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Rotello1
SignalDetectionTheoriesofRecognitionMemory
CarenM.RotelloDepartmentofPsychological&BrainSciences
UniversityofMassachusetts
June21,2016–toappearas:Rotello,C.M.(inpress).Signaldetectiontheoriesof
recognitionmemory.ToappearinJ.T.Wixted(Ed.),LearningandMemory:AComprehensiveReference,2ndedition(Vol.4:CognitivePsychologyofMemory).Elsevier.
Pleasereadandcitethepublishedversion.Correspondence:
CarenM.RotelloDepartmentofPsychological&BrainSciencesUniversityofMassachusetts135HicksWayAmherst,MA01003-9271(413)[email protected]
Rotello2
Abstract
Signaldetectiontheoryhasguidedthinkingaboutrecognitionmemorysinceitwas
firstappliedbyEganin1958.Essentiallyatoolformeasuringdecisionaccuracyin
thecontextofuncertainty,detectiontheoryoffersanintegratedaccountofsimple
old-newrecognitionjudgments,decisionconfidence,andtherelationshipofthose
responsestomorecomplexmemoryjudgmentssuchasrecognitionofthecontextin
whichaneventwaspreviouslyexperienced.Inthischapter,severalcommonlyused
signaldetectionmodelsofrecognitionmemory,andtheirthreshold-based
competition,arereviewedandcomparedagainstdatafromawiderangeoftasks.
Overall,thesimplersignaldetectionmodelsarethemostsuccessful.
Keywords:
Associativememoryd'DiscriminationaccuracyDual-processrecognitionmemoryItemmemoryFamiliarityMixturemodelsModelingPluralitydiscriminationRecollectionRecognitionmemorySignaldetectiontheorySourcememoryThresholdmodels
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1 Introduction
Recognitionmemoryerrorsareunavoidable.Sometimeswefailtorecognize
anindividualwe’vehadacasualconversationwith;othertimesweinitiatea
conversationwithastranger,erroneouslythinkingwemethimatacampusevent.
Theseerrorsarenotlimitedtoweakmemories:LachmanandField(1965)asked
subjectstostudyasinglelistof50commonwordsasmanyas128timesandfound
thatthepercentageofstudiedwordsthatarecalled“old”reachedanmaximumof
88%,whilethefalserecognitionofanunstudiedwordhoveredaround2%.
Althoughthisperformancelevelisexcellent,freerecallofthosestudiedwords
underthesameconditionswas98%correctwithnointrusionerrors.Thedifference
ofmemoryaccuracybetweenrecallandrecognitionsuggeststhatthedecision
processitselfplaysanimportantroleinrecognitionmemory.
Signaldetectiontheory(SDT:Green&Swets,1966;Macmillan&Creelman,
2005)providesatheoreticalframeworkforquantifyingmemoryaccuracyaswellas
theroleofdecisionprocesses.Itmakesexplicitthebalancebetweenpossible
memoryerrors(missedstudieditemsandfalsealarmstolures),aswellasthe
inevitabilityofthoseerrors.Insomeapplications,suchaseyewitness
identifications,thedifferenterrortypescomewithvariableimplicitcosts:failingto
identifytheguiltysuspectinalineupallowsacriminaltogofree;falselyaccusing
thewrongindividualleavesthetruecriminalunpunishedandmaysendaninnocent
persontojail.Inexperimentalsettings,theremaybeperformancepenalties(cash
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orpointdeductions,delayedonsetofthesubsequenttrial)associatedwithmissed
opportunitiestorecognizeastudieditemorwithfalseidentificationsofunstudied
memoryprobes.Theseconsiderationsmaysuggesttheonetypeoferrorismore
desirable–or,atleast,lessundesirable–thantheother,anddecisionmakerscan
shifttheirstrategytoreducetheprobabilityofthecostliererror.Modeling
recognitionmemoryusingsignaldetectionallowsindependentassessmentofthe
decisionprocessandtheabilityoftheindividualtodiscriminatecategoriesofitems.
Competingmodelsofrecognitionmemorymakedifferentassumptionsabout
thenatureofmemoryerrors.Discretestate,orthreshold,models(e.g.,Krantz,
1969)assumethatprobingmemorywithastudieditemcaneitherresultinits
detectionasapreviouslyexperienceditem,orinnoinformationatallbeing
availableaboutitsstatus.Forthisreason,thesemodelsareoftendescribedas
havingcompleteinformationlossbelowarecollectionthreshold.Inthemost
commonversionofthesemodels,errorsoccureitherbecauseofarandomguessing
process,or,sometimes,becausearesponseisofferedthatdirectlycontradictsthe
evidenceavailablefrommemory.Therelationshipbetweenmissesandfalsealarms
isnotspecifiedinadvancebythresholdmodels;aswe'llsee,differentparameter
choicesallowagooddealofflexibility.Inparticular,certainparametersettings
alloweithermissesorfalsealarmstobeavoidedentirely.
Asecondtypeofcompetingmodelassumesthatmorethanoneprocess
contributestorecognitionmemorydecision,inagreementwithMandler’s(1980)
well-knownbutcheronthebusexample.Themanonthebusmayberecognized
becauseheseemsfamiliar;bothmodelsinthisclassassumethatfamiliarity
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operatesasasignaldetectionprocess.Themanmayalsoberecognizedbecausewe
rememberhowweknowhim;thatheisthebutcher.Thisrecollectionprocesshas
beendescribedasoperatingeitherasasecondsignaldetectionprocess(Wixted&
Mickes,2010)orasathresholdprocess(Yonelinas,1994).Therecognitionmemory
errorsthatarepredictedbythesemodelsvarywiththeirassumptions,aswillbe
describedinsection2.
Finally,athirdtypeofcompetingmodelassumesthatrecognitiondecisions
forstudieditemsarebasedonamixtureoftwotypesoftrials,thoseonwhichthe
studyitemwasattended,andthoseforwhichitwasnot.Aswewillsee,these
mixturemodelsinheritmostofthepropertiesofthesignaldetectionmodels,
includingtheinabilitytoavoidatrade-offbetweenthetwotypesofrecognition
errors.
Thischapterisdividedintothreemainsections.Ibeginbydescribingthe
competingmodelsindetail.Next,Ireviewtheempiricalevidencethatdiscriminates
themodels,concludingthatthetraditionalsignaldetectionapproachprovidesthe
bestoveralldescriptionoftheliterature.Finally,Iconsidersomechallengesfor
signaldetectionmodels.
2 TheModels
2.1Equal-(EVSDT)andUnequal-Variance(UVSDT)Signal
DetectionModels
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Theearliestsignaldetectionmodelsofrecognitionmemoryassume
recognitiondecisionsaremadebasedonasingleunderlyingevidencedimension
(seeFigure1).Bothstudieditems(targets)andunstudieditems(lures)areassumed
toresonatewithmemorytovaryingdegrees,resultinginadistributionofobserved
memorystrengths;thestrengthoftargetsisincreasedbytheirrecentstudy
exposure,shiftingthatdistribution'smeantoagreatervaluethanthatofthelures.
Recognitiondecisionsarebasedonacriterionlevelofevidence,withpositive
("old")decisionsgiventoallmemoryprobeswhosestrengthsexceedthatcriterion,
otherwisenegative("new")responsesaremade.Theproportionofthetarget
distributionthatexceedsthecriterionequalsthetheoreticalproportionofstudied
itemsthatareidentifiedas"old",whichisthehitrate(H).Themissrateisthe
proportionoftargetsthatareerroneouslycalled"new,"soH+missrate=1.
Similarly,theproportionoftheluredistributionthatexceedsthatsamecriterion
providesthefalsealarmrate(F),whichistheproportionofluresthatfalselyelicit
an"old"response.Finally,theproportionofluresthatarecalled"new"isthecorrect
rejectionrate.Byvaryingthelocationofthecriterion,thehitandfalsealarmrates
canbeincreasedordecreased.
<InsertFigure1nearhere>
TherearetwoimportantpointstomakeabouttheSDTmodel.First,changes
inthecriterionlocationalwayschangehitandfalsealarmratesinthesame
direction(bothincreasing,formoreliberally-placedcriteria,orbothdecreasing,for
moreconservativecriteria),thoughtheobserveddifferencesmaynotbestatistically
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significant.Second,errorsareimpossibletoavoid.Acriterionthatisliberalenough
toyieldalowrateofmissedtargetswillnecessarilyresultinaveryhighfalsealarm
rate,andonethatisconservativeenoughtoresultinalowfalsealarmratewill
necessarilyproduceahighmissrate.
Wecanmeasureparticipants'discriminationaccuracy–thatis,theirability
todistinguishthetargetsfromthelures–intermsofthedistancebetweenthe
meansofthedistributions,instandardized(z-score)units.Whenthetwo
distributionshavethesamevariance(asintheupperrowofFigure1),thisdistance
iscalledd'anditisindependentofthecriterionlocation,k.Inthatcase,themodel
canbedefinedwithonlythosetwoparameters.Settingthemeanofthelure
distributionto0anditsstandarddeviationto1(withoutlossofgenerality),the
falsealarmrateisdefinedby
(1)
whereFisthecumulativenormaldistributionfunction.Similarly,thehitrateis
definedbythesamecriterionrelativetothemean,d’,ofthetargetdistribution:
. (2)
Wecancombineequations1and2toseethat
(3)
wherezistheinverseofthenormalCDF.Becausethecriterionlocation,k,drops
outofcalculationsinEquation3,itsvaluedoesnotaffectourestimateof
discriminationaccuracy:responsebias(k)andmemorysensitivity(d')are
independentinthismodel.Effectively,thismeansthatthereisasetof(F,H)points
F =Φ −k( )
H =Φ "d − k( )
!d = zH − zF
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thatallyieldthesamevalueofd';eachpointsimplyreflectsadifferentwillingness
oftheparticipanttosay“old.”Connectingallofthesepossible(F,H)pairsyieldsa
theoreticalcurvecalledareceiveroperatingcharacteristic(ROC);transformingboth
FandHtotheirz-scoreequivalentsyieldsazROC.
SeveralexampleROCsandcorrespondingzROCsareshownintheupperrow
ofFigure1,fordifferentvaluesofd'.TheROCsandzROCsassociatedwithhigher
decisionaccuracyfallabovethosewithloweraccuracy:foranygivenfalsealarm
rate,theROCyieldinghigheraccuracyhasagreaterpredictedhitrate.Thepoints
oneachROCandzROCvaryonlyincriterionlocation,k,withmoreconservative
responsebiases(largerk)yieldingpointsthatfallonthelowerleftendoftheROC
becauselargervaluesofkresultinlowerFandH.Inprobabilityspace,theROCsare
curvedandsymmetricabouttheminordiagonal.Innormal-normalspace,wecan
useEquation3toseethatthezROCisaline,zH=d'+zF,forwhichthey-intercept
equalsd'andtheslopeis1.ThemodelintheupperrowofFigure1,andthus
equations1-3,appliesonlywhenthevariabilityofthetargetdistributionequalsthat
oftheluredistribution.Forthisreason,thismodeliscalledtheequal-varianceSDT
(EVSDT)model.Aswewillsoonsee,theequalvariancepropertyofthisbasicmodel
causesthesymmetryinthetheoreticalROC.
Egan(1958)wasthefirsttoapplythismodeltorecognitionmemorydata.
Participantsintwoexperimentsstudied100wordseitheronceortwice,andthen
madeold-newdecisionsonthosestudiedwordsmixedwith100lures.Their
responsesweremadeonaconfidenceratingscalerangingfrom“positive”thatthe
testprobewasstudiedto“positive”thatitwasnew.Theresponseprobabilitiesin
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eachoftheseconfidencebinscanbemodeledwiththesameoveralldiscrimination
value(d')butadifferentcriterion(k1-km,seeFigure1).Egan'sdataimmediately
suggestedaproblemwiththemodel:theROCswerenotsymmetric,eitherfor
individualdataorfortheaverageacrossparticipants,andthereforewerenot
consistentwiththeequal-varianceSDTmodel.(Figure6showstheROCproduced
byoneofhisparticipants.)Fortunately,itisstraightforwardtomodifythemodelto
allowforunequal-variancedistributions.
Againassuming(withoutlossofgenerality)thattheluredistributionis
normalwithameanof0andastandarddeviationof1,wecansetthemeanofthe
targetdistributiontobedanditsstandarddeviationtobes.Thelowerrowof
Figure1showswhatthesedistributionsmightlooklike.Inthisunequal-variance
versionoftheEVSDTmodel,theUVSDT,Equation1stillholdsbecausethefalse
alarmrateisdefinedbythemeanandstandarddeviationoftheluredistribution,
andthosehaven’tchanged.Thehitratecalculationintheunequal-variancemodel
musttakeaccountofthestandarddeviationofthetargetdistribution,s,yielding
. (4)
Noticethatdiscriminationaccuracy,whichisthedistancebetweenthemeansofthe
targetandluredistributions,nowcanbedefinedinseveralways.Thetwomost
obviousapproachesaretomeasurethedistanceinunitsofthestandarddeviationof
theluredistribution(d'1),
H =Φd − ks
#
$%
&
'(
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, (5)
orinunitsofthestandarddeviationofthetargetdistribution(d'2),
. (6)
SeveralexampleROCsareshowninthelowerrowofFigure1,fordifferentvaluesof
d'1(and,equivalently,d'2).ThecorrespondingzROCsarealsoshown.They-
interceptisthevalueofzHwhenzF=0;Equation5tellsusthatzH=d'2atthat
point.ItalsoshowsthatthezROC,zH=d'2+(1/s)zF,isalinewithslopeequaltothe
ratioofthelureandtargetdistributionsstandarddeviations.Thisconnectionofthe
slopeofthezROCandtheratioofstandarddeviationsisahandypropertythathas
theoreticalsignificance.ThelinearformofthezROC,anditsslope,areheavily
studiedaspectsofrecognitionROCs.
Athirdstrategyformeasuringthedistancebetweenthetargetandlure
distributionmeansistouseunitsthatreflectacompromisebetweenthetwo
standarddeviations.Thebeststrategyfordoingsoinvolvestherootmeansquare
standarddeviation,yieldingda,
(7)
becauseofitsrelationshiptotheareaundertheROC,Az:
. (8)
!d1 = s ⋅ zH − zF
!d2 = zH −1s⋅ zF
da = 21+s2!
"#
$
%& zH−1
s⋅zF
!
"#
$
%&
Az =Φda2
"
#$
%
&'
Rotello11
Azisequalstheproportioncorrectanunbiasedparticipantwouldachieveinatask
involvingselectionofthetargetinasetoftarget-lurepairs.Noticethatda=d'when
thevarianceofthetargetandluresdistributionsareequal(s=1).
2.2Dual-processandMixtureSignalDetectionModels
2.2.1Thehigh-thresholdsignaldetectionmodel(HTSDT)
Yonelinas(1994)proposedaverydifferentexplanationoftheasymmetryin
therecognitionROC,namelythatparticipantssometimesrecollectstudieditems.
Becauserecollectioncan'toccurforluresandbecauseit'slikelytoresultinhigh
confidenceresponses,onlythehighest-confidencehitrateisincreasedbythe
contributionofrecollection.ThiscausestheleftendoftheROCtobeshifted
upwards,resultinginanasymmetricfunction.Yonelinasassumedthat,inthe
absenceofrecollection,responsesarebasedonanequal-variancesignaldetection
processthatassessesthefamiliarityofthememoryprobe.Inthisdual-process
model,recollectionoperatesasahigh-thresholdprocess(lurescan'tberecollected),
sowe'llcallitthehighthresholdsignaldetection(HTSDT)model.Accordingto
HTSDT,thehitrateisdefinedby
, (9)
whereRistheprobabilityofrecollection,andthefalsealarmrateisgivenby
Equation1;themodelcanbedescribedbytheparametersRandd'.Someexample€
H = R + (1− R)⋅ Φ % d − k( )
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ROCsandzROCsareshowninFigure2.NoticethatzROCfortheHTSDTmodelis
curved.Inthismodel,familiarity-basedrecognitionerrorsoccurtradeoffagainst
oneanother,exactlyasintheEVSDTandUVSDTmodels.However,therecollection
processcannotresultinfalsealarms,andifallresponsestotargetsarebasedon
recollection,therecanbenomisses.1
<InsertFigure2nearhere>
2.2.2 Thecontinuousdualprocesssignaldetectionmodel(CDP)
Theideathatsomeitemsonarecognitiontestmayberecollectedhasalong
history(e.g.,Mandler,1980).However,nothingaboutrecollectiondemandsthatit
isahigh-thresholdprocess.WixtedandMickes(2010)proposedadual-process
modelinwhichbothrecollectionandfamiliarityarebasedonunderlyingsignal
detectionprocesses,theresultsofwhicharesummedtoyieldanold-newresponse.
Forthisreason,theCDPmodelisidenticaltotheUVSDTmodelforitemrecognition.
However,theCDPmodelalsoallowsthetwoprocessestobequeriedseparately.
2.2.3Themixturesignaldetectionmodel(MSDT)
DeCarlo(2002,2003,2007)proposedanextensionofthestandardEVSDT
1TheSourcesofActivationConfusion(SAC)Model(Rederetal.,2000)isaprocessmodelsimilartotheHTSDTmodel.Thischapterwillnotdiscussprocessmodels.
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modelinwhichstudyitemsarenotalwaysfullyencoded.Onsometrials,theitemis
fullyencoding(resultinginarelativelylargeincrementinmemorystrength,dFull),
whereasonothertrialsthestudyitemisonlypartiallyencoded(leadingtoasmall
incrementinstrength,dPartial).Theprobabilityoffullencodingisgivenbythe
parameterl,whichcanbeinterpretedasameasureofattention.Attest,thetarget
distributionreflectsamixtureofresponsesfromthesetwodistributions.This
mixturedistributionforthetargetsisnotGaussian,anditspreciseformdependson
both landthedistancebetweenthemeansofthefull-andpartially-encoded
distributions.Thehitrateisdefinedasfollows:
(10)
ThefalsealarmrateisdefinedasinEquation1.Noticethecloserelationship
betweentheMSDTandHTSDTmodels:whendFullisverylarge(asisoftenthecase
whenfittoempiricaldata),thenthefirstcomponentofthehitrateisessentiallyjust
l,analogoustotheRparameteroftheHTSDTmodel.
ThedecisionspaceassumedbytheMSDTmodelisshowninFigure3,aswell
asseveralexampleROCsandzROCs.NotetheunusualformofthezROCs,whichwill
becomeimportantinthediscussionofassociativeandsourcerecognition.
<InsertFigure3nearhere>
2.3 TheDoubleHigh-Threshold(2HT)Model
H = λ ⋅Φ dFull − k( )+ 1−λ( ) ⋅Φ dPartial − k( )
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Theremainingmodelofrecognitionmemorythathasbeenpopularinrecent
yearsisadiscretestatemodel.Thedoublehigh-threshold(2HT:Snodgrass&
Corwin,1988)modelassumesthatmemoryprobesresultindifferentinternalstates
(seeFigure4).Targetscaneitherberecollected,inwhichcasetheyarealways
judgedtobe“old,”ortheyresultinastateofuncertaintyfromwhichtheparticipant
mustguess"old"or"new."Lurescanbedetectedasnew,resultingina"new"
decision,ortheyresultinthesamestateofuncertaintyasun-recollectedtargets.
Themodeliscalledadoublehigh-thresholdmodelbecausetherearetwo
thresholds:thelurescan'tcrosstherecollectionthresholdandbecalled"old"from
thatstate,andthetargetscan'tbedetectedasnew.Memoryerrorsalwaysresult
fromtheuncertainstate.Inthe2HTmodel,thehitratedependsontheprobability
thattargetsarerecollected(po)andtheprobabilitythat,ifnotrecollected,they
resultinaguess"old"decision(g):
. (11)
An"old"responsetoalurecanonlyoccurbecauseofguessing,sothefalsealarm
rateisdeterminedbytheprobabilitythatluresfailtobedetectedasnewandthe
rateof"old"guessing:
. (12)
Inthisform,the2HTmodelpredictsthattheROCisalinewithy-interceptequalto
poandslopeof(1-po)/(1-pn).Differentresponsebiasescanoccurinsimpleold-new
decisiontaskswhentheguessingrate,g,isvaried.Sensiblechangesingoccurwhen
differentbase-ratesoftargetsandluresappearonamemorytest,orwhen
€
H = po + 1− po( )g
€
F = 1− pn( )g
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participantsareoffereddifferentpenaltiesandrewardsforspecificresponses.
However,it’spossiblewithinthismodelforthegparametertobesetto0,sothat
falsealarmsareentirelyavoided,atthepriceofanincreaseinthemissrate.
Similarly,there’snothingaboutthemodelitselfthatpreventsthegparameterfrom
beingsetto1,sothatmissesareeliminatedatthepriceofanincreaseinfalse
alarms.2
<InsertFigure4nearhere>
The2HTmodeldoesnotnaturallypredictconfidenceratings,thoughitcan
beextendedtodosobyaddingparametersfromtheinternalstates(recollect,
uncertain,detect-new)tothepossibleconfidencejudgments,asinFigure5.If
recollectedtargetsarealwaysgivenhighest-confidence"old"responses,thenthe
confidence-basedROCpredictedthismodified2HTmodelisstilllinear.However,
themodelcanaccommodatethecurvedconfidence-basedROCsthatareobserved
empirically,ifrecollectedtargets(whichlogicallyshouldreceivethehighest-
confidenceresponse)areallowtoyieldlower-confidence"old"responses(e.g.,
Malmberg,2002;Bröder&Schütz,2009).Similarly,thedetectedluresareallowed
toresultinlower"new"decisions.(Someresearchersevenallowresponsesto
detecteditemstofallinthe"opposite"responsecategory,sothatrecollectedtargets
maystillyielda"new"decision.)Thismodifiedmodelrequiresmoreparametersto
describethemappingfromtheinternalstates,buttheincreaseinfreeparameters
resultsinmuchbetterfitstodata(andgreatermodelflexibility,ofcourse).
2Morecomplexversionsofthebasic2HTmodelhavealsobeenproposed(e.g.,Brainerd,Reyna,&Mojardin,1999).Testingthesevariantsrequireexperimentalconditionsbeyondthoseconsideredinthischapter.
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<InsertFigure5nearhere>
3 TheEvidence
In1970,Banksexpressedtheoptimisticviewthatsignaldetectionmodeling
wouldultimatelyallowustoidentifythenumberandnatureofprocessesinvolved
inrecognitionmemorydecision.Atthetime,themodelsunderconsideration
includedtheSDTandthresholdmodels(includingthe2HTmodelandseveralother
variants).Thosemodelsdomakequitedistinctpredictionsabouttheformofthe
ROC(seePazzaglia,Dube,andRotello,2013,fordetails).Specifically,the2HTmodel
canaccommodateacurvedROCbasedonconfidenceratings,butitmustpredicta
linearROCifparticipantsmakebinaryold-newdecisionsandtheresponsesthat
definethedifferentoperatingpointsarecollectedindependently.Incontrast,the
SDTmodelalwayspredictsacurvedROCwillresult,regardlessofwhether
confidenceratingsorbinaryold-newdecisionsarecollected.Aswe’llsee,Banks’s
optimismwasreasonablywellplacedforthesemodels.
WiththeadditionofthehybridHTSDTandmixtureMSDTmodels,however,
thelandscapebecamemorechallenging.Thesemodelsdomakepredictionsthat,in
principle,allowthemtobedistinguishedfromtheothers.Forexample,thezROCis
predictedtobelinearforSDTandtohaveanupwardcurvaturefortheHTSDT
model,andtheHTSDTmodelspredictsthatboththeslopeofthezROCandits
curvaturearesystematicallyinfluencedtheprobabilityofrecollection.Despite
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theseapparentlycontrastingpredictions,themodelsturnouttofitbasicitem
recognitiondataquitewell,requiringthattheexperimentalparadigmsbeexpanded.
Insection3.1,Ireviewtherelevantdatafromitemrecognitionexperimentsbefore
turning,insection3.2,tonewparadigmsdesignedtoinfluencerecollection
probabilitiesand,insection3.3,toexperimentsthatrelyondifferentialmodel
predictionsinparadigmsthatdonotyieldROCdata.Topreviewtheresultsofthis
literaturesurvey,theUVSDTmodelcomesoutaheadonnearlyeverymeasure.
However,section4willconsidersomepotentialchallengestothesuccessofthe
UVSDTmodel.
3.1 TraditionalItemRecognitionTasks
Standarditemrecognitionexperiments,likeEgan's(1958),provideawealth
ofdatathatcanbereasonablywelldescribedbyallofthemodelsconsideredhere.
Intheseexperiments,participantsstudyasetofitems(typicallywords)oneata
time.Attest,theyareaskedtoidentifythestudiedwordsfromatestlistthat
includesbothtargetsandlures.Subjects'responsesmaybesimpleold-new
decisionsforeachmemoryprobe,butmorecommonlytheyareratingsof
confidencethattheprobewasstudied.Theseratingsarethenusedtogenerate
ROCs,astrategythathasrevealedanumberof"regularities"inthedata.For
example,thezROCistypicallylinearwithaslopeofabout0.8aslongasmemory
accuracyiswellabovechance(e.g.,Ratcliff,Sheu,&Gronlund,1992;Glanzer,Kim,
Hilford,&Adams,1999;Yonelinas&Parks,2007).
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3.1.1 ConfidencebasedROCs
3.1.1.1 Fitsofthemodelstodata
ConfidencebasedROCsaregeneratedbyaskingparticipantstoratetheir
confidencethateachmemoryprobewasstudied(e.g.,6=“sureold”,5=“probably
old”,4=“maybeold”,3=“maybenew”,2=“probablynew”,1=“surenew”).The
probabilityofahitandafalsealarmineachconfidencebinisthencalculated;these
valuesareincrementallysummedtoyieldtheoperatingpointsontheROC.For
example,themostconservativepoint,yieldingthelowesthitandfalsealarmrates,
isbasedonresponsesinthe“sureold”category;thesecondpointontheROC
dependsonthesumoftheresponseprobabilitiesinthe“sureold”and“probably
old”bins,etc.ThefinalpointontheconfidenceROCisalways(1,1),whenall
responsesareincluded.
Pazzagliaetal.(2013)suggestedthatdiscriminatingtheUVSDTandHTSDT
modelswithROCswouldbeextremelydifficultbecausetheymakeverysimilar
predictions.Indeed,bothmodelshaveaparametertosummarizeold-new
discriminationaccuracy(d',d)andaparametertocapturetheasymmetryofthe
ROC(R,s).Similarly,theMSDTmodelcanbeviewedasaversionoftheHTSDT
modelifthefullattentiontrialsyield(essentially)perfectencoding.Whenapplied
todata,allofthesemodelsfitwell.Figure6showsthefitofeachofthesemodels,as
wellasthe2HTmodel,tothedataofasinglesubjectinEgan’s(1958,Exp.1)study.
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Asisobviousinthefigure,allofthemodelsprovideexcellentdescriptionsofthese
data;onlytheEVSDTmodelcanberejectedbasedonagoodnessoffitstatistic.
<InsertFigure6nearhere>
High-fidelityfitslikethoseinFigure6areroutinelyobserved.Forexample,
DeCarlo(2002)comparedtheMSDTandUVSDTmodels’abilitytofitdata,finding
themtobeessentiallytied.Yonelinas(1999b,p.514)notedthattheHTSDTand
UVSDT“modelsprovidedanaccurateaccountoftheROCs,capturingmorethan
99.9%ofthevarianceoftheaverageROCs.”Fortheverysamestudies,however,
Glanzeretal.(1999)foundthattheUVSDTmodelprovidedabetterfitinall10data
sets.Glanzeretal.(1999)alsotestedspecificHTSDTpredictionsaboutthe
relationshipbetweentheprobabilityofrecollection,theslopeofthezROC,andthe
curvatureofthezROC,findingnosupportforthosepredictions.Similarly,
Heathcote(2003)comparedthefitsoftheUVSDTandHTSDTmodelsforasetof
experimentsinwhichthetargetsandluresweresimilartoanother.Thesimilarity
manipulationwasintendedtoincreasetheprobabilitythatrecollectionwouldplay
aroleintherecognitionoftargets(Westerman,2001),yetthezROCsshowedno
evidenceofthecurvaturethatispredictedbytheHTSDTmodel.Othercomparisons
oftheUVSDTandHTSDTmodelshavealsofavoredthesignaldetectionview(e.g.,
Kelley&Wixted,2001;Healey,Light,&Chung,2005;Rotello,Macmillan,Hicks,&
Hautus,2006;Dougal&Rotello,2007;Kapucu,Rotello,Ready,&Seidl,2008;Jang,
Wixted,&Huber,2011).
3.1.1.2 Assessmentsofmodelflexibility
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TheUVSDT,HTSDT,2HT,andMSDTmodelsallprovidereasonablefitsto
data,buttheydohavedifferentassumptionsandthereforecan’tallprovidean
accurateaccountoftheunderlyingrecognitionmemoryprocesses.AsRobertsand
Pashler(2000)pointedout,agoodfittodatadoesnotimplythatthemodelitselfis
agoodone;itmighthaveenoughflexibilitytofitawiderangeofpossibledata,for
example,includingrandomnoise.Theflexibilityofamodelcomesfromitsnumber
offreeparametersanditsfunctionalform(Pitt,Myung,&Zhang,2002).Increasinga
model’sparametersgenerallyincreasesitsabilitytofitdata,buttwomodelswith
thesamenumberofparametersmaynonethelessdifferinflexibility.Forexample,a
sinusoidalmodely=asin(bx)canexactlyfitanydatageneratedbythelinearmodel
y=cx+d,aswellasfittingdatathatarenon-linear;thesinusoidalmodelhasgreater
flexibilitybecauseofitsfunctionalform.Forthisreason,wemustdeterminethe
relativelyflexibilityofthecompetingmodelsofrecognitionmemorybeforewecan
concludethattheUVSDTmodelprovidesthebestdescriptionofthedata.
ThenumberofparametersforeachmodelisshowninTable1fora
confidence-ratingold-newtask.TheUVSDTandHTSDTmodelshavethesame
numberofparameters,whereastheEVSDTmodelhasonefewer,andtheMSDT
modelonemore.The2HTmodelhasahighdegreeofflexibilitybecausethestate-
responsemappingparametersareselectedbytheexperimenter.Wixted(2007)
reportedasmall-scalemodel-recoverysimulationoftheUVSDTandHTSDTmodels
thatconcludedthatthetwomodelswereaboutequallyflexible,aconclusionthat
hasbeenmodifiedonlyslightlyinsubsequentwork.
Rotello21
<InsertTable1nearhere>
Jangetal.(2011)usedaparametricbootstrapcross-fittingmethod(PBCM:
Wagenmakersetal.,2004)tocomparetheflexibilityoftheUVSDTandHTSDT
models.ThePBCMhasseveralsteps.Essentially,modelparametersaresampled
fromtherangethatwouldbeestimatedfromfitstorealdata,andthoseparameters
areusedtogeneratesimulateddatafromthemodels.Then,bothmodelsarefitto
thesimulateddataandthedifferenceintheresultinggoodnessoffitmeasures
(DGOF)iscomputed.Thisprocessisrepeatedmanytimestogenerateadistribution
ofobservedDGOFvalueswheneachmodelgeneratedthedata.Thedegreeof
overlapofthesedistributionsisameasureofhowwellthemodelsmimiceachother
(seeWagenmakersetal.,2004;Cohen,Rotello,&Macmillan,2008,fordetails).For
group-leveldata,Jangetal.concludedthatmodelscouldbereadilydistinguished,
andthattheUVSDTmodelwasveryslightlymoreflexiblethantheHTSDTmodel.In
contrast,asimilaranalysisbyCohenetal.(2008)concludedthattheUVSDTmodel
wasslightlylessflexible.Arelatedbutsmaller-scalecomparisonofaversionofthe
2HTandUVSDTmodelsconcludedthatthe2HTmodelhasgreaterflexibility(Dube,
Rotello,&Heit,2011).
Whenanindividualsubjectprovidestheinitialdatathatareusedtoestimate
themodelparametersfromwhichsimulateddataaregenerated,thedistributionsof
DGOFvaluesalsoprovidequantitativeinformationabouthowdiagnosticthosedata
are.Diagnosticdataarethoseforwhichthedistributionshavelittletonooverlap;
fornon-diagnosticdata,theoverlapmaybesubstantial.Theextentofoverlapcan
beusedasameasureoftheprobabilitythatthewrongmodelisidentifiedbythe
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GOFmeasures.Jangetal.(2011)usedthisapproachtoassessthediagnosticityof
97individualparticipants’ROCs,findingthatmanyprovidednon-diagnosticdata.
Forthoseindividuals,thereweretwocommonfindings:theslopeofthezROCwas
likelytobenear1,andtheHTSDTmodelwasmorelikelytobeselected.For
individualswhoprovidedmorediagnosticdata(theDGOFdistributionsoverlapped
less),theslopeofthezROCtendedtobeshallower,andtheUVSDTmodelwas
usuallyselected.TheclearimplicationofJangetal.’sworkisthattheUVSDTmodel
isthebetter-fittingmodelwhenthedataactuallyallowastrongconclusiontobe
drawn.
Overall,theanalysesofmodelflexibilitysuggestthatthesuccessofthe
UVSDTmodelcannotbeattributedtogreaterflexibility.Forgroup-leveldata,the
UVSDTandHTSDTmodelshavesimilardegreesofflexibility,andforindividual
subjects’data,theUVSDTmodelisselectedonlywhenthedataareactually
informative.
3.1.1.3 ExplanationsofthezROCslope
TherearequalitativereasonstoprefertheUVSDTmodelovertheHTSDT
model,aswellasthequantitativereasonsinsection3.1.1.2.Forone,theslopeof
thezROChasanaturalexplanationintermsofvariabilityintheincrementtoan
item'sstrengththatoccursduringstudy(Wixted,2007);thisideaisreflectedinthe
assumptionsofrecentprocessmodelsofmemory(e.g.,Shiffrin&Steyvers,1997).
Incontrast,theHTSDTmodelassumesthattheslopeofthezROCisdirectlyrelated
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totheprobabilityofrecollection,ahypothesisthathasnotsurvivedinspection(e.g.,
Glanzeretal.,1999).
Thevariableencodinghypothesisisthatduringstudythestrengthofthe
itemisincrementedbyanamountsampledfromabaselinedistributionappropriate
fortheencodingtask,plusanamountsampledatrandomfromanoisedistribution
withameanofzero.KoenandYonelinas(2010)attemptedtodiscreditthis
hypothesisbyaskingonegroupsubjectstostudyitemsforeitherashorter(1sec)
orlonger(4sec)amountoftime,andanothergrouptostudythesameitemsfor2.5
secondseach.TheslopeofthezROCdidnotdifferacrossgroups.However,their
experimentassessedtheimpactofmixingtwodistributionsontheslopeofthe
zROC,ratherthantestingthevariableencodinghypothesis(Jang,Mickes,&Wixted,
2012;Starns,Rotello,&Ratcliff,2012).AmixtureoftwoGaussiandistributions
(oneforstrongitemsandanotherforweak)isn’tGaussianandthustheslopeofthe
resultingzROCdoesn’tprovideavalidestimateoftheratiooflureandtarget
standarddeviations,1/s.Thus,thereisstillnodefinitivetestofencoding
variability.AlthoughtheKoenandYonelinas(2010)experimentappearstoprovide
agoodtestoftheMSDTmodel,Starnsetal.(2012)showedthattheirmanipulation
ofencodingstrengthlackedpower.
OneinterestingtestoftheHTSDT,2HT,andUVSDTaccountsofzROCslopeis
this:Doestherelativevariabilityintheobservedconfidenceratingsfortargetsand
lurescorrespondtotheslopeofthezROC?Mickes,Wixted,&Wais(2007)asked
exactlythisquestion.Participantsinastandardold-newrecognitionexperiment
madetheirresponsesoneithera20-or99-pointconfidencescale.Theseconfidence
Rotello24
ratingswereusedtogenerateempiricalROCs,whichwerewell-describedbythe
UVSDTmodel.Theestimatedslopeparameter,whichequalstheratioofstandard
deviationsofthelureandtargetdistributions,wasabout0.8,asusual.Mickesetal.
alsocalculatedtheratioofthestandarddeviationsofeachsubject'sconfidence
ratingstotheluresandtothetargets,independentlyoftheROCanalysis.The
HTSDTdoesnotpredictanyrelationshipbetweenthesetworatios,becauseit
assumesthatthezROCslopeisdeterminedbytheprobabilityofrecollection(which
doesn'tdependontheconfidenceratings).Similarly,the2HTmodeldoesnot
predictarelationshipbetweenthetwomeasuresofvariabilitybecausethe
confidenceratingsarenotbasedonmemorystrength.EventheUVSDTmodeldoes
notconstrainthetworatiostoyieldthesamevalue:Ifthecriteriaaretightly-spaced
forhighermemorystrengthsandspreadoutforweakerstrengths,thentheratings-
basedratiomayunderestimatetheROC-basedvalue.Ontheotherhand,the
ratings-basedratiomayoverestimatetheROC-basedvalueifthecriteriaarewidely-
spacedforhighevidencevaluesandcompressedforlowerevidencevalues.Overall,
however,theaveragevalueofthetwoestimatesofthestandarddeviationratios
wasidenticalinoneexperimentandhighlysimilarintheother.Acrossparticipants,
thecorrelationsofthetwoestimateswere.61and.83inthetwoexperiments,
providingstrongsupportfortheUVSDTmodeloverthecompetitors.
3.1.1.4 Atestofthe2HTmodel:conditionalindependence
Liketheothermodels,the2HTmodelcanfittheconfidence-basedROCs(see
Figure6),atthepriceofadditionalparameterstomapfrominternalstatesto
Rotello25
responseratings(compareFigures4and5).Moreover,tofitthecurvaturethatis
ubiquitousintheseconfidenceROCs,the2HTmodelmustassumethatparticipants
giveatleastsomelower-confidenceresponsestostudieditemsthattheyhave
detectedasold(e.g.,Erdfelder&Buchner,1998;Malmberg,2002;Bröder&Schütz,
2009).Saiddifferently,tofittheconfidence-basedROCs,the2HTmodelmust
assumethatparticipantssometimesgivelow-confidenceresponsesevenintheface
ofinfallibleevidencethattheitemwasstudied.
The2HTmodelallowsforthepossibilitythatitemsthatareencodedwith
greaterstrengthmayhaveahigherprobabilityofbeingdetectedthanmoreweakly-
encodeditems(i.e.,thevalueofpomaydifferforstrongandweakitems;seeFig.5),
butresponsesfromthedetect-oldstatedependonlyonthearbitrarystate-response
mappingparameters(e.g.,Klauer&Kellen,2010;Bröder,Kellen,Schütz,&
Rohrmeier,2013).Thedistributionofconfidenceratingsmustbethesameforall
detectedtargets,regardlessoftheirencodingstrength,becausethereisonlyone
detect-oldstateandonlyonesetofresponseprobabilitiesthatleadfromthatstate
totheconfidenceratings(Fig.5).3Thisaspectofthe2HTmodelisknownasthe
conditionalindependenceassumption(Province&Rouder,2012)
ProvinceandRouder(2012)testedtheconditionalindependence
assumptionofthe2HTmodelbypresentingparticipantswithabout240unique
studyitemsavariablenumberoftimes(1,2,or4timeseach)onasinglelist.The
recognitiontestwasatwo-alternativeforcedchoicetask:atargetandalurewere
3Theoveralldistributionofconfidenceratingsforstrongandweaktargetsmayvarybecausetheyreflectdifferentmixturesofresponsesbasedondetectionandguessing.
Rotello26
testedtogether,andparticipantswereaskedtoselectthetargetfromeachpair.
Responsesweremadeonacontinuousscaletoindicateconfidenceinthedecision
("suretargetonleft"to"suretargetonright").ProvinceandRouderalsoincluded
sometestpairsthatcontainedtwolures,forcingparticipantstoguess;responsesto
thesetrialsprovideimportantdataabouthowconfidenceratingsweredistributed
fromtheuncertainstate.Acrossthreeexperiments,theyreportedthatthe
distributionofconfidenceratings(conditionalonadetection-basedresponse)was
independentofencodingstrength:theROCswerecurvedinallstrengthconditions
exceptforthelure-luretrials.
WhileProvinceandRouder’s(2012)datasupportthe2HTmodel,Chen,
Starns,andRotello(2015)alsotestedtheconditionalindependenceassumption,
reachingadifferentconclusion.TwoprimarychangesweremadetoProvinceand
Rouder'sapproach.First,thememorytestusedasimpleold-newrecognition
procedurewithconfidenceratings.Second,andmoreimportantly,multipleshort
studylistswereused(14listswith42uniqueitemseach)thatincludedasmall
numberof"superstrong"studyitems.Thesuperstrongstimuliwereshownfour
timeseachwithadifferentencodingtaskeachtime(e.g.,ratehoweasyitistoform
amentalimageofthisitem;rateitforsurvivalrelevance).Thesesuperstrongitems
wereexpectedtohaveahighprobabilityofbeingdetected,andtheydidformost
participants.Fortheseparticipants,thesuperstrongitemswerealmostinvariably
giventhehighest-confidence"old"response.Formoreweaklyencodedstimuli
(thosestudied1,2,or4timeswithoutaspecificencodingtask),theprobabilityofa
highest-confidenceoldratingwasmuchlower,evenfordetecteditems.Most
Rotello27
participants’datawerebetterfitbytheUVSDTmodel,becausetheconditional
independenceassumptionofthe2HTmodelwasviolated:thedistributionof
confidenceratingsvariedwiththeencodingstrengthofthetargets.
3.1.2 BinaryresponseROCs
TheROCsdescribedsofarweregeneratedfromconfidenceratings.Itisalso
possibletogenerateROCsfromresponsebiasmanipulations,suchaspresenting
differentproportionsoftargetsandluresacrosstests,orbyofferingdifferent
incentivesfor“old”or“new”responses;confidenceratingsarenotcollected.Inthis
second“binaryresponse”typeofROC,theoperatingpointsaregenerated
independentlyofoneanother,eitherindifferenttestsorevenfromdifferentgroups
ofparticipants.
BinaryresponseROCsareimportantdatathatcandiscriminatesignal
detectionmodelsfromthethresholdmodels(Banks,1970).AsFigures4and5
show,confidence-basedROCscangenerallybefitwiththresholdmodelsby
assumingthattherearestate-responseparameterstogeneratetheprobabilitiesof
theratingsresponses(Erdfelder&Buchner,1998;Malmberg,2002;Bröder&
Schütz,2009).Ineffect,thoseextraparametersgivethe2HTmodeltheflexibilityit
needstofitthecurvedconfidenceROCsthatareconsistentlyobserved.Thestoryis
differentwhentheROCsaregeneratedfrombinaryold-newdecisionsindifferent
biasconditions,becauseinthatcasethereareonlytworesponsebins(“old,”“new”)
andadditionalstate-responseparameterscan'tbeaddedtoredistributeresponses
Rotello28
fromonecategorytoanother.TheROCpredictedbythe2HTinthiscaseisalwaysa
linewithslopeequalto(1-po)/(1-pn),asshowninFigure4.Incontrast,theSDT
modelsmakethesamepredictionofcurvedROCSregardlessofwhethertheyare
confidence-basedorgeneratedfromindependentbiasconditions.
3.1.2.1 Fitsofthemodelstodata
Bröder&Schütz(2009)fitallbinaryresponseROCsintherecognition
memoryliterature,concludingthatthe2HTmodelfitaswellastheUVSDTmodel.
However,theiranalysesincludedalargenumberofROCsthatcontainedonlytwo
points.AsDubeandRotello(2012)noted,two-pointROCscannotdiscriminatethe
2HTfromUVSDTmodelsbecausetwopointscanbefitbyeitheralineoracurve.
Afterexcludingthosetwo-pointROCsandrunningtwonewexperiments,Dubeand
Rotello(2012)fitthe2HTandUVSDTmodelstoallavailabledataonbinary-
responseROCsreportedforindividualsubjectsinthedomainsofperceptionand
recognitionmemory.TheresultingbinaryROCswerecurved,notlinear,and
stronglysupportedtheUVSDTmodelforthevastmajorityofparticipants.4Dube,
Starns,Rotello,andRatcliff(2012)alsoreportedROCsbasedonbinaryresponses.
Theyincludedawithin-listmanipulationofencodingstrength(wordswerestudied
onceor5timeseach);becauseasinglesetoflureswasused,the2HTmodelis
constrainedtoasinglevalueofpn.DubeandcolleaguestestedtheUVSDTand2HT
4DubeandRotello(2012)basedtheirconclusionontheAICandBICfitstatistics.Kellenetal.(2013)usednormalizedmaximumlikelihood(NML)formodelselection,andonthatbasisconcludedinfavorofthe2HTmodel.Inthenextsection,wewillevaluatetheplausibilityoftheNMLconclusion.
Rotello29
models,againfindingthattheROCswerecurvedandinconsistentwiththe2HT
model.Thus,themodel-fittingevidenceisstronglyinfavoroftheUVSDTmodel
(Dube&Rotello,2012;Dubeetal.,2012).
OneadditionalstudyprovidesstrongevidenceinfavoroftheUVSDTmodel
andagainstboththe2HTandHTSDTmodels.Starns,Ratcliff,andMcKoon(2012)
collectedbothold-newrecognitiondecisionsandreactiontimesinanexperiment
thatmanipulatedresponsebiasbyvaryingtheproportionoftargetsonthetest.In
addition,participantswereaskedtorespondquicklyonsometests,andto
emphasizeaccuracyonothertests.FitsoftheHTSDTmodelrevealedthatthe
probabilityofrecollectionincreasedwithencodingstrength(whichwas
manipulatedwithin-studylist),butwasnotaffectedbythespeedandaccuracy
instructions.Theabsenceofareductioninrecollectionunderspeedinstructionsis
problematicfortheHTSDTmodelbecausemostofthoseresponsesweremadein
lesstimethanrecollectionappearstorequire(e.g.,McElree,Jacoby&Dolan,1999).
ThezROCswerealsolinearinallconditions,withslopeslessthan1,contradicting
thepredictionsoftheHTSDTand2HTmodels.
PerhapsthemostinterestingaspectoftheStarnsetal.(2012)study,
however,isthatthediffusionmodel(Ratcliff,1978)wasfittotheresponse
probabilitiesandreactiontimedistributionssimultaneously.Thediffusionmodelis
asequentialsamplingmodelthatassumesinformationaccumulatesovertime
accordingtoanaveragedriftratethatreflectsthequalityoftheevidencefortargets
andlures.Acrosstrials,adistributionofdriftratesisassumed;thevarianceofthis
distributioncanbeinterpretedasmeasuringthevariabilityinevidencevaluesfor
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targetsandlures.Theratioofluretotargetdriftratestandarddeviationswasless
thanonefor9ofthe12conditions,providingconvergingevidencefortheUVSDT
model.
3.1.2.2 Assessmentsofmodelflexibility
Asfortheconfidenceratingparadigm,theflexibilityofthemodelstofitthe
binaryresponseROCsshouldbeconsidered.Dube,Rotello,andHeit(2011)
reportedacomparisonofthe2HTandUVSDTmodelsasfittobinaryROCswith
threeoperatingpointsthatwereeithercloselyspacedormorespreadout.They
concludedthatthemodelsweredifficulttodiscriminate,especiallywhenthe
operatingpointswereclosetogether,butthatthe2HTandUVSDTmodelswere
approximatelyequallyflexible.Alarge-scaleevaluationoftheflexibilityofthe
HTSDT,UVSDT,2HT,andMSDTmodelswasreportedbyKellen,Klauer,andBröder
(2013).Theyusednormalizedmaximumlikelihood(NML;seeMyung,Navarro,&
Pitt,2006)formodelselection,andonthatbasisconcludedinfavorofthe2HT
model.OnechallengefortheconclusionsbasedonNMListhattheyshowastrong
preferencefortheequal-variance(orpo=pn)versionsofthemodelsthatpredict
symmetricROC.Aswe'veseen,symmetricrecognitionROCsarenotobserved
empirically.
3.1.3 Summaryoftheitemrecognitiondata
Overall,theevidencereviewedsofarsupportstheUVSDTmodeloverthe
others.Criticaltestsofthemostpopularthresholdmodel,the2HTmodel,reveal
Rotello31
deepproblems:empiricaldataviolateboththeconditionalindependence
assumptionforthestate-responsemappingparameters(Chenetal.,2015)andthe
predictionoflinearbinaryROCs(Dube&Rotello,2012;Dubeetal.,2012).The
HTSDTmodelfaressomewhatbetterwiththeseitemrecognitionROC,butit
predictsadecreaseinzROCslopeswithincreasingprobabilityofrecollectionthat
hasnotbeenobserved(e.g.,Glanzeretal.,1999).TheHTSDTmodelalsopredicts
thatcurvedzROCsshouldbeobservedwhenrecollectionisneededtodistinguish
targetsfromlures,aswhentheyaresimilartooneanother.However,thatzROC
curvatureistypicallynotobserved(e.g.,Glanzeretal.,1999;Heathcote,2003).
StrongertestsoftheHTSDTmodelcomeintheformofassessmentsofthe
contributionofrecollection,whichwillbeconsideredinthenextsection.
3.2 ExpandingtheData:TheContributionofRecollection
ThebasicpredictionsoftheHTSDTandUVSDTmodelshavebeentestedin
numerousitemrecognitionmemoryexperimentsthatdidnotspecifically
manipulaterecollection(seeWixted,2007;Yonelinas&Parks,2007,forreviews).
Instead,recollectionestimateswerebasedsolelyontheparametersoftheHTSDT
model'sbestfittothedata.OneproblemwiththisapproachisthatboththeUVSDT
andHTSDTmodelsfitthedatawell,qualitativelyandquantitatively(seeFigure6).
Twostrategieshavebeenusedtodistinguishthesemodels.Thefirstapproachisto
obtainmeasuresofrecollectionthatareindependentoftheHTSDT'sparameter
estimates(e.g.,Yonelinas,2001),toassesstheirconvergence.Theprimarysuch
Rotello32
measureofrecollectionhascomefromaskingparticipantstoprovideremember-
knowjudgmentstosupplementtheirold-newdecisions.Thesecondstrategyfor
expandingthedataistotakeadvantageofempiricaltasksthatappearedtorequire
recollectionforaccurateresponses.Threepopulartasksareassociativerecognition
decisions,whichrequiretheparticipanttodecidewhethertwostudieditems
appearedtogetheronthelist,plurality-discrimination,andsourcememory
judgmentsthatasktheparticipanttorecognizenotonlythatanitemwasstudied
butalsotoreportsomethingspecificaboutthatpresentation.We'llconsidereachof
theseapproachesinturn.Whereappropriate,we'llalsoconsiderthreshold
modelingapproachestothesetasks.
3.2.1Remember-knowjudgments
Tulving(1985)proposedthatweaskparticipantstoreportthebasisoftheir
"old"recognitiondecisions:dotheyremembersomethingspecificaboutthe
encodingexperience,ordoestheirmemorylackparticulardetailsyettheyknow
thatthememoryprobewasstudied?Rajaram(1993)developedextensive
instructionsontheremember-knowdistinction,whichhavesincebeenusedin
hundredsofexperiments.Foraboutthefirstfifteenyearsofremember-know
research,mostexperimentsfocusedonidentifyingvariablesthatdissociatedthe
rememberandknowjudgments,influencingonetypeofresponsewithoutaffecting
theotherormovingtheresponseprobabilitiesinoppositedirections.Thisgoalwas
readilyachieved,andallpossiblecombinationsofinfluenceonrememberandknow
Rotello33
responseshavebeenobtained(seeGardiner&Richardson-Klavehn,2000,fora
summary).Theconclusionintheliteraturewasthattheseexperimentsidentified
thevariablesthatselectivelyinfluenceeitherrecollectionorfamiliarity.
FromtheperspectiveoftheHTSDTmodel,theseremember-know
dissociationexperimentsprovideawealthofevidenceinfavoroftherecollection
process(Yonelinas,2002).Rememberhitstendtoincreasewithvariablesthat
increasememorystrength(e.g.,fullratherthandividedattention:Yonelinas,2001),
whereasknowresponsestendtoincreasemoreasafunctionofsuperficial
manipulationssuchasperceptualsimilarity(e.g.,fluencymanipulations:Rajaram&
Geraci,2000).OneparticularaspectofthedatathatisconvincingtoHTSDT
proponentsisthatfalsealarmsoccurprimarilywith“know”justificationsrather
than“remember”responses(Dunn,2004).Thisfindingisimportantbecauseahigh-
thresholdprocesscannotproduceanyfalsealarms:if“remember”responsesreflect
recollection,thentheymustonlyoccuraftercorrect“old”decisions(i.e.,hits).In
addition,rememberresponsesgivenafterhitsshouldbehighconfidencedecisions
becausetherecollectionprocess“trumps”thefamiliarityprocess;thisassumption
ofhighest-confidencerememberingisoftenbuiltintothemodeling(e.g.,Yonelinas
&Jacoby,1995;Yonelinas,2001).Ontheotherhand,directcomparisonsof
estimatesofrecollectionbasedonrememberresponsesandonROCparameters
havenotprovidedaconvincinglevelofagreement(e.g.,Rotello,Macmillan,Reeder,
&Wong,2005).
OtherproblemsfortheHTSDTmodelweresoonidentified.Thedissociation
evidenceseemstostronglysuggestthattherearedistinctunderlyingprocessesof
Rotello34
recollectionandfamiliarity,butdissociationsareweakandfrequentlyinconclusive
evidenceformultipleprocesses(Dunn&Kirsner,1988).Strongerevidenceforthe
presenceofmultipleprocessescomesfromstate-traceanalysis(Bamber,1979;
Dunn&Kirsner,1988).State-traceplotsshowhowperformanceononetaskrelates
toperformanceonanothertask,asfunctionofmanipulationsintendedtoselectively
influenceoneofthepresumedunderlyingprocesses.Monotonicstate-traceplots
areconsistentwithasingleunderlyingprocessthatmayhaveanon-linear
relationshipwiththelevelsoftheexperimentalfactors.Incontrast,non-monotonic
statetraceplotsimplythatmorethanoneunderlyingprocessdetermines
performance.Dunn(2008)appliedthelogicofstate-traceanalysistoremember-
knowdata,findingonlymonotonicfunctions;thisanalysisisconsistentwiththe
UVSDTmodelandinconsistentwiththeHTSDTview.Astrongertestreachedthe
sameconclusion:PrattandRouder(2012)showedthatevenwhenahierarchical
modelisapplied,eliminatingpotentialconfoundsthatmightoccurfromaveraging
dataoversubjectsortrials,thestate-traceanalysisoffersnosupportforthedual-
processview.
Theremember-knowdatadonotdemandadual-processinterpretation,and
infactcanbereadilyaccountedforbytheUVSDTmodel.Donaldson(1996)wasthe
firsttosuggestthisinterpretationofremember-knowdata:heproposedthatthe
datacouldbeaccountedforbyasignaldetectionmodelwithtwodecisioncriteria,a
conservativecriterionthatdividesold-rememberfromold-knowresponses,anda
moreliberalcriterionthatprovidesanold-newboundary.Indeed,Dunn(2004)
showedthatalloftheexistingpatternsofremember-knowdissociationswerewell-
Rotello35
describedbytheUVSDTmodel.Dunnalsotackledfourothercommonarguments
againsttheSDTmodelofremember-knowjudgments,showingthemalltobefaulty.
OneofthesedemonstrationsisparticularlychallengingfortheHTSDTmodel:old-
newdiscriminationaccuracymeasuredwiththerememberhitandfalsealarmrates
isequaltoaccuracymeasuredfromtheoverallhitandfalsealarmrates(seealso
Macmillan,Rotello,&Verde,2005).TheUVSDTmodelpredictsthisresultbecause
responsebiasandaccuracyareindependent,butitiscontrarytotheassumption
thatrecollectionisahigh-accuracy(orhigh-threshold)process.
Thecompetinginterpretationsofremember-knowjudgmentshavebeen
extendedtoaccountfortheinclusionofconfidenceratingsinseveraldifferent
experimentalparadigms(Rotello&Macmillan,2006;Rotelloetal.,2006).For
example,participantsmightbeaskedtofirstdecideiftheyrememberamemory
probe,andifnot,toratetheirconfidencethattheyknowtheystudieditorthatit'sa
lure(Yonelinas&Jacoby,1995).Alternatively,subjectsmightbeaskedtodecide
amongthreeresponsealternatives(remember,know,new)andthentoratetheir
confidenceinthatdecision(Rotello&Macmillan,2006),ortheymightfirstmakean
old-newdecisionandthenratetheirconfidencealongaremember-knowdimension
foritemsjudgedtobeold.Acrossarangeoftasksandcorrespondingmodel
versions,theone-dimensionalUVSDTmodelconsistentlyprovidesthebest
quantitativefittodata(e.g.,Rotello&Macmillan,2006;Rotelloetal.,2006).This
generalfindingaccordswellwiththeobservationthatrememberresponsesare
easilyinfluencedbymanipulationsintendedtoaffectonlyold-newresponsebias
(Rotelloetal.,2006;Dougal&Rotello,2007;Kapucuetal.,2008),andwiththe
Rotello36
observationthatROCsbasedonlyonrememberresponsesarestronglycurved
(Slotnick,Jeye,&Dodson,2016).Importantly,Cohenetal.(2008)showedthatthese
conclusionsdonotreflectdifferencesinmodelcomplexity:theUVSDTmodelof
remember-knowjudgmentsissomewhatlessflexiblethantheHTSDTmodel.
Finally,oneothertypeofevidencearguesinfavoroftheUVSDT
interpretationofremember-knowjudgments.Reactiontimesforremember
responseshavelongbeenknowntobeshorterthanthoseforknowdecisions
(Dewhurst&Conway,1994;Wixted&Stretch,2004;Dewhurst,Holmes,Brandt,&
Dean, 2006);onthesurface,thiseffectsuggeststhatrememberandknowresponses
reflectdistinctprocesses.However,higherconfidencedecisionsarealsomade
morequicklythanlowerconfidenceresponses(Petrusic&Baranski,2003),andthe
probabilityofarememberresponseiscorrelatedwithresponseconfidence(Rotello,
Macmillan,&Reeder,2004).Whenconfidenceiscontrolled,RotelloandZeng(2008)
foundthatthereactiontimedistributionsforrememberandknowresponsesdonot
differsignificantly.Inaddition,WixtedandMickes(2010)foundthatremember
falsealarmsaremademorequicklythaneitherknowhitsorknowfalsealarms,
consistentwiththeUVSDTmodel.
Insummary,alloftheobservedremember-knowdata,frombasic
dissociationeffects(Dunn,2004)toreactiontimes(Rotello&Zeng,2008;Wixted&
Mickes,2010)andconfidenceratings(e.g.,Dougal&Rotello,2007;Slotnicketal.,
2016)canbeaccountedforwiththeUVSDTmodel.ThesuccessoftheUVSDTmodel
occursinspiteofitsslightlylowerflexibilitythantheHTSDTmodel(Cohenetal.,
2008).Finally,state-traceanalysesofremember-knowdataconcludethatasingle
Rotello37
processissufficient(Dunn,2008;Pratt&Rouder,2012).Thereislittlereasonto
believethatrememberresponsesreflectthreshold-basedrecollection;theyare
easilyinfluencedbymanipulationsofold-newresponsebias(Rotelloetal.,2005).
3.2.2Associativerecognitionandpluralitydiscriminationtasks
Abetterwayofassessingtheroleofrecollectioninrecognitiondecisionsisto
designtasksinwhichanaccurateresponserequiresrecollection.Onecandidate
taskisassociativerecognition.Participantsstudypairsofitems(A-B,C-D),usually
words,andareaskedtorememberthemtogether.Attest,theymustselectthe
intactpairsthatappearexactlyasstudied(A-B)whilerejectingthosethatare
completelynew(X-Y).Theinterestingchallengepresentedtoparticipantsisthat
someoftheluresarerearrangedpairs(C-B)inwhichbothwordswerestudied,but
withdifferentpartners.Theassumptionisthatrejectionoftherearrangedpairs
requiresmorethananassessmentoffamiliarity.Becausebothofthewordswere
studied,correctdecisionsaboutrearrangedpairsrequiresrecollectionofthe
specificstudiedcombinations.Acloselyrelatedargumenthasbeenmadeabout
pluralitydiscrimination(e.g.,Hintzman&Curran,1994),ataskinwhichparticipants
studynounsintheirsingularorpluralform(trucks,frog),andthenmustrecognize
targetspresentedintheirstudiedform(trucks)amidplurality-changed(frogs)and
completelynewlures.
Earlyevidenceconsistentwiththedual-processviewofassociative
Rotello38
recognitioncomesfromresponsesignalexperimentsinwhichparticipantsare
askedtomaketheirrecognitionjudgmentsimmediatelyafteranunknown,variable,
amountoftime.Onsometrials,theresponsesignaloccursverysoonafterthe
memoryprobeispresented(i.e.,within50-100msofprobeonset),allowingonlya
smallamountofprocessingtimepriortodecision,whereasonothertrials
processingmaycompletebecausethesignaloccursafteralonglag(2000ormore
msafterprobeonset).Thesignallagvariesrandomly,sothatparticipantscannot
anticipatetheamountofdecisiontimethatwillavailableonanygiventesttrial.
Responsesignaldatafromassociativerecognitionparadigmsaresuggestiveof
multipleprocesseswithdifferenttimecourses:foraboutthefirst600or700msof
processingtime,"old"responsestobothintactandrearrangedpairsincrease,asif
familiarityforthosememoryprobesdevelopsovertime.Afterthatpoint,however,
additionalprocessingtimeyieldsadecreasein"old"responsestorearrangedpairs,
asiftheresultsofarecollectionprocess("recall-to-reject")begintocontributeto
thedecision(e.g.,Gronlund&Ratcliff,1989;Rotello&Heit,2000).
Pluralitydiscriminationresponse-signalexperimentshaverevealedthesame
typeofnon-monotonicresponsestoplurality-changedluresasafunction
processingtime(Hintzman&Curran,1994).However,RotelloandHeit(1999)
suggestedthatdynamicresponsebiaschangesmaybesufficienttoexplainthose
data.Arecollectionprocessisnotrequiredbythedatabecausethefalsealarmrate
tothecompletelynewluresdecreasesinthesamewayasthefalsealarmratetothe
plurality-changedlures,consistentwithanincreasinglyconservativeresponsebias
asprocessingtimeelapses.Ausefulrecollectionprocessmustdomorethanmimica
Rotello39
familiarityprocess;itshoulddominatethedecisionoutcome.
ROCshavealsobeenusedtoassesswhetherahigh-thresholdrecollection
processcontributestoassociativerecognitionorpluralitydiscrimination,with
somewhatmixedconclusions.Ifrecollectionisrequiredtodiscriminateintactfrom
rearrangedtestprobes,andifrecollectionisahigh-thresholdprocessastheHTSDT
modelassumes,thenalinearROCshouldresultif“old”responsestointactpairsare
plottedagainst“old”responsestorearrangedpairs.Becauserecollectionshouldbe
morelikelywhenitemsarestronglyencoded,aclearpredictionoftheHTSDTmodel
isthatassociativeROCsshouldbeincreasinglylinearwithgreatermemorystrength.
ThefirstreportedassociativerecognitionROCswerelinear(Yonelinas,1997;
Yonelinas,Kroll,Dobbins,&Soltani,1999,upside-downfaces;Rotello,Macmillan,&
VanTassel,2000)butvirtuallyallsubsequentlyreportedROCshavebeencurved
(Yonelinasetal.,1999,right-sideupfaces;Kelley&Wixted,2001;Verde&Rotello,
2004;Healy et al., 2005; Quamme,Yonelinas,&Norman,2007;Voskuilen&Ratcliff,
2016;foranexception,seeBastinetal.,2013).Inaddition,thedegreeofcurvature
oftheassociativerecognitionROCincreaseswithmemorystrength(Kelley&
Wixted,2001;Mickes,Johnson,&Wixted,2010;seealsoQuammeetal.,2007),in
contrasttothemostnaturalpredictionoftheHTSDTmodel.Macho(2004)showed
thattheHTSDTmodelcouldfittheseassociativeROCs,butonlybyadopting
implausibleparametervaluessuchasgreaterrecollectionforthemoreweakly
encodeditems.
Asimplerandbriefer,butotherwisesimilar,historyexistsforplurality-
discriminationROCs.TheHTSDTpredictionsabouttheformoftheplurality-change
Rotello40
ROCareanalogoustoitspredictionsforassociativerecognition:target-similar
ROCsbasedonresponsestotargetsandplurality-changedluresshouldbelinear,
especiallyasmemorystrengthincreases.Rotello(2000),Rotelloetal.(2000),and
ArndtandReder(2002)reportedthattarget-similarROCsintheplurality-
discriminationtaskwerelinear,butthosereportedbyHeathcote,Raymond,and
Dunn(2006)arecurved.TheROCsfromtheseexperimentsareactuallyquite
similarlooking,despitethedifferentconclusionsthatwerereached(seeKapucu,
Macmillan,&Rotello,2010,Figure1).Recently,Slotnicketal.(2016)reported
stronglycurvedplurality-discriminationROCs,evenwhentheywerebasedonlyon
trialsforwhicha"remember"responsewasgiven.
ThereisoverwhelmingevidenceforcurvedROCsinbothassociative
recognitionandplurality-discriminationtaskswhenthestudyitemsarewell-
learned,whichisclearlyachallengefortheHTSDTmodel.Ontheotherhand,for
moreweaklyencodingitems,detailedquantitativefitsofthedataalsoreveal
systematicdeviationsfromthepredictionsofboththeUVSDTandHTSDTmodels.
TheROCsforthesemorepoorlylearneditemsarebothmorelinearthantheUVSDT
modelpredictsandmorecurvedthanHTSDTexpects,leadingtocurvilinearzROCs
(e.g.,DeCarlo,2007).
Anumberofexplanationshavebeenofferedforthesesystematicdistortions
intheROCs.Oneaccountassumesachangeinthedecisioncriteria(Hautus,
Macmillan,&Rotello,2008;Starns,Pazzaglia,Rotello,Hautus,&Macmillan,2013),
aswillbedescribedindetailinthesectiononsourcerecognition.Theother
accountsallrelyonchangestotheeffectivetargetdistributionasaconsequenceof
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mixingtrialssampledfromafully-encodeddistribution(e.g.,itemandassociative
informationavailable)andtrialssampledfromadistributionthatassumesthestudy
itemswereonlypartiallyencoded(DeCarlo,2002,2003,2007).Accordingtothe
HTSDTmodel,ofcourse,wecouldcallthefully-encodeddistribution"recollection"
andtheitem-informationdistributions"familiarity"(Yonelinas,1994,1997,1999a;
seesection2.2.3).Otheraccountsassumethattheassociativeinformationis
continuously-valued(Kelley&Wixted,2001;DeCarlo,2002,2003;Greve,
Donaldson,&vanRossum,2010;Mickes,Johnson,&Wixted,2010).Mixing
responsesfrommultipledistributions(thosewithandwithoutassociative
information)changesthedistributionofevidenceassociatedwithatargetfromits
presumedGaussianformtosomethingthatisnon-Gaussian,thuschangingthe
predictedformoftheROC(seeFigure3).Allofthesemixturemodelscangenerate
ROCsthathaveacharacteristic"flattened"shapeforweakeritems.Forstronger
items,theprobabilitythatassociativeinformationisunavailableisgreatlyreduced,
sothemixturedistributionpredominantlyreflectsthefully-encodeddistribution.
Thus,strongitemsyieldROCsthatarewelldescribedbythestandardUVSDTmodel.
UnusualROCshapescanalsobeobservedifparticipantsmakerandom
responseonsomeproportionoftrials,effectivelyshiftingprobabilitymassfromone
partofthetargetdistributiontoanother(Ratcliff,McKoon,&Tindall,1994).The
impactofthisrandomguessingontheexactshapeoftheROCvariesasafunctionof
howthoseguessesaredistributedoverconfidenceratings(Malmberg&Xu,2006).
HarlowandDonaldson(2012)providedarecentempiricaldemonstrationofthis
consequenceofguessing.Inacleverassociativerecognitionexperiment,
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participantsviewedaseriesofstudywordsthatwerepairedwithaspecificlocation
indicatedonacircularsurround.(Wordsandlocationsdidnotappearonthescreen
atthesametime.)Inasubsequentmemorytest,participantswereshownastudied
wordandaskedtoclickthecorrespondinglocationontestcircle,thentoratetheir
confidenceintheirresponse.Thedistributionofmemoryerrorswasbestdescribed
asamixtureofpureguesses(randomlyspreadaroundthecircle,30-40%oftrials,
dependingontestlag)andcorrectresponses(withacertainspreadaboutthetrue
location,about10°,duetomemory-basedlossofprecision).Thecorresponding
ROCswereflatterthantheUVSDTmodelpredicts,consistentwiththepresenceof
thoserandomguesses.
Insummary,theevidencefromtheassociativerecognitionandplurality-
detectiontasksissomewhatmixed.TheROCsareincreasinglycurvedand
consistentwithUVSDTasmemorystrengthincreases(Mickesetal.,2010),and
ROCsbasedonlyonrememberresponsesarealsocurvedandinconsistentwiththe
HTSDTinterpretation(Slotnicketal.,2016).However,theflattenedROCsthatare
consistentlyobservedformoreweaklyencodeditemssuggestthattheresponses
mayreflectamixtureoftrialsforwhichtheassociativedetailisandisnotavailable
forreport(e.g.,DeCarlo,2002;Harlow&Donaldson,2012).Theideathatsome
responsesarepureguessesismoreconsistentwithathresholdviewthanasignal
detectionprocess(seeFigure4).Wewillrevisitthisissueafterreviewingthedata
fromanothertaskdesignedtorequirerecollection,namelysourcerecognitiontasks.
3.2.3 Sourcerecognition
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Anothercommontaskthatappearstorequirerecollectionisasource
memorytask.Inthisparadigm,participantsareaskedtojudgethecontext(or
source)inwhichamemoryprobewaspresented.Forexample,wasitshownin
greenorinred?Heardinawoman’svoiceoraman’s?ThesimplestSDTmodelof
sourcerecognitionsimplyreplacesthetargetdistributioninFigure1withatarget
source(say,malevoice)andtheluredistributionwiththealternativesource
(femalevoice).ThesimplestHTSDTmodelassumesthatcorrectsource
identificationrequiresrecollection;thusthesourceROC,whichplotscorrectsource
identificationsagainsterrors,isassumedtobelinear.Ifthetwosourcesareequally
strong,thentheHTSDTmodelfurtherassumesthattheROCwillbesymmetric
becausepo=pn;otherwiseitwillbeasymmetric(withpo>pnontheassumptionthat
thetargetsourceisthestrongerofthetwo:Yonelinas,1999a).ThesimpleSDT
modelpredictsacurvedROC,asusual.
3.2.3.1SourcerecognitionROCs
Asintheassociativerecognitionandplurality-discriminationliteratures,the
earliestreportedsourceROCssupportedtheHTSDTmodel.Yonelinas(1999a)
reportedthreeexperimentsinwhichlinearsourceROCswereobserved.Intwo
experiments,studyitemswerepresentedinthetwosourcesinarandomorderon
thesamestudylist,andtheresultingsourceROCsweresymmetricandlinear.In
theremainingexperiments,studyitemsappearedontwolists,whichservedasthe
Rotello44
sources.Whenthelistswerepresentedduringthesameexperimentalsession,the
sourceROCwaslinearandslightlyasymmetric,butwhenthestudylistswere
separatedbyfivedays,thesourceROCwascurvedandmorestronglyasymmetric.
Alsoechoingtheassociativerecognitionandplurality-discriminationliteratures,all
subsequentlypublishedsourceROCshavebeencurvedandinconsistentwiththe
HTSDTmodel(e.g.,Slotnicketal.,2000;Qinetal.,2001;Hilford,Glanzer,Kim&
DeCarlo,2002;Dodson,Bawa,&Slotnick,2007;Onyper,Zhang,&Howard,2010;
Slotnick,2010;Parks,Murray,Elfman,&Yonelinas,2011;Schütz&Bröder,2011;
Starnsetal.,2013;Starns&Ksander,2016).
Importantinsightonthediscrepancybetweenthelinearandcurvedsource
ROCscomesfromSlotnicketal.(2000).LikeYonelinas(1999a,Exps.2&3),they
askedtheirparticipantstomakebothold-newconfidenceratingsandsource
confidenceratings(“suresourceA”to“suresourceB”)foreverymemoryprobe.
WhereasYonelinasignoredtheold-newratingswhenplottinghissourceROCs,
Slotnicketal.tookadvantageofthem.Theyassessedtheformoftheoverallsource
ROC(exactlyasinYonelinas,1999)andthe"refined"sourceROCthatresultsfrom
includingonlyitemsforwhichparticipantshadmadethehighest-confidenceold
decisions.Slotnicketal.reasonedthatifahigh-thresholdprocesscontributesto
responses,thenthatprocessshouldbereflectedinboththeold-newdecisionsand
inthesubsequentsourcejudgmentsontheverysameitems.Accordingtothe
HTSDTmodel,aswellasthe2HTmodelofsourcememory(Bayen,Murnane,&
Erdfelder,1996),therefinedsourceROCshouldbelinear.However,asSlotnicket
al.(2000,seeMickes,Wais,&Wixted,2009,forarelatedargument)showed,the
Rotello45
refinedsourceROCisactuallystronglycurvedandreasonablyconsistentwiththe
EVSDTmodel.5Are-analysisoftheYonelinas(1999a)datashowsthatthesource
ROCbecomesmorelinear-notmorecurved-astrialsareincludedforwhichlower-
confidence-old(oreven"new")decisionsaremade(Slotnick&Dodson,2005).This
resultisperfectlysensible:asresponsestoweakermemoryitemsareaddedtothe
ROC,discriminationisreducedtowardschancelevels,andthechance-levelROCisa
line(seeFigure1).
InanoveldefenseoftheHTSDTmodel,ParksandYonelinas(2007)argued
thatthecurvedsourceROCsweretheresultofdecisionsthatwerebasedon
"unitized"familiarityratherthanrecollection.Ineffect,thisargumentassumesthat
item-sourcepairs(oritem-itempairsinanassociativerecognitiontask)aresowell-
encodedthattheybecomeasinglehighly-familiarunit.Ifthatweretrue,thenthose
refinedsourcejudgmentsshouldreflectknowresponsesinaremember-knowtask;
sourceROCsbasedonrememberdecisionsshouldbelinearbecauseremember
responsesareahallmarkofrecollection(Yonelinas,2002).ParksandYonelinas’s
(2007)claimwastestedbySlotnick(2010),whoreportedsourceROCsconditional
ona"remember"response.TheseconditionalROCSarestronglycurvedandwell
describedbytheUVSDTmodel.ThesameconclusionwasreachedbyMickesetal.
(2010)inasimilaranalysisofassociativerecognitionROCs.
5Slotnicketal.(2000)claimedthatthe2HTmodelcouldnotfittheirconfidence-basedsourceROCs.Asdescribedearlier,onlybinary-responseROCsmustbelinearaccordingtothresholdmodels,sotheSlotnicketal.dataarenotconvincing.Asitturnsout,neitherarethebinary-responsesourceROCs:SchützandBröder(2011)presentedbinary-responsesourceROCSfromfiveexperiments.AlthoughtheyclaimedtheROCswerelinear,comparativemodelfittingofthe2HTandSDTmodelswasinconclusive(Pazzagliaetal.,2013).
Rotello46
ConsiderationoftherefinedROCsledtoeffortstomodelthefullsetofold-
newandsourcememoryconfidenceratingssimultaneously.Thiseffortexpandson
Banks(2000),whowasthefirsttoshowthatold-newrecognitionandbinarysource
judgmentscouldbemodeledwithinasingletwo-dimensionaldecisionspace.Inthis
space,onedimensiondefinestheinformationthatdistinguishedtargetsfromlures,
andtheotherdimensiondefinestheinformationthatdistinguishesthetwosources.
Asonemightexpect,thereisnowacompletemodelofrecognitionandsource
memoryineachmodelflavor:abivariatesignaldetectionmodel(Banks,2000;
DeCarlo,2003;Glanzer,Hilford,&Kim,2004;Hautusetal.2008),adiscrete-state
modelthatassumesbothrecognitionandsourcejudgmentsare2HTprocesses
(Klauer&Kellen,2010),andahybridmodelthatassumesahigh-threshold
recollectionprocessandcontinuousfamiliarity(Onyper,Zhang,&Howard,2010).
RepresentationsoftheSDTandhybridmodelsareshownschematicallyinFigures7
and8.
<InsertFigures7and8nearhere>
Acarefulcomparisonofthesemodelsonthesamedatasets(e.g.,Yonelinas,
1999a;Slotnicketal.,2000)concludedthattheexistingdatawerenotpowerful
enoughtoallowselectionofthebestmodel(Klauer&Kellen,2010).Despitebeing
unabletoidentifya"winner,"someconclusionsabouttheplausibilityofthemodels
maybedrawn(seealsoPazzagliaetal.,2013).First,thethresholdmodelofKlauer
andKellen(2010)facesthesamechallengesasthesimplerthresholdmodels
discussedearlier,includingtheobservedcurvatureofbinaryrecognitionROCs
(Dube&Rotello,2012;Dubeetal.,2012)andtheviolationoftheconditional
Rotello47
independenceassumptionthatiscentraltothisclassofmodels(Chenetal.,2015).
Abroadercriticismofthethresholdapproachisitstremendousflexibility:different
parametersettingscanyieldROC-formsthathaveneverbeenobservedempirically.
Similarly,thehybridsourcemodelofOnyperetal.(2010)inheritsthechallengesof
theHTSDTmodel.
3.2.3.2Sourcedecisionstomissedtargets
ThereareafewadditionalargumentsthatdiscriminatetheSDTapproach
fromtheHTSDTmodelforsourcememory.Thefirstpointisquitesimple:because
bothold-newandsourcejudgmentsarebasedoncontinuousinformationaccording
totheSDTview(e.g.,Banks,2000;DeCarlo,2003;Hautusetal.,2008),participants
whosetaconservativecriterionandrespond"new"toastudieditemshould
nonethelessbeabletomakeasourcejudgmentforthatitemwithaccuracythatis
abovechance.OneeasywaytounderstandthispredictionistoconsiderSlotnick
andDodson's(2005)refinedsourceROCs.Aconservativeold-newcriterioncould
beplacedsimilarlytothehighest-confidenceoldcriterion.AsSlotnickandDodson
showed,sourceROCsconditiononsomewhatlowerconfidenceresponsesstill
discriminatedthetwosources.Incontrast,thresholdmodelsofsourcejudgment
predictthat"new"decisionsarebasedonguessing,andthusmemoryforthose
itemswillcontainnosourcedetails.
Starns,Hicks,Brown,&Martin(2008)testedthispredictioninthree
experiments.Toinduceaconservativeorliberalold-newbias,theymanipulated
participants’expectationsabouttheproportionoftargetsandluresonthe
Rotello48
recognitiontest.Participantswerethenaskedforbothold-newjudgmentsand,for
studiedwords,forsourcedecisions.Participantsintheconservativeconditions(but
notthoseintheliberalconditions)wereabletodiscriminatethesourceofstudied
wordstheyhadmissedonthetest,exactlyastheSDTmodelpredicts.Thisresult
waschallengedbyMalejkaandBröder(2016),whoarguedthataskingforsource
judgmentsonlyforstudieditemsprovidedsomefeedbacktoparticipantsaboutthe
accuracyoftheirold-newresponse,whichmayhavecausedthemtore-evaluate
memoryonthosetrials.Theyre-ranStarnsetal.'s(2008)experiments,askingfor
sourcejudgmentsforalltestitemsandfindingnodifferenceinsourceaccuracyasa
functionofbias.However,theirbiasmanipulationwaslesseffectivethanthatof
Starnsetal.(2008);inparticular,theirconservativeconditionwasnotnearlyas
conservative,whichmayaccountforthereducedsourceaccuracy.
3.2.3.3zROCslopesandcurvatureareaffectedbydecisionprocesses
AthirdargumentinfavoroftheSDTmodelsovertheHTSDTmodelstems
fromapredictionabouthowtheslopeofthesourcezROCisinfluencedbythe
relativestrengthsofthetwosources(S1andS2).Ifitemsappearingineachsource
arestudiedthesamenumberoftimes,thenthesourceinformationshouldbe
equallyeasy(orhard)torecollect.Inotherwords,RS1=RS2andtheslopeofthe
zROCis1.Ontheotherhand,supposethattheitemsstudiedinonesource(say,S2)
arestrengthenedrelativetothoseintheothersource(S1),perhapsbypresenting
theitemsinS2twiceeachandtheitemsinS1onlyonceeach.Inthatcase,the
Rotello49
HTSDTmodelpredictsthatrecollectionshouldbeincreasedforthestrongersource,
soRS2>RS1.TheslopeofthezROCwillthendependonwhichsourceisselectedto
bethe“target”sourcethatdefinesthey-axis.IfS2isthetargetsource,thenthe
slopeofthezROCwillbelessthan1,andifS1isthetargetsource,theslopeofthe
zROCwillbegreaterthan1.Starnsetal.(2013)calledthisexperimentaldesign
“unbalanced”becausethesourcestrengthsarenotequal;theyconfirmedthatthe
sourceslopedependsonwhichsourceisthetarget.
AninterestingtestoftheHTSDTmodelcomesfromexperimentswith
balancedbutvariablesourcestrengths.Inthisdesign,bothS1andS2itemsare
studiedanequalnumberoftimes,butforhalfoftheitemsineachsourcethe
encodingisweak(onestudyexposure)andfortheremainingitemstheencodingis
stronger(twostudyexposures).Becausethesourcestrengthsareequaloverall,the
HTSDTmodelpredictsthesourcezROCslopewillbe1.ThepredictionsoftheSDT
modelsaredifferent.AccordingtoSDT,theoptimaldecisionboundsforthesource
decisionarelikelihood-based(theseareshowninFigure7foraspecificdataset).
Thesecurveddecisionboundsnaturallycapturetheintuitionthatparticipants
shouldbeunwillingtomakehigh-confidencesourcedecisionsforweakly-encoded
itemsthattheyhavelow-confidencethey’veevenstudied.Forstrongeritems,
confidenceintheolddecisionishigher,andtheprobabilityofahigher-confidence
sourcedecisionincreases;becauseitemandsourcestrengthsarecorrelated,these
higher-confidencesourceresponsesarealsolikelytobeaccurate.Starnsetal.
(2013)showedthattheSDTmodelpredictsthesourcezROCslopesinthebalanced
designwilldifferasafunctionofwhetherthestrongerorweakeritemsourceserves
Rotello50
asthetargetsource,exactlyliketheHTSDTmodel’spredictionsfortheunbalanced
design.Inthreeexperiments,thebalanceddesignproduced“crossed”sourcezROC
slopesaspredictedbytheSDTmodelbutnotbytheHTSDTmodel.
StarnsandKsander(2016)showedthatthesourcezROCslopeeffect
dependsonitemstrength,notsourcestrength.Thus,theslopeeffectmustbedueto
thedecisionprocessratherthantheunderlyingevidencedistributions.Starnsand
Ksander(2016)hadparticipantsstudywordspairedwithamaleorfemaleface,or
withapictureofabirdorafish.Intheno-repetitioncondition,eachitem-face
combinationwasstudiedonce.Inthesame-sourcerepetitioncondition,item-face
pairswerestudiedthreetimeseach.Andinthedifferent-sourcerepetition
condition,eachwordwasstudiedtwicewitheitherabirdorafishimage,andthen
oncewithamaleorfemaleface.Althoughmale-femalesourceaccuracywaslower
inthedifferent-sourcerepetitionconditionthanintheno-repetitioncondition,high-
confidencemale-femalesourcejudgmentsweremorefrequent.Inaddition,the
zROCslopescrossedexactlyasinStarnsetal.(2013).Bothoftheseeffectsare
consistentwiththepredictionsofthebivariateSDTmodelwithlikelihood-type
decisionbounds(e.g.,Hautusetal.,2008).6
Intheassociativerecognitionliterature,theappearanceofrelatively
flattenedROCsandcurvedzROCshasbeeninterpretedintermsofmixturesoftrials
drawnfromdistributionsthatdoanddon’tcontainassociativeinformation.The
6Whenfittodata,thethreshold(Klauer&Kellen,2010)andhybrid(Onyperetal.,2010)bivariatemodelsofitemandsourcememoryalsoyieldparametersconsistentwiththeideathatparticipantsarereluctanttogivehigh-confidencesourcejudgmentstoitemstheydonotrememberwell(seeFigure8).Forthesemodels,however,theparametersarearbitrary;unlikethebivariateSDTmodel(e.g.,Hautusetal.,2008),nothingaboutthestructureofthethresholdandhybridmodelsdictatesthelikelihood-typedecisionbounds.
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bivariateSDTmodelsofsourcememorysuggestanalternativeexplanationthat
restsinthenatureofthedecisionboundsratherthantheevidencedistributions.
Specifically,theconvergenceofthedecisionboundsinthebivariateSDTmodel(Fig.
7)thatpredictstheobservedsourcezROCslopes(Starnsetal.,2013;Starns&
Ksander,2016)alsoaccountsfortherelativelyflattenedsourceROCshapeandthe
presenceofcurvatureinthezROC(Hautusetal.,2008).AsStarns,Rotello,and
Hautus(2014)explained,thatcurvatureoccursbecausestronglyencodeditems
tendtoreceivebothhigh-confidenceoldandhigh-confidence(andcorrect)source
decisions,whereasmoreweaklyencodeditemstendtobeassignedlower-
confidenceresponsesonbothscales.Thismeansthattheendpointsofthesource
ROCtendtobebasedonresponsestomorewell-learneditems(withhighersource
accuracy),andthemid-pointsoftheROCtendtobebasedonresponsestomore
poorly-learnedstimuli(withsourceaccuracyclosertochance);aflattenedROCand
curvedzROCaretheresult.
3.2.3.4Sourcememoryprovidessomeevidencefor(continuous)recollection
ThedatadiscussedsofarhaveconsistentlysupportedtheUVSDTmodelover
itscompetitors.ParticularlyproblematicfortheHTSDTmodelhasbeenits
assumptionofathresholdrecollectionprocess.AsWixtedandMickes(2010)
pointedout,however,thereisnoreasontoassumethatarecollectionprocesshas
thresholdcharacteristics.Theysuggestedthealternativeviewthatrecollection
operatesasacontinuous,signaldetectionprocess,theresultofwhichisusually
Rotello52
summedwiththeresultofthefamiliarityprocess.Together,thesetwoprocesses
areusuallycompletelyconsistentwiththeUVSDTmodel;WixtedandMickes
termedthismodelthecontinuousdualprocess(CDP)model(seesection2.2.2).
TherearesomelimitedcircumstancesinwhichtheUVSDTandCDPmodels
maybedistinguished.WixtedandMickes(2010)partitionedthehighest-confidence
“old”decisionsthatwereassociatedwithrememberandknowresponses,andthen
separatelycalculatedrecognitionandsourcememoryaccuracyforthosetwotypes
ofsubjectivereport.Sourceaccuracywashigherafterrememberthanknow
responses,eventhoughoverallrecognitionaccuracywasequated.Thesedata
providesomeevidencethatrememberdecisionsmayreflectrecollectionafterall,
albeitinacontinuousform.Thatbasiceffectwasreplicatedandstrengthenedby
Ingram,Mickes,andWixted(2012),whoreportedthatsourceaccuracywashigher
afterlower-confidencerememberjudgmentsthanafterhighconfidenceknow
decisions.Evenmoreconvincingarethestate-traceanalysesforallofthese
experiments,whichwerenon-monotonicandconsistentwiththecontributionof
morethanprocesstotheserecognitionandsourcedecisions(Dunn&Kirsner,
1988).
3.2.3.5Summaryofthesourcerecognitiondata
Overall,thesourcerecognitiondataaremoreconsistentwiththeUVSDT
approachthanwitheithertheHTSDTor2HTmodels.Theslopesofthesource
zROCsaresystematicallyaffectedbyitemstrengthandthedecisionboundsinthe
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bivariateUVSDTmodel(Starnsetal.,2012;Hautusetal.,2008).TheflattenedROC
shapes(andslightlycurvedzROCs)arealsoexplainedbythedecisionboundsinthe
bivariatemodel,orbyamixtureprocessasassumedbytheMSDTmodel(DeCarlo,
2003).
3.3 ExpandingtheData:BeyondROCs
ThedatadiscussedsofarhavelargelycomefromROCexperiments,andhave
providedevidenceinfavoroftheUVSDTmodelovertheothers.Apowerful
advantageofsignaldetectionmodelsisthattheynotonlyseparateresponsebias
fromdecisionaccuracywithinataskandshowhowdifferenttypesoferrorstrade
offagainstoneanother,theyalsomakespecificpredictionsabouthowaccuracy
shouldcompareacrosstasks.Comparingmodelparametersacrossdifferent
empiricalparadigmsprovidesconvergingevidenceonthequalityofamodel,inthe
formofatestofitsgeneralizationability.Inthissection,datafromseveraldifferent
paradigmswillbeconsidered,includingthecommonly-usedtwo-alternativeforced
choice(2AFC)task.We’llalsoconsidertwolessfamiliarparadigms:theodditytask,
inwhichparticipantsseethreetestitems(2luresandatargetor2targetsanda
lure)andmustchoosethe“oddoneout,”andtheso-calledsecondchoiceparadigm
inwhichparticipantsaregivenfourmemoryprobes(3ofwhicharelures)andthey
gettwochancestoidentifythetarget.Finally,datafromsomerecentexperimental
testsofthemodelsunder“minimalassumptions”willbediscussed.
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3.3.1Two-alternativeforcedchoicerecognition
3.3.1.1Accuracycomparisonwithold-newrecognition
Ina2AFCrecognitiontask,participantsarepresentedwithastudylistand
thenfaceatestonwhichthememoryprobesarepresentedinpairs.Typically,only
oneofthetestitemswasstudied,andtheparticipants’taskistoselectthatitem,the
target.Thistaskcanbeaccomplishedbycomparingthememorystrengthsofthe
twostimuli,selectingtheonewithgreaterstrengthasthe“old”memberofthepair.
Theone-dimensionalmodelinFigure1servesasourtheoreticalstartingpoint.The
targetcomesfromaNormaldistributionthathasameanofd'YesNoandastandard
deviationof1;thelurecomesfromaNormaldistributionwithameanof0and
standarddeviationof1.Thedifferencebetweenthetwostrengths,target-lureor
lure-target,isalsonormallydistributedwithameanofd'YesNo(or-d'YesNo)anda
standarddeviationof√2.Theparticipants’taskistodiscriminatethetarget-lure
pairsfromthelure-targetpairs;Figure9showsthattheiroverallaccuracyis
predictedtobe
!d2AFC =2 !dYesNo2
= 2 !dYesNo (13)
Inotherwords,SDTtellsusthatperformanceinthe2AFCtaskshouldbeeasierthan
inanold-newrecognitiontask,byafactorof√2:ad'scoreof1.5ina2AFCtaskis
equivalenttoad'YesNoof1.06=1.5/√2.
<InsertFigure9nearhere>
Rotello55
Thetheoreticalrelationshipbetweenold-newrecognitionand2AFC
performanceisclearlyestablishedbySDT.Earlytestsofthisprediction,using
auditoryandvisualdetectiontasks,weresuccessful(seeGreen&Swets,1966,fora
summary).Inthedomainofrecognitionmemory,theassessmentoftheSDT
predictionhasruninparallelwithanassessmentofcompetingmodelssuchasthe
HTSDTandMSDTmodels.
Kroll,Yonelinas,Dobbins,andFrederick(2002)usedold-newrecognition
responsestoestimatetheparametersoftheHTSDTandEVSDTmodels.Those
parameterswerethenusedtopredictthepercentageofcorrectresponsesona
2AFCtaskwiththesamematerials.Krolletal.(2002)concludedthattheHTSDT
modelmoreaccuratelypredicted2AFCperformancethantheEVSDTmodel.
However,asSmithandDuncan(2004)noted,therearetwomajorproblemswith
thatanalysis.First,theUVSDTmodelismoreappropriatethanitsequal-variance
cousinforrecognitionmemorytasks(seesection3.1),andsecond,astrongertestof
themodelsfocusesonwhetheritsparametersareconsistentacrosstasks.Many
differentcombinationsofparametervaluesintheold-newrecognitionmodelcan
resultinthesamevalueofpercentcorrectonthe2AFCtest,makingpercentcorrect
aweaktargetformodelassessment.
Jang,Wixted,andHuber(2009)hadparticipantscompletebothaconfidence-
ratingitemrecognitiontaskanda2AFCrecognitiontaskwithconfidenceratings;
thetwotypesoftrialswererandomlyintermixedonthetest.Theresultingold-new
recognitionROCwascurvedwithazROCslopeof0.7,whereasthe2AFCROCwas
curvedandsymmetric.Threedifferentmodels(UVSDT,HTSDT,andMSDT)werefit
Rotello56
tobothROCssimultaneously,sothatthesameparameterswererequiredtofitboth
tasks.Forexample,theUVSDTwasconstrainedtohaveasinglediscrimination
parameterthatwasrelatedacrosstasksasdescribedbyEquation13.Forthe
HTSDTmodel,therecollectionparameterwassettobeconstantacrosstasks;
becausethefamiliarityprocessoperatesasasignaldetectionmodel,thed’
parameterineachtaskwasdefinedbyEquation13.Finally,thesignaldetection
componentoftheMSDTmodelwasalsoassumedtocomplywithEquation13,and
theattentionparameterwasfixedtobeequalinbothold-newand2AFC
recognition.InbothanewexperimentandareanalysisofSmithandDuncan’s
(2004)data,theUVSDTmodelclearlyprovidedthebestfitofindividual
participants’data.
3.3.1.2 Therelationshipofaccuracyandconfidencein2AFCtasks
Forcedchoicetaskshaveplayedanotherinterestingroleintherecognition
literature.Ratherthanfocusingonthepredictedaccuracyrelationshipacrosstasks,
these2AFCstudieshaveinvestigatedtherelationshipbetweenparticipants’
decisionaccuracyandtheirconfidence.Allofthesignaldetectionmodelswe’ve
consideredmaketheassumptionthatold-newmemorydecisionsandconfidence
ratingsarebasedonthesameunderlyingevidenceaxis;confidencecriteriaandthe
old-newcriterionaresimplydifferentlocationsonthataxis.Forthisreason,the
SDTmodelspredictthatempiricalfactorsthatinfluenceaccuracyshouldalso
Rotello57
influenceconfidenceinthesamemanner,withhigherlevelsofconfidence
correspondingtohigherlevelsofaccuracy.
Tulving(1981)wasthefirsttoreportthataccuracyandconfidenceina2AFC
recognitionmemorytaskhadan“inverted”relationship:confidencewashigherin
theconditionwithloweraccuracy.InTulving’sexperiment,participantsstudieda
seriesofphotographsandthenweretestedina2AFCtaskinwhichthelureitem
waseitherhighly-similartothetargetinthatpair(A/A'pairs,whereAwasstudied)
orwashighly-similartoadifferentstudieditem(A/B'pairs,wherebothAandB
werestudied).ParticipantsweremoreconfidentintheirresponsestotheA/B'
pairs,butweremoreaccuratefortheA/A'pairs.Thisbasiceffecthasbeen
replicatedseveraltimes(Chandler,1989,1994;Dobbins,Kroll,&Liu,1998;
Heathcote,Freeman,Etherington,Tonkin,&Bora,2009;Heathcote,Bora,&
Freeman,2010),andappearstoofferatruepuzzleforSDTmodels.
Asitturnsout,though,SDTcaneasilyandsimultaneouslyaccountforboth
theconfidenceandaccuracyeffects.Signaldetection’sdescriptionofthe2AFCtask
isthatparticipantsselectthetargetbycalculatingthedifferenceinstrengthsofthe
twoitemsattest(seesection3.3.1.1).AsClark(1997)pointout,however,theA/A'
pairsarenotindependentrandomvariables:theysharevariancebyvirtueoftheir
similaritytooneanother,andthereforethevarianceoftheA-A'strengthdifference
iss2A+s2A' -2cov(A,A').Incontrast,theA-B'differencehasalargervariance:s2A+
s2B'.TherearetwoconsequencesofthisreducedvariancefortheA/A'testpairs.
First,selectionofthestudiedphotofromtheA/A'pairsiseasierthanforA/B'pairs.
That’sbecausethemeanstrengthdifferenceisthesameforbothtests(A'andB'are
Rotello58
bothequallysimilartotheircorrespondingstudieditem),butthevariabilityis
lower,whichincreasesdiscrimination.Thataccountsfortheaccuracyeffect,as
showninFigure10.Second,assumingconfidenceisroughlydeterminedby
distancefromthedecisioncriterion,whichcouldplausiblybesetatthezeropoint
wherethere’snostrengthdifferencebetweenthetestitems,thentheaverage
confidencelevelfortheA/A'pairswillbehigherthanfortheA/B'pairs.So,the
samecovariancedifferenceaccountsforboththeincreasedaccuracyandthe
decreasedconfidence.Indeed,Heathcoteetal.(2010)successfullymodeledthe
resultsoftheirexperimentsandDobbinsetal.’s(1998),allofwhichinvolved
remember-knowjudgments,usingClark’smodelplusaremember-knowcriterion
withalocationthatvariedrandomlyfromtrialtotrial.ThatSDTmodelfitthedata
betterthananHTSDTvariantproposedbyDobbinsetal.(1998).
<InsertFigure10nearhere>
3.3.2 OddityTask
O'Connor,Guhl,Cox,andDobbins(2011)testedparticipantsonanunusual
task,usingtheoddityparadigm.Inanodditytask,participantsareshownthree
memoryprobessimultaneously.Thereareeithertwotargetsandalure,ortwo
luresandatarget;theparticipant'staskistoselectthe"odd"itemthatisofa
differentstimulusclassthantheothers.Thistaskisnotincommonuseoutsideof
thefoodscienceliterature,buthasbeenarguedtobeappropriateforrequesting
Rotello59
discriminationsthataredifficulttodescribe.Forexample,MacmillanandCreelman
(2005)suggestedthatanodditytaskmightbeappropriatefortestingtheabilityof
novicestodiscriminatetwodifferenttypesofredwine.
O'Connoretal.generatedpredictionsoftheHTSDTmodelfortheodditytask,
concludingthatthemodelexpectshigheraccuracywhenalureistheodditem.
Essentially,thispredictionarisesbecauseonlytargetscanberecollected:on
average,theHTSDThasmoreinformationabouttargetsthanaboutlures.According
totheUVSDTmodel,ontheotherhand,decisionsmaybemadebasedona
differencingstrategylikethatusedfor2AFCparadigm,exceptthattwodifferences
arerequired(item1–item2;item2–item3).Eachpossiblecombinationoftrial
types(i.e.,lure-target-target,target-lure-target,etc)producesauniquecombination
ofexpecteddifferencescores,allowingidentificationoftheodditem(seeMacmillan
&Creelman,2005,fordetails).Alternatively,participantsmaysimplyorderthe
memorystrengthsofthethreeitemsandthencomparethemiddlestrengthtoan
unbiasedold-newdecisionbound.Ifthemiddleitemfallsabove(below)that
criterion,thentheweakest(strongest)itemshouldbeselectedastheodditem.
Becausethetargetdistributionisknowntobemorevariablethanthelure
distributioninrecognitionmemorytasks,bothSDTdecisionrulesleadtothe
predictionthataccuracywillbehigherwhenthetargetistheodditem:inthatcase
thetwolureswilllikelybeclosertogetherinstrengththantwotargetswouldbe.
Inaseriesofexperimentsandsimulations,O'Connoretal.foundthatthe
lureswereeasiertoidentifyasodd,consistentwithamodelthatassumes
recollectioncontributestothedecision.Giventheevidenceagainstthreshold
Rotello60
recollection,however,WixtedandMickes'(2010)continuousdual-processmodelis
likelytobemoresuccessfuloverallthantheHTSDTmodel.AndasO'Connoretal.
(2011)realized,thereisalsoaversionoftheUVSDTmodelthatcanaccountforthe
higheraccuracyonlure-oddtrials:iftheold-newdecisioncriterionissetliberally,
thenmosttargetswillfallabovethatcriterion,allowingtheluretobereadily
identified.
3.3.3 Secondchoicetasks
ParksandYonelinas(2009)broughtadifferenttaskfromtheperception
literature(Swets,Tanner,&Birdsall,1961)totherecognitionmemoryliterature,
andappliedittobothitemandassociativerecognition.Theygaveparticipantsfour
memoryprobestochoosefrom(onetargetand3lures),andtwotriestoselectthe
target.ThresholdandSDTmodelsmakedifferentpredictionsabouthowthesecond
choiceresponsesshouldberelatedtothefirstchoice.Forthethresholdmodelin
whichonlytargetscanbedetected,thefirstselectionshouldbethetarget,ifitis
detected(Kellen&Klauer,2011).Lurescanneverbedetectedasoldinthismodel,
sothatresponsestrategywouldalwaysleadtoacorrectdecisionontheinitial
response.Becauseonlyoneoftheresponseoptionsisatarget,failuretoselectit
firstmeansthatboththefirstandsecondchoicesmustbeaconsequenceofa
randomguessingprocessfromastateofuncertainty.Thus,firstandsecondchoices
willbeunrelatedtooneanother.
Rotello61
IntheSDTmodel,thesecondchoicewillbesystematicallyrelatedtothefirst.
Theparticipantisassumedtoselecttheoptionthathasthegreateststrength,which
willusuallybeatarget(DeCarlo,2013).If,duetodistributionaloverlap,the
strongestitemhappenstobealure,thenthesecondchoiceislikelytobethetarget,
becausetheprobabilitythattwolureswillfallintheuppertailofthedistributionis
low.
Initemrecognition,ParksandYonelinas(2009,seealsoKellen&Klauer,
2014)foundthatthesecondchoiceresponseswererelatedtofirstchoice,
consistentwiththeUVSDTmodelandinconsistentwiththeHTSDTmodel.In
contrast,associativerecognitionsecond-choiceswereunrelatedtofirstchoice
responses,aresultthatseemstosuggestathresholdinterpretationconsistentwith
recollectioncontributingtoassociativeresponses.Theproblemwiththat
conclusion,ofcourse,isthattheHTSDTaccountoftheassociativerecognitionROCs
(seesection3.2.2)assumesthat"unitization"leadsparticipantstorespondtobased
onfamiliarity,aUVSDTprocess(seeEquation9).
Anotherchallengefortheinterpretationofthesesecondchoiceresponsesis
thatthattheanalysesfailtoaccountformodelcomplexity.Consistentwithearlier
analysesforconfidence-basedrecognitionROCs(Jangetal.,2011),butnot
remember-knowdata(Cohenetal.,2008),KellenandKlauer(2011)arguedthatthe
UVSDTmodelismoreflexiblethantheothermodelswhenappliedtodatafromthis
second-choicetask.Forthisreason,theyconcludethateithertheHTSDTorMSDT
modelprovidesthebestdescriptionofthedata.However,theirconclusionsare
basedonnormalizedmaximumlikelihood.Thiscriterionmayhavetoostrongofa
Rotello62
preferenceforsimplemodels,becausewhenappliedtoold-newrecognitiondatait
concludesinfavorofmodelsthatgeneratesymmetricROCs(Kellenetal.,2013).
3.3.4Minimalassumptiontests
Manyofthepredictionsforparticularmodeloutcomesdependon
assumptionsaboutthemodelthatmaynotbeessentialpropertiesofthatmodel.
Forexample,theassumptionthattheSDTmodelsinvolveGaussianevidence
distributionsisaconvenienceratherthananecessityofthemodel.So-called
minimalassumptiontestsofthesemodelattempttosidesteptheseancillary
assumptions,thusmakingpredictionsthatreflectthecorepropertiesofthemodel,
ratherthanthedetailsofhowithappenstobeimplemented.
OneminimalassumptiontestisthattheSDTmodelspredictthatfewer
extremeerrors(high-confidencemissesorfalsealarms)shouldbemadeasmemory
strengthincreases.Thispredictionfollowsdirectlyfromthedecreasingoverlapof
thetargetandluredistributions(seeFigure1).Incontrast,the2HTmodelassumes
thatextremeerrorsresultfromguessing;theconditionalindependenceassumption
requiresthatresponsesbasedonguessingareindependentofmemorystrength
(seesection3.1.2).KellenandKlauer(2015)testedthesecompetingpredictionsby
focusingonhigh-confidencemisses("surenew"decisionsfortargets).Theirdata
wereconsistentwiththe2HTmodel'spredictions,leadingthemtoconcludethat
thereisnodirectmappingofmemoryevidencetoresponseconfidence.Ofcourse,
Rotello63
thisconclusioncontradictstheresultsofagreatmanyotherexperimentson
recognitionmemory.
4 Challenges
We'veseenthattheevidencefromavarietyofmemorytaskssupportedthe
UVSDTmodeloveritscompetitors.Despitethenearunanimityofthatsuccess,
therearesomechallengesthatmustbefaced.Severalofthesechallengesstemfrom
afailureofvirtuallyallrecognitionmemorystudiestoconsiderallvariablesinthe
experiment,includingboththosethatarepartofthedesign(e.g.,itemandsubject
effects)andallpossibledependentmeasures(i.e.,reactiontimes).
4.1 AggregationEffects
Oneissuefacedbyallofthemodelsistheproblemofdataaggregation(Pratt,
Rouder,&Morey,2010;DeCarlo,2011;Pratt&Rouder,2011).Ourmodeling
effortsusuallyinvolvecollapsingresponsesovertrials,subjects,orboth.Weknow
thatthereareindividualdifferencesinparticipants'responsestrategiesinthese
tasks(e.g.,Kapucuetal.,2010;Jangetal.,2011;Kantner&Lindsay,2012),yetwe
typicallyignorethosedifferencesandconsideronlygroup-levelbehavior.The
consequencesforthemodelfitsarenotnecessarilybad(Cohen,Sanborn,&Shiffrin,
2008;Cohenetal.,2008),butcertainlyshouldbeevaluated.Likewise,wealmost
Rotello64
invariablyignoreitemeffectsthatalsooccur(e.g.,Freeman,Heathcote,Chalmers,&
Hockley,2010;Isola,Xiao,Parikh,Torralba,&Oliva,2014).Prattetal.(2010;see
alsoDeCarlo,2011)demonstratedthataggregationofdataoveritemsandsubjects
cansystematicallydistortourconclusions:Initemrecognitiontasks,overestimation
ofaccuracyeffectsandunderestimationofzROCslopescanresult.Aggregation
disguisesvariability,meaningthatwealsohavetoomuchconfidenceinthestability
ofourparameterestimates.Hierarchicalmodelingapproacheshavebeen
developedtoaddressthesechallenges(e.g.,Klauer,2006,2010;Prattetal.,2010;
Pratt&Rouder,2011),buthaveyettobewidelyadopted.
4.2 ReactionTimes
Wesawearlierthatreactiontimeshavesuccessfullydiscriminateddifferent
interpretationsofremember-knowresponses,concludinginfavoroftheUVSDT
model(Wixted&Stretch,2004;Rotello&Zeng,2008;Wixted&Mickes,2010).In
addition,diffusionmodelfitstobinary-responserecognitionmemorydataprovide
convergingevidencefortheUVSDTmodel(Starnsetal.,2012).Despitethese
positives,newermodelsdevelopedtosimultaneouslyfitbothconfidenceratings
andreactiontimedistributionspresentaninterpretivechallengetothosestudies
(Ratcliff&Starns,2009;Voskuilen&Ratcliff,2016;seealsoVanZandt,2000;
Pleskac&Busemeyer,2010).Ratcliff'sRTCONmodelincludestwosetsofcriteria
thattogetherpredicttheROCandRTdistributionsforthetask.Theconfidence
Rotello65
criteriaarelikethoseinFigure1;theypartiallydeterminethepredictedpointson
theROC.Theareasunderthecurvebetweenthoseconfidencecriteriaalsoyieldthe
meandriftratesforasetofdiffusionprocesses,oneforeachconfidencelevel.
Responsesaremadewhenthefirstdiffusionprocesshitsitsdecisioncriterion,
resultinginbotharesponsetimeandaconfidencerating.Thus,thedecisioncriteria
determinethereactiontimedistributions,butbecausethemodelisfittoallofthe
datasimultaneously,theconfidenceparametersareconstrainedbydecision
parameters,andviceversa,andbothsetsofcriteriaconstraintheestimated
evidencedistributions.AconsequenceisthattheslopeofthezROCdoesnot
correspondtotheratioofstandarddeviationsofthelureandtargetdistributions,as
theUVSDTmodelassumes.Forthisreason,Ratcliffandcolleagues(Ratcliff&
Starns,2009;Voskuilen&Ratcliff,2016)cautionagainstrelyingonzROCslopesasa
basisfortheoreticalconclusions.
4.3. CriterionVariability
AdifferentcriticismofusingzROCslopestodrawtheoreticalconclusions
comesfromexperimentsinwhichconfidenceratingsarecollectedacrosstestlists
thatvaryintheirbaserateoftargetsandlures(Schulman&Greenberg,1970;Van
Zandt,2000).Thesestudiesyielddatathatappeartoviolatethecoreassumptions
ofsignaldetectiontheory.Asdescribedinsections3.1.1and3.1.2,zROCscanbe
constructedacrosslists,usingthedifferentbaseratestogeneratetheoperating
Rotello66
points,andtheycanalsobeconstructedwithinlistsusingtheconfidenceratings.
AccordingtoSDTmodels,bothzROCsarebasedonthesameunderlyingevidence
distributions,sothesameslopeshouldbeestimatedfrombothmethods.In
contrasttothisprediction,steeperconfidence-basedzROCslopeswereobservedon
teststhatincludedahigherproportionoftargets.Forthisreason,VanZandt
(2000)concludedthattheUVSDTmodelcouldnotaccountforthedata.However,
thisconclusionfailstoconsidertheinfluenceofcriterionvariability.AsRotelloand
Macmillan(2008)argued,TreismanandWilliams'(1984)modelofcriterion
variabilitypredictstheobservedpatternofslopes,withoutanymodificationtothe
underlyingsignaldetectionmodel.
Essentially,TreismanandWilliams(1984)arguedthatcriterionlocationis
determinedbythreefactors.Taskdemandsandthefirstfewtesttrialssetthe
criterioninitially,thenoneachtrialthecriterionisshiftedtowardtheaverageofthe
recentlyobservedevidencevaluessothatfinerdiscriminationsmaybemade.The
shifttowardtherecent-meanisoffsetbyatendencytoadjustthecriterionsothat
thesameresponseismorelikelyonthenexttrial,allowingsequentialdependencies
tooccur(Malmberg&Annis,2012).Whenconfidencecriteriaarerequired,the
moreextremecriteriatendtohavegreatervariabilitybecausetheprobabilityof
observingatestitemfromtheuppertailofthetargetdistribution(orthelowertail
ofthelures)islow.TheoveralleffectofTreismanandWilliams’sthreefactorsis
thatthepresenceofmoretargetsthanluresincreases"old"confidencecriterion
variabilitytoagreaterextentthan"new"confidencecriterion,andtheoppositeis
trueforteststhatincludearelativelymorelures.
Rotello67
Acrosstrials,thismeansthatthereisnoiseinthelocationofthecriterionas
wellastheevidence(Wickelgren&Norman,1966;Norman&Wickelgren,1969).
ThismeansthattheslopeofthezROCisnotjusttheratioofthestandarddeviation
ofthelures(1)tothetargets(s),it’sactually
(14)
wheres2cisthevarianceofthecriterionlocation.Theseevidenceandcriterion
componentsofvariancecannotbeseparatedempiricallyusingastandard
experimentaldesign(butseeBenjamin,Diaz,&Wee,2009andMueller&
Weidemann,2008,fortwoattempts,andKellen,Klauer,&Singmann,2012,for
criticism).Infact,wedon'tneedtomeasurebothevidenceandcriterionnoise
separatelytoknowthatbotharepresent:thedatareportedbyVanZandt(2000)
andbySchulmanandGreenberg(1970)confirmearliersimulationworkby
TreismanandFaulkner(1984)anddemonstratethatthecriterionnoiseisboth
presentandsystematic.
4.4 ResidualAnalysesRevealPotentialProblemsforAllModels
Recently,Dede,Squire,andWixted(2014)proposedanewstrategyfor
evaluatingtherelativefitofmodelsofrecognitionmemory.Specifically,they
suggestedlookingatthepatternofresidualsbetweenobserveddataandthe
models’bestfittingpredictions.Iftheresidualsforaparticularmodelare
slope =1+σ c
2( )s2 +σ c
2
Rotello68
systematicacrossdatasets,thenthatindicatesaprobleminherenttothemodel.On
theotherhand,iftheresidualsarenotsystematicthentheyreflectrandomnoisein
anygivenexperimentaloutcome,lendingcredibilitytothatmodel.Dedeetal.
(2014)appliedthisstrategytofourrecognitionmemorydatasets,withthegoalof
decidingwhethertheHTSDTorUVSDTmodeloffersthebetterexplanation.The
HTSDTfitsyieldedthesamesystematicpatternofresidualsacrossallfourdatasets,
whereastheresidualsfortheUVSDTmodelappeartoreflectonlystatisticalnoise,
suggestingthattheUVSDTmodelprovidesthebetteroverallaccountofthesedata.
Dedeetal.’s(2014)resultsarepromising.Ontheotherhand,Kellenand
Singmann(2016)adoptedthesamebasicstrategyofanalyzingresidualsand
reachedadifferentconclusion.KellenandSingmannfitalargernumberofdata
sets,includedtheMSDTmodelintheevaluation,andusedadifferentcriterionfor
definingsystematicresiduals.Theyfoundthatallofthemodelsunderconsideration
displayedatleastsomesystematicdeviationsfromthedata.Itremainsanopen
questionwhethertheseresidualsreflectcoreassumptionsofeachofthemodels,or
whethertheyreflectancillarydetailssuchastheassumedformoftheevidence
distributions.
5 Conclusion
Acrossawiderangeofrecognitionmemorytasks,includingthosethoughtto
relyheavilyonarecollectionprocess,theunequal-variancesignaldetectionmodel
Rotello69
providesaconsistently–almostunanimously–betterfittodatathanthatofferedby
competingmodels.Assessmentsofmodelflexibilityindicatethatthesuccessofthe
UVSDTmodelisnotduetointrinsicallygreaterflexibility.Instead,thissimple
modelappearstoprovideanexcellentdescriptionofrecognitionmemory
performance.Assuch,itshouldserveasthefoundationforresearchonrecognition
memoryindomainsasvariedas"real-world"applicationsofmemory(i.e.,
eyewitnessidentificationdecisions:Mickes,Flowe,&Wixted,2012,)andthe
neurologicalbasisofrecognition(e.g.,Squire,Wixted,&Clark,2007).
Comment [CR1]: Crossreferencechapter02025. Eyewitness Identification byLauraMickes
Rotello70
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Table1.Parametersofthemodelswhenfittoaconfidence-ratingROCwithmconfidencebins.Model Sensitivity
Parameter(s)VarianceorMixtureParameter
CriterionLocations
State-responsemappingparameters
EVSDT d’ -- m-1 --UVSDT d s m-1 --HTSDT R,d’ -- m-1 --MSDT dFull,dPartial l m-1 --2HT po,pn -- -- Varies.
Maximum=3(m-1).
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FigureCaptions
Figure1.Toprow:Equal-variancesignaldetection(EVSDT)modeldecisionspace
(leftpanel),exampleROCs(middlepanel),andcorrespondingzROCs(rightpanel).
Bottomrow:Unequal-variancesignaldetection(UVSDT)modeldecisionspace(left
panel),exampleROCs(middlepanel),andcorrespondingzROCs(rightpanel).
Figure2.High-thresholdsignaldetection(HTSDT)model.Leftpanel:decision
spacefortargets.LuredecisionspaceisidenticaltoEVSDT.Middlepanel:example
ROCsforthreerecollectionprobabilities(.2,.4,.6)andaconstantd’(1.5).Right
panel:correspondingzROCs.
Figure3.Mixturesignaldetection(MSDT)model.Leftpanel:decisionspace.Lure
distributionontheleft,distributionforunattendedtargets(dasheddistribution),
andattendedtargetdistributionontheright.Middlepanel:ExampleROCsforthree
valuesofl(.2,.4,.6).Rightpanel:correspondingzROCs.
Figure4.Doublehigh-threshold(2HT)modelforbinary(old-new)decisiontask.
Leftpanel:decisionspace,T=Target;L=Lure;?=uncertainstateMiddlepanel:
ExampleROCsforthreevaluesofpo(.2,.4,.6)andthreevaluesofpn(.05,.25,.45).
Rightpanel:correspondingzROCs.
Figure5.Doublehigh-threshold(2HT)modelforconfidenceratingtask.Left
panel:decisionspace,T=Target;L=Lure;?=uncertainstate.Middlepanel:
ExampleROCsforpo=.6,pn=.45andthreedifferentsetsofdetectstatetoresponse
mappingparameters.Rightpanel:correspondingzROCs.
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Figure6.Examplefitsofthecompetingmodelstoanitemrecognitiontask.Data
(circles)arefromasinglesubjectinEgan(1958,Exp.1),reportedinhisTable1.
Best-fittingmodelpredictionsareshown.TheMSDTandHTSDTmodelsmake
identicalpredictionsforthesedata,thoughtheMSDTrequiresanextraparameter
todoso.AllmodelsexcepttheEVSDTprovideacceptablefits(theycannotbe
rejectedbyaG2goodnessoffitmeasure).
Figure7.DecisionspaceforHautusetal.’s(2008)bivariatemodelofitemand
sourcerecognition.Horizontallinesreflecttheold-newconfidencecriteria,which
dependonlyontheold-newevidencedimension.Curvedboundariesindicatethe
optimal(likelihood-based)sourceconfidencecriteria(“1”=SureSourceB;“6”=
SureSourceA).From:Hautus,M.,Macmillan,N.A.,&Rotello,C.M.(2008).Toward
acompletedecisionmodelofitemandsourcerecognition.PsychonomicBulletin&
Review,15,889-905.Figure8.ReprintedwithpermissionofSpringer.
Figure8.DecisionspaceforOnyperetal.’s(2010)modelofsourceanditem
recognition.LiketheHTSDTmodel,thismodelassumessourceinformationis
recollectedwithsomeprobability(upperdistributions).Intheabsenceof
recollection,responsesarebasedonfamiliarity(lowerdistributions).Confidence
ratings(‘1’though‘9’)dependonlyontheitemorsourcedimension.From:Onyper,
Zhang,&Howard(2010).Some-or-nonerecollection:Evidencefromitemand
sourcememory,JournalofExperimentalPsychology:General,139,341–364,Figure
6A.ReprintedwithpermissionoftheAmericanPsychologicalAssociation.
Figure9.Two-alternativeforcedchoice(2AFC)decisionspace.
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Figure10.Heathcoteetal.’s(2010)modelofthe2AFCconfidence-accuracy
inversiondata.Positivedifferencesresultincorrectdecisions;negativedifferences
inerrors.Confidenceisdefinedbydistancetothecriterion(0-point).Remember
responsesaremadefordifferenceslargerthantheR/Kcriterion,andknow
responsesforsmalldifferences.Thearrowindicatestrial-to-trialvariabilityinthe
locationoftheR/Kcriterion.Adaptedfrom:Clark,S.E.(1997).AFamiliarity-Based
AccountofConfidence-AccuracyInversionsinRecognitionMemory.Journalof
ExperimentalPsychology:Learning,Memory,&Cognition,23,232-238.Adaptedwith
permissionoftheAmericanPsychologicalAssociation.
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