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1、MultipleCorrespondenceAnalysisMultipleCorrespondenceAnalysisHervéAbdi1&DominiqueValentin1OverviewMultiplecorrespondenceanalysis(MCA)isanextensionofcorre-spondenceanalysis(CA)whichallowsonetoanalyzethepatternofrelationshipsofseveralcategoricaldependentvariables.Assuch,itcanalsobeseenasagenera
2、lizationofprincipalcomponentanal-ysiswhenthevariablestobeanalyzedarecategoricalinsteadofquantitative.BecauseMCAhasbeen(re)discoveredmanytimes,equivalentmethodsareknownunderseveraldifferentnamessuchasoptimalscaling,optimalorappropriatescoring,dualscaling,homogeneityanalysis,scalogramanalysis,andq
3、uantificationme-thod.TechnicallyMCAisobtainedbyusingastandardcorrespon-denceanalysisonanindicatormatrix(i.e.,amatrixwhoseentriesare0or1).Thepercentagesofexplainedvarianceneedtobecor-rected,andthecorrespondenceanalysisinterpretationofinter-pointdistancesneedstobeadapted.1In:NeilSalkind(Ed.)(2007)
4、.EncyclopediaofMeasurementandStatistics.ThousandOaks(CA):Sage.Addresscorrespondenceto:HervéAbdiPrograminCognitionandNeurosciences,MS:Gr.4.1,TheUniversityofTexasatDallas,Richardson,TX75083–0688,USAE-mail:herve@utdallas.edu//.utd.edu/??herve1H.Abdi&D.Valentin:MultipleCorrespondenceAnalysis2Whe
5、ntouseitMCAisusedtoanalyzeasetofobservationsdescribedbyasetofnominalvariables.Eachnominalvariablecomprisesseverallev-els,andeachoftheselevelsiscodedasabinaryvariable.Forex-amplegender,(Fvs.M)isonenominalvariablewithtwolevels.Thepatternforamalerespondentwillbe01and10forafemale.Thecompletedatatabl
6、eiscomposedofbinarycolumnswithoneandonlyonecolumntakingthevalue“1”pernominalvariable.MCAcanalsoaccommodatequantitativevariablesbyrecod-ingthemas“bins.”Forexample,ascorewitharangeof??5to+5couldberecodedasanominalvariablewiththreelevels:lessthan0,equalto0,ormorethan0.Withthisschema,avalueof3willbe
7、expressedbythepattern001.ThecodingschemaofMCAimpliesthateachrowhasthesametotal,whichforCAimpliesthateachrowhasthesamemass.3AnexampleWeillustratethemethodwithanexamplefromwinetesting.Sup-posethatwewanttoevaluatetheeffectofthe
