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Analysis of Categorical Data from Historical Perspectives [[electronic resource] ] : Essays in Honour of Shizuhiko Nishisato / / edited by Eric J. Beh, Rosaria Lombardo, Jose G. Clavel
| Analysis of Categorical Data from Historical Perspectives [[electronic resource] ] : Essays in Honour of Shizuhiko Nishisato / / edited by Eric J. Beh, Rosaria Lombardo, Jose G. Clavel |
| Autore | Beh Eric J |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (0 pages) |
| Disciplina | 519 |
| Altri autori (Persone) |
LombardoRosaria
ClavelJose G |
| Collana | Behaviormetrics: Quantitative Approaches to Human Behavior |
| Soggetto topico |
Statistics
Social sciences - Statistical methods Quantitative research Psychometrics Applied Statistics Statistics in Social Sciences, Humanities, Law, Education, Behavorial Sciences, Public Policy Statistical Theory and Methods Data Analysis and Big Data |
| ISBN | 981-9953-29-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Gratitude: A Life Relived -- Nishisato’s Psychometric World -- My Recollections of People in the World of Data Science -- A Straightforward Approach to Chi-Squared Analysis of Associations in Contingency Tables -- Contrasts for Neyman’s Modified Chi-Square Statistic in One-Way Contingency Tables. |
| Record Nr. | UNINA-9910806195503321 |
Beh Eric J
|
||
| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Correspondence analysis : theory, practice and new strategies / / Eric Beh, Rosaria Lombardo
| Correspondence analysis : theory, practice and new strategies / / Eric Beh, Rosaria Lombardo |
| Autore | Beh Eric J. |
| Pubbl/distr/stampa | Chichester, England : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (593 p.) |
| Disciplina | 519.5/37 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico | Correspondence analysis (Statistics) |
| ISBN |
1-118-76287-8
1-118-76289-4 |
| Classificazione | MAT029020 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Correspondence Analysis: Theory, Practice and New Strategies; Contents; Foreword; Preface; Part One: Introduction; 1 Data Visualisation; 1.1 A Very Brief Introduction to Data Visualisation; 1.1.1 A Very Brief History; 1.1.2 Introduction to Visualisation Tools for Numerical Data; 1.1.3 Introduction to Visualisation Tools for Univariate Categorical Data; 1.2 Data Visualisation for Contingency Tables; 1.2.1 Fourfold Displays; 1.3 Other Plots; 1.4 Studying Exposure to Asbestos; 1.4.1 Asbestos and Irving J. Selikoff; 1.4.2 Selikoff's Data; 1.4.3 Numerical Analysis of Selikoff's Data
1.4.4 A Graphical Analysis of Selikoff's Data1.4.5 Classical Correspondence Analysis of Selikoff's Data; 1.4.6 Other Methods of Graphical Analysis; 1.5 Happiness Data; 1.6 Correspondence Analysis Now; 1.6.1 A Bibliographic Taste; 1.6.2 The Increasing Popularity of Correspondence Analysis; 1.6.3 The Growth of the Correspondence Analysis Family Tree; 1.7 Overview of the Book; 1.8 R Code; References; 2 Pearson's Chi-Squared Statistic; 2.1 Introduction; 2.2 Pearson's Chi-Squared Statistic; 2.2.1 Notation; 2.2.2 Measuring the Departure from Independence; 2.2.3 Pearson's Chi-Squared Statistic 2.6.3 The Cressie--Read StatisticReferences; Part Two: Correspondence Analysis of Two-Way Contingency Tables; 3 Methods of Decomposition; 3.1 Introduction; 3.2 Reducing Multidimensional Space; 3.3 Profiles and Cloud of Points; 3.4 Property of Distributional Equivalence; 3.5 The Triplet and Classical Reciprocal Averaging; 3.5.1 One-Dimensional Reciprocal Averaging; 3.5.2 Matrix Form of One-Dimensional Reciprocal Averaging; 3.5.3 M-Dimensional Reciprocal Averaging; 3.5.4 Some Historical Comments; 3.6 Solving the Triplet Using Eigen-Decomposition; 3.6.1 The Decomposition; 3.6.2 Example 3.7 Solving the Triplet Using Singular Value Decomposition3.7.1 The Standard Decomposition; 3.7.2 The Generalised Decomposition; 3.8 The Generalised Triplet and Reciprocal Averaging; 3.9 Solving the Generalised Triplet Using Gram--Schmidt Process; 3.9.1 Ordered Categorical Variables and a priori Scores; 3.9.2 On Finding Orthogonalised Vectors; 3.9.3 A Recurrence Formulae Approach; 3.9.4 Changing the Basis Vector; 3.9.5 Generalised Correlations; 3.10 Bivariate Moment Decomposition; 3.11 Hybrid Decomposition; 3.11.1 An Alternative Singly Ordered Approach; 3.12 R Code 3.12.1 Eigen-Decomposition in R |
| Record Nr. | UNINA-9910132173303321 |
|
Beh Eric J.
|
||
| Chichester, England : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Correspondence analysis : theory, practice and new strategies / / Eric Beh, Rosaria Lombardo
| Correspondence analysis : theory, practice and new strategies / / Eric Beh, Rosaria Lombardo |
| Autore | Beh Eric J. |
| Pubbl/distr/stampa | Chichester, England : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (593 p.) |
| Disciplina | 519.5/37 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico | Correspondence analysis (Statistics) |
| ISBN |
1-118-76287-8
1-118-76289-4 |
| Classificazione | MAT029020 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Correspondence Analysis: Theory, Practice and New Strategies; Contents; Foreword; Preface; Part One: Introduction; 1 Data Visualisation; 1.1 A Very Brief Introduction to Data Visualisation; 1.1.1 A Very Brief History; 1.1.2 Introduction to Visualisation Tools for Numerical Data; 1.1.3 Introduction to Visualisation Tools for Univariate Categorical Data; 1.2 Data Visualisation for Contingency Tables; 1.2.1 Fourfold Displays; 1.3 Other Plots; 1.4 Studying Exposure to Asbestos; 1.4.1 Asbestos and Irving J. Selikoff; 1.4.2 Selikoff's Data; 1.4.3 Numerical Analysis of Selikoff's Data
1.4.4 A Graphical Analysis of Selikoff's Data1.4.5 Classical Correspondence Analysis of Selikoff's Data; 1.4.6 Other Methods of Graphical Analysis; 1.5 Happiness Data; 1.6 Correspondence Analysis Now; 1.6.1 A Bibliographic Taste; 1.6.2 The Increasing Popularity of Correspondence Analysis; 1.6.3 The Growth of the Correspondence Analysis Family Tree; 1.7 Overview of the Book; 1.8 R Code; References; 2 Pearson's Chi-Squared Statistic; 2.1 Introduction; 2.2 Pearson's Chi-Squared Statistic; 2.2.1 Notation; 2.2.2 Measuring the Departure from Independence; 2.2.3 Pearson's Chi-Squared Statistic 2.6.3 The Cressie--Read StatisticReferences; Part Two: Correspondence Analysis of Two-Way Contingency Tables; 3 Methods of Decomposition; 3.1 Introduction; 3.2 Reducing Multidimensional Space; 3.3 Profiles and Cloud of Points; 3.4 Property of Distributional Equivalence; 3.5 The Triplet and Classical Reciprocal Averaging; 3.5.1 One-Dimensional Reciprocal Averaging; 3.5.2 Matrix Form of One-Dimensional Reciprocal Averaging; 3.5.3 M-Dimensional Reciprocal Averaging; 3.5.4 Some Historical Comments; 3.6 Solving the Triplet Using Eigen-Decomposition; 3.6.1 The Decomposition; 3.6.2 Example 3.7 Solving the Triplet Using Singular Value Decomposition3.7.1 The Standard Decomposition; 3.7.2 The Generalised Decomposition; 3.8 The Generalised Triplet and Reciprocal Averaging; 3.9 Solving the Generalised Triplet Using Gram--Schmidt Process; 3.9.1 Ordered Categorical Variables and a priori Scores; 3.9.2 On Finding Orthogonalised Vectors; 3.9.3 A Recurrence Formulae Approach; 3.9.4 Changing the Basis Vector; 3.9.5 Generalised Correlations; 3.10 Bivariate Moment Decomposition; 3.11 Hybrid Decomposition; 3.11.1 An Alternative Singly Ordered Approach; 3.12 R Code 3.12.1 Eigen-Decomposition in R |
| Record Nr. | UNINA-9910822547203321 |
|
Beh Eric J.
|
||
| Chichester, England : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo
| An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo |
| Autore | Beh Eric J. |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] |
| Descrizione fisica | 1 online resource (243 pages) : illustrations |
| Disciplina | 519.537 |
| Collana | Wiley Series in Probability and Statistics Ser. |
| Soggetto topico | Correspondence analysis (Statistics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-119-04196-1
1-119-04448-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910555118003321 |
|
Beh Eric J.
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo
| An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo |
| Autore | Beh Eric J. |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] |
| Descrizione fisica | 1 online resource (243 pages) : illustrations |
| Disciplina | 519.537 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico | Correspondence analysis (Statistics) |
| ISBN |
1-119-04196-1
1-119-04448-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910676630003321 |
|
Beh Eric J.
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo
| An introduction to correspondence analysis / / Eric J. Beh and Rosaria Lombardo |
| Autore | Beh Eric J. |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] |
| Descrizione fisica | 1 online resource (243 pages) : illustrations |
| Disciplina | 519.537 |
| Collana | Wiley Series in Probability and Statistics |
| Soggetto topico | Correspondence analysis (Statistics) |
| ISBN |
1-119-04196-1
1-119-04448-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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. |
| Record Nr. | UNINA-9910807726803321 |
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Beh Eric J.
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| Hoboken, New Jersey : , : John Wiley & Sons, Incorporated, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Modern Quantification Theory : Joint Graphical Display, Biplots, and Alternatives
| Modern Quantification Theory : Joint Graphical Display, Biplots, and Alternatives |
| Autore | Nishisato Shizuhiko |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore Pte. Limited, , 2021 |
| Descrizione fisica | 1 online resource (242 pages) |
| Altri autori (Persone) |
BehEric J
LombardoRosaria ClavelJose G |
| Collana | Behaviormetrics: Quantitative Approaches to Human Behavior |
| Soggetto topico | Càlcul |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-2470-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface -- Acknowledgements -- Contents -- Part I Joint Graphical Display -- 1 Personal Reflections -- 1.1 Early Days -- 1.2 Internationalization -- 1.3 Books in French, Japanese and English -- 1.4 Names for Quantification Theory -- 1.5 Two Books with Different Orientations -- 1.6 Joint Graphical Display -- 1.7 A Promise to J. Douglas Carroll -- 1.8 From Dismay to Encouragement -- References -- 2 Mathematical Preliminaries -- 2.1 Graphs with Orthogonal Coordinates -- 2.1.1 Linear Combination of Variables -- 2.1.2 Principal Axes -- 2.2 Correlation and Orthogonal Axes -- 2.3 Standardized Versus Non-standardized PCA -- 2.4 Principal Versus Standard Coordinates -- References -- 3 Bi-modal Quantification and Graphs -- 3.1 Likert Scale -- 3.1.1 Its Ubiquitous Misuse -- 3.1.2 Validity Check -- 3.2 Quantification Theory -- 3.2.1 Quantification by Reciprocal Averaging -- 3.2.2 Simultaneous Linear Regressions -- 3.3 Bi-linear Decomposition -- 3.3.1 Key Statistic: Singular Values -- 3.4 Bi-modal Quantification and Space -- 3.5 Step-by-Step Numerical Illustrations -- 3.5.1 Basic Quantification Analysis -- 3.6 Our Focal Points -- 3.6.1 What Does Total Information Mean? -- 3.6.2 What is Joint Graphical Display -- 3.7 Currently Popular Methods for Graphical Display -- 3.7.1 French Plot or Symmetric Scaling -- 3.7.2 Non-symmetric Scaling (Asymmetric Scaling) -- 3.7.3 Comparisons -- 3.7.4 Rational 2-D Symmetric Plot -- 3.7.5 CGS Scaling -- 3.8 Joint Graphs and Contingency Tables -- 3.8.1 A Theorem on Distance and Dimensionality -- References -- 4 Data Formats and Geometry -- 4.1 Contingency Table in Different Formats -- 4.2 Algebraic Differences of Distinct Formats -- 4.3 CGS Scaling: Incomplete Theory -- 4.4 More Information on Structure of Data -- References -- 5 Coordinates for Joint Graphs -- 5.1 Coordinates for Rows and Columns.
5.2 One-Component Case -- 5.3 Theory of Space Partitions -- 5.4 Two-Component Case -- 5.5 Three-Component Case -- 5.6 Wisdom of French Plot -- 5.7 General Case -- 5.8 Further Considerations -- 5.8.1 Graphical Approach and Further Problems -- 5.8.2 Within-Set Distance in Dual Space -- References -- 6 Clustering as an Alternative -- 6.1 Decomposition of Input Data -- 6.1.1 Rorschach Data -- 6.1.2 Barley Data -- 6.2 Partitions of Super-Distance Matrix -- 6.3 Outlines of Cluster Analysis -- 6.3.1 Universal Transform for Clustering (UTC) -- 6.4 Clustering of Super-Distance Matrix -- 6.4.1 Hierarchical Cluster Analysis: Rorschach Data -- 6.4.2 Hierarchical Cluster Analysis: Barley Data -- 6.4.3 Partitioning Cluster Analysis: Rorschach Data -- 6.4.4 Partitioning Cluster Analysis: Barley Data -- 6.5 Cluster Analysis of Between-Set Relations -- 6.5.1 Hierarchical Cluster Analysis of Rorschach Data (UTC) -- 6.5.2 Hierarchical Cluster Analysis of Barley Data (UTC) -- 6.5.3 Partitioning Cluster Analysis: Rorschach Data and Barley Data (UTC) -- 6.5.4 Effects of Constant Q for UTC on Cluster Formation -- 6.6 Overlapping Versus Non-overlapping Clusters -- 6.7 Discussion and Conclusion -- 6.8 Final Comments on Part 1 -- References -- Part II Scoring Strategies and the Graphical Display -- 7 Scoring and Profiles -- 7.1 Introduction -- 7.2 Profiles -- 7.3 The Method Reciprocal Averaging -- 7.3.1 An Overview -- 7.3.2 Profiles -- 7.3.3 The Iterative Approach -- 7.3.4 The Role of Eigendecomposition -- 7.3.5 The Role of Singular Value Decomposition -- 7.3.6 Models of Correlation and Association -- 7.4 Canonical Correlation Analysis -- 7.4.1 An Overview -- 7.4.2 The Method -- 7.5 Example -- 7.5.1 One-Dimensional Solution via Reciprocal Averaging -- 7.5.2 K-Dimensional Solution via SVD -- 7.5.3 On Reconstituting the Cell Frequencies -- 7.6 Final Remarks -- References. 8 Some Generalizations of Reciprocal Averaging -- 8.1 Introduction -- 8.2 Method of Reciprocal Medians (MRM) -- 8.3 Reciprocal Geometric Averaging (RGA) -- 8.3.1 RGA of the First Kind (RGA1) -- 8.3.2 RGA of the Second Kind (RGA2) -- 8.3.3 RGA of the Third Kind (RGA3) -- 8.4 Reciprocal Harmonic Averaging (RHA) -- 8.5 Final Remarks -- References -- 9 History of the Biplot -- 9.1 Introduction -- 9.2 Biplot Construction -- 9.3 Biplot for Principal Component Analysis -- 9.4 Final Remarks -- References -- 10 Biplots for Variants of Correspondence Analysis -- 10.1 Introduction -- 10.2 Biplots for Simple Correspondence Analysis-The Symmetric Case -- 10.3 Biplots for Simple Correspondence Analysis-The Asymmetric Case -- 10.4 Ordered Simple Correspondence Analysis -- 10.4.1 An Overview -- 10.4.2 Biplots for Ordered Simple Correspondence Analysis -- 10.4.3 The Biplot and a Re-Examination of Table3.1摥映數爠eflinktab3.13.13 -- 10.5 The Biplot for Multi-Way Correspondence Analysis -- 10.5.1 An Overview -- 10.5.2 TUCKER3 Decomposition -- 10.6 The Interactive Biplot -- 10.6.1 The Biplot and Three-Way Correspondence Analysis -- 10.6.2 Size and Nature of the Dependence -- 10.6.3 The Interactive Biplot -- 10.7 Final Remarks -- References -- 11 On the Analysis of Over-Dispersed Categorical Data -- 11.1 Introduction -- 11.2 Generalized Pearson Residual -- 11.3 Special Cases -- 11.3.1 Generalized Poisson Distribution -- 11.3.2 Negative Binomial Distribution -- 11.3.3 Conway-Maxwell Poisson Distribution -- 11.4 Over-Dispersion, the Biplot and a Re-Examination of Table3.5摥映數爠eflinktab3.53.53 -- 11.5 Stabilizing the Variance -- 11.5.1 The Adjusted Standardized Residual -- 11.5.2 The Freeman-Tukey Residual -- 11.6 Final Remarks -- References. |
| Record Nr. | UNINA-9910735395803321 |
|
Nishisato Shizuhiko
|
||
| Singapore : , : Springer Singapore Pte. Limited, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Modern Quantification Theory : Joint Graphical Display, Biplots, and Alternatives
| Modern Quantification Theory : Joint Graphical Display, Biplots, and Alternatives |
| Autore | Nishisato Shizuhiko |
| Pubbl/distr/stampa | Singapore : , : Springer Singapore Pte. Limited, , 2021 |
| Descrizione fisica | 1 online resource (242 pages) |
| Altri autori (Persone) |
BehEric J
LombardoRosaria ClavelJose G |
| Collana | Behaviormetrics: Quantitative Approaches to Human Behavior |
| Soggetto topico | Càlcul |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-2470-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface -- Acknowledgements -- Contents -- Part I Joint Graphical Display -- 1 Personal Reflections -- 1.1 Early Days -- 1.2 Internationalization -- 1.3 Books in French, Japanese and English -- 1.4 Names for Quantification Theory -- 1.5 Two Books with Different Orientations -- 1.6 Joint Graphical Display -- 1.7 A Promise to J. Douglas Carroll -- 1.8 From Dismay to Encouragement -- References -- 2 Mathematical Preliminaries -- 2.1 Graphs with Orthogonal Coordinates -- 2.1.1 Linear Combination of Variables -- 2.1.2 Principal Axes -- 2.2 Correlation and Orthogonal Axes -- 2.3 Standardized Versus Non-standardized PCA -- 2.4 Principal Versus Standard Coordinates -- References -- 3 Bi-modal Quantification and Graphs -- 3.1 Likert Scale -- 3.1.1 Its Ubiquitous Misuse -- 3.1.2 Validity Check -- 3.2 Quantification Theory -- 3.2.1 Quantification by Reciprocal Averaging -- 3.2.2 Simultaneous Linear Regressions -- 3.3 Bi-linear Decomposition -- 3.3.1 Key Statistic: Singular Values -- 3.4 Bi-modal Quantification and Space -- 3.5 Step-by-Step Numerical Illustrations -- 3.5.1 Basic Quantification Analysis -- 3.6 Our Focal Points -- 3.6.1 What Does Total Information Mean? -- 3.6.2 What is Joint Graphical Display -- 3.7 Currently Popular Methods for Graphical Display -- 3.7.1 French Plot or Symmetric Scaling -- 3.7.2 Non-symmetric Scaling (Asymmetric Scaling) -- 3.7.3 Comparisons -- 3.7.4 Rational 2-D Symmetric Plot -- 3.7.5 CGS Scaling -- 3.8 Joint Graphs and Contingency Tables -- 3.8.1 A Theorem on Distance and Dimensionality -- References -- 4 Data Formats and Geometry -- 4.1 Contingency Table in Different Formats -- 4.2 Algebraic Differences of Distinct Formats -- 4.3 CGS Scaling: Incomplete Theory -- 4.4 More Information on Structure of Data -- References -- 5 Coordinates for Joint Graphs -- 5.1 Coordinates for Rows and Columns.
5.2 One-Component Case -- 5.3 Theory of Space Partitions -- 5.4 Two-Component Case -- 5.5 Three-Component Case -- 5.6 Wisdom of French Plot -- 5.7 General Case -- 5.8 Further Considerations -- 5.8.1 Graphical Approach and Further Problems -- 5.8.2 Within-Set Distance in Dual Space -- References -- 6 Clustering as an Alternative -- 6.1 Decomposition of Input Data -- 6.1.1 Rorschach Data -- 6.1.2 Barley Data -- 6.2 Partitions of Super-Distance Matrix -- 6.3 Outlines of Cluster Analysis -- 6.3.1 Universal Transform for Clustering (UTC) -- 6.4 Clustering of Super-Distance Matrix -- 6.4.1 Hierarchical Cluster Analysis: Rorschach Data -- 6.4.2 Hierarchical Cluster Analysis: Barley Data -- 6.4.3 Partitioning Cluster Analysis: Rorschach Data -- 6.4.4 Partitioning Cluster Analysis: Barley Data -- 6.5 Cluster Analysis of Between-Set Relations -- 6.5.1 Hierarchical Cluster Analysis of Rorschach Data (UTC) -- 6.5.2 Hierarchical Cluster Analysis of Barley Data (UTC) -- 6.5.3 Partitioning Cluster Analysis: Rorschach Data and Barley Data (UTC) -- 6.5.4 Effects of Constant Q for UTC on Cluster Formation -- 6.6 Overlapping Versus Non-overlapping Clusters -- 6.7 Discussion and Conclusion -- 6.8 Final Comments on Part 1 -- References -- Part II Scoring Strategies and the Graphical Display -- 7 Scoring and Profiles -- 7.1 Introduction -- 7.2 Profiles -- 7.3 The Method Reciprocal Averaging -- 7.3.1 An Overview -- 7.3.2 Profiles -- 7.3.3 The Iterative Approach -- 7.3.4 The Role of Eigendecomposition -- 7.3.5 The Role of Singular Value Decomposition -- 7.3.6 Models of Correlation and Association -- 7.4 Canonical Correlation Analysis -- 7.4.1 An Overview -- 7.4.2 The Method -- 7.5 Example -- 7.5.1 One-Dimensional Solution via Reciprocal Averaging -- 7.5.2 K-Dimensional Solution via SVD -- 7.5.3 On Reconstituting the Cell Frequencies -- 7.6 Final Remarks -- References. 8 Some Generalizations of Reciprocal Averaging -- 8.1 Introduction -- 8.2 Method of Reciprocal Medians (MRM) -- 8.3 Reciprocal Geometric Averaging (RGA) -- 8.3.1 RGA of the First Kind (RGA1) -- 8.3.2 RGA of the Second Kind (RGA2) -- 8.3.3 RGA of the Third Kind (RGA3) -- 8.4 Reciprocal Harmonic Averaging (RHA) -- 8.5 Final Remarks -- References -- 9 History of the Biplot -- 9.1 Introduction -- 9.2 Biplot Construction -- 9.3 Biplot for Principal Component Analysis -- 9.4 Final Remarks -- References -- 10 Biplots for Variants of Correspondence Analysis -- 10.1 Introduction -- 10.2 Biplots for Simple Correspondence Analysis-The Symmetric Case -- 10.3 Biplots for Simple Correspondence Analysis-The Asymmetric Case -- 10.4 Ordered Simple Correspondence Analysis -- 10.4.1 An Overview -- 10.4.2 Biplots for Ordered Simple Correspondence Analysis -- 10.4.3 The Biplot and a Re-Examination of Table3.1摥映數爠eflinktab3.13.13 -- 10.5 The Biplot for Multi-Way Correspondence Analysis -- 10.5.1 An Overview -- 10.5.2 TUCKER3 Decomposition -- 10.6 The Interactive Biplot -- 10.6.1 The Biplot and Three-Way Correspondence Analysis -- 10.6.2 Size and Nature of the Dependence -- 10.6.3 The Interactive Biplot -- 10.7 Final Remarks -- References -- 11 On the Analysis of Over-Dispersed Categorical Data -- 11.1 Introduction -- 11.2 Generalized Pearson Residual -- 11.3 Special Cases -- 11.3.1 Generalized Poisson Distribution -- 11.3.2 Negative Binomial Distribution -- 11.3.3 Conway-Maxwell Poisson Distribution -- 11.4 Over-Dispersion, the Biplot and a Re-Examination of Table3.5摥映數爠eflinktab3.53.53 -- 11.5 Stabilizing the Variance -- 11.5.1 The Adjusted Standardized Residual -- 11.5.2 The Freeman-Tukey Residual -- 11.6 Final Remarks -- References. |
| Record Nr. | UNISA-996466404403316 |
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Nishisato Shizuhiko
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| Singapore : , : Springer Singapore Pte. Limited, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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