Table Of ContentI n t e rd i s c i p l i n a r y S t a t i s t i c s
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 (cid:54)(cid:18)(cid:42)(cid:18)(cid:3)(cid:43)(cid:69)(cid:80)(cid:70)(cid:86)(cid:69)(cid:77)(cid:88)(cid:76)
TRACK ANALYSIS
© 2007 by Taylor & Francis Group, LLC
I n t e rd i s c i p l i n a r y S t a t i s t i c s
CORRESPONDENCE
ANALYSIS in
PRACTICE
Second Edition
Michael Greenacre
Universitat Pompeu Fabra
Barcelona, Spain
Boca Raton London New York
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© 2007 by Taylor & Francis Group, LLC
First edition published by Academic Press in 1993.
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v
To Franc¸oise, 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
9 Two-dimensional Maps . . . . . . . . . . . . . . . . . . . . . 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
ThisbookisthetotallyrevisedandextendededitionofCorrespondenceAnaly-
sisinPractice,firstpublishedin1993.InthefirsteditionIwrotethefollowing
in the Preface, which is still relevant today:
Correspondenceanalysis isastatistical techniquewhichisusefultoallstudents, ExtractfromPrefaceof
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-
spondenceanalysis was given bytheFrench linguist and dataanalyst Jean-Paul
Benz´ecri and his colleagues and students, working initially at the University of
Rennesintheearly1960sandsubsequentlyattheJussieucampusoftheUniver-
sity of Paris. Parallel developments of correspondence analysis have taken place
intheNetherlandsandJapan,centredaroundsuchpioneeringresearchersasJan
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
widerandmoreroutineapplicationofcorrespondenceanalysisinthefuture.The
subsequentevolutionandgrowingpopularityofthemethodcouldnothavebeen
more gratifying, as hundreds of researchers were introduced to the method and
became familiar with its ability to communicate complex tables of numerical
datatonon-specialiststhroughtthemediumofgraphics.Researcherswithwhom
Ihavecommunicatedcomefromsuchvaryingbackgroundsassociology, ecology,
paleontology, archeology, geology, education, medicine, biochemistry, microbiol-
ogy,linguistics,marketingresearch,advertising,religiousstudies,philosophy,art
and music. ... In 1989 I was invited by Jay Magidson of Statistical Innovations
Inc.tocollaboratewithLeoGoodmanandCliffordClogginthepresentationofa
two-dayshortcourseinNewYork,entitled“CorrespondenceAnalysisandAsso-
ciation Models: Geometric Representation and Beyond”. The participants were
mostly marketingprofessionals frommajorAmericancompanies. Forthiscourse
Ipreparedasetofnoteswhichreinforcedthepractical,user-orientedapproachto
correspondence analysis. ... The positive reaction of the audience was infectious
andinspiredmesubsequentlytopresentshortcoursesoncorrespondenceanalysis
inSouthAfrica,EnglandandGermany.Itisfromthenotespreparedfromthese
courses that this book has grown.
In1991Prof.WalterKristofofHamburgUniversityproposedthatweorganize The Cologne and
a conference on correspondence analysis, with the assistance of Jo¨rg Blasius Barcelona conferences
oftheZentralarchiv fu¨r Empirische Sozialforschung (CentralArchiveforEm-
piricalSocialResearch)attheUniversityofCologne.Thisconferencewasthe
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 in2007atthe ErasmusUniversityin Rotterdam.The 1991confer-
ence ledto the publicationofthe book Correspondence Analysis in the Social
Sciences, while the 1995 conference gave birth to another book Visualization
of Categorical Data, both of which received excellent reviews. For the 1999
conference on Large Scale Data Analysis participants had to present analy-
ses of data from the multinational International Social Survey Programme
(ISSP). This interdisciplinarymeeting includedpresentationsnot onlyonthe
latest methodological developments in survey data analysis, but also topics
as diverse as religion, the environment and social inequality. In 2003 we re-
turnedtotheoriginalthemefortheBarcelonaconference,whichwasbaptized
withtheCatalangirl’snameCARME(CorrespondenceAnalysisandRelated
MEthods);hence the formationofthe CARME network(www.carme-n.org).
This led to J¨orgBlasius andmyselfediting a thirdbook,Multiple Correspon-
dence Analysis and Related Methods, which was published by Chapman &
HallinJune2006.Aswiththetwopreviousvolumes,ourideawastoproduce
a multi-authored book, inviting experts in the field to contribute, with our
task being to write the introductory and linking material, unifying the no-
tation and compiling a common reference list and index. These books mark,
in some sense, the pace of development of the subject, at least in the social
sciences,andarehighlyrecommendedtoanyoneinterestedindeepeningtheir
knowledge on correspondence analysis and methods related to it.
New material in I have been very gratified to rewrite Correspondence Analysis in Practice,
Second Edition havingaccumulatedconsiderablymoreexperienceinsocialandenvironmental
researchin the 13 yearssince the publication of the firstedition. I have given
more short courses across the world, including Spain, Italy, Belgium, Brazil,
Canada and Australia, and also courses on multivariate analysis for environ-
mentalbiologistsin Norway,IcelandandSpain,withcorrespondenceanalysis
as one of the major topics. The experience of giving these courses has pro-
vidednewapplicationsandnewideasforthisnewedition,sothatIhavebeen
able to bring the material right up to date. Apart from completely revising
the original chapters and changing several examples, five new chapters have
been added, on “Transition and Regression Relationships” (showing how the
results and the data are linked by linear functions), “Stacked Tables” (show-
inghowseveralcross-tablescanbeanalysedjointly),“SubsetCorrespondence
Analysis” (a simple but highly effective variationof the correspondenceanal-
ysis algorithm to analyse selected parts of a data set), “Analysis of Square
Tables” (showing how square tables — e.g., social mobility tables, brand-
switching matrices — can be decomposed into parts that can be visualized
separately using correspondence analysis), and “Canonical Correspondence
Analysis” (showinghow to take into accountrelationshipsto externalpredic-
tor variables, an extension of correspondence analysis that is very popular in
© 2007 by Taylor & Francis Group, LLC
Preface xi
ecology). All in all, I can say that this second edition contains almost all my
practical knowledge of the subject, after 33 years working in this area.
At aconferenceI attendedinthe 1980s,I wasgiventhis lapelbutton withits Comparison of first
nicely ambiguous maxim, which could well be the motto of correspondence and second editions
analysts all over the world:
To illustrate the more obvious meaning of this motto, and to give a simple
example of correspondence analysis, I counted how many tables and figures
there werein eachof the chapters ofthe firsteditionand intheir counterpart
chaptersinthesecondedition.Foravalidcomparisonbetweenthetwoeditions
Iexpressedtheserelativetothetotalnumberofpagesineachchapterandthen
performedavariationofthetechniquecalled“subsetcorrespondenceanalysis”
(described in Chapter 21), using the standard biplot presentation (described
in Chapter 13), leading to the data map shown on the following page (you
willunderstandtheseideasafteryoureadthebook,butforthemomentthink
of this example as a type of scatterplot). The two vectors Figures and Tables
pointtotheright,sochapterstotherighthavehigherthanaveragepercentage
of figures and tables. For example, Chapters 9 and 11 in the second edition
have the highest percentage of figures and tables, respectively. In fact, about
three quarters of the second edition’s chapters represented in the map are to
the right of the centre of the map (the centre represents the average), with
onlyonequarterofthe firstedition’schapterstotheright,demonstratingthe
substantial increase in figures and tables in the second edition. In fact, the
information content and applications component of the book have increased
substantiallycomparedtothefirstedition,whichhadamainbody(excluding
appendices) of 177 pages — in the second edition this has increased to 200
pages,anincreaseof13%,whiletherehasbeenanincreaseof25%inchapters
and topics, 18% in data sets, 44% in figures and 63% in tables.
Thisbookhassomeinnovationsthatdeservementioning.Likethefirstedition, Format of second
it is intended to be didactic, but this edition is even more so. I wanted each edition
chapterto representafixedamounttoreadorteach,andtherewasno better
way to do that than to limit the length of each chapter — each chapter is
exactly eight pages in length. This was one of the most interesting aspects of
© 2007 by Taylor & Francis Group, LLC
xii Preface
Exhibit 0.1:
1
Subset 0.0946 (33.2%) B11
correspondence
analysis map of A20
percentages of A7 Tables
figures and tables in
20 comparable 0.5
B7 A12
chaptersfrom first
A11
and second editions, A18 B4 A3
presented as a A4 B12 B15 A10
standard biplot. B20 B16
Only chaptersof the B1 A19
present second 0 A6 B3B1B98 B18 0.1899 (66.8%)
edition (denoted by A8 A23 B10
A9 A13 B2
B) that havea A5 A1 B6 A2
B23
counterpart in the A16
A25 A15B25
first edition B5
(denoted by A) are -0.5 B13 B9
analysed. The
chapternumbers
correspond to the
Figures
present edition,
giving the same
-1
numbersto the
-1 -0.5 0 0.5 1 1.5
corresponding
chapters in the first
edition.
the project and evolved naturally as I was writing it. One of my colleagues
remarkedthatitwaslikewriting14-linesonnetswithstrictrulesforrhyming,
which was certainly true in my case: the format definitely contributed to the
creativeprocess.Another innovationwasthe extensive use ofmarginalnotes.
Every paragraph of the book has a heading which is placed in the margin.
Then to summarize each chapter, these paragraph headings are all gathered
into a “Contents” section on the first page of every chapter. All figure and
table captions are also placed in the margins, so that the captions are often
muchlongerandmoreinformativethanconventionalcaptionsthattendtobe
one-liners. Finally, each chapter ends with a summary in the form of a list.
Theoretical appendix As in the first edition, the book’s main thrust is still toward the practice of
correspondence analysis, so most technical issues and mathematical aspects
aregatheredinanAppendixattheendofthebook.Thistheoreticalappendix
ismoreextensivethanthatofthe firstedition,includingadditionaltheoryon
the new topics in the book such as canonical correspondence analysis.
Computational Oneofthemainfeaturesofthiseditionwhichdistinguishesitfromtheoriginal
appendix one, and which clearly marks the present digital era, is the lengthy compu-
tational appendix, using the freely available R program, which has become
the de facto standardin statistical computing. Almost all the analyses in the
© 2007 by Taylor & Francis Group, LLC
