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.

CORRESPONDENCE ANALYSIS AND RELATED METHODS IN PRACTICE, Jörg Blasius and Michael GreenacreA simple exampleBasic method Concepts of correspondence analysisStacked tables Multiple correspondence analysisCategorical principal components analysisActive and supplementary variablesMultiway data Content of the bookFROM SIMPLE TO MULTIPLE CORRESPONDENCE ANALYSIS, Michael GreenacreCanonical correlation analysisGeometric approach Supplementary pointsDiscussion and conclusions DIVIDED BY A COMMON LANGUAGE: ANALYZING AND VISUALIZING TWO-WAY ARRAYS, John C. GowerIntroduction: two-way tables and data matricesQuantitative variables Categorical variables Fit and scaling Discussion and conclusionNONLINEAR PRINCIPAL COMPONENTS ANALYSIS AND RELATED TECHNIQUES, Jan de LeeuwLinear PCALeast-squares nonlinear PCA Logistic NLPCADiscussion and conclusions Software Notes THE GEOMETRIC ANALYSIS OF STRUCTURED INDIVIDUALS o VARIABLES TABLES, Henry RouanetPCA and MCA as geometric methodsStructured data analysis The basketball study The EPGY study Concluding commentsCORRELATIONAL STRUCTURE OF MULTIPLE-CHOICE DATA AS VIEWED FROM DUAL SCALING, Shizuhiko NishisatoPermutations of categories and scaling Principal components analysis and dual scalingStatistics for correlational structure of data Forced classificationCorrelation between categorical variables Properties of squared item-total correlationStructure of nonlinear correlation Concluding remarksVALIDATION TECHNIQUES IN MULTIPLE CORRESPONDENCE ANALYSIS, Ludovic LebartExternal validation Internal validation (resampling techniques) Example of MCA validation ConclusionMULTIPLE CORRESPONDENCE ANALYSIS OF SUBSETS OF RESPONSE CATEGORIES, Michael Greenacre and Rafael PardoCorrespondence analysis of a subset of an indicator matrixApplication to women's participation in labor forceSubset MCA applied to the Burt matrixDiscussion and conclusions SCALING UNIDIMENSIONAL MODELS WITH MULTIPLE CORRESPONDENCE ANALYSIS, Matthijs J. Warrens and Willem J. HeiserThe dichotomous Guttman scale The Rasch modelThe polytomous Guttman scale The graded response modelUnimodal models ConclusionTHE UNFOLDING FALLACY UNVEILED: VISUALIZING STRUCTURES OF DICHOTOMOUS UNIDIMENSIONAL ITEM-RESPONSE-THEORY DATA BY MULTIPLE CORRESPONDENCE ANALYSIS, Wijbrandt van Schuur and Jörg BlasiusItem 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 scaleConsequences for unfolding analysis DiscussionREGULARIZED MULTIPLE CORRESPONDENCE ANALYSIS, Yoshio Takane and Heungsun HwangThe methodExamples Concluding remarksTHE EVALUATION OF "DON'T KNOW" RESPONSES BY GENERALIZED CANONICAL ANALYSIS, Herbert Matschinger and Matthias C. AngermeyerMethodResults DiscussionMULTIPLE FACTOR ANALYSIS FOR CONTINGENCY TABLES, Jérôme Pagès and Mónica Bécue-BertautTabular conventionsInternal 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 setConclusion SIMULTANEOUS ANALYSIS: A JOINT STUDY OF SEVERAL CONTINGENCY TABLES WITH DIFFERENT MARGINS, Amaya Zárraga and Beatriz GoitisoloSimultaneous analysisInterpretation rules for simultaneous analysisComments on the appropriateness of the method Application: study of levels of employment and unemployment according to autonomous community, gender, and training levelConclusionsMULTIPLE FACTOR ANALYSIS OF MIXED TABLES OF METRIC AND CATEGORICAL DATA, Elena Abascal, Ignacio García Lautre, and M. Isabel LandaluceMultiple factor analysisMFA of a mixed table: an alternative to PCA and MCAAnalysis of voting patterns across provinces in Spain's 2004 general electionConclusionsCORRESPONDENCE ANALYSIS AND CLASSIFICATION, Gilbert Saporta and Ndèye NiangLinear methods for classificationThe "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 QannariMultiblock canonical correlation analysisApplicationDiscussion and perspectivesPROJECTION-PURSUIT APPROACH FOR CATEGORICAL DATA, Henri Caussinus and Anne Ruiz-GazenContinuous variables Categorical variables Conclusion CORRESPONDENCE ANALYSIS AND CATEGORICAL CONJOINT MEASUREMENT, Anna Torres-LacombaCategorical conjoint measurement Correspondence analysis and canonical correlation analysisCorrespondence analysis and categorical conjoint analysisIncorporating interactionsDiscussion and conclusions A THREE-STEP APPROACH TO ASSESSING THE BEHAVIOR OF SURVEY ITEMS IN CROSS-NATIONAL RESEARCH, Jörg Blasius and Victor ThiessenData MethodSolutions DiscussionADDITIVE AND MULTIPLICATIVE MODELS FOR THREE-WAY CONTINGENCY TABLES: DARROCH (1974) REVISITED, Pieter M. Kroonenberg and Carolyn J. AndersonData and design issuesMultiplicative and additive modeling Multiplicative models Additive models: three-way correspondence analysisCategorical principal components analysisDiscussion and conclusions A NEW MODEL FOR VISUALIZING INTERACTIONS IN ANALYSIS OF VARIANCE, Patrick J.F. Groenen and Alex J. KoningHoliday-spending dataDecomposing interactionsInteraction decomposition of holiday spending ConclusionsLOGISTIC BIPLOTS. José L. Vicente-Villardón, M. Purificación Galindo-Villardón, and Antonio Blázquez-ZaballosClassical biplots Logistic biplotApplication: microarray gene expression data Final remarksReferencesAppendixIndex