Interdisciplinary Statistics CORRESPONDENCE ANALYSIS in PRACTICE Second Edition © 2007 by Taylor & Francis Group, LLC CHAPMAN & HALL/CRC Interdisciplinary Statistics Series Series editors: N. Keiding, B. Morgan, T. Speed, P. van der Heijden AN INVARIANT APPROACH TO S. Lele and J. Richtsmeier STATISTICAL ANALYSIS OF SHAPES ASTROSTATISTICS G. Babu and E. Feigelson BIOEQUIVALENCE AND S. Patterson and STATISTICS IN CLINICAL B. Jones PHARMACOLOGY CLINICAL TRIALS IN ONCOLOGY J. Crowley, S. Green, SECOND EDITION and J. Benedetti CORRESPONDENCE ANALYSIS M. Greenacre IN PRACTICE, SECOND EDITION DESIGN AND ANALYSIS OF D.L. Fairclough QUALITY OF LIFE STUDIES IN CLINICAL TRIALS DYNAMICAL SEARCH L. Pronzato, H. Wynn, and A. Zhigljavsky GENERALIZED LATENT VARIABLE A. Skrondal and MODELING: MULTILEVEL, S. Rabe-Hesketh LONGITUDINAL, AND STRUCTURAL EQUATION MODELS GRAPHICAL ANALYSIS OF K. Basford and J. Tukey MULTI-RESPONSE DATA INTRODUCTION TO M. Waterman COMPUTATIONAL BIOLOGY: MAPS, SEQUENCES, AND GENOMES MARKOV CHAIN MONTE CARLO W. Gilks, S. Richardson, IN PRACTICE and D. Spiegelhalter MEASUREMENT ERROR AND P. Gustafson MISCLASSIFICATION IN STATISTICS AND EPIDEMIOLOGY: IMPACTS AND BAYESIAN ADJUSTMENTS STATISTICAL ANALYSIS OF GENE T. Speed EXPRESSION MICROARRAY DATA STATISTICAL CONCEPTS J. Aitchison, J.W. Kay, AND APPLICATIONS IN and I.J. Lauder CLINICAL MEDICINE STATISTICAL AND PROBABILISTIC P.J. Boland METHODS IN ACTUARIAL SCIENCE STATISTICS FOR ENVIRONMENTAL A. Bailer and W. Piegorsch BIOLOGY AND TOXICOLOGY STATISTICS FOR FISSION 6*+EPFVEMXL TRACK ANALYSIS © 2007 by Taylor & Francis Group, LLC Interdisciplinary Statistics CORRESPONDENCE ANALYSIS in PRACTICE Second Edition Michael Greenacre niversitat Pompeu Fabra Barcelona, Spain Boca Raton London New York Chapman & Hall/CRC is an imprint of the Taylor & Francis Group, an informa business © 2007 by Taylor & Francis Group, LLC First edition published by Academic Press in 1993. Chapman & Hall/CRC Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 1-58488-616-1 (Hardcover) International Standard Book Number-13: 978-1-58488-616-7 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com © 2007 by Taylor & Francis Group, LLC v To Fran¸coise, Karolien and Gloudina © 2007 by Taylor & Francis Group, LLC Contents Preface ................................ ix 1 Scatterplots and Maps ...................... 1 2 Profiles and the Profile Space ................. 9 3 Masses and Centroids ...................... 17 4 Chi-square Distance and Inertia ................ 25 5 Plotting Chi-square Distances ................. 33 6 Reduction of Dimensionality .................. 41 7 Optimal Scaling .......................... 49 8 Symmetry of Row and Column Analyses .......... 57 9Two-dimensionalMaps ..................... 65 10 Three More Examples ...................... 73 11 Contributions to Inertia ..................... 81 12 Supplementary Points ...................... 89 13 Correspondence Analysis Biplots ............... 97 14 Transition and Regression Relationships .......... 105 15 Clustering Rows and Columns ................. 113 16 Multiway Tables .......................... 121 17 Stacked Tables ........................... 129 18 Multiple Correspondence Analysis .............. 137 19 Joint Correspondence Analysis ................ 145 20 Scaling Properties of MCA ................... 153 21 Subset Correspondence Analysis ............... 161 22 Analysis of Square Tables .................... 169 23 Data Recoding ........................... 177 24 Canonical Correspondence Analysis ............. 185 25 Aspects of Stability and Inference .............. 193 A Theory of Correspondence Analysis ............. 201 B Computation of Correspondence Analysis ......... 213 C Bibliography of Correspondence Analysis .......... 259 D Glossary of Terms ......................... 263 E Epilogue ............................... 267 vii © 2007 by Taylor & Francis Group, LLC Preface This book is the totally revised and extended edition of Correspondence Analy- sis in Practice, first published in 1993. In the first edition I wrote the following in the Preface, which is still relevant today: Correspondence analysis is a statistical technique which is useful to all students, Extract from Preface of researchers and professionals who collect categorical data, for example data col- First Edition of Corre- lected in social surveys. The method is particularly helpful in analysing cross- spondence Analysis in tabular data in the form of numerical frequencies, and results in an elegant but Practice simple graphical display which permits more rapid interpretation and under- standing of the data. Although the theoretical origins of the technique can be traced back over 50 years, the real impetus to the modern application of corre- spondence analysis was given by the French linguist and data analyst Jean-Paul Benz´ecriand his colleagues and students, working initially at the University of Rennes in the early 1960s and subsequently at the Jussieu campus of the Univer- sity of Paris. Parallel developments of correspondence analysis have taken place in the Netherlands and Japan, centred around such pioneering researchers as Jan de Leeuw and Chikio Hayashi. My own involvement with correspondence anal- ysis commenced in 1973 when I started my doctorate in Benz´ecri’s Laboratory of Data Analysis in Paris. The publication of my first book Theory and Appli- cations of Correspondence Analysis in 1984 coincided with the beginning of a wider dissemination of correspondence analysis outside of France. At that time I expressed the hope that my book would serve as a springboard for a much wider and more routine application of correspondence analysis in the future. The subsequent evolution and growing popularity of the method could not have been more gratifying, as hundreds of researchers were introduced to the method and became familiar with its ability to communicate complex tables of numerical data to non-specialists throught the medium of graphics. Researchers with whom I have communicated come from such varying backgrounds as sociology, ecology, paleontology, archeology, geology, education, medicine, biochemistry, microbiol- ogy, linguistics, marketing research, advertising, religious studies, philosophy, art and music. ... In 1989 I was invited by Jay Magidson of Statistical Innovations Inc. to collaborate with Leo Goodman and Clifford Clogg in the presentation of a two-day short course in New York, entitled “Correspondence Analysis and Asso- ciation Models: Geometric Representation and Beyond”. The participants were mostly marketing professionals from major American companies. For this course I prepared a set of notes which reinforced the practical, user-oriented approach to correspondence analysis. ... The positive reaction of the audience was infectious and inspired me subsequently to present short courses on correspondence analysis in South Africa, England and Germany. It is from the notes prepared from these courses that this book has grown. In 1991 Prof. Walter Kristof of Hamburg University proposed that we organize The Cologne and a conference on correspondence analysis, with the assistance of J¨org Blasius Barcelona conferences of the Zentralarchiv f¨ur Empirische Sozialforschung (Central Archive for Em- pirical Social Research) at the University of Cologne. This conference was the ix © 2007 by Taylor & Francis Group, LLC x Preface first international one of its kind and drew a large audience to Cologne from Germany and neighbouring European countries. This initial meeting devel- oped into a series of quadrennial conferences, repeated in 1995 and 1999 in Cologne, in 2003 at the Pompeu Fabra University in Barcelona and due to take place in 2007 at the Erasmus University in Rotterdam. The 1991 confer- ence led to the publication