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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)545-1543caren@psych.umass.edu

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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

"

#$

%

&'

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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

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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

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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

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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

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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

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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

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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

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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).

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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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,

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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

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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

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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

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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

6 References

Arndt,J.,&Reder,L.M.(2002).Wordfrequencyandreceiveroperating

characteristiccurvesinrecognitionmemory:Evidenceforadual-process

interpretation.JournalofExperimentalPsychology:Learning,Memory,&

Cognition,28,830-842.DOI:10.1037//0278-7393.28.5.830

Banks,W.P.(1970).Signaldetectiontheoryandhumanmemory.Psychological

Bulletin,74,81-99.

Banks,W.P.(2000).Recognitionandsourcememoryasmultivariatedecision

processes.PsychologicalScience,11,267–273.

Bamber,D.(1979).State-traceanalysis:Amethodoftestingsimpletheoriesof

causation.JournalofMathematicalPsychology,19,137-181.

Bastin,C.,Diana,R.A.,Simon,J.,Collette,F.,Yonelinas,A.P.,&Salmon,E.(2013).

Associativememoryinaging:Theeffectofunitizationonsourcememory.

PsychologyandAging,28,275-283.doi:10.1037/a0031566

Bayen,U.J.,Murnane,K.,&Erdfelder,E.(1996).Sourcediscrimination,item

detection,andmultinomialmodelsofsourcemonitoring.Journalof

ExperimentalPsychology:Learning,Memory,&Cognition,22,197-215.

Benjamin,A.S.,Diaz,M.,&Wee,S.(2009).Signaldetectionwithcriterionnoise:

Applicationstorecognitionmemory.PsychologicalReview,116,84-115.Doi:

10.1037/a0014351

Brainerd,C.J.,Reyna,V.F.,&Mojardin,A.H.(1999).Conjointrecognition.

PsychologicalReview,106,160-179.

Rotello71

Bröder,A.,Kellen,D.,Schütz,J.,&Rohrmeier,C.(2013).Validatingatwo-high-

thresholdmeasurementmodelforconfidenceratingdatainrecognition.

Memory,21,916- ︎944.Doi:10.1080/09658211.2013.767348

Bröder,A.&Schütz,J.(2009).RecognitionROCsarecurvilinear-orarethey?On

prematureargumentsagainstthetwo-high-thresholdmodelofrecognition.

JournalofExperimentalPsychology:Learning,Memory&Cognition,35,587-

606.[seealsocorrectiontoBröderandSchütz(2009).JEP:LMC,47(5),1301]

Buchner,A.,&Erdfelder,E.(1996).Ontheassumptionsof,relationsbetween,and

evaluationsofsomeprocessdissociationmeasurementmodels.

ConsciousnessandCognition,5,581-594.

Chandler,C.C.(1989).Specificretroactiveinterferenceinmodifiedrecognition

tests:Evidenceforanunknowncauseofinterference.JournalofExperimental

Psychology:Learning,Memory,andCognition,15,256-265.

Chandler,C.C.(1994).Studyingrelatedpicturescanreduceaccuracy,butincrease

confidence,inamodifiedrecognitiontest.Memory&Cognition,22,273-280.

Chen,T.,Starns,J.J.,&Rotello,C.M.(2015).Aviolationoftheconditional

independenceassumptionofdiscretestatemodelsofrecognitionmemory.

JournalofExperimentalPsychology:Learning,Memory,&Cognition,41,1215-

1222.doi:10.1037/xlm0000077

Clark,S.E.(1997).AFamiliarity-BasedAccountofConfidence-AccuracyInversions

inRecognitionMemory.JournalofExperimentalPsychology:Learning,

Memory,&Cognition,23,232-238.

Rotello72

Cohen,A.L.,Rotello,C.M.,&Macmillan,N.A.(2008).Evaluatingmodelsof

remember-knowjudgments:Complexity,mimicry,anddiscriminability.

PsychonomicBulletin&Review,15,906-926.

Cohen,A.L.,Sanborn,A.N.,&Shiffrin,R.M.(2008).Modelevaluationusinggrouped

orindividualdata.PsychonomicBulletin&Review,15,692-712.doi:

10.3758/PBR.15.4.692

DeCarlo,L.T.(2002).Signaldetectiontheorywithfinitemixturedistributions:

Theoreticaldevelopmentswithapplicationsto

recognitionmemory.PsychologicalReview,109,710-721.

DeCarlo,L.T.(2003).Anapplicationofsignaldetectiontheorywithfinitemixture

distributionstosourcediscrimination.Journalof

ExperimentalPsychology:Learning,Memory,andCognition,29,767-778.

DeCarlo,L.T.(2007).Themirroreffectandmixturesignaldetectiontheory.Journal

ofExperimentalPsychology:Learning,Memory,andCognition,33,18-33.

DeCarlo,L.T.(2011).Signaldetectiontheorywithitemeffects.Journalof

MathematicalPsychology,55,229-239.

DeCarlo,L.T.(2012).Onasignaldetectionapproachtom-alternativeforcedchoice

withbias,withmaximum likelihoodandBayesianapproachestoestimation.

JournalofMathematicalPsychology,56,196-207.

Dede,A.J.O.,Squire,L.R.,&Wixted,J.T.(2014).Anovelapproachtoanold

problem:Analysisofsystematicerrorsintwomodelsofrecognitionmemory.

Neuropsychologia,52,51–56.doi:10.1016/j.neuropsychologia.2013.10.012

Rotello73

Dewhurst,S.A.,&Conway,M.A.(1994).Pictures,images,andrecollective

experience.JournalofExperimentalPsychology:Learning,Memory,&

Cognition,20,1088-1098.

Dewhurst,S.A.,Holmes,S.J.,Brandt,K.R.,&Dean,G.M.(2006).Measuringthe

speedoftheconsciouscomponentsofrecognitionmemory:Rememberingis

fasterthanknowing.Consciousness&Cognition,15,147-162.

Dobbins,I.G.,Kroll,N.E.A.,&Liu,Q.(1998).Confidence–accuracyinversionsin

scenerecognition:Aremember–knowanalysis.JournalofExperimental

Psychology:Learning,Memory,andCognition,24,1306–1315.

Dodson,C.S.,Bawa,S.,&Slotnick,S.D.(2007).Aging,sourcememory,and

misrecollections.JournalofExperimentalPsychology:Learning,Memory,&

Cognition,33,169-181.

Donaldson,W.(1996).Theroleofdecisionprocessesinrememberingandknowing.

Memory&Cognition,24,523-533.

Dougal,S.,&Rotello,C.M.(2007).“Remembering”emotionalwordsisbasedon

responsebias,notrecollection.PsychonomicBulletin&Review,14,423-429.

Dube,C.,&Rotello,C.M.(2012).BinaryROCsinperceptionandrecognition

memoryarecurved.JournalofExperimentalPsychology:Learning,Memory,

andCognition,38,130-151.

Dube,C.,Rotello,C.M.,&Heit,E.(2011).Thebeliefbiaseffectisaptlynamed:A

replytoKlauerandKellen(2011).PsychologicalReview,118,155-163.

Rotello74

Dube,C.,Starns,J.J.,Rotello,C.M.,&Ratcliff,R.(2012).BeyondROCcurvature:

Strengtheffectsandresponsetimedatasupportcontinuous-evidencemodels

ofrecognitionmemory.JournalofMemory&Language,67,389-406.

Dunn,J.C.(2004).Remember-know:Amatterofconfidence.PsychologicalReview,

111,524-542.

Dunn,J.C.(2008).ThedimensionalityoftheRemember-Knowtask:Astate-trace

analysis.PsychologicalReview,115,426-446.

Dunn,J.C.&Kirsner,K.(1988).Discoveringfunctionallyindependentmental

processes:Theprincipleofreversedassociation.PsychologicalReview,95,

91-101.

Egan,J.P.(1958).Recognitionmemoryandtheoperatingcharacteristic(Technical

NoteAFCRC-TN-58-51).Bloomington,IN:IndianaUniversityHearingand

CommunicationLaboratory.

Erdfelder,E.,&Buchner,A.(1998).Process-dissociationmeasurementmodels:

Thresholdtheoryordetectiontheory?JournalofExperimentalPsychology:

General,127,83–97.doi:10.1037/0096-3445.127.1.83

Freeman,E.,Heathcote,A.,Chalmers,K.,&Hockley,W.(2010).Itemeffectsin

recognitionmemoryforwords.JournalofMemoryandLanguage,62,1–18.

Doi:10.1016/j.jml.2009.09.004

Gardiner,J.M.,&Richardson-Klavehn,R.(2000).Rememberingandknowing.InE.

Tulving&F.I.M.Craik(Eds.),TheOxfordhandbookofmemory(pp.229–244).

Oxford,England:OxfordUniversityPress.

Rotello75

Glanzer,M.,Hilford,A.,&Kim,K.(2004).Sixregularitiesofsourcerecognition.

JournalofExperimentalPsychology:Learning,Memory,andCognition,30,

1176–1195.

Glanzer,M.,Kim,K.,Hilford,A.,&Adams,J.K.(1999).Slopeofthereceiver-operating

characteristicinrecognitionmemory.JournalofExperimentalPsychology:

Learning,Memory,&Cognition,25,500–513.

Green,D.M.&Swets,J.A.(1966).Signaldetectiontheoryandpsychophysics.New

York:Wiley.Reprinted1974byKrieger,Huntington,NY.

Greve,A.,Donaldson,D.I.,&vanRossum,M.C.W.(2010).Asingle-tracedual-

processmodelofepisodicmemory:Anovelcomputationalaccountof

familiarityandrecollection.Hippocampus,20,235-251.Doi:

10.1002/hipo.20606

Gronlund,SD.,Ratcliff,R.(1989).Timecourseofitemandassociativeinformation:

Implicationsforglobalmemorymodels.JournalofExperimentalPsychology:

Learning,Memory,andCognition,15,846-858.

Harlow,I.M.,&Donaldson,D.I.(2013).Sourceaccuracydatarevealthethresholded

natureofhumanepisodicmemory.PsychonomicBulletin&Review,20,318–

325.doi:10.3758/s13423-012-0340-9

Hautus,M.,Macmillan,N.A.,&Rotello,C.M.(2008).Towardacompletedecision

modelofitemandsourcerecognition.PsychonomicBulletin&Review,15,

889-905.

Healy,M.R.,Light,L.L.,&Chung,C.(2005).Dual-processmodelsofassociative

recognitioninyoungandolderadults:Evidencefromreceiveroperating

Rotello76

characteristics.JournalofExperimentalPsychology:Learning,Memory,and

Cognition,31,768-788.DOI:10.1037/0278-7393.31.4.768

Heathcote,A.(2003).ItemRecognitionMemoryandtheReceiverOperating

Characteristic.JournalofExperimentalPsychology:Learning,Memory,&

Cognition,29,1210-1230.DOI:10.1037/0278-7393.29.6.1210

Heathcote, A., Bora, B., & Freeman, E. (2010). Recollection and confidence in

two-alternative forced choice episodic recognition. Journal of Memory and

Language, 62, 183-203.doi:10.1016/j.jml.2009.11.003

Heathcote,A.,Raymond,F.,&Dunn,J.(2006).Recollectionandfamiliarityin

recognitionmemory:EvidencefromROCcurves.JournalofMemoryand

Language,55,495-514.

Hilford,A.,Glanzer,M.,Kim,K.,&DeCarlo,L.T.(2002).Regularitiesofsource

recognition:ROCanalysis.JournalofExperimentalPsychology:General,131,

494-510.

Hintzman,D.L.,&Curran,T.(1994).Retrievaldynamicsofrecognitionand

frequencyjudgments:Evidenceforseparateprocessesoffamiliarityand

recall.JournalofMemory&Language,33,1-18.

Ingram,K.M.,Mickes,L.,&Wixted,J.T.(2012).Recollectioncanbeweakand

Familiaritycanbestrong.JournalofExperimentalPsychology:Learning,

Memory,andCognition,38,325-339.Doi:10.1037/a0025483

Isola,P.,Xiao,J.,Parikh,D.,Torralba,A.&Oliva,A.(2014).Whatmakesaphotograph

memorable?PatternAnalysisandMachineIntelligence.1-14.

Rotello77

Jang,Y.,Mickes,L.&Wixted,J.T.(2012).Threetestsandthreecorrections:

CommentonKoenandYonelinas(2010).JournalofExperimentalPsychology:

Learning,Memory,andCognition,38,513–523.

Jang,Y.,Wixted,J.T.,&Huber,D.E.(2009).Testingsignal-detectionmodelsof

yes/noandtwo-alternativeforced-choicerecognitionmemory.Journalof

ExperimentalPsychology:General,138,291–306.

Jang,Y.,Wixted,J.T.,&Huber,D.E.(2011).Thediagnosticityofindividualdatafor

modelselection:Comparingsignal-detectionmodelsofrecognitionmemory.

PsychonomicBulletin&Review,18,751–757.DOI10.3758/s13423-011-

0096-7

Kantner,J.,&Lindsay,D.S.(2012).Responsebiasinrecognitionmemoryasa

cognitivetrait.Memory&Cognition,40,1163-1177.

Kapucu,A.,Macmillan,N.A.,&Rotello,C.M.(2010).Positiveandnegative

rememberjudgmentsandROCsinthepluralsparadigm:Evidencefor

alternativedecisionstrategies.Memory&Cognition,38,541-554.

PMCID2887610

Kapucu,A.,Rotello,C.M.,Ready,R.E.,&Seidl,K.N.(2008).Responsebiasin

‘remembering’emotionalstimuli:Anewperspectiveonagedifferences.

JournalofExperimentalPsychology:Learning,Memory,&Cognition,34,703-

711.

Kellen,D.,&Klauer,K.C.(2011).Evaluatingmodelsofrecognitionmemoryusing

first-andsecond-choiceresponses.JournalofMathematicalPsychology,55,

251–266.http://dx.doi.org/10.1016/j.jmp.2010.11.004

Rotello78

Kellen,D.,&Klauer,K.C.(2014).Discrete-stateandcontinuousmodelsof

recognitionmemory:Testingcorepropertiesunderminimalassumptions.

JournalofExperimentalPsychology:Learning,Memory,andCognition,40,

1795–1804.http://dx.doi.org/10.1037/xlm0000016

Kellen,D.,&Klauer,K.C.(2015).Signaldetectionandthresholdmodelingof

confidence-ratingROCs:Acriticaltestwithminimalassumptions.

PsychologicalReview,122,542–557.Doi:10.1037/a0039251

Kellen,D.,Klauer,K.C.,&Broder,A.(2013).Recognitionmemorymodelsand

binary-responseROCs:Acomparisonbyminimumdescriptionlength.

PsychonomicBulletin&Review,20,693-719.Doi:10.3758/s13423-013-0407-

2

Kellen,D.,Klauer,K.C.,&Singmann,H.(2012).Onthemeasurementofcriterion

noiseinSignalDetectionTheory:Thecaseofrecognition

memory.PsychologicalReview,119,457-479.

Kellen,D.,&Singmann,H.(2016).ROCresidualsinsignal-detectionmodelsof

recognitionmemory.PsychonomicBulletin&Review,23,253-264.Doi:

10.3758/s13423-015-0888-2

Kelley,R.,&Wixted,J.T.(2001).Onthenatureofassociativeinformationin

recognitionmemory.JournalofExperimentalPsychology:Learning,Memory,

andCognition,27,701–722.Doi:10.1037//0278-7393.27.3.701

Klauer,K.C.(2006).Hierarchicalmultinomialprocessingtreemodels:alatent-class

approach.Psychometrika,71,1–31.

Rotello79

Klauer,K.C.(2010).Hierarchicalmultinomialprocessingtreemodels:alatent-trait

approach.Psychometrika,75,70-98.DOI:10.1007/S11336-009-9141-0

Klauer,K.C.&Kellen,D.(2010).Towardacompletedecisionmodelofitemand

sourcerecognition:Adiscrete-stateapproach.PsychonomicBulletin&Review,

17,465-478.

Koen,J.D.,&Yonelinas,A.P.(2010).Memoryvariabilityisduetothecontributionof

recollectionandfamiliarity,notencodingvariability.JournalofExperimental

Psychology:Learning,Memory,andCognition,36,1536–1542.

doi:10.1037/a0020448

Krantz,D.H.(1969).Thresholdtheoriesofsignaldetection.PsychologicalReview,

76,308–324.doi:10.1037/h0027238

Kroll,N.E.A.,Yonelinas,A.P.,Dobbins,I.G.,&Frederick,C.M.(2002).Separating

sensitivityfromresponsebias:Implicationsofcomparisonsofyes-noand

forced-choicetestsformodelsandmeasuresofrecognitionmemory.Journal

ofExperimentalPsychology:General,131,241-254.Doi:10.1037/0096-

3445.131.2.241

Lachman,R.,&Field,W.H.(1965).Recognitionandrecallofverbalmaterialsasa

functionofdegreeoftraining.PsychonomicScience,2,225-226.

Macho,S.(2004).Modelingassociativerecognition:Acomparisonoftwo-high-

threshold,two-high-thresholdsignaldetection,andmixturedistribution

models.JournalofExperimentalPsychology:Learning,Memory,andCognition,

30,83–97.DOI:10.1037/0278-7393.30.1.83

Rotello80

Macmillan,N.A.,&Creelman,C.D.(2005).Detectiontheory:Auser’sguide(2nded.).

Mahwah,NJ:Erlbaum.

Macmillan,N.A.,Rotello,C.M.,&Verde,M.F.(2005).Ontheimportanceofmodels

ininterpretingremember-knowexperiments:CommentsonGardineretal.’s

(2002)meta-analysis.Memory,13,607-621.

Malejka,S.,Bröder,A.(2016).Nosourcememoryforunrecognizeditemswhen

implicitfeedbackisavoided.Memory&Cognition,44,63-72.Doi:

10.3758/s13421-015-0549-8

Malmberg,K.J.(2002).OntheformofROCsconstructedfromconfidenceratings.

JournalofExperimentalPsychology:Learning,Memory,andCognition,28,

380-387.

Malmberg,K.J.,&Annis,J.(2012).OntheRelationshipbetweenMemoryand

Perception:Sequentialdependenciesinrecognitiontesting.Journalof

ExperimentalPsychology:General,141,233-259.

Malmberg,K.J.&Xu,J.(2006).TheInfluenceofAveragingandNoisyDecision

StrategiesontheRecognitionMemoryROC,PsychonomicBulletin&Review,

13,99-105.

Mandler,G.(1980).Recognizing:Thejudgmentofpreviousoccurrence.

PsychologicalReview,87,252–271

McElree,B.,Dolan,P.O.,&Jacoby,L.L.(1999).Isolatingthecontributionsof

familiarityandsourceinformationtoitemrecognition:Atimecourse

analysis.JournalofExperimentalPsychology:Learning,Memory,and

Cognition,25,563–582.

Rotello81

Mickes,L.,Flowe,H.D.,&Wixted,J.T.(2012).Receiveroperatingcharacteristic

analysisofeyewitnessmemory:Comparingthediagnosticaccuracyof

simultaneousversussequentiallineups.JournalofExperimentalPsychology:

Applied,18,361-376.Doi:10.1037/a0030609

Mickes,L.,Johnson,E.M.,&Wixted,J.T.(2010).Continuousrecollectionversus

unitizedfamiliarityinassociativerecognition.JournalofExperimental

Psychology:Learning,Memory,andCognition,36,843–863.doi:

10.1037/a001975

Mickes,L.,Wais,P.E.,&Wixted,J.(2009).Recollectionisacontinuousprocess:

Implicationsfordual-processtheoriesofrecognitionmemory.Psychological

Science,20,509-515.

Mickes,L.,Wixted,J.T.&Wais,P.E.(2007).ADirectTestoftheUnequal-Variance

Signal-DetectionModelofRecognitionMemory.PsychonomicBulletin&

Review,14,858-865.

Mueller,S.T.,&Weidemann,C.T.(2008).Decisionnoise:Anexplanationfor

observedviolationsofsignaldetectiontheory.PsychonomicBulletin&

Review,15,465-494.doi:10.3758/PBR.15.3.465

Myung,J.I.,Navarro,D.J.,&Pitt,M.A.(2006).Modelselectionbynormalized

maximumlikelihood.JournalofMathematicalPsychology,50,167-179.

Norman,D.A.,&Wickelgren,W.A.(1969).Strengththeoryofdecisionrulesand

latencyinretrievalfromshort-termmemory.JournalofMathematical

Psychology,6,192-208.

Rotello82

O’Connor,A.R.,Guhl,E.N.,Cox,J.C.,&Dobbins,I.G.(2011).Somememoriesare

odderthanothers:Judgmentsofepisodicoddityviolateknowndecision

rules.JournalofMemoryandLanguage,64,299–315.Doi:

10.1016/j.jml.2011.02.001

Onyper,S.V.,Zhang,Y.X.,&Howard,M.W.(2010).Some-or-nonerecollection:

Evidencefromitemandsourcememory.JournalofExperimentalPsychology:

General,139,341–364.doi:10.1037/a0018926

Parks,C.M.,&Yonelinas,A.P.(2007).Movingbeyondpuresignaldetectionmodels:

CommentonWixted(2007).PsychologicalReview,114,188–202.

doi:10.1037/0033-295X.114.1.188

Parks,C.M.,&Yonelinas,A.P.(2009).Evidenceforamemorythresholdinsecond-

choicerecognitionmemoryresponses.ProceedingsoftheNationalAcademy

ofSciences,106,11515-9.

Parks,C.M.,Murray,L.J.,Elfman,K.,&Yonelinas,A.P.(2011).Variationsin

recollection:Theeffectsofcomplexityonsourcerecognition.Journalof

ExperimentalPsychology:Learning,Memory,andCognition,37,861-873.

Doi:10.1037/a0022798

Pazzaglia,A.M.,Dube,C.,&Rotello,C.M.(2013).Acriticalcomparisonofdiscrete-

stateandcontinuousmodelsofrecognitionmemory:Implicationsfor

recognitionandbeyond.PsychologicalBulletin,139,1173-1203.

Petrusic,W.M.,&Baranski,J.V.(2003).Judgingconfidenceinfluencesdecision

processingincomparativejudgments.PsychonomicBulletin&Review,10,

177–183.doi:10.3758/BF03196482

Rotello83

Pitt,M.A.,Myung,I.J.,&Zhang,S.(2002).Towardamethodofselectingamong

computationalmodelsofcognition.PsychologicalReview,109,472-491.

Pleskac,T.J.,&Busemeyer,J.R.(2010).Two-stagedynamicsignaldetection:A

theoryofchoice,decisiontime,andconfidence.PsychologicalReview,117,

864-901.DOI:10.1037/a0019737

Pratte,M.S.,&RouderJ.N.(2011).Hierarchicalsingle-anddual-processmodelsof

recognitionmemory.JournalofMathematicalPsychology,55,36-46.

Pratte,M.S.,&Rouder,J.N.(2012).Assessingthedissociabilityofrecollectionand

familiarityinrecognitionmemory.JournalofExperimentalPsychology:

Learning,Memory,andCognition,38,1591-1607.10.1037/a0028144

Pratte,M.S.,RouderJ.N.,&MoreyR.D.(2010).Separatingmnemonicprocessfrom

participantanditemeffectsintheassessmentofROCasymmetries.Journalof

ExperimentalPsychology:Learning,Memory,andCognition,36,224--232.

Province,J.M.,&Rouder,J.N.(2012).Evidencefordiscrete-stateprocessingin

recognitionmemory,ProceedingsoftheNationalAcademyofSciences,109,

14357–14362.doi:10.1073/pnas.1103880109

Qin,J.,Raye,C.L.,Johnson,M.K.,&Mitchell,K.J.(2001).Source ROCsare(typically)

curvilinear:CommentonYonelinas(1999). JournalofExperimental

Psychology:Learning,Memory,&Cognition, 27,1110-1115.

Quamme,J.R.,Yonelinas,A.P.,&Norman,K.A.(2007).Effectofunitizationon

associativerecognitioninamnesia.Hippocampus,17,192-200.Doi:

10.1002/hipo.20257

Rotello84

Rajaram,S.(1993).Rememberingandknowing:Twomeansofaccesstothe

personalpast.Memory&Cognition,21,89–102.

Rajaram,S.,&Geraci,L.(2000).Conceptualfluencyselectivelyinfluencesknowing.

JournalofExperimentalPsychology:Learning,Memory,andCognition,26,

1070-1074.

Ratcliff,R.(1978).Atheoryofmemoryretrieval.PsychologicalReview,85,59–108.

Ratcliff,R.,McKoon,G.,&Tindall,M.(1994).Theempiricalgeneralityofdatafrom

recognitionmemoryreceiver-operatingcharacteristicfunctionsand

implicationsforglobalmemorymodels.JournalofExperimentalPsychology:

Learning,Memory,andCognition,20,763–785.

Ratcliff,R.,Sheu,C.-F.,&Gronlund,S.D.(1992).Testingglobalmatchingmemory

modelsusingROCcurves.PsychologicalReview,99,518-535.

Ratcliff,R.,&Starns,J.J.(2009).Modelingconfidenceandresponsetimein

recognitionmemory.PsychologicalReview,116,59–83.

Reder,L.M.,Nhouyvanisvong,A.,Schunn,C.D.,Ayers,M.S.,Angstadt,P.,&Hiraki,K.

(2000).Amechanisticaccountofthemirroreffectforwordfrequency:A

computationalmodelofremember–knowjudgmentsinacontinuous

recognitionparadigm.JournalofExperimentalPsychology:Learning,Memory,

&Cognition,26,294-320.

Roberts,S.,&Pashler,H.(2000).Howpersuasiveisagoodfit?Acommentontheory

testing.PsychologicalReview,107,358–367.DOI:10.1037//0033-

295X.107.2.358

Rotello85

Rotello,C.M.(2000).Recallprocessesinrecognitionmemory.InD.L.Medin(Ed.),

ThePsychologyofLearningandMotivation,Vol.40(pp.183-221).SanDiego,

CA:AcademicPress.

Rotello,C.M.,&Heit,E.(1999).Two-processmodelsofrecognitionmemory:

EvidenceforRecall-to-reject?JournalofMemoryandLanguage,40,432-453.

Rotello,C.M.,&Heit,E.(2000).Associativerecognition:Acaseofrecall-to-reject

processing.MemoryandCognition,28,907-922.

Rotello,C.M.,&Macmillan,N.A.(2006).Remember-knowmodelsasdecision

strategiesintwoexperimentalparadigms.JournalofMemory&Language,55,

479-494.

Rotello,C.M.,&Macmillan,N.A.(2008).Responsebiasinrecognitionmemory.InA.

S.Benjamin&B.H.Ross(Eds.),ThePsychologyofLearningandMotivation:

SkillandStrategyinMemoryUse,Vol.48(pp.61-94).London:Academic

Press.

Rotello,C.M.,&Zeng,M.(2008).AnalysisofRTdistributionsintheremember-

knowparadigm.PsychonomicBulletin&Review,15,825-832.

Rotello,C.M.,Macmillan,N.A.,Hicks,J.L.,&Hautus,M.(2006).Interpretingthe

effectsofresponsebiasonremember-knowjudgmentsusingsignal-

detectionandthresholdmodels.Memory&Cognition,34,1598-1614.

Rotello,C.M.,Macmillan,N.A.,Reeder,J.A.,&Wong,M.(2005).Theremember

response:Subjecttobias,graded,andnotaprocess-pureindicatorof

recollection.PsychonomicBulletin&Review,12,865-873.

Rotello86

Rotello,C.M.,Macmillan,N.A.,&VanTassel,G.(2000).Recall-to-rejectin

recognition:EvidencefromROCcurves.JournalofMemoryandLanguage,43,

67-88.

Schulman,A.I.,&Greenberg,G.Z.(1970).Operatingcharacteristicsandapriori

probabilityofthesignal.Perception&Psychophysics,8,317-320.

Schütz,J.&Bröder,A.(2011).Signaldetectionandthresholdmodelsofsource

memory.ExperimentalPsychology,58(4),293-311.

Shiffrin,R.M.,&Steyvers,M.(1997).Amodelforrecognitionmemory:REM–

Retrievingeffectivelyfrommemory.PsychonomicBulletin&Review,4,145-

166.

Slotnick,S.D.(2010)."Remember"sourcememoryROCsindicaterecollectionisa

continuousprocess.Memory,18,27−39.doi:10.1080/09658210903390061

Slotnick,S.D.,&Dodson,C.S.(2005).Supportforacontinuous(singleprocess)

modelofrecognitionmemoryandsourcememory.Memory&Cognition,33,

151–170.

Slotnick,S.D.,Jeye,B.M.,&Dodson,C.S.(2016).Recollectionisacontinuous

process:Evidencefrompluralitymemoryreceiveroperatingcharacteristics.

Memory,24,2-11.Doi:10.1080/09658211.2014.971033

Slotnick,S.D.,Klein,S.A.,Dodson,C.S.,&Shimamura,A.P.(2000).Ananalysisof

signaldetectionandthresholdmodelsofsourcememory.Journalof

ExperimentalPsychology:Learning,Memory,andCognition,26,1499–1517.

Smith,D.G.,&Duncan,M.J.J.(2004).Testingtheoriesofrecognitionmemoryby

predictingperformanceacrossparadigms.JournalofExperimental

Rotello87

Psychology:Learning,Memory,&Cognition,30,615-625.Doi:10.1037/0278-

7393.30.3.615

Snodgrass,J.G.,&Corwin,J.(1988).Pragmaticsofmeasuringrecognitionmemory:

Applicationstodementiaandamnesia.JournalofExperimentalPsychology:

General,117,34–50.doi:10.1037/0096-3445.117.1.34

Squire,L.R.,Wixted,J.R.,&Clark,R.E.(2007).Recognitionmemoryandthemedial

temporallobe:Anewperspective.NatureReviewsNeuroscience,8,872-883.

10.1038/nrn2154

Starns,J.J.,&Ksander,J.C.(2016).Itemstrengthinfluencessourceconfidenceand

alterssourcememoryzROCslopes.JournalofExperimentalPsychology:

Learning,Memory,andCognition,42,351-365.Doi:10.1037/xlm0000177

Starns,J.J.,Hicks,J.L.,Brown,N.L.,&Martin,B.A.(2008). Sourcememoryfor

unrecognizeditems:Predictionsfrommultivariate signaldetectiontheory.

Memory&Cognition,36,1-8.

Starns,J.J.,Pazzaglia,A.M.,Rotello,C.M.,Hautus,M.J.,&Macmillan,N.A.(2013).

Unequal-strengthsourcezROCslopesreflectcriteriaplacementandnot

(necessarily)memoryprocesses.JournalofExperimentalPsychology:

Learning,Memory,andCognition,39,1377-1392

Starns,J.J.,Ratcliff,R.,&McKoon,G.(2012).Evaluatingtheunequal-varianceand

dual-processexplanationsofzROCslopeswithresponsetimedataandthe

diffusionmodel.CognitivePsychology,64,1–34.doi:

10.1016/j.cogpsych.2011.10.002

Rotello88

Starns,J.J.,Rotello,C.M.,&Hautus,M.J.(2014).RecognitionmemoryzROCslopes

foritemswithcorrectversusincorrectsourcedecisionsdiscriminatethe

dualprocessandunequalvariancesignaldetectionmodels.Journalof

ExperimentalPsychology:Learning,Memory,&Cognition,40,1205-1225.

Starns,J.J.,Rotello,C.M.,Ratcliff,R.(2012).Mixingstrongandweaktargets

providesnoevidenceagainsttheunequal-varianceexplanationofzROC

slopes:AcommentonKoen&Yonelinas(2010).JournalofExperimental

Psychology:Learning,Memory,andCognition,38,793-801.

Swets,J.A.,Tanner,W.P.,Jr.,&Birdsall,T.G.(1961).Decisionprocessesin

perception.PsychologicalReview,68,301–340.doi:10.1037/h0040547

Treisman,M.,&Faulkner,A.(1984).Theeffectsofsignalprobabilityontheslopeof

thereceiveroperatingcharacteristicgivenbytheratingprocedure.British

JournalofMathematicalandStatisticalPsychology,37,199-215.

Treisman,M.,&Williams,T.C.(1984).Atheoryofcriterionsettingwithan

applicationtosequentialdependencies.PsychologicalReview,91,68-111.

Tulving,E.(1981).Similarityrelationsinrecognition.JournalofVerbalLearningand

VerbalBehavior,20,479-49.

Tulving,E.(1985).Memoryandconsciousness.CanadianPsychology,26,1-12.

VanZandt,T.(2000).ROCcurvesandconfidencejudgmentsinrecognitionmemory.

JournalofExperimentalPsychology:Learning,Memory,andCognition,26,

582-600.

Verde,M.F.,&Rotello,C.M.(2004).ROCcurvesshowthattherevelationeffectis

notasinglephenomenon.PsychonomicBulletin&Review,11,560-566.

Rotello89

Voskuilen,C.,&Ratcliff,R.(2016).Modelingconfidenceandresponsetimein

associativerecognition.JournalofMemoryandLanguage,86,60-96.doi:

10.1016/j.jml.2015.09.006

Wagenmakers,E.-J.,Ratcliff,R.,Gomez,P.,&Iverson,G.J.(2004).Assessingmodel

mimicryusingtheparametricbootstrap.JournalofMathematicalPsychology,

48,28-50.

Westerman,D.L.(2001).Theroleoffamiliarityinitemrecognition,associative

recognition,andpluralityrecognitiononself-pacedandspeededtests.

JournalofExperimentalPsychology:Learning,Memory,andCognition,27,

723-732.DO1:10.1037//0278-7393.27.3.723

Wickelgren,W.A.,&Norman,D.A.(1966).Srengthmodelsandserialpositionin

short-termrecognitionmemory.JournalofMathematicalPsychology,3,316-

347.

Wixted,J.T.(2007).Dual-processtheoryandsignal-detectiontheoryofrecognition

memory.PsychologicalReview,114,152-176.

Wixted,J.T.&Mickes,L.(2010).Usefulscientifictheoriesareuseful:Areplyto

Rouder,PratteandMorey(2010).PsychonomicBulletin&Review,17,436-

442.

Wixted,J.T.&Mickes,L.(2010).Acontinuousdual-processmodelof

remember/knowjudgments.PsychologicalReview,117,1025-1054.

Wixted,J.T.&Stretch,V.(2004).Indefenseofthesignal-detectioninterpretationof

Remember/Knowjudgments.PsychonomicBulletin&Review,11,616-641.

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Yonelinas,A.P.(1994).Receiver-operatingcharacteristicsinrecognitionmemory:

Evidenceforadual-processmodel.JournalofExperimentalPsychology:

Learning,Memory,andCognition,20,1341-1354.

Yonelinas,A.P.(1997).RecognitionmemoryROC’sforitemandassociative

information:Thecontributionofrecollectionandfamiliarity.Memory&

Cognition,25,747–763.

Yonelinas,A.P.(1999a).Thecontributionofrecollectionandfamiliarityto

recognitionandsource-memoryjudgments:Aformaldual-processmodel

andanalysisofreceiveroperatingcharacteristics.JournalofExperimental

Psychology:Learning,Memory,andCognition,25,1415–1434.

Yonelinas,A.P.(1999b).RecognitionmemoryROCsandthedual-process signal

detectionmodel:CommentonGlanzer,Kim,Hilford,andAdams.Journalof

ExperimentalPsychology:Learning,Memory,andCognition,25,514–521.

Yonelinas,A.P.(2001).Consciousness,controlandconfidence:ThethreeCsof

recognitionmemory.JournalofExperimentalPsychology:General,130,361-

379.

Yonelinas,A.P.(2002).Thenatureofrecollectionandfamiliarity:Areviewof30

yearsofresearch.JournalofMemoryandLanguage,46(3),441-517.

Yonelinas,A.P.,&Jacoby,L.L.(1995).Therelationbetweenrememberingand

knowingasbasesforrecognition:Effectsofsizecongruency.Journalof

MemoryandLanguage,34,622-643.doi:10.1006/jmla.1995.1028

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Yonelinas,A.P.,KrollN.E.A.,DobbinsI.G.,&Soltani,M.(1999).Recognition

MemoryforFaces:WhenFamiliaritySupportsAssociativeRecognition

Judgments.PsychonomicBulletinandReview,6,654-661.

Yonelinas,A.P.,&Parks,C.M.(2007).Receiveroperatingcharacteristics(ROCs)in

recognitionmemory:Areview.PsychologicalBulletin,133,800–832.

doi:10.1037/0033-2909.133.5.800

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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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