An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo

• Record Nr.: UNINA9910555118003321
• Autore: Beh Eric J.
• Pubbl/distr/stampa: Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021]; ©2021
• ISBN: 1-119-04196-1; 1-119-04448-0
• Descrizione fisica: 1 online resource (243 pages) : illustrations
• Collana: Wiley Series in Probability and Statistics Ser.
• Disciplina: 519.537
• Soggetti: Correspondence analysis (Statistics); Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction -- 1.1 Data Visualisation -- 1.2 Correspondence Analysis in a "Nutshell" -- 1.3 Data Sets -- 1.3.1 Traditional European Food Data -- 1.3.2 Temperature Data -- 1.3.3 Shoplifting Data -- 1.3.4 Alligator Data -- 1.4 Symmetrical Versus Asymmetrical Association -- 1.5 Notation -- 1.5.1 The Two‐way Contingency Table -- 1.5.2 The Three‐way Contingency Table -- 1.6 Formal Test of Symmetrical Association -- 1.6.1 Test of Independence for Two‐way Contingency Tables -- 1.6.2 The Chi‐squared Statistic for a Two‐way Table -- 1.6.3 Analysis of the Traditional European Food Data -- 1.6.4 The Chi‐squared Statistic for a Three‐way Table -- 1.6.5 Analysis of the Alligator Data -- 1.7 Formal Test of Asymmetrical Association -- 1.7.1 Test of Predictability for Two‐way Contingency Tables -- 1.7.2 The Goodman-Kruskal tau Index -- 1.7.3 Analysis of the Traditional European Food Data -- 1.7.4 Test of Predictability for Three‐way Contingency Tables -- 1.7.5 Marcotorchino's Index -- 1.7.6 Analysis of the Alligator Data -- 1.7.7 The Gray-Williams Index and Delta Index -- 1.8 Correspondence Analysis and R -- 1.9 Overview of the Book -- Part I Classical Analysis of Two Categorical Variables -- Chapter 2 Simple Correspondence Analysis -- 2.1 Introduction -- 2.2 Reducing Multi‐dimensional Space -- 2.2.1 Profiles Cloud of Points -- 2.2.2 Profiles for ; the Traditional European Food Data -- 2.2.3 Weighted Centred Profiles -- 2.3 Measuring Symmetric Association -- 2.3.1 The Pearson Ratio -- 2.3.2 Analysis of the Traditional European Food Data -- 2.4 Decomposing the Pearson Residual for Nominal Variables -- 2.4.1 The Generalised SVD of γij−1 -- 2.4.2 SVD of the Pearson Ratio's -- 2.4.3 GSVD and the Traditional European Food Data -- 2.5 Constructing a Low‐Dimensional Display.; 2.5.1 Standard Coordinates -- 2.5.2 Principal Coordinates -- 2.6 Practicalities of the Low‐Dimensional Plot -- 2.6.1 The Two‐Dimensional Correspondence Plot -- 2.6.2 What is NOT Being Shown in a Two‐Dimensional Correspondence Plot? -- 2.6.3 The Three‐Dimensional Correspondence Plot -- 2.7 The Biplot Display -- 2.7.1 Definition -- 2.7.2 Isometric Biplots of the Traditional European Food Data -- 2.7.3 What is NOT Being Shown in a Two‐Dimensional Biplot? -- 2.8 The Case for No Visual Display -- 2.9 Detecting Statistically Significant Points -- 2.9.1 Confidence Circles and Ellipses -- 2.9.2 Confidence Ellipses for the Traditional European Food Data -- 2.10 Approximate p‐values -- 2.10.1 The Hypothesis Test and its p‐value -- 2.10.2 P‐values and the Traditional European Food Data -- 2.11 Final Comments -- Chapter 3 Non‐Symmetrical Correspondence Analysis -- 3.1 Introduction -- 3.2 Quantifying Asymmetric Association -- 3.2.1 The Goodman-Kruskal tau Index -- 3.2.2 The τ Index and the Traditional European Food Data -- 3.2.3 Weighted Centred Column Profile -- 3.2.4 Profiles of the Traditional European Food Data -- 3.3 Decomposing πi|j for Nominal Variables -- 3.3.1 The Generalised SVD of πi|j -- 3.3.2 GSVD and the Traditional Food Data -- 3.4 Constructing a Low‐Dimensional Display -- 3.4.1 Standard Coordinates -- 3.4.2 Principal Coordinates -- 3.5 Practicalities of the Low‐Dimensional Plot -- 3.5.1 The Two‐Dimensional Correspondence Plot -- 3.5.2 The Three‐Dimensional Correspondence Plot -- 3.6 The Biplot Display -- 3.6.1 Definition -- 3.6.2 The Column Isometric Biplot for the Traditional Food Data -- 3.6.3 The Three‐Dimensional Biplot -- 3.7 Detecting Statistically Significant Points -- 3.7.1 Confidence Circles and Ellipses -- 3.7.2 Confidence Ellipses for the Traditional Food Data -- 3.8 Final Comments.; Part II Ordinal Analysis of Two Categorical Variables -- Chapter 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 -- 4.3.1 Profiles of the Temperature Data -- 4.3.2 Defining Scores -- 4.3.3 On the Mean of the Profiles -- 4.3.4 On the Variation of the Profiles -- 4.3.5 Mean and Variation of Profiles for the Temperature Data -- 4.4 Decomposing the Pearson Residual for Ordinal Variables -- 4.4.1 The Bivariate Moment Decomposition of γij−1 -- 4.4.2 BMD and the Temperature Data -- 4.5 Constructing a Low‐Dimensional Display -- 4.5.1 Standard Coordinates -- 4.5.2 Principal Coordinates -- 4.5.3 Practicalities of the Ordered Principal Coordinates -- 4.6 The Biplot Display -- 4.6.1 Definition -- 4.6.2 Ordered Column Isometric Biplot -- 4.6.3 Ordered Row Isometric Biplot -- 4.6.4 Ordered Isometric Biplots for the Temperature Data -- 4.7 Final Comments -- Chapter 5 Ordered Non‐symmetrical Correspondence Analysis -- 5.1 Introduction -- 5.2 The Goodman-Kruskal tau Index Revisited -- 5.3 Decomposing πi|j for Ordinal and Nominal Variables -- 5.3.1 The Hybrid Decomposition of πi|j -- 5.3.2 Hybrid Decomposition and the Shoplifting Data -- 5.4 Constructing a Low‐Dimensional Display -- 5.4.1 Standard Coordinates -- 5.4.2 Principal Coordinates -- 5.5 The Biplot -- 5.5.1 An Overview -- 5.5.2 Column Isometric Biplot -- 5.5.3 Column Isometric Biplot of the Shoplifting Data -- 5.5.4 Row Isometric Biplot -- 5.5.5 Row ; Isometric Biplot of the Shoplifting Data -- 5.5.6 Distance Measures and the Row Isometric Biplots -- 5.6 Some Final Words -- Part III Analysis of Multiple Categorical Variables -- Chapter 6 Multiple Correspondence Analysis -- 6.1 Introduction -- 6.2 Crisp Coding and the Indicator Matrix -- 6.2.1 Crisp Coding.; 6.2.2 The Indicator Matrix -- 6.2.3 Crisp Coding and the Alligator Data -- 6.2.4 Application of Multiple Correspondence Analysis using the Indicator Matrix -- 6.3 The Burt Matrix -- 6.4 Stacking -- 6.4.1 A Definition -- 6.4.2 Stacking and the Alligator Data - Lake(Size)× Food -- 6.4.3 Stacking and the Alligator Data - Food(Size)× Lake -- 6.5 Final Comments -- Chapter 7 Multi‐way Correspondence Analysis -- 7.1 An Introduction -- 7.2 Pearson's Residual γijk−1 and the Partition of X2 -- 7.2.1 The Pearson Residual -- 7.2.2 The Partition of X2 -- 7.2.3 Partition of X2 for the Alligator Data -- 7.3 Symmetric Multi‐way Correspondence Analysis -- 7.3.1 Tucker3 Decomposition of γijk−1 -- 7.3.2 T3D and the Analysis of Two Variables -- 7.3.3 On the Choice of the Number of Components -- 7.3.4 Tucker3 Decomposition of γijk−1 and the Alligator Data -- 7.4 Constructing a Low‐Dimensional Display -- 7.4.1 Principal Coordinates -- 7.4.2 The Interactive Biplot -- 7.4.3 Column‐Tube Interactive Biplot for the Alligator Data -- 7.4.4 Row Interactive Biplot for the Alligator Data -- 7.5 The Marcotorchino Residual πi|j,k and the Partition of τM -- 7.5.1 The Marcotrochino Residual -- 7.5.2 The Partition of τM -- 7.5.3 Partition of τM for the Alligator Data -- 7.6 Non‐symmetrical Multi‐way Correspondence Analysis -- 7.6.1 Tucker3 Decomposition of πi|j,k -- 7.6.2 Tucker3 Decomposition of πi|j,k and the Alligator Data -- 7.7 Constructing a Low‐Dimensional Display -- 7.7.1 On the Choice of Coordinates -- 7.7.2 Column-Tube Interactive Biplot for the Alligator Data -- 7.8 Final Comments -- References -- Author Index -- Subject Index -- EULA.