of 7.6 Non-symmetrical Multi-way Correspondence Analysis 7.7 Constructing a Low-Dimensional Display 7.8 Final Comments

10 References

11 Author Index

12 Subject Index

13 End User License Agreement

1 Chapter 1 Table 1.1 Cross-classification of Country of origin of the participants and th... Table 1.2 Temperature by Month in La Guardia airport, . Table 1.3 Men’s shoplifting data: Item stolen versus mid-point of the perpetra... Table 1.4 Cross-classification of 219 alligators by their Size , primary Food o... Table 1.5 Notation used for a contingency table. Table 1.6 Expected cell counts, under independence, for the traditional Europ...Table 1.7 R packages and some variants of correspondence analysis for two var...Table 1.8 R packages and some variants of correspondence analysis for multipl...

2 Chapter 2Table 2.1 The Pearson standardised residuals, , for Table 1.1.Table 2.2 The Pearson residuals, , for the traditional European food data of ...Table 2.3 The values from the GSVD of for Table 1.1.Table 2.4 The values from the GSVD of for Table 1.1.Table 2.5 The principal coordinates, , of Table 1.1.Table 2.6 The principal coordinates, , of Table 1.1.Table 2.7 The values of Table 1.1.Table 2.8 Contribution and percentage contribution, of each Country catego...Table 2.9 Contribution and percentage contribution of each Free-word categ...Table 2.10 Features of the confidence ellipses for the Free-word categories ...Table 2.11 Features of the confidence ellipses for the Country categories li...

3 Chapter 3Table 3.1 The weighted centred column profiles, , of Table 1.1.Table 3.2 The values from the GSVD of for Table 1.1.Table 3.3 The values from the GSVD of