1st Edition
Multiple Correspondence Analysis and Related Methods
As a generalization of simple correspondence analysis, multiple correspondence analysis (MCA) is a powerful technique for handling larger, more complex datasets, including the high-dimensional categorical data often encountered in the social sciences, marketing, health economics, and biomedical research. Until now, however, the literature on the subject has been scattered, leaving many in these fields no comprehensive resource from which to learn its theory, applications, and implementation.
Multiple Correspondence Analysis and Related Methods gives a state-of-the-art description of this new field in an accessible, self-contained, textbook format. Explaining the methodology step-by-step, it offers an exhaustive survey of the different approaches taken by researchers from different statistical "schools" and explores a wide variety of application areas. Each chapter includes empirical examples that provide a practical understanding of the method and its interpretation, and most chapters end with a "Software Note" that discusses software and computational aspects. An appendix at the end of the book gives further computing details along with code written in the R language for performing MCA and related techniques. The code and the datasets used in the book are available for download from a supporting Web page.
Providing a unique, multidisciplinary perspective, experts in MCA from both statistics and the social sciences contributed chapters to the book. The editors unified the notation and coordinated and cross-referenced the theory across all of the chapters, making the book read seamlessly. Practical, accessible, and thorough, Multiple Correspondence Analysis and Related Methods brings the theory and applications of MCA under one cover and provides a valuable addition to your statistical toolbox.
A simple example
Basic method
Concepts of correspondence analysis
Stacked tables
Multiple correspondence analysis
Categorical principal components analysis
Active and supplementary variables
Multiway data
Content of the book
FROM SIMPLE TO MULTIPLE CORRESPONDENCE ANALYSIS, Michael Greenacre
Canonical correlation analysis
Geometric approach
Supplementary points
Discussion and conclusions
DIVIDED BY A COMMON LANGUAGE: ANALYZING AND VISUALIZING TWO-WAY ARRAYS, John C. Gower
Introduction: two-way tables and data matrices
Quantitative variables
Categorical variables
Fit and scaling
Discussion and conclusion
NONLINEAR PRINCIPAL COMPONENTS ANALYSIS AND RELATED TECHNIQUES, Jan de Leeuw
Linear PCA
Least-squares nonlinear PCA
Logistic NLPCA
Discussion and conclusions
Software Notes
THE GEOMETRIC ANALYSIS OF STRUCTURED INDIVIDUALS o VARIABLES TABLES, Henry Rouanet
PCA and MCA as geometric methods
Structured data analysis
The basketball study
The EPGY study
Concluding comments
CORRELATIONAL STRUCTURE OF MULTIPLE-CHOICE DATA AS VIEWED FROM DUAL SCALING, Shizuhiko Nishisato
Permutations of categories and scaling
Principal components analysis and dual scaling
Statistics for correlational structure of data
Forced classification
Correlation between categorical variables
Properties of squared item-total correlation
Structure of nonlinear correlation
Concluding remarks
VALIDATION TECHNIQUES IN MULTIPLE CORRESPONDENCE ANALYSIS, Ludovic Lebart
External validation
Internal validation (resampling techniques)
Example of MCA validation
Conclusion
MULTIPLE CORRESPONDENCE ANALYSIS OF SUBSETS OF RESPONSE CATEGORIES, Michael Greenacre and Rafael Pardo
Correspondence analysis of a subset of an indicator matrix
Application to women's participation in labor force
Subset MCA applied to the Burt matrix
Discussion and conclusions
SCALING UNIDIMENSIONAL MODELS WITH MULTIPLE CORRESPONDENCE ANALYSIS, Matthijs J. Warrens and Willem J. Heiser
The dichotomous Guttman scale
The Rasch model
The polytomous Guttman scale
The graded response model
Unimodal models
Conclusion
THE UNFOLDING FALLACY UNVEILED: VISUALIZING STRUCTURES OF DICHOTOMOUS UNIDIMENSIONAL ITEM-RESPONSE-THEORY DATA BY MULTIPLE CORRESPONDENCE ANALYSIS, Wijbrandt van Schuur and Jörg Blasius
Item response models for dominance data
Visualizing dominance data
Item response models for proximity data
Visualizing unfolding data
Every two cumulative scales can be represented as a single unfolding scale
Consequences for unfolding analysis
Discussion
REGULARIZED MULTIPLE CORRESPONDENCE ANALYSIS, Yoshio Takane and Heungsun Hwang
The method
Examples
Concluding remarks
THE EVALUATION OF "DON'T KNOW" RESPONSES BY GENERALIZED CANONICAL ANALYSIS, Herbert Matschinger and Matthias C. Angermeyer
Method
Results
Discussion
MULTIPLE FACTOR ANALYSIS FOR CONTINGENCY TABLES, Jérôme Pagès and Mónica Bécue-Bertaut
Tabular conventions
Internal correspondence analysis
Balancing the influence of the different tables
Multiple factor analysis for contingency tables (MFACT)
MFACT properties
Rules for studying the suitability of MFACT for a data set
Conclusion
SIMULTANEOUS ANALYSIS: A JOINT STUDY OF SEVERAL CONTINGENCY TABLES WITH DIFFERENT MARGINS, Amaya Zárraga and Beatriz Goitisolo
Simultaneous analysis
Interpretation rules for simultaneous analysis
Comments on the appropriateness of the method
Application: study of levels of employment and unemployment according to autonomous community, gender, and training level
Conclusions
MULTIPLE FACTOR ANALYSIS OF MIXED TABLES OF METRIC AND CATEGORICAL DATA, Elena Abascal, Ignacio García Lautre, and M. Isabel Landaluce
Multiple factor analysis
MFA of a mixed table: an alternative to PCA and MCA
Analysis of voting patterns across provinces in Spain's 2004 general election
Conclusions
CORRESPONDENCE ANALYSIS AND CLASSIFICATION, Gilbert Saporta and Ndèye Niang
Linear methods for classification
The "Disqual" methodology
Alternative methods
A case study
Conclusion
MULTIBLOCK CANONICAL CORRELATION ANALYSIS FOR CATEGORICAL VARIABLES: APPLICATION TO EPIDEMIOLOGICAL DATA, Stéphanie Bougeard, Mohamed Hanafi, Hicham Noçairi, and El-Mostafa Qannari
Multiblock canonical correlation analysis
Application
Discussion and perspectives
PROJECTION-PURSUIT APPROACH FOR CATEGORICAL DATA, Henri Caussinus and Anne Ruiz-Gazen
Continuous variables
Categorical variables
Conclusion
CORRESPONDENCE ANALYSIS AND CATEGORICAL CONJOINT MEASUREMENT, Anna Torres-Lacomba
Categorical conjoint measurement
Correspondence analysis and canonical correlation analysis
Correspondence analysis and categorical conjoint analysis
Incorporating interactions
Discussion and conclusions
A THREE-STEP APPROACH TO ASSESSING THE BEHAVIOR OF SURVEY ITEMS IN CROSS-NATIONAL RESEARCH, Jörg Blasius and Victor Thiessen
Data
Method
Solutions
Discussion
ADDITIVE AND MULTIPLICATIVE MODELS FOR THREE-WAY CONTINGENCY TABLES: DARROCH (1974) REVISITED, Pieter M. Kroonenberg and Carolyn J. Anderson
Data and design issues
Multiplicative and additive modeling
Multiplicative models
Additive models: three-way correspondence analysis
Categorical principal components analysis
Discussion and conclusions
A NEW MODEL FOR VISUALIZING INTERACTIONS IN ANALYSIS OF VARIANCE, Patrick J.F. Groenen and Alex J. Koning
Holiday-spending data
Decomposing interactions
Interaction decomposition of holiday spending
Conclusions
LOGISTIC BIPLOTS. José L. Vicente-Villardón, M. Purificación Galindo-Villardón, and Antonio Blázquez-Zaballos
Classical biplots
Logistic biplot
Application: microarray gene expression data
Final remarks
References
Appendix
Index
Biography
Michael Greenacre, Jorg Blasius
