Beh E.J., Lombardo R. Correspondence Analysis: Theory, Practice and New Strategies

NY: John Wiley & Sons Ltd., 2014. — 592 p. — (Wiley Series in Probality and Statistics). — ISBN: 978-1-119-95324-1.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.Introduction
Data Visualisation
A Very Brief Introduction to Data Visualisation
Data Visualisation for Contingency Tables
Other Plots
Studying Exposure to Asbestos
Happiness Data
Correspondence Analysis Now
Overview of the Book
R CodePearson’s Chi-Squared StatisticPearson’s Chi-Squared Statistic
The Goodman--Kruskal Tau Index
The 2 х 2 Contingency Table
Early Contingency Tables
R CodeCorrespondence Analysis of Two-Way Contingency Tables
Methods of DecompositionReducing Multidimensional Space
Profiles and Cloud of Points
Property of Distributional Equivalence
The Triplet and Classical Reciprocal Averaging
Solving the Triplet Using Eigen-Decomposition
Solving the Triplet Using Singular Value Decomposition
The Generalised Triplet and Reciprocal Averaging
Solving the Generalised Triplet Using Gram--Schmidt Process
Bivariate Moment Decomposition
Hybrid Decomposition
R Code
A Preliminary Graphical Summary
Analysis of Analgesic DrugsSimple Correspondence AnalysisNotation
Measuring Departures from Complete Independence
Decomposing the Pearson Ratio
Coordinate Systems
Distances
Transition Formulae
Moments of the Principal Coordinates
How Many Dimensions to Use?
R Code
Other Theoretical Issues
Some Applications of Correspondence Analysis
Analysis of a Mother’s Attachment to Her ChildNon-Symmetrical Correspondence AnalysisThe Goodman--Kruskal Tau Index
Non-Symmetrical Correspondence Analysis
The Coordinate Systems
Transition Formulae
Moments of the Principal Coordinates
The Distances
Comparison with Simple Correspondence Analysis
R Code
Analysis of a Mother’s Attachment to Her ChildOrdered Correspondence AnalysisPearson’s Ratio and Bivariate Moment Decomposition
Coordinate Systems
Artificial Data Revisited
Transition Formulae
Distance Measures
Singly Ordered Analysis
R CodeOrdered Non-Symmetrical Correspondence AnalysisGeneral Considerations
Doubly Ordered Non-Symmetrical Correspondence Analysis
Singly Ordered Non-Symmetrical Correspondence Analysis
Coordinate Systems for Ordered Non-Symmetrical Correspondence Analysis
Tests of Asymmetric Association
Distances in Ordered Non-Symmetrical Correspondence Analysis
Doubly Ordered Non-Symmetrical Correspondence of Asbestos Data
Singly Ordered Non-Symmetrical Correspondence Analysis of Drug Data
R Code for Ordered Non-Symmetrical Correspondence AnalysisExternal Stability and Confidence RegionsOn the Statistical Significance of a Point
Circular Confidence Regions for Classical Correspondence Analysis
Elliptical Confidence Regions for Classical Correspondence Analysis
Confidence Regions for Non-Symmetrical Correspondence Analysis
Approximate 𝑝-values and Classical Correspondence Analysis
Approximate 𝑝-values and Non-Symmetrical Correspondence Analysis
Bootstrap Elliptical Confidence Regions
Ringrose’s Bootstrap Confidence Regions
Confidence Regions and Selikoff’s Asbestos Data
Confidence Regions and Mother--Child Attachment Data
R CodeVariants of Correspondence AnalysisCorrespondence Analysis Using Adjusted Standardised Residuals
Correspondence Analysis Using the Freeman--Tukey Statistic
Correspondence Analysis of Ranked Data
R Code
The Correspondence Analysis Family
Other TechniquesCorrespondence Analysis of Multi-Way Contingency Tables
Coding and Multiple Correspondence Analysis
Introduction to Coding
Coding Data
Coding Ordered Categorical Variables by Orthogonal Polynomials
Burt Matrix
An Introduction to Multiple Correspondence Analysis
Multiple Correspondence Analysis
Variants of Multiple Correspondence Analysis
Ordered Multiple Correspondence Analysis
Analysis
Applications
R CodeSymmetrical and Non-Symmetrical Three-Way Correspondence AnalysisNotation
Symmetric and Asymmetric Association in Three-Way Contingency Tables
Partitioning Three-Way Measures of Association
Formal Tests of Predictability
Tucker3 Decomposition for Three-Way Tables
Correspondence Analysis of Three-Way Contingency Tables
Modelling of Partial and Marginal Dependence
Graphical Representation
On the Application of Partitions
On the Application of Three-Way Correspondence Analysis
R CodeThe Computation of Correspondence Analysis
Computing and Correspondence AnalysisA Look Through Time
The Impact of R
Some Stand-Alone Programs