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Description

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.

Contents

CORRESPONDENCE ANALYSIS AND RELATED METHODS IN PRACTICE, Jörg Blasius and Michael Greenacre

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

Name: Multiple Correspondence Analysis and Related Methods (Hardback)Chapman and Hall/CRC 
Description: Edited by Michael Greenacre, Jorg BlasiusSeries Editor: Andrew Gelman, Sophia Rabe-Hesketh, Anders Skrondal, J. Scott LongContributors: Shizuhiko Nishisato, Elena Abascal Fernandez, Carolyn Anderson, Matthias Angermeyer, Monica Becue Bertaut, Antonio Blaquez Zaballos, Stephanie Bougeard, Henri Caussinus, Jan de Leeuw, M. Purificacion Galindo Villardon, Ignacio Garcia Lautre, Beatriz Goitisolo, John Gower, Patrick J. F. Groenen, Mohamed Hanafi, Willem Heiser, Alex Koning, Pieter Kroonenberg, Isabel Calvo, Ludovic Lebart, Herbert Matschinger, Oleg Nenadic, Ndeye Niang, Hicham Nocairi, Jerome Pages, Rafael Pardo, Mostafa Qannari, Henry Rouanet, Anne Ruiz-Gazen, Gilbert Saporta, Yoshio Takane, Victor Thiessen, Anna Torres Lacomba, Wijbrandt Schuur, Jose Luis Vicente Villardon, Matthijs J. Warrens, Amaya Zarraga, Heungsun Hwang. 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,...
Categories: Psychological Methods & Statistics, Statistical Theory & Methods, Quantitative Methods, Statistics for the Biological Sciences