SawtoothSoftwareRESEARCHPAPERSERIESProductMappingwithPerceptionsandPreferencesRichardM.Johnson,SawtoothSoftware,Inc.1998©Copyright1998-2001,SawtoothSoftware,Inc.530W.FirSt.Sequim,WA98382(360)681-2300www.sawtoothsoftware.comProductMappingwithPerceptionsandPreferencesRichardM.JohnsonSawtoothSoftware,Inc.BackgroundInthe‘50sand‘60s,mathematicalpsychologistsdevelopedtheoriesabouthowperceptionsandpreferencesmightberelated.Theyconsideredobjectstobearrangedinsomekindofperceptualspace,determinedeitherwithrespecttoperceivedsimilarities,orwithrespecttoratingsondescriptiveattributes.Eachindividualwasalsothoughttohaveanidealdirectioninthespaceandtopreferobjectsthatwerefartherinthatdirection,ortohaveanidealpointinthespaceandtopreferobjectsclosertothatpoint.Marketresearchershavefoundtheseideasveryfruitful.Useofproductmapsbecamewidespreadinmarketingresearchinthe‘60sand‘70s,andtheyhaveprovedtobeusefulaidsforthinkingaboutdifferencesamongproducts,customerdesires,andwaysinwhichproductsmightbemodifiedtobecomemoresuccessful.Perceptualdatahavebeenusedmostoftentocreateproductspaces.Inearlyyearsjudgementsaboutoverallsimilarityofpairsofproductswereusedwithmultidimensionalscalingtechniques.However,inlateryearsattributeratingshavebeenusedmorewidely,analyzedwithfactoranalysis,discriminantanalysis,orcorrespondenceanalysis.Preferencedatahavealsobeenusedtodevelopproductspacesinmarketingresearch.Thefirsttechniquesformakingmapsbasedonpreferencesweredevelopedintheearly‘60s:Coombs’Unfoldingmethod(whichassumedeachindividualhadanidealpoint)andTucker’sPointsofViewapproach(whichassumedeachindividualhadapreferreddirectioninspace).Inanimportantcontributionin1970,CarrollandChangshowedthatvectormodelscanberegardedasspecialcasesofgeneralizedidealpointmodels,andtheyalsoprovidedthefirstpracticalmethodforestimatingidealpoints.Mostmethodsformakingproductmapshaveusedeitherperceptualdataorpreferencedata,butseldomboth.Andtherehavebeenproblemswithmapsofbothtypes.Mapsbasedonperceptionsareeasytointerpretandgoodatconveyinginsights,buttheyareoftenlessgoodatpredictingindividualpreferences.Onereasonisthattheymayfocusondifferencesthatareeasytoseebutlessimportantindeterminingpreferences.Mapsbasedonpreferencesarebetterataccountingforpreferences,buttheirdimensionsaresometimeshardtointerpret.Forexample,considercupscoffeewithdifferencesintemperaturerangingfromboilingtotepid.Mostofuswouldprobablyprefersomemiddletemperatureandrejectbothextremes.Butifnoperceptualinformationisavailabletoestablishtheirdifferencesontheunderlyingtemperaturescale,themostextremecupsmaybeclosetogetherinapreference-basedmap,becausetheironlyrecognizedpropertyisthattheyarebothrejectedbynearlyeveryone.2Thereisstillanotherproblemwithaggregatemapsofbothtypes:aproduct’spositiononamapisbasedontheaverageofmanyindividuals’perceptionsorpreferences.Becauseindividualsdiffer,asinglemapcanseldomdescribedifferentindividuals’perceptionsorpreferencesveryprecisely.Attheprevious(1997)SawtoothSoftwareConference,JohnFiedlerandTerryElrodpresentedpapersanalyzingthesamedatabutusingdifferentmethods.Johnusedadiscriminant-basedmethodwhichconsideredonlyperceptualdataintheformofattributeratings,andTerryusedatechniquehehaddevelopedwhichconsideredonlypreferencedata.Theirmapsweresurprisinglysimilar.Thisreinforcedtheunderlyingtheoryrelatingperceptionsandpreferences,andsuggestedthate...
