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Submittedforpublication.Pleasedonotquote.VersionofApril26,2001.Commentswelcome.Cuecompetitioninfunctionlearning:BlockingandhighlightingJohnK.KruschkeIndianaUniversity,BloomingtonInfunctionlearning,peoplelearntopredictacontinuousoutcomefromcontinuouscues.Incategorylearning,peoplelearntopredictanominaloutcome.Thepresentresearchdemon-stratesthattwocomplementaryformsofcuecompetition,previouslyfoundincategorylearn-ing,alsooccurinfunctionlearning.Oneformofcuecompetitionisblockingoflearningaboutaredundantcue(Kamin,1968).Asecondformofcuecompetitionishighlightingofadiagnosticcue(a.k.a.theinversebaserateeffect;Medin&Edelson,1988).Fortestswithconictingcues,theresultsshowbimodalityofresponses,asopposedtoaveraging,whichimpliesexclusiveselectivitythatcannotbediscernedfromcategorylearningparadigms.Itisarguedthattheseeffectsarecaused,inbothcategoryandfunctionlearning,byattentionalshifts.Nopreviouslypublishedmodeloffunctionlearningcanaccountfortheseeffects,butamodelbyKalish,Lewandowsky,andKruschke(2001)ispromising.Thisarticlereportsevidenceoftwotypesofstrongcuecom-petitioninfunctionlearning.Oneeffectis“blocking”oflearningaboutaredundantrelevantcue(Kamin,1968).TheothereffectiswhatIcall“highlighting,”previouslyreferredtoastheinversebaserateeffect(Medin&Edelson,1988).Therearetwomainimplicationsofthiswork.First,becausetheeffectsarenowevidentinbothfunctionlearningandcategorylearning,theresultssuggestthatfuturetheoriesoflearningineitherdomainshouldbedesignedtoaddresstheotherdomainaswell.Second,becausetheoriesofthesecuecompetitioneffectsincategorylearningpositacentralroleforselectiveattention(Kruschke,1996;Kruschke&Blair,2000),theoriesoffunctionlearningshouldalsoincorporateselectiveattention.Thenewdataalsoindicatemutualexclusivityincuecom-petition,asopposedtoaveraging,thatcannotbemeasuredincategorylearningparadigms.Considerwhatmighthap-penwhenanobserverisconfrontedbytwoconictingcuessimultaneously.Forexample,supposethatthepersonhaspreviouslylearnedthatcueAindicatesoutcome1,andcueCindicatesoutcome3,whereoutcomes1and3arevaluesonametricscale.SupposethatthepersonisthenconfrontedbyatestcaseinwhichtheconictingcuesAandCarepaired.TheobservermightcontemplatetheresponsesforbothcuesThisresearchwassupportedinpartbyNSFgrantBCS9910720.TheauthorthanksMichaelKalishandStephanLewandowskyformotivationtopursuethisresearch.Forhelpfulcommentsondraftsofthisarticle,theauthorthanksJeromeBusemeyerandStephanLewandowsky.Forassistanceadministeringtheexperiment,theauthorthanksTwannaAllen,ColinCampbell,DanHall,KaraKohnen,IndyaWattsandMaxineWeiss.CorrespondencecanbeaddressedtoJohnK.Kruschke,De-partmentofPsychology,1101E.10thSt.,IndianaUniver-sity,BloomingtonIN47405-7007,orviaelectronicmailtokr-uschke@indiana.edu.Theauthor'sworldwidewebpageisathttp://www.indiana.edu/kruschke/andgeneratearesponsethatbestreectsanaverageofthetwo,i.e.,response2.Alternatively,theobservermightexclu-sivelyselectoneortheothercue(orcue-outcomelink)andgenerateeitherresponse1orresponse3,perhapsbimodally.Yetanotherpossibilityisthatthepersoncouldjustdecidethattheconictingcuesimplythatallbetsareoff,andsos/hejustchoosesrandomly(uniformly)fromtheavailablere-sponseoptions.Stillotherpossibilitiesexist,ofcourse.Mypointisthatthesethreedifferentresponsetendencies,whichleavedifferentsignaturesinthefunctionlearningparadigm,cannotbesoeasilydistinguishedinthestandardcategorylearningparadigm.Thisisbecauseincategorylearningtherearenointermediateresponseoptionsbetweenthenominalcategorylabels.Theresultsreportedbelowaremostconsis-tentwithmutualexclusivityincueselection,asopposedtoaveraging.BackgroundFunctionlearningiscommonineverydaytasks.Asjustafewexamples,considerthatpeoplecanlearnhowhardtothrowaballinresponsetovisualcuesaboutthedistanceofthecatcher,paramedicscanlearnhowmuchmedicationtoadministerinresponsetocuesabouttheweightofthepa-tient,andinvestorscanlearnhowmuchstocktopurchaseinresponsetocuesaboutmarkettrends.Categorylearningisdistinctfromfunctionlearningonlyinthattheoutcomesarecategoricalvaluesinsteadofmetricvalues.Thatis,theoutcomesaremerelylabels(withoutsizeororder),insteadofmagnitudes.Thisseeminglysmalldifferencesuggeststhatsimilarpsychologicalmechanismsshouldbeinvolvedinboth,andthatresearchaboutthetwotypesoflearningshouldmutuallyinformeachother(seereviewbyBusemeyer,Byun,Delosh,&McDaniel,1997).Oneofthecentraltypesofphenomenaobservedincategorylearningiscuecompetition,whereinalternativecuesapparentlycompetetogainassocia-tivepredictivenessoftheoutcome.Itseemsreasonabletoex-pectthatcuecompetitionshouldalsooccurinfunctionlearn-1 2KRUSCHKEing.Cuecompetitionisfundamentalinassociativelearning,butonlyalittleworkhasfoundcuecompetitioninfunctionlearning(e.g.Birnbaum,1976;Busemeyer,Myung,&Mc-Daniel,1993;Mellers,1986).Perhapsthemostwellknownexampleofcuecompeti-tionincategorylearningisblocking,whichhasbeenob-servedinavarietyofspeciesandprocedures(e.g.Dickin-son,Shanks,&Evenden,1984;Kamin,1968;Kruschke&Blair,2000;Shanks,1985),andwhichrevolutionizedtheo-riesofassociativelearning.Inblocking,theparticipantrstlearnsthatacue,denotedhereasA,perfectlypredictsanoutcome.Insubsequenttraining,theparticipantexperiencescasesofcueApairedwithanothercue,denotedB,stillper-fectlypredictiveoftheoutcome.DespitethefactthatBper-fectlypredictstheoutcome,peopleapparentlydonotlearntostronglyassociateitwiththeoutcome.Thatis,learningaboutBhasbeenblockedbypreviouslearningaboutA.Tomyknowledge,blockinghasneverbeensoughtinthecontextoffunctionlearning,yetitshouldexistifblockingistrulyafundamentalandpervasivephenomenoninlearning.AnotherdramaticcaseofcuecompetitionincategorylearningiswhatIcallhighlighting,previouslyreferredtoastheinversebaserateeffect(Medin&Edelson,1988).Inthisparadigm,peopleinitiallylearnthatapairofcues,de-notedI.E,indicateoutcomeOE.Inthenextphaseoftrain-ing,newcasesareintroducedinwhichcuepairI.LindicatesoutcomeOL.Thus,cueIisanimperfectpredictor,whilecueEisaperfectpredictorofoutcomeOEandcueLisaperfectpredictorofoutcomeOL.Despitethesymmetryofeachoutcomehavingonesharedcueandoneperfectlypre-dictivecue,peopleseemtolearnastrongerassociationfromLtoOLthanfromEtoOE,andastrongerassociationfromItoOEthanfromItoOL.ThisisevidencedbythefactthatpeopletendtorespondwithOEwhentestedonIalone,andtendtorespondwithOLwhentestedonthepairE.L.Thiseffect,whereincueLappearstobeselectivelyhigh-lightedwhenlearningI.LOL(andcueIisselectivelyig-noredwhenlearningI.LOL)hasbeendocumentedinava-rietyofcircumstances(Dennis&Kruschke,1998;Fagot,Kr-uschke,Depy,&Vauclair,1998;Kalish&Kruschke,2000;Kruschke,1996,2002;Medin&Bettger,1991;Shanks,1992).Highlightingiscomplementarytoblocking,becausethesecondcue(L)experiencesenhancedlearningratherthandiminishedlearning.Likeblocking,highlightinghasneverbeensoughtinthecontextoffunctionlearning,yetitshouldexistifitreectsafundamentalcuecompetitioneffect.Experiment:blockingandhighlightingTable1showsthedesignoftheblockingcomponentoftheexperiment.Theleftmostcolumnindicatesthephaseoftheblockingcomponent;thereweretwotrainingphasesfol-lowedbyatestphase.Eachrowofthetrainingphasesshowsasingletrainingtrial.Forexample,therowwithcueA3andoutcome3indicatesthatthethirdlevelofcueAoccurredwithoutcomelevel3.ThecorrectoutcomeleveldependedonthegrouptowhichTable1Designoftheblockingcomponentoftheexperiment.CorrectResponsePositiveNegativeFunctionFunctionPhaseCue(s)GroupGroupTrain1A336A445A554A663Train2A3.B336A4.B445A5.B554A6.B663Ca3.Cb336Ca4.Cb445Ca5.Cb554Ca6.Cb663Test2ndphasetrainingitems,plus:B1.Ca8,B1.Cb8,A1.Ca8,A1.Cb8B3.Ca6,B3.Cb6,A3.Ca6,A3.Cb6B6.Ca3,B6.Cb3,A6.Ca3,A6.Cb3B8.Ca1,B8.Cb1,A8.Ca1,A8.Cb1Note.A1-A8denotetheeightlevelsofthecuethatactedastheblocker.B1-B8denotetheeightlevelsofthecuethatwasblocked.Ca1-Ca8andCb1-Cb8denotetheeightlevelsofthetwocontrolcues.Adot(period)separatestwocuesthatappearedtogether.theparticipantwasassigned.Halftheparticipantslearnedpositivefunctionsofthecues,andtheotherhalflearnedneg-ativefunctions.TheseoutcomesareindicatedinthetworightmostcolumnsofTable1.Thismanipulationisimpor-tantbecause,ifanalogouseffectsareobservedforbothpos-itiveandnegativefunctions,thenwehaveevidencethattheeffectsareduetolearnedfunctionalrelationships,andarenotanartifactofpreviouslyexistingbiasestowardpositivelinearrelationships(e.g.Sawyer,1991;Summers,Summers,&Karkau,1969).Intheblockingdesign(Table1),noticethatcueBistheblockedcue,completelyredundantwithcueAbutalsoper-fectlypredictiveoftheoutcome.CuesCaandCbarecontrolcues,whichoccurasoftenascueB.CuesCaandCbarestructurallyequivalentinthedesign,andsotheresultswillbecollapsedacrossoccurrencesofCaandCbanddenotedsimplyascueC.Thevariousitemswerepresentedinrandomorderacrosstrialsoftraining.Ifblockingoccurs,thenresponsestocueBwillbeweakcomparedtothecontrolcuesC.Thisisassessedinthetestphasebypresentingpeoplewithconictingcues,suchasB3.C6.(B3.C6denotescasesofB3.Ca6andB3.Cb6.)IfcueBhasbeenblocked,thenthecontrolcuewilldominate,andtheresponsesshouldtendtobelevel6andnotlevel3.Table2showsthedesignforthehighlightingcomponentoftheexperiment.Allparticipantsdidboththeblocking CUECOMPETITIONINFUNCTIONLEARNING3Table2Designofthehighlightingcomponentoftheexperiment.CorrectResponsePositiveNegativeFunctionFunctionPhaseCue(s)GroupGroupTrain1I3.E336I4.E445I5.E554I6.E663Train2I3.E336I4.E445I5.E554I6.E663I3.L363I4.L454I5.L545I6.L636Test2ndphasetrainingitems,plus:E1,L1,I1,E1.L1E3,L3,I3,E3.L3E6,L6,I6,E6.L6E8,L8,I8,E8.L8Note.I1-I8denotetheeightlevelsoftheimperfectlypredic-tivecue.E1-E8denotetheeightlevelsoftheearlierlearnedperfectlypredictivecue.L1-L8denotetheeightlevelsofthelaterlearnedperfectlypredictivecue.Adot(period)sepa-ratestwocuesthatappearedtogether.andhighlightingcomponents,incounterbalancedorder.Liketheblockingcomponent,inthehighlightingcomponentthereweretwophasesoftrainingfollowedbyatestingphase.Alsoasintheblockingcomponent,halftheparticipantslearnedpositivefunctions,andtheotherhalflearnednegativefunc-tions.InTable2,noticeintrainingphase2thatcueIisimper-fectlypredictiveoftheoutcome.Forexample,inthepos-itivefunctiongroup,whenI3occurswithE3,itindicatesoutcome3,butwhenI3occurswithL3,itindicatesout-come6.ThisistrueforeverylevelofcueI,suchthathalfthetimeitindicatesoneoutcomelevel,andhalfthetimethecomplementaryoutcomelevel.BothcuesEandL,ontheotherhand,areperfectlypredictive.Theyindicateoppositesignfunctions,however.Thus,forparticipantsintheposi-tivefunctiongroup,cueE3indicatesoutcome3butcueL3indicatesoutcome6.Inboththeblockingandhighlightingcomponents,peo-pleweretrainedonthemiddlefourlevelsofaneight-levelscale.Thetestphasesprobedlevelsaboveandbelowthetraininglevels,therebycheckingforextrapolationofthelin-earfunctionrelatingthecuesandtheresponses.Theextrap-olationtestsareespeciallyimportant,becausetheytestthatpeopleactuallylearnedafunctionalrelationshipbetweencueandoutcome,asopposedtomerelymemorizingthepartic-ularcue-outcomecorrespondencesexperiencedintraining.Iftestsofthevaluesoutsidethetrainingrangedonotshowextrapolation,thenanyobservationofblockingorhighlight-ingcouldbeexplainedawayasjustthesameoldblockingandhighlightingalreadyknowntooccurincategorylearn-ing.Theimportanceofextrapolationinfunctionlearninghasbeenpointedoutbyotherauthorsinothercontexts,bothinfunctionlearningandincategorylearning(e.g.Delosh,Busemeyer,&McDaniel,1997;Erickson&Kruschke,1998;Kalishetal.,2001).MethodParticipantsFiftysevenstudentsfromintroductorypsychologycoursesatIndianaUniversityparticipatedforpartialcoursecredit.Agesrangedfrom17to52years,withamedianof19.Therewere33femalesand24males.ApparatusandstimuliParticipantsweretrainedindividuallyindimlylit,sound-dampenedcubicles.Theysatinfrontofastandarddesktopcomputeratacomfortableviewingdistance,andmadere-sponsesbypressingkeysonthestandardkeyboard.Thecueswereverbal-numerical,anddisplayedasthecuenameandvalue;e.g.,“BodyTemp:95.0deg.F”.Thesevencuesincludedthefollowing:BodyTemp,from95.0deg.Fto102.0inincrementsof1.0;GPA,from0.5to4.0inin-crementsof0.5;MileTime,from5:30to9:00inincrementsof0:30;Income,from$28,000to70,000inincrementsof6,000;SoundThreshold,from2.0dBto23.0inincrementsof3.0;HairLength,from2.0cmto37.0inincrementsof5.0;ShoeSize,from5+1/2to12+1/2inincrementsof1.Therefore,therewere8levelsofeachcue.Theresponsewasa“mysterymeter”levelfrom1to8,madebypressingthecorrespondingkeyonthetoprowofthekeyboard.ProcedureThedesignsoftheblockingandhighlightingcomponentsareshowninTables1and2.Thesevencuetermswererandomlyassignedtoabstractcuetypes,independentlyforeveryparticipant.Theorderingofblockingandhighlight-ingwascounterbalancedacrosssubjects,aswastheas-signmenttonegativeorpositivefunctionsforeachcompo-nent.Thus,therewereeightpossibleorderings(counterbal-ancedacrosssubjects):blockingpositivefunctionfollowedbyhighlightingpositivefunction;highlightingpositivefol-lowedbyblockingpositive;blockingpositivefunctionfol-lowedbyhighlightingnegativefunction;highlightingneg-ativefollowedbyblockingpositive;etc.Ineveryphaseoftheexperiment,thevariousitemswererandomlypermutedwithineachblock.Inthehighlightingprocedure,therewere10repetitionsofTrain1and15repetitionsofTrain2.TheTestphaseincludedonetrialofeachofthetrainingitems1,1Forsomeparticipants,thehighlightingtestphaseinadvertentlyincludedmoreI.EitemsthanI.Litems(becauseofavestigefromearlyexperimentsthatuseddifferentbaseratesforI.EandI.L).This 4KRUSCHKEonetrialofeachoftheEandLitems,andtwotrialseachoftheIandE.Litems.Intheblockingprocedure,therewere10repetitionsofTrain1,10repetitionsofTrain2,andinthetestphasetherewasonetrialofeachofthetrainingitemsplusonetrialofeachofthetestitems.Thistotalof336tri-alsproceededseamlesslywithoutinterruptionaftertheinitialinstructions.Theexperimenttookabout30minutes.Theinitialinstructions,writtenonthecomputerscreen,statedthatparticipantswouldseeinformationaboutahy-potheticalperson,andwouldneedtopredictthelevelofa“mysterymeter”thatmeasuredsomethingabouttheperson.Theinstructionstoldtheparticipant,“Yousimplyneedtoob-servetheinformationabouteachpersonandlearntopredictthemysterymeterlevel.”Onatrial,thecueswouldappear,oneperline,centeredhorizontallyonthescreen.Whenthereweretwocues,theirlocation(toporbottom)wasrandomoneachtrial.Afterapredictionwasmade,thecuesstayedonthescreenalongwithfeedbackthatindicatedthecorrectan-swer.Feedbacktoerroneousresponseswasaccompaniedbyabriefbuzzingsound.Ontesttrialswithoutcorrectanswers,thefeedbackindicatedthatnoofcialmeterlevelwasyetavailablebuttheirpredictionwasrecorded.Theparticipantpressedthespacebartomovetothenexttrial.ResultsBlocking,positivefunctiongroupBecauseIaminterestedineffectsoflearning,dataanal-ysisexcludedparticipantswhodidnotlearntorespondataccuracysignicantlyabovechance.Fortheblockingde-sign,Iwantedtobesurethatpeoplehadlearnedthecontrolcues,whichoccurredlaterintrainingthantheblocker.Isetchanceat25%correctbecauseonly4outcomeshadoccurredduringthetrainingphases.Torejectthenullhypothesisofchanceperformanceonthecontrol-cueitemsinthelasttwoblocksoftraining,apersonmustgetatleast5of8occur-rencescorrect.2Only1participantof29inthisconditionfailedtoachievethislevelofaccuracy,leavingN28.Inthetestingphase,performancecontinuedtobehighlyaccurateonthetrainingitems,averaging91%fortheblock-ingcuesand85%forthecontrolcues.CompleteresultsareshownintheAppendixinTable3.Figure1showsresultsfornovelcuecombinationsinthetestphase.Eachrowinthegurecorrespondstoaparticu-larcuecombination.Thewidthofthecirclesineachrowindicatesthepercentageofresponsesateachoftheeightoutcomelevels.ThelowerpanelofFigure1showsthattherewasrobustblocking,withtheresponseappropriateforthecontrolcuedominatingtheresponseappropriatetotheblockedcue.Forexample,withtestcuesB6.C3,thecircleatresponselevel3ismuchlargerthanthecircleatresponselevel6.Therewasdistinctextrapolationofcontrolcuedomi-nancebeyondthetrainingrange.Forexample,withtestcuesB8.C1,themodalresponseislevel1,whichwasneverexpe-riencedduringtraining.Inferentialstatisticsbolsterthesedescriptiveobservationsthatblockingoccurredandwasextrapolated.Blockingoc-12345678Figure1.ResponsepercentagesforA.CandB.Ctesttrialsofblocking,positivefunctiongroup.Diameterofcirclecorrespondstoresponsepercentage.SeetheAppendixfornumericalvalues.curredatthescalelevelsofthetrainingitems,insofarasthefrequencyof”5”or”6”responsestoB3.C6and”3”or”4”responsestoB6.C3wassignicantlygreaterthanthefrequencyof”3”or”4”responsestoB3.C6and”5”or”6”responsestoB6.C3,c2
df1N104650,p012.Therewasalsoextrapolationofblocking,inthatthefrequencyofrespondingwithextreme(nevertrained)scalevalues(”1”or”2”responsestoB8.C1and”7”or”8”responsestoB1.C8)wassignicantlyhigherthanwouldbeexpectedbychancerespondingacrosstheentirescale,c2
df1N1121376,p001.ThetoppanelofFigure1showsthatdespitethecontrolcues'dominanceoftheblockedcueB,thecontrolcuesdidnotdominatetheblockingcueA.(Intheterminologyofasso-proceduralinfelicitywasdetectedandcorrectedfortheremainingparticipants.TheincreasedexposuretoI.Eitemsduringtestonlymakestheresultsmoreremarkable,becausethepreferenceforthelater-trainedresponsesontheconictingcuesE.LmustovercomethisextratrainingwithI.E.2Analternativemeasureoflearningaccuracyismeanabso-lutedeviationbetweencorrectandselectedresponselevels.The“hit/miss”measurewasusedinsteadbecauseofitssimplicityandconservativeness. CUECOMPETITIONINFUNCTIONLEARNING5ciativelearningtheory,thiscanbedescribedasthetwocon-trolcuesmutuallyovershadowingeachotherduringlearning,althoughtheeffectmightalsobedueinparttothegreateroverallexposuretoA.)Forexample,withcuecombinationA6.C3,themodalresponseislevel6.ThemodalresponseineachcasefollowsthelinearfunctionappropriatetotheblockingcueA,evenintheextrapolationregion.Inferentialstatisticsconcurwiththisdescriptionoftheblockingcue'sdominanceandextrapolation.Atthescalelevelsofthetrainingitems,thefrequencyof”5”or”6”re-sponsestoA6.C3and”3”or”4”responsestoA3.C6wassig-nicantlygreaterthanthefrequencyof”3”or”4”responsestoA6.C3and”5”or”6”responsestoB3.C6,c2
df1N1101424,p001.Therewasalsoextrapolationofblockerdominance,inthatthefrequencyofrespondingwithextreme(nevertrained)scalevalues(”1”or”2”responsestoA1.C8and”7”or”8”responsestoA8.C1)wassignicantlyhigherthanwouldbeexpectedbychancerespondingacrosstheen-tirescale,c2
df1N1122976,p001.Blocking,negativefunctiongroupTheresultsforthenegative-functionversionofblockingwereentirelyanalogoustothepositive-functionversion.Thecontrolcuesdominatedtheblockedcue,andtheblockingcuedominatedthecontrolcues.Therewasextrapolationofthedominanceintotheuntrainedregionsofthescales.Thus,theresultsfromthepositive-functionversioncannotbeat-tributedtopriorbiasesaboutpositivefunctions.CompletedetailsarepresentedintheAppendix.Highlighting,positivefunctiongroupToexcludenon-learners,thesamecriterionwasusedasfortheblockingcomponents:Participantshadtoshowsignicantlyabovechanceperformanceonthelater-traineditemsinthelasttwoblocksoftraining.Thismeansatleast5of8correctontheI.Ltrialsinthelasttwoblocksoftraining.Of29participants,4failedtoreachthiscriterion,yieldingN=25forsubsequentanalyses.Performanceonthetrainingitemscontinuedtobegoodinthetestphase,averaging98%correctontheI.Eitemsand88%correctontheI.Litems.Figure2showsresultsfromsomeofthecriticaltestcases.(Table5intheAppendixshowscompleteresults.)ResponsestocueIbyitselfshowedaclearpreferencefortheearly-learnedoutcome.Forexample,intheupperpanelofFig-ure2,itcanbeseenthatthemodalresponsetocueI6wasoutcomelevel6(whichwastheearly-learnedoutcome).Thelineartrendcontinuesintotheextrapolationregions.Importantly,responsestoconictingcuesE.Lshowedapreferenceforthelaterlearnedoutcome.Forexample,inthelowerpanelofFigure2,itcanbeseenthatthemodalresponsetocuecombinationE6.L6wasoutcomelevel3,whichcorrespondswithcueL6.Thereisclearextrapola-tionofcueL'sdominanceintountrainedextremitiesofthescales.Oneaspectworthemphasizingisthatthedominantcue,L,indicatedanegativefunction,whichisafunctional12345678Figure2.ResponsepercentagesforIandE.Ltesttrialsofhigh-lighting,positivefunctiongroup.Diameterofcirclecorrespondstoresponsepercentage.SeetheAppendixfornumericalvalues.formknowntobedifculttolearnandapply(e.g.Brehmer,1971,1973).Itsdominanceoverthepositivecueisthereforequiteremarkable.Interestingly,responsestotheconictingcuesE.Lshowedaweaker,secondarypeakalongthefunctionfortheearlylearnedoutcome.InthelowerpanelofFigure2thiscanbeseenasanegativelinearfunctionconnectingthelargestcirclesineachrow,butapositivelinearfunctionconnectingthesecond-largestcirclesineachrow.Therearerelativelyfewresponsesoffofthesetwolinearfunctions.Thus,fortheconictingcues,itseemsthatparticipantstendedtoselectcueLtodictateresponding,butoccasionallyselectedcueEtodictateresponding.Itseemsthatpeoplerarelyifeverse-lectedbothcuesandaveragedtheirpredictedoutcomes.Thisobservationcouldnothavebeenfoundintraditionalcategorylearningexperiments,becausetherearenointermediatere-sponselevelsbetweencategories.Inferentialstatisticssupporttheseobservations.ForcueIbyitself,thefrequencyof”1”or”2”responsestoI1and”7”or”8”responsestoI8wasgreaterthanuniformrespondingacrossthescalerange,c2
df1N1001229,p001.Thefrequencyof”3”or”4”responsestoI3and”5”or”6”re-sponsestoI6wasgreaterthanthefrequencyof”5”or”6”re- 6KRUSCHKEsponsestoI3and”3”or”4”responsestoI6,c2
df1N93542,p001.ForconictingcuesE.L,thefrequencyofrespondingalongthenegativediagonalwassignicantlygreaterthanthefrequencyofrespondingalongthepositivediagonal3,c2
df1N176100,p001.Highlighting,negativefunctiongroupTheresultsforthenegative-functionversionofthehigh-lightingcomponentwereentirelyanalogoustotheresultsfromthepositive-functionversion.ForcueIbyitself,theearly-learned(negativefunction)outcomewasdominant.ForcuecombinationE.L,thelater-learned(positivefunc-tion)outcomewasdominant.Inbothcasestherewasclearextrapolationtotheuntrainedregionsofthescales.Thus,theresultsfromthepositivefunctionversioncannotbeat-tributedtopriorbiasesaboutpositivefunctions,ortosomeprior“distinctiveness”ofnegativefunctions.CompletedataarepresentedintheAppendix.ConclusionTheresultsshowedstrongevidenceofblockingandhigh-lightinginfunctionlearning.Thisisthersttimethattheseeffectsofcuecompetitionfromcategorylearninghavebeenfoundinfunctionlearning.Previousresearchershavedemonstratedformsofcuecompetitioninfunctionlearn-ing(e.g.Birnbaum,1976;Busemeyeretal.,1993;Mellers,1986),buttheyhavenotshownbridgesfromtheseparticulardramaticcuecompetitioneffectsincategorylearning.Theresultsalsoshoweddeniteextrapolationtonovelvaluesaboveandbelowthetraineddomain.Hencetheblock-ingandhighlightingreportedherecannotbeexplainedasmerelyaconagrationofseveralinstancesofcategorylearn-ing.Itappears,instead,thatpeoplereallydidlearnfunctionalrelationshipsbetweencuesandoutcomes,andthattherewasstrongcompetitionbetweenthecues.Therewasalsobimodalityinresponsesforsometestcasesthatusedconictingcues.Inparticular,forcasesofE.Linthehighlightingdesign,themaintrendwasforresponsestofollowthefunctionappropriatetocueL,buttherewasalsoaweakerpeakalongthefunctionappropriatetothecueE.Thatis,peopleappearedtoselectprimarilycueLtodom-inatetheresponse,orsecondarilycueE.Therewasnotastrongtendencytoselectbothcuesandaveragetheirimpliedresponses.Thisbimodalityindicatesexclusiveselectionofcuesthatcannotbediscernedfrompreviousdemonstrationsofhighlightingincategorylearningparadigms,becausecat-egorylearningparadigmsdonothaveresponseoptionsthatareintermediatebetweenthetrainedoutcomes.Theoriesofblockingandhighlightingincategorylearn-ingpositacentralroleforattentionalshiftingandlearning(Kruschke,1996;Kruschke&Blair,2000;Kruschke,2001).Thepresentresultsaddtoevidencethatselectiveattentionplaysasignicantroleinfunctionlearning.Theimportanceofcueselectionhasbeenrecognizedbymanyresearchersoffunctionlearning(e.g.Klayman,1988),butthenewdatapresentedinthisarticlemaketheconnectiontoattentionalselectionincategorylearningthatmuchstronger.Therehavebeenanumberofthoughtfulandsuccessfulmodelsoffunctionlearningpreviouslydescribedintheliter-ature,butnoneofthem,tomyknowledge,canaccountforthepresentresults.Theadaptiveregressionmodel(ARM)ofKoh(1993),forexample,hasmanyattractiveproperties,andbecauseofitserror-drivenlearningalgorithmmightbeanticipatedtobeabletoshowblockinginfunctionlearn-ing,analogouslytohowtheerror-drivenRescorla-Wagnermodel(1972)canshowblockingincategorylearning.ThereisspaceinthisarticleonlyforacursoryindicationofARM'spredictions,derivedherebyarmchairanalysis,notbynu-mericalsimulation.WhereasARMcan,appropriately,learnalargerregressioncoefcientfortheblockingcuethanfortheblockedcue,themodeldoesnotlearnaboutthecontrolcuesappropriately.ARMlearnshalf-strengthcoefcientsforeachofthetwocontrolcues(assumingthatthetwocon-trolcuesareequallysalient).ThiscausesARMtogeneratehalf-strengthoutputsfortheconicting-cuetestcases,unlikethefull-strengthmodalresponsesproducedbypeople.Moredramatically,ARMisunabletoproducethehighlightingef-fect,evenqualitatively,becauseitpredictsthattheunpre-dictivecueIshouldconvergetoaregressioncoefcientofzero,andthetwopredictivecues,EandL,shouldconvergetoequalstrength(butoppositesign)regressioncoefcients.Theextrapolationassociationmodel(EXAM;Deloshetal.,1997)hasbeenshowntotawidevarietyofphenom-enainfunctionlearning(forareview,seeBusemeyeretal.,1997).EXAMcanbethoughtofasanerror-drivenexem-plarbasedmodel(ALCOVE;Kruschke,1992)withanad-ditionalresponsemechanismthatextrapolateslinearlyfromlearnedexemplars.ArmchairanalysissuggeststhatEXAMcanshow,atleastqualitatively,theresultsfromtheblock-ingcomponentoftheexperiment.ButEXAMisnotabletoexhibithighlighting.Theexemplarrepresentationanderror-drivenlearningalgorithmmakesthemodelrespondambiva-lentlytoambiguouscues.Thisfailuretocapturehighlight-inginfunctionlearningisadirectextensionofALCOVE's(Kruschke,1992)failuretocapturehighlightingincategorylearning.Kruschke(e.g.,1996,2002)hasarguedthathighlightingisbestexplainedbyrapidshiftsofattentionduringlearning.Intheearlyphaseoflearning,thesharedcueIisassociatedwiththeearlyfunctionaloutcome.Inthelaterphaseoflearn-ing,whenstudyingcuecombinationsI.L,attentionshiftstothedistinctivecueL,inordertoreduceinterferencefromthepreviouslylearnedknowledgeaboutcueI.Inthisway,cueIremainsassociatedwiththeearlierlearnedoutcome,whilecueLbecomesstronglyassociatedwiththelaterlearnedout-come.KruschkeandBlair(2000;seealsoKruschke,2001)3Thefrequencyofrespondingalongthepositivediagonalwascomputedasthefrequencyofresponding”1”or”2”toE1L1,”3”or”4”toE3L3,”5”or”6”toE6L6,and”7”or”8”toE8L8.Thefrequencyofrespondingalongthenegativediagonalwascomputedasthefrequencyofresponding”1”or”2”toE8L8,”3”or”4”toE6L6,”5”or”6”toE3L3,and”7”or”8”toE1L1. 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8KRUSCHKETable3Choicepercentagesfromtestphaseofblockingcomponent,positivefunctiongroup.ResponseCues12345678A3.B3008677000A4.B4004894400A5.B5004089700A6.B60000010000Ca3.Cb30482411000Ca4.Cb40411757400Ca5.Cb5004789000Ca6.Cb6000449300A1.C838977144913A3.C600631172000A6.C32291347100A8.C123479541632B1.C87414111491329B3.C6201323134640B6.C3454314161800B8.C12514916119413Note.A1-A8denotetheeightlevelsofthecuethatactedastheblocker.B1-B8denotetheeightlevelsofthecuethatwasblocked.Ca1-Ca8andCb1-Cb8denotetheeightlevelsofthetwocontrolcues.Adot(period)separatestwocuesthatappearedtogether.Numbersinboldfontindicatethemodalresponseineachrow.Appendix:CompleteDataBlocking,positivefunctiongroupTable3showstheresultsfromtheblockingcomponentforparticipantswhoweretrainedwithapositivefunction.Blocking,negativefunctiongroupItiswellknownthatnegativefunctionsaremoredif-culttolearnthanpositivefunctions(e.g.Brehmer,1971,1973).Thereforeitisnotsurprisingthatfewerpeoplepassedthelearningcriterionforthenegativefunctionversionoftheblockingdesignthanthepositivefunctionversion.Of28participants,11failedtoreachthelearningcriterion(5cor-rectoutof8controltrialsinthenaltwotrainingblocks).Thus,N17inthedatareported.Table4showstheresultsfromthetestphase.Performancecontinuedtobehighlyaccurateonthetrainingitems,aver-aging91%fortheblockingcues(denotedA3B3-A6B6)and85%forthecontrolcues(denotedCa3Cb3-Ca6Cb6).Forthetestsofblocking,involvingablockedcue(de-notedB)andacontrolcue(denotedC),twoeffectsstandout,directlyanalogoustothepositivefunctionresults.First,therewasrobustblocking,withtheresponseappropriateforthecontrolcuedominatingtheresponseappropriatetotheblockedcue.Second,therewasdistinctextrapolationofthecontrolcuebeyondthetrainingrange.ThesetwoeffectscanTable4Choicepercentagesfromtestphaseofblockingcomponent,negativefunctiongroup.ResponseCues12345678A3.B3006068800A4.B4000694000A5.B50008812000A6.B6009406000Ca3.Cb3006068800Ca4.Cb40001276660Ca5.Cb5066826000Ca6.Cb6009406000A1.C82412612001533A3.C600261265303A6.C303623122100A8.C14763939024B1.C83531515091212B3.C630382461866B6.C3002118184400B8.C1159126931235Note.A1-A8denotetheeightlevelsofthecuethatactedastheblocker.B1-B8denotetheeightlevelsofthecuethatwasblocked.Ca1-Ca8andCb1-Cb8denotetheeightlevelsofthetwocontrolcues.Adot(period)separatestwocuesthatappearedtogether.Numbersinboldfontindicatethemodalresponseineachrow.beseenclearlyinTable4,wherethemodalresponseforeachcuecombination,setinboldfont,followsexactlythe(nega-tive)linearfunctionappropriatetothecontrolcue.Inferentialstatisticsbolsterthesedescriptiveobservationsthatblockingoccurredandwasextrapolated.Blockingoc-curredatthescalelevelsofthetrainingitems,insofarasthefrequencyof”3”or”4”responsestoB3C6and”5”or”6”responsestoB6C3wassignicantlygreater(becauseofthenegativefunctionlearned)thanthefrequencyof”5”or”6”responsestoB3C6and”3”or”4”responsestoB6C3,c2
df1N6370,p01.Therewasalsoextrapolationofblocking,inthatthefrequencyofrespondingwithextreme(nevertrained)scalevalues(”1”or”2”responsestoB1C8and”7”or”8”responsestoB8C1)wassignicantlyhigherthanwouldbeexpectedbychancerespondingacrosstheen-tirescale,c2
df1N681129,p001.AlsoevidentinTable4isthedominanceoftheblocker(denotedA)overthecontrolcues.Themodalresponseineachcase,setinboldfontinTable4followsthe(negative)linearfunctionappropriatetotheblocker.Inferentialstatisticsconcurwiththisdescriptionoftheblocker'sdominanceandextrapolation.Forscalelevelsinthetrainingrange,thefrequencyof”3”or”4”responsestoA6C3and”5”or”6”responsestoA3C6wassignicantlygreaterthanthefrequencyof”3”or”4”responsestoA3C6and”5”or”6”responsestoA6C3,c2
df1N66490, CUECOMPETITIONINFUNCTIONLEARNING9Table5Choicepercentagesfromtestphaseofhighlightingcompo-nent,positivefunctiongroup.ResponseCue(s)12345678I3.E3209620000I4.E4002962000I5.E50000100000I6.E6000009802I3.L3048008800I4.L40002080000I5.L5000924400I6.L6009204400E14828088008E30076124800E6400807288E84040881660L112400801264L3040887640L6008044444L852320000412I15024882026I30468180622I600610205842I84642842052E1.L1248122201240E3.L30224865820E6.L62258282440E8.L834864100632Note.I1-I8denotetheeightlevelsoftheimperfectlypredic-tivecue.E1-E8denotetheeightlevelsoftheearlierlearnedperfectlypredictivecue.L1-L8denotetheeightlevelsofthelaterlearnedperfectlypredictivecue.Adot(period)sepa-ratestwocuesthatappearedtogether.Numbersinboldfontindicatethemodalresponseineachrow.p05.Therewasalsoextrapolationofblockerdomi-nance,inthatthefrequencyofrespondingwithextreme(nevertrained)scalevalues(”1”or”2”responsestoA8C1and”7”or”8”responsestoA1C8)wassignicantlyhigherthanwouldbeexpectedbychancerespondingacrosstheen-tirescale,c2
df1N682267,p001.Highlighting,positivefunctiongroupTable5showscompleteresults.ForcuesEandLbythemselves,therewasclearextrapolationofthepositiveandnegativefunctions,respectively,ashighlightedinTable5bytheboldfontforthemodalresponsetoeachcue.Inferen-tialstatisticsconrmthisobservation,inthatthefrequencyofresponding”1”or”2”toE1,and”7”or”8”toE8,wassignicantlygreaterthanwhatwouldbeexpectedfromuni-formrespondingacrossthescalerange,c2
df1N50694,p001;and,thefrequencyofresponding”1”or”2”toL8Table6Choicepercentagesfromtestphaseofhighlightingcompo-nent,negativefunctiongroup.ResponseCue(s)12345678I3.E30011278000I4.E4002789200I5.E5004849200I6.E6008742420I3.L301163551600I4.L40058411000I5.L5005589000I6.L600111607400E151601111111632E3011526114700E6055311111605E82121110215165L1472105016011L301168511005L600516116350L805551116553I1518838111829I3051613135300I60547248835I82913115516813E1.L1341113588813E3.L305501682100E6.L600291105803E8.L8855516111634Note.I1-I8denotetheeightlevelsoftheimperfectlypredic-tivecue.E1-E8denotetheeightlevelsoftheearlierlearnedperfectlypredictivecue.L1-L8denotetheeightlevelsofthelaterlearnedperfectlypredictivecue.Adot(period)sepa-ratestwocuesthatappearedtogether.Numbersinboldfontindicatethemodalresponseineachrow.and”7”or”8”toL1wassignicantlygreaterthanuniformresponding,c2
df1N50807,p001.Otherresultsarediscussedinthebodyofthearticle.Highlighting,negativefunctiongroupOf28participantswhoexperiencedthenegativefunctionfortheearlytrainedcues,9failedtoreachthelearningcri-terion,yieldingN=19forsubsequentanalyses.Thislowerproportionoflearnersistobeexpectedbecauseitiswellknownthatlearninganegativefunctionismoredifcultthanlearningapositivefunction(e.g.Brehmer,1971,1973).Ta-ble6showstheresultsfromthetestphase.Performanceonthetrainingitemswasfairinthetestphase,averaging85%correctontheI.Eitemsand78%cor-rectontheI.Litems.ForcuesEandLbythemselves,therewasextrapolationofthenegativeandpositivefunctions,respectively,ashigh- 10KRUSCHKElightedinTable6bytheboldfontforthemodalresponsetoeachcue,althoughtheextrapolationwasnotassharpforE(thenegativefunction)asforL(thepositivefunction).Infer-entialstatisticsconrmthisobservation,inthatthefrequencyofresponding”1”or”2”toE8,and”7”or”8”toE1,wassignicantlygreaterthanwhatwouldbeexpectedfromuni-formrespondingacrossthescalerange,c2
df1N38789,p001;and,thefrequencyofresponding”1”or”2”toL8and”7”or”8”toL1wassignicantlygreaterthanuniformresponding,c2
df1N382951,p001.Mostimportantly,responsestocueIbyitselfshowedaclearpreferencefortheearly-learnedoutcome,andre-sponsestoconictingcuesE.Lshowedapreferenceforthelaterlearnedoutcome.Forbothtypesofcues,therewasrobustextrapolationofthesetrendsbeyondthetrainingdo-main.ThesetrendscanbeseenclearlyinTable6bythebold-fontmodalresponses.Asobservedpreviouslyforthepositive-functioncase,responsestotheconictingcuesE.Lshowedaweaker,secondarypeakalongthefunctionfortheearlylearnedoutcome.Inferentialstatisticssupporttheseobservations.ForcueIbyitself,thefrequencyof”1”or”2”responsestoI8and”7”or”8”responsestoI1wasgreaterthanuniformrespondingacrossthescalerange,c2
df1N76158,p001.Thefrequencyof”3”or”4”responsestoI6and”5”or”6”re-sponsestoI3wasgreaterthanthefrequencyof”5”or”6”re-sponsestoI6and”3”or”4”responsestoI3,c2
df1N69178,p001.ForconictingcuesE.L,thefrequencyofrespondingalongthepositivediagonalwassignicantlygreaterthanthefrequencyofrespondingalongthenegativediagonal,c2
df1N122159,p001.