Psychological Review

Transcription

1 Psychlgical Review VOLUME 88 NUMBER 2 MARCH 1981 Jeren G. W. Raaijmakers University f Nijmegcn Nijmegen, The Netherlands Search f Assciative Memry Richard M. Shiffrin Indiana University A general thery f retrieval frm lng-term memry cmbines features f assciative netwrk mdels and randm search mdels. It psits cue-dependent prbabilistic sampling and recvery frm an assciative netwrk, but the netwrk is specified as a retrieval structure rather than a strage structure. The thery is labeled SAM, meaning Search f Assciative Memry. A quantitative simulatin f SAM is develped and applied t the part-list cuing paradigm. When free recall f a list f wrds is cued by a randm subset f wrds frm that list, the prbability f recalling ne f the remaining wrds is less than if n cues are prvided at all. SAM predicts this effect in all its variatins by making extensive use f interwrd assciatins in retrieval, a prcess that previus therizing has dismissed. A cue-dependent prbabilistic search thery f retrieval has been develped t perate within a retrieval structure based n an assciative netwrk. This thery, referred t as SAM (Search f Assciative Memry), has been applied t the results f studies investigating free recall, paired-assciate recall, and recgnitin. The thery is capable f fitting the results simultaneusly, with n essential change in prcesses r parameters. Raaijmakers (1979) and Raaijmakers and Shiffrin (1980) give early results supprting these cntentins. In the present article, ur gal is the delineatin f the general thery and a thr- This research was supprted in part by a fellwship frm the Netherlands Organizatin fr the Advancement f Pure Research t the first authr and Public Health Service Grant and Natinal Science Fundatin Grant BNS t the secnd authr. We gratefully acknwledge the help f Henry Rediger HI, Edward Rskam, Susan Dumais, David Fyle, Bruce Williams, and Gary Gillund, wh assisted us in the varius stages f develpment f this wrk. Requests fr reprints shuld be sent t R. M. Shiffrin, Psychlgy Department, Indiana University, Blmingtn, Indiana ugh expsitin f an applicatin t ne particular research setting. Fr expsitry purpses, we begin with a simplified mdel and applicatin and then turn t the general thery. The first sectin f the article describes a relatively simple cmputer simulatin prgram fr free recall that serves t illustrate the main features f the thery. The pwer f the apprach is then illustrated by applying the simulatin mdel t a puzzling phenmenn knwn as the part-list cuing effect (e.g., Slamecka, 1968). Sectin II f the paper discusses in detail research and thery directed tward the part-list cuing effect; Sectin III explres in depth the way in which the simulatin mdel deals with this phenmenn. It shuld be nted that the mdel presented in Sectins I and III is a precisely stated, carefully delineated, scaled-dwn versin f the general thery aimed at a limited set f paradigms. Discussin f the ratinale behind many f the assumptins, the ways in which the thery handles ther types f paradigms, the strengths and weaknesses f the apprach, and cmparisns with ther theries are reserved fr Sectin IV. Cpyright 1981 by the American Psychlgical Assciatin, Inc X/81/ $

2 94 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN I. A Simulatin Mdel fr Free and Cued Recall The general thery will be abbreviated as SAM (Search f Assciative Memry); the simulatin mdel fr free recall will be abbreviated as SAMS (SAM Simulatin). The Paradigms SAMS is develped t deal with the paradigms f free verbal recall and free recall with added cues. In free recall, a list f «wrds is presented in randm rder at a rate f t sec per wrd. Bth t and n may be varied between lists. In immediate free recall, the subject is asked t recall as many wrds as pssible, in any rder, immediately fllwing list presentatin. In this case, the mst recently presented wrds are recalled at an enhanced level (the recency effect), presumably reflecting the presence f thse wrds in a shrt-term stre. In delayed free recall, an interplated task, usually arithmetic, is interpsed between presentatin and test. The interplated task is presumed t clear shrt-term stre f the list wrds s that all recall is frm lng-term stre. Indeed, the recency effect is eliminated in this case. The part-list cuing paradigm will be described in detail in Sectin II. In brief, at the time f testing, sme f the list wrds are presented t the subject, suppsedly as helpful aids t enable recall f the remaining list wrds. The data frm such experiments are typically analyzed in terms f the number f recalled wrds r in terms f the prbability f recall (which is smetimes analyzed in terms f the presentatin psitin r the utput psitin f particular wrds). In additin, the rate f utput is ften analyzed, smetimes in terms f interrespnse times, but mre ften in terms f the cumulative number f items recalled as a functin f utput time. Shrt-Term Stre and Lng-Term Stre SAMS utilizes a tw-phase memry system (Atkinsn & Shiffrin, 1968; Shiffrin, 1975). Shrt-term stre (STS) is the temprary stre int which infrmatin abut presented items is placed and in which cntrl prcesses such as cding and rehearsal are carried ut. Lng-term stre (LTS) is the permanent stre, cntaining all prir infrmatin plus new infrmatin transferred frm STS. Retrieval frm LTS is quite fallible, as described belw. STS is limited in capacity (Shiffrin, 1976), s that nly a limited number f items may be retained, rehearsed, and cded at ne time. In particular, SAMS assumes a buffer rehearsal system perating as fllws: Each presented wrd enters STS, jining previus wrds there, until the buffer size, r, is reached. Then each new wrd entering the buffer replaces ne f the r wrds already present. The wrd t be replaced is chsen with prbability l/r. If immediate testing is used, the r items currently in the buffer are all crrectly recalled, and then retrieval frm LTS begins. If delayed testing is used, it is assumed that the arithmetic clears the buffer at the same rate that wuld have btained had the list cntinued. After a lng perid f arithmetic, the buffer will be empty f list items at test, and retrieval will begin frm LTS at nce. Strage in Lng-Term Stre What is stred in LTS are assciative relatinships between cntext and wrd infrmatin, and between a set f cntext-pluswrd infrmatin fr ne wrd and a set f cntext-plus-wrd infrmatin fr anther wrd. The frmer is termed wrd-cntext infrmatin, and the latter is termed wrdwrd infrmatin. The amunt f wrd-cntext infrmatin stred is assumed t be prprtinal t the ttal amunt f time a given wrd remains in the rehearsal buffer. The amunt f wrd-wrd infrmatin stred is assumed t be prprtinal t the ttal amunt f time thse tw wrds are simultaneusly present in the rehearsal buffer. Wrd infrmatin is infrmatin that enables the subject t prduce the name f the encded wrd. Cntext infrmatin refers t tempral and situatinal factrs that might als be present in STS at a given time, including envirnmental details, physical sensatins, emtinal feelings, and all thught prcesses nt directly relevant t name prductin.

3 Besides the strage that takes place during list presentatin, additinal strage may ccur during the lng-term retrieval prcess itself. The assumptins gverning such strage are given belw. Lng-Term Retrieval LTS retrieval is assumed t be a cue-dependent prcess perating n a retrieval structure based n an assciative memry. At each step f the search prcess, cues are assembled in STS and used as a prbe f LTS. A lcalized set f infrmatin in LTS, called an image, is sampled. The sampling prbabilities are a functin f the strength f assciatin between the prbe cues and the varius images in LTS. The infrmatin in the sampled image is then accessed and evaluated in a prcess called recvery. The prbability that enugh infrmatin is recvered t enable the name f the encded wrd t be recalled is a functin f the strength f assciatin between the prbe cues and the sampled image. In SAMS, the nly cues cnsidered are the general cntext cues, called C T, and the wrds frm the presented list, termed W, T, W 2T,... W nt. The subscript T indicates the wrd at test. A prbe set always cnsists f C T alne r f C T alng with ne f the wrd cues, fr example, (C T, W/T). The images that can be sampled cnsist f the stred infrmatin abut each f the n wrds in the presentatin list, including the cntext at that time; these are dented W 1S, W 2S,... W ns. The subscript S indicates the infrmatin as it is stred. The Retrieval Structure SAMS assumes that relatinships between the prbe cues and the images may be cmpletely summarized in a retrieval structure that gives the strengths f relatinship between each pssible prbe cue and each pssible image. This is illustrated in the matrix f Figure 1. In the figure, S(C T, W s ) represents the strength with which the cntext cue tends t sample the image f Wrd SEARCH OF ASSOCIATIVE MEMORY 95 C T 1T W nt is IMAGES ns s ( c r w ls ) s(c r w ns ) s(w 1T,w ns ) S(W nr W ls' /; SCW/T, W(s) represents the strength with P S (W /S C T ) = which Cue- wrd j tends t sample the image f Wrd /. Figure 1. The strength matrix the matrix f strengths that determine the prbabilities f selectin and recvery f list images (hrizntal margin) when varius cues (vertical margin) are used in the cue set. (Entries in the cells are strengths frm individual cues t individual images; when multiple cues are used in the cue set, then the strengths are cmbined accrding t Equatins 1 and 2 in the text. C T refers t the cntext cue; Wfr and W s refer t the Cue Wrd i and the image f Wrd /.) The strengths in this matrix are assumed in SAMS t be prprtinal t the amunts f infrmatin stred during presentatin. Let t, be the time that Wrd i stays in the buffer, and let t tj be the time that Wrds i and j are tgether in the buffer simultaneusly. Then S(Cr, W (S ) = at,; S(W,r, W, s ) = bt lf, S(W /T, W s ) = ct h where a, b, and c are parameters t be estimated. It shuld be nted that many pairs f wrds will never ccupy the buffer simultaneusly. In all such cases, a small residual strength value is assumed. In particular, if tu = 0, S(W,r, Wys) = d, where d is anther parameter t be estimated (but is presumably smaller than a, b, r c). The Sampling Rule Equatins la and Ib give the quantitative sampling rules: S(C T, W <s ) 2 S(C T, w, s ) (la)

4 96 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN Ps(W /s C T, W CT ) S(Cr. W 8 )S(WH, W, s ) = ~s - 2 S(C T, W, S )S(W, T) W, s ) In Equatin 1, P s indicates the sampling prbability. The left-hand sides f these equatins give the prbability f sampling the image f Wrd i, given that the prbe cues cnsist f C T in Equatin la, r C T and W* T in Equatin Ib. Equatin la is a simple rati rule fr strengths. Equatin Ib is a rati rule fr the prducts f strengths. This prduct rule has the effect f fcusing the search s that there is a tendency t sample images with high strengths t bth cues, rather than images with high strengths t nly ne f the cues. It shuld be nted that when at t is substituted fr the strengths in Equatin la, the a cancels, and the rule becmes a rati f rehearsal times. Hwever, when similar substitutins are made in Equatin Ib, the parameters a, b, c, and d d nt cancel (except fr special cmbinatins f values). The Recvery Rule Equatins 2a and 2b give the prbability that the subject will be able t generate the name f the wrd encded in Image /, given the cue (r cues) that made up the prbe set during sampling, and given that this recvery instance is the first fr Image / with that prbe set. In Equatin 2, P R indicates the recvery prbability. P R (W ( C T ) = 1 - exp{-s(c T, W, s )} P R (W ( C T, W w ) = 1 - exp{-s(c T, W s ) -S(W OT,W«)} (2a) (2b) These equatins essentially say that recvery prbabilities rise as the cue-t-image strengths rise. Nte that the parameters a, b, and c d nt cancel ut f these recvery equatins; in fact, these parameters may be viewed as recvery parameters. SAMS makes special assumptins when an image that has already been sampled with a given prbe set is again sampled with that same prbe set later in the search. These "cnditinalizatin" assumptins hld that the utcme f the secnd and subsequent recvery attempts will match the utcme f the first recvery attempt. In additin, if the cntext cue and any ther wrd cue tgether d nt lead t recvery f Image /, then it is assumed that any subsequent recvery attempt fr Image i with the cntext cue nly will als fail. Thus a new independent recvery chance ccurs whenever the prbe set cntains a new cue (i.e., ne nt utilized befre fr the image sampled). These assumptins represent an assumptin that successive recvery attempts f the same image with the same prbe set are based n essentially the same infrmatin. Strage During Retrieval Whenever a successful recvery ccurs, the strengths f the prbe set t the recvered image are increased. This prcess is termed incrementing and beys the fllwing rules: S'(C T, W s ) = S(Cr, W s ) + e; S'(W, T, W, s ) = S'(W A, W s ) -S(Wn,Wjs)+/; S'(W, T, W«) = S(W, T, W, s ) + g. (3) Here the primes represent the strengths after incrementing, and e, f, and g are the incrementing parameters. Tw special assumptins are made cncerning incrementing: First, any increment f a cntext t wrd strength is always linked t an increment f the recvered image's self strength. That is, the e and g increments always ccur tgether. Secnd, nly ne increment can ever take place fr any given cue-t-image strength. (See Sectin IV, Incrementing, fr further discussin.) The Search Prcess The retrieval prcess invlves an extended search that requires a series f decisins n the part f the subject cncerning what cues t use during each sampling phase and when t stp searching. The retrieval prcess in an arbitrary setting is diagrammed in Figure 2. The subject makes a plan, chses a set

5 SEARCH OF ASSOCIATIVE MEMORY 97 f prbe cues, samples and tries t recver, decides whether t stp searching, and then lps back t the retrieval plan t begin the next phase. This general system will be discussed in Sectin IV. The specific decisins and cntrl prcesses used in SAMS are given in the flw chart shwn in Figure 3. The stpping rule. A failure is defined as any sampling and recvery attempt that des nt result in recall f a new wrd. The main phase f the retrieval prcess is assumed t end whenever the cumulative ttal f failures in the search reaches a value termed A: MAX. Selectin f prbe cues. If cues are nt prvided, the subject begins by using cntext nly as a cue. This prbe set cntinues t be used until sme new wrd is recalled. Whenever a new wrd is recalled, the next prbe set cnsists f tw cues: the cntext cue and the wrd just recalled. This rule applies even when the previus prbe set cnsisted f cntext plus a different wrd. Stpping rule fr wrd cues. L M \x is the stpping criterin fr a wrd cue. If a given cmbinatin f cntext plus wrd serves as a prbe set fr LMAX cnsecutive lps f the search, and n new wrd is recalled, then the subject drps the wrd frm the prbe set and uses cntext alne. Rechecking. When the main search phase ends (when AMAX is reached), then rechecking begins. In this phase, each previusly recalled wrd (either frm the main phase r rechecking) is used alng with cntext in a prbe set. Each such prbe set is utilized until Z-MAX failures accumulate. Any new wrds recalled during this perid are saved and are used as cues during later rechecking. The ratinale fr the rechecking prcess is based n a certain arbitrariness in the assumptins cncerning selectin f cues fr prbe sets. A wrd may be recalled and used as a cue. Then it may happen that a new wrd is recalled n the very next lp f the search. Our rules require that the prbe set be changed t use this new wrd, but it culd be argued that the previus wrd cue is still f value and has nt been "used up." The incrpratin f a rechecking prcess allws us t argue that all assciative retrieval rutes have been checked thrughly, at least up t an LMAX stpping criterin. RETRIEVAL (NO) SEARCH FROM LONG-TERM-STORE QUESTION RETRIEVAL PLAN ASSEMBLE PROBE CUES IN STS SEARCH -SET SELECTION [RESTRICTION TO RELEVANT! L LTS REGION J i SAMPLING OF ITEM [/».OF AGGREGATE OF FEATURES] RECOVERY * OF CONTEXT AND ITEM FEATURES] [CONTEXT COMPARISONS] ITEM DECISIONS j TERMINATION DECISION Figure 2. A generalized depictin f the varius phases f retrieval in the thery. (STS = shrt-term search; LTS = lng-term search.) Parameters The SAMS mdel described abve is ready t be applied t the data frm freerecall studies. The parameters are a (cntext-cue-t-image strength), b (wrd-cue-timage strength), c (wrd-cue-t-self-image strength), d (residual-wrd-cue-t-image strength), e (cntext-t-image increment), / (wrd-cue-t-image increment), g (wrdcue-t-self-image increment), /sf M Ax (ttal failure stpping criterin), Z, MAX (stpping criterin fr a wrd cue), and r (buffer size). At first glance, 10 parameters seems quite a high number t fit the results frm freerecall studies, especially since Shiffrin (1970)

6 98 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN ( START J ( STOP J sample item i using cntext-cue YES increase assciatin t cntext sample item j using Item i and cntext as cues increase assciatin t cntext and t item i Figure 3. A flwchart fr Phase 1.f the retrieval prcess in the cmputer simulatin f SAMS develped fr free recall. (K and L are cunters f failures. Old r nt recvered refers t a failure t recall a new item.) used a much simpler search mdel with just three parameters t fit a great deal f freerecall data. This bjectin is amelirated by the fllwing factrs. We can shw that mst f the present parameters, and their precise values, are nt essential fr the fit f the mdel t mst f the data. The parameters are listed abve fr generality, even thugh sme are never varied and thers are equated befre fits t the data are begun. Sme f the parameters are given nnzer values and included in the fit merely t demnstrate that the presence f the prcesses they represent will nt harm the ability f the mdel t predict the data. In fact, we have set many f these parameters t zer, and n harm t the mdel's predictins has resulted. Hwever, each f these parameters represents prcesses that we feel are needed n lgical grunds, r needed t deal with data that will nt be discussed in detail in this article (see Raaijmakers & Shiffrin, 1980). The rles played by the varius parameters have been extensively explred by simulatin means, as have certain prcess assumptins, and the results f these explratins will be either summarized briefly r reprted in detail in the remainder f the article. Free-Recall Data In this sectin we will apply SAMS t free-recall data in rder t get a set f reasnable parameter estimates. A set f data particularly well suited fr the initial explratins f the mdel was cllected by Rberts (1972). Fur list lengths (10, 20, 30, r 40 wrds) and five presentatin rates (.5, 1,

7 SEARCH OF ASSOCIATIVE MEMORY 99 2, 4, r 8 sec per wrd) were cvaried. N interplated arithmetic task was used (s bth shrt- and lng-term cmpnents are assumed in recall). Bth visual and auditry presentatin mdes were utilized, but we have averaged the results fr these tw mdes. Our main cncern is average recall perfrmance fr each type f list (rather than perfrmance as a functin f serial presentatin psitin). The results are given in the upper panels f Figures 4 and 5. Clearly, mean number f wrds recalled is a negatively accelerated functin f ttal presentatin time fr a fixed list length (Figure 4; see als Waugh, 1967). Als, equal ttal presentatin times fr different list lengths d nt yield equal recall; rather, lnger lists yield mre ttal wrds recalled (Figure 4). Finally, as list length increases fr fixed presentatin time per item, ttal recall increases almst linearly, thugh with a slight hint f negatively accelerated grwth (Figure 5). The "list length effect" is als implicit in these data: The prbability f recall f a given wrd decreases as list length increases. 25 LL=40 20 LL=30 UJ OT 15 <E UJ CD O (K 10 L!_=IO UJ rr a e i LL = 30 LL=40 UJ "; 15 - O 10 LL=IO ii I i TOTAL PRESENTATION TIME (secnds) Figure 4. Observed data (Rberts, 1972; tp panel) and predictins f SAM (lwer panel) fr mean wrds free recalled as a functin f presentatin time and list length (LL). (The parameters f the mdel are r = 4; K MAX = 30; Z-MAX = 3; a = c =.10; 6 =.10; rf =.02; e =/= g =.70. These parameters are used t generate predictins in all the fllwing figures, except where indicated differently.)

8 100 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN 25 PT= PT=2.0 UJ CC LU CD ci 10 PT=I.O PT = 0.5 a(e (0 Q CK O UJ ~. 15 UJ O O PT=I.O PT= 5,0 -* PT = TOTAL PRESENTATION TIME (secnds) Figure 5. The same data are presented as in Figure 4, except that the label f each curve is presentatin time (PT) per item. Parameter Estimatin The mdel has characteristics that make analytical derivatins infeasible; it is therefre cnstructed as a cmputer simulatin prgram. Predictins are derived by Mnte Carl methds by averaging the results f large numbers f "statistical subjects." Parameter estimates are btained by generating predictins fr varius cmbinatins f parameter values and chsing the best cmbinatin. The number f simulatins (NSIM) was 300 fr the predictins shwn in the figures. Nthing like an exhaustive search was used t btain parameter estimates: Sme parameters were set n the basis f past data and mdels, sme were arbitrarily set equal t thers, and sme were varied ver small regins f values. Surely, then, the fits are nt ptimal. They are, hwever, quite satisfactry fr ur purpses. The parameter values, methds f estimatin, and sme general cmments are discussed next. Parameter r. The buffer size was set equal t 4 n the basis f previus fits t serial psitin curves and n the basis f numerus estimates f shrt-term capacity as 2.5 (see Crwder, 1976). Typical methds f estimating shrt-term capacity, such as that f Waugh and Nrman (1965), prduce values much lwer than the buffer size; it can be shwn that ur predictins, using a

9 SEARCH OF ASSOCIATIVE MEMORY 101 buffer size f 4, when analyzed accrding t the Waugh and Nrman prcedure, result in an estimate f shrt-term capacity f 2.5. It shuld be mentined als that ur mdel gives an excellent accunt f the Murdck (1962) serial psitin data when r is set equal t 4. Value f #MAX- The criterin fr cessatin f search was set equal t 30 failures. This value was chsen in part because Shiffrin (1970) fit Murdck's data with an assumptin f abut 36 samples (crrespnding t abut 30 failures). It can be shwn that the chice f stpping rule and the value f 30 are nt crucial fr predicting the qualitative and quantitative effects in the present data (nr in much ther data, as well). Of curse, if the value f XMAX is raised, predicted recall will increase slightly, but the increase may be cunterbalanced by small changes in the ther parameters. In general, XMAX is a decisin criterin, whse value may be chsen by the subject and manipulated by instructins. Value f LMAX- The number f failures f an item cue befre it is discarded and cntext nly is utilized as a cue was set equal t 3. The perfrmance changes expected as a result f changes in LMAX are fairly difficult t ascertain, especially since increases in LMAX extend the perid f rechecking. With the help f simulatins, the fllwing general prperties have been determined: When interitem strength attains values near r belw thse estimated fr Rberts' (1972) data, then a wrd cue's tendency t sample itself is fairly high, and a cntext cue alne can lead t mre efficient sampling. (This reasning des nt hld if interitem strength r residual strength is raised.) Since large values f LMAX reduce bth the number f cntext cues utilized in the search, and als the number f different wrd cues utilized, increases in LMAX tend t decrease perfrmance. This effect is cunterbalanced smewhat by the fact that recvery prbability fr wrd-plus-cntext cue sets is greater than fr cntext-nly cue sets. The net result is that, withut rechecking, increases in LMAX frm 1 t 5 have nly a small effect, a slight decrease in perfrmance. Hwever, the amunt f search during rechecking increases as L MAX increases, s in the mdel as it stands, perfrmance turns ut t be a weakly inverted-u-shaped functin f L M AX» with a maximum near 3. Thus we frtuitusly chse a value f L MAX that maximizes perfrmance. Als, it certainly is the case that extensive use f interwrd assciatins is made during the search when LMAX = 3, a desirable prperty f the mdel. The value f LMAX is a chice f the subject and may be manipulated by instructin. Parameter a. The cntext-t-image strength per secnd f rehearsal time was ne f the three estimated parameters and attained a value f.10. Sampling prbabilities are nt affected by changes in a (unless c is set equal t a, in which case wrd-cue sampling is affected because c changes; see belw). Hwever, recvery prbabilities depend directly n a. Thus a strngly influences bth the verall level f recall and the dependence f recall n presentatin time. The value f a shuld depend n the cding r rehearsal technique used, n the nature f the wrds, and n the distinctiveness f the list cntext. Parameter b. The interwrd strength per secnd f jint rehearsal time was estimated t be. 10. The value f this parameter directly influences recvery prbabilities whenever a wrd is used as a cue and an image is sampled that had been rehearsed with the cue wrd. Hwever, if a wrd cue is used, b als affects the sampling prbabilities. The reasn fr this depends n the three types f samples: It is pssible t selfsample, t sample a wrd that had nt been rehearsed with the cue wrd, r t sample a wrd that had been rehearsed with the cue wrd. As the value f b rises, the prbability f the last f these pssibilities rises. The value f b shuld depend n cntext distinctiveness t a small degree but shuld depend primarily n the ease with which the list wrds may be cded tgether. Fr example, increases in the similarity f the list wrds t each ther shuld prbably increase the value f b fr that list. Parameter c. The wrd's self-sampling strength per unit f rehearsal time was set equal t the cntext-t-wrd strength, a. The self-sampling strength gives the relative tendency fr a wrd t sample its wn image, and it seems reasnable that this tendency

10 102 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN <fl 1.0.a OS 0.6 U. 0.4 H _1 ffi PROBABILITY OF RECALL (Mdel) Figure 6. Cmparisn f the predicted and bserved prbabilities f recall, crrespnding t each f the 20 pints in Figures 4 and 5. shuld grw with rehearsal time. Setting c equal t a accmplishes this gal, but there is n real reasn t believe these parameters shuld be equal (rather than, say, linearly related). If c is raised fr fixed a, then selfsampling rises and recall perfrmance drps (thugh recgnitin perfrmance wuld rise). Fr the recall tasks t which the mdel has been fit, the value f c des nt seem t be crucial. Evidence abut the relatinship f c t a can best be btained frm recgnitin tasks, but fr the present n harm is dne by setting c equal t a. In general, we expect c and a t vary in similar ways as the experimental cnditins are changed. Parameter d. The residual interwrd strength value fr wrds nt rehearsed tgether was set equal t.02. The value was chsen n the basis f applicatins f the mdel t data frm paired-assciate paradigms (nt discussed in this article). This value is lw relative t a, b, and c, as shuld be the case. In fact, the precise value is nt imprtant fr the present applicatin: Almst identical predictins f Rberts' data are btained when d is set equal t.0, the value f a is raised t.12, and the ther parameters are unchanged. The effect n perfrmance f raising d is cmplex. Sampling will be directed away frm wrds rehearsed with a cue wrd, which culd hurt perfrmance in a cued-recall r recgnitin task. Hwever, in the present free-recall task, perfrmance is imprved slightly because mre retrieval rutes are made likely, because self-sampling is reduced, and because recvery prbability is raised. It is presumed that d reflects preexperimental factrs and shuld be higher fr wrds that are already strngly related, es-" pecially if that relatinship was frmed in a cntext similar t the test cntext. Als, factrs that affect the value f b shuld usually affect d similarly. Parameters e, f, and g. The increments in strength fllwing recall were all set equal and then estimated, attaining a value f.70. The particular value chsen is nt very imprtant fr the present applicatin. Hwever, an increase in these incrementing values des lwer verall recall levels, s they must be estimated jintly with a and b. Incrementing is included in this applicatin and set t a fairly high value t achieve cnsistency with applicatins t ther paradigms, in which incrementing is essential t predict the data (see Sectin I, Discussin). The amunt f incrementing is suppsed t reflect the amunt f attentin given t any wrd as it is recalled and after it has been recalled. Predictins fr Free Recall The predictins f SAMS with these parameter values are shwn in Figures 4 and 5 in the lwer panels. Since direct cmparisn f bserved and predicted pints is difficult in these figures, Figure 6 shws a cmparisn f the predicted and bserved pints fr all 20 cnditins. Clearly the fit f the mdel is quite adequate. Discussin Our parameter estimatin prcedures make it clear that this mdel is far mre pwerful than it needs t be t fit free-recall data. Many f the mdel's prcesses and

11 SEARCH OF ASSOCIATIVE MEMORY 103 parameters are included t deal with data frm ther paradigms that we d nt have the space t discuss here. Hwever, we will present a brief survey f certain findings that help illuminate the rles played by these prcesses. First, cnsider the search stpping criterin. One prblem with a search mdel such as that f Shiffrin (1970) was its dependence n the number f samples made frm memry: The number f samples was equated fr all lists. Perhaps such an assumptin is defensible if the recall perid is shrt and equal fr all lists. Hwever, in almst all studies the recall perid is set lng enugh that the subject ceases attempts t recall befre time expires. The present mdel incrprates a stpping criterin based n the prgress f retrieval during any given search. Furthermre, the criterin is a subject chice that shuld be alterable by the experimenter. Rediger (1978) and Rediger and Thrpe (1978), fr example, have examined bth the time curse f retrieval and the effect f instructing subjects t cntinue recall attempts beynd the pint at which retrieval nrmally ceases. In bth cases, ur mdel predicts the data with n changes in assumptins and nly minr changes in parameter values. It is wrth nting that ur assumptin f ^MAX = 30 causes recall t cease during a perid when new recalls are ccurring at a very slw rate relative t the rate ccurring earlier in the search. This cmment is supprted by the bservatin that an alternative stpping rule, in which search ceases when 12 cnsecutive failures ccur, prduces predictins almst identical t thse btained fr a rule f 30 ttal failures. Cnsider next the purpse f rechecking and the effects f this prcess n the predictins. Rechecking was included initially s that it culd be argued that the subject had exhausted all available retrieval rutes. Rechecking is nt essential t predict Rberts' (1972) data; the eliminatin f rechecking can be handled withut difficulty by increasing the value f AMAX r raising the values f a and b. Rechecking des play an imprtant rle in ther situatins, hwever. Fr example, withut rechecking, cumulative recall functins can be predicted t grw t asymptte t sharply; rechecking prvides new retrieval rutes that allw ttal recall t cntinue t grw (albeit slwly) fr lng perids f time (Buschke, 1975, Rediger & Thrpe, 1978). Cnsider incrementing next. Althugh nt really crucial fr predicting Rberts' data, this prcess is essential fr predicting a number f effects frm ther paradigms. Fr example, tw cnsecutive tests f the same list may be given, ne by the technique f free recall and ne by sme srt f cued recall (e.g., categry cues r part-list cues), in either rder. Quite large rder effects have been fund in ur wn research, and these can be explained quite well by the effects f incrementing. A smewhat smaller effect is that f test rder f categries in cued recall f categrized wrd lists. Slight drps in recall are fund fr categries that are delayed in testing (e.g., Rediger, 1973; Smith, 1971). This effect als is well predicted by incrementing. The reasn why incrementing explains these effects is straightfrward: Recall leads t incrementing that increases the sampling prbability fr the items already recalled. Interwrd assciatins and their use in retrieval are a crnerstne f SAMS, but even these are nt needed t predict Rberts' data. Such assciative rutes are needed, hwever, t predict many results, including thse cncerning paired-assciate paradigms and the effects f variatins in interwrd assciatin values. Perhaps mst intriguing is the manner in which such interwrd retrieval rutes explain the part-list cuing effect, which is discussed in the next tw sectins. Finally, cnsider the residual strengths between list wrds nt rehearsed tgether. We include such retrieval rutes in part because it seems lgical that they shuld be present. Hwever, many results shw the need fr such rutes. Fr example, if a list f wrd pairs is studied, with instructins t frm cdes fr each pair, and ne member f a pair is presented at test, recall prbability depends strngly n list length (Raaijmakers & Shiffrin, 1980). This effect is due within the mdel t the assumptin that the cue wrd is assciated nt just t the

12 104 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN respnse wrd but als, residually, t each wrd n the list. We realize, f curse, that n serius supprt fr ur present mdel can be btained frm ur fit t Rberts' free-recall data. Hwever, the applicatins t part-list cuing discussed in the next tw sectins help shw the value f the present apprach. II. Part-List Cuing A Survey f the Literature One f the mre intriguing results btained in the free-recall paradigm is the scalled "part-list cuing" effect, first reprted by Slamecka (1968). The effect is imprtant because it is cunterintuitive and seemingly incnsistent with many theries f human memry. In the prttypical part-list cuing experiment, subjects are given a list f wrds fr study and are later tested fr recall f these items in ne f tw ways: One grup f subjects, the cntrl grup, simply recalls as many items as pssible; that is, this grup is given the usual free-recall instructins. A secnd grup is given a randmly chsen subset f the list items as cues, suppsedly t aid retrieval f the remaining items. The recall by this latter, part-list cued grup f the remaining r critical items (als called target items) is then cmpared with the perfrmance f the cntrl grup n the same items. This paradigm was devised by Slamecka (1968) as a rather direct test f the rle f interitem assciatins in recall. Slamecka reasned that any thery that assumes that interitem assciatins are used in recall shuld predict that at least sme f these cues wuld facilitate recall f items that wuld therwise nt have been recalled. Failure t find recall facilitatin shuld (accrding t Slamecka) lead t the cnclusin that interitem assciatins are nt frmed during study r nt used during recall. The result that is btained quite reliably in this paradigm and in a number f variants shws that recall f the critical items is nt better fr the cued grup than fr the cntrl grup (even when shrt-term memry effects are cntrlled). In fact, there is usually a slight negative effect, with the cntrl grup shwing superir recall (Rediger, Stelln, & Tulving, 1977; Slamecka, 1969). What is surprising abut this result is nt s much the small superirity f the cntrl grup, but the fact that n reliable cuing facilitatin is fund. Mst cnventinal theries assume that during study f a list f wrds a netwrk f interitem assciatins is frmed. A mdel pstulating that the list cues simply give a number f additinal entry pints int the netwrk shuld predict a large advantage fr the cued grup. Fr example, Andersn's FRAN mdel, which makes exactly this assumptin, predicts much better critical wrd recall by the cued grup than by the cntrl grup (Andersn, 1972, p. 362). In the early experiments n part-list cuing (Slamecka, 1968), a rather large advantage was fund fr the cntrl grup. Hwever, Slamecka (1968, Experiments V and VI) shwed that this was because the cntrl grup had the advantage f being able t reprt the items still in shrt-term stre, whereas the cued grup had t prcess the list cues. When this artifact was eliminated, n significant differences were bserved between the tw cnditins. Mrever, the lack f a psitive cuing effect did nt seem t depend n the interitem assciative strength. Fr example, in ne f Slamecka's experiments (Slamecka, 1968, Experiment VI), three types f lists were used: a list f 30 rare wrds, a list f 30 cmmn wrds, and a list cmpsed f the wrd butterfly and 29 f its mst frequently named assciates. The mean number f target items recalled by the cntrl grup was 5.58 fr the rare wrd list, 7.04 fr the cmmn wrd list, and 8.50 fr the butterfly list. Fr the cued grup these means were 4.70, 6.79, and 8.97, respectively. The difference between the cued and the nncued cnditins was nt significant (F < 1), nr was the interactin between this cuing factr and the type f list (F < 1). The differences between the three lists were, hwever, highly significant. Thus, the part-list cuing effect des nt seem t depend very much n the interitem strength. Althugh the cntrl grup advantage des seem t diminish smewhat r even reverse slightly with higher interitem strength, n large psitive effect f cuing

13 SEARCH OF ASSOCIATIVE MEMORY 105 appears, even when the variatin in interitem strengths between cnditins is enugh t make ttal recall differ by a factr f nearly tw. Such a result has been thught by previus investigatrs t be at dds with the typical assciative netwrk theries^ Similar results have been reprted by a number f ther researchers. Rediger et al. (1977) reprted a cntrl grup advantage that increased slightly with the number f cues prvided. They als bserved that the advantage f the nncued ver the cued cnditin did nt disappear r reverse even when very lng recall perids were used (up t 10 minutes). Slight psitive effects f cuing (ften nt significant) have been reprted, but nly in special cnditins. Andersn (1972) and Wd (1969) reprted a very slight psitive effect after multitrial free-recall learning. In a similar experiment, Slamecka (1969) bserved a slight negative effect f cuing. Allen (1969) presented subjects with a list cmpsed f cntiguus pairs f items, which were judged t be either related r unrelated. After an initial recall fr bth grups, he cued the subjects in ne grup with ne member f each wrd pair and fund greater recall fr the cue grup, especially with related pairs. Nte, hwever, that this prcedure is quite different frm the nrmal prcedure, in which a randm subset f wrds is given as cues. The nly paradigms in which a reasnably large advantage appears fr the cued cnditin are retractive interference paradigms. Blake and Okada (1973) reprted an experiment in which subjects were given 10 study-test trials n a 6-item list, fllwed by 10 study-test trials n a secnd, interplated list. Fllwing this interplated learning they were tested n the first list. In this experiment, cuing n the final test trial did have a psitive effect. Similar results were reprted by Basden (1973). Rediger (1974) has summarized a number f experiments with categrized lists in which the number f cues per categry varied. In these paradigms, cuing may help in retrieving categries when there are t many categries in the list t be retrieved unaided, but cuing has n beneficial effect at all n within-categry recall, that is, n the number f wrds recalled per categry f which at least ne member was recalled. In fact, a slight negative effect is cnsistently fund in within-categry recall. Results cnsistent with this generalizatin have been reprted by Hudsn and Austin (1970), Mueller and Watkins (1977), Rediger (1973, 1974), Rundus (1973), Slamecka (1972), and Watkins (1975). Mrever, it is usually fund that the negative effect f cuing n within-categry recall increases slightly with the number f cues prvided (Mueller & Watkins, 1977; Rediger, 1973, 1974; Watkins, 1975). Rediger (1974, Table 1) summarized a number f experiments that shw that the higher the prprtin f items frm a particular categry that are given as recall cues, the lwer the prbability f recalling the remaining items frm that categry. Fr example, Rundus (1973) btained recall prbabilities fr the remaining categry members f.36,.34,.29, and.28 fr cuing with 1, 2, 3, and 4 categry instances, respectively. Explanatins fr the Part-List Cuing Effect The basic part-list cuing result the lack f an advantage fr the cued grup is interpreted by researchers in this area as evidence against the rle f interitem assciatins in free recall. Slamecka (1972), Rundus (1973), Rediger (1974) and Watkins (1975) assume nly vertical r hierarchical assciatins. Thus, Slamecka (1972) writes: A truly assciative thery f learning, ne which identities learning with the active elabratin and strengthening f interitem linkages, cannt, in ur pinin, cnvincingly incrprate these findings withut abandning a central feature f the term "assciatin." The unique frce f the prpsitin that A and B are assciated is that presence f A has the pwer t elicit B; that A can "pull ut" B. (p. 331) This cnclusin is shared by mst ther researchers in the area: It shuld be nted that the results... cntradict predictins f theries pstulating direct assciatins between items. If items were directly interlinked in memry, it shuld be the case that presentatin f sme items as cues wuld increase the likelihd f ther items being recalled. (Rediger, 1974, p. 265) Hwever, we will shw in the next sectin that this reasning is quite incrrect. Despite Slamecka's cntentin that the part-list cuing

14 106 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN effect shws that interitem assciatins are nt used in recall, the effect is cmpletely cnsistent with a mdel that relies heavily n the use f interitem retrieval rutes. In fact, we shall see that the effect is virtually an inevitable cnsequence f mdels like SAM. First, let us cnsider the explanatins that have been develped by therists wh have decided t abandn the rle f interitem assciatins. These explanatins have tended t pstulate hierarchical, r "vertical," assciatins in place f interitem, r "hrizntal," assciatins. Such theries have nt been wrked ut in detail, s it is nt clear hw they prpse t handle the part-list cuing effect. One hypthesis wuld assume that a retrieval path frm an item t a nde at anther level and then back t anther item at the initial level is either difficult r impssible t fllw: Thus a wrd cue at ne level will nt effectively cue anther wrd at the same level. Whatever the merits f this hypthesis fr part-list cuing, it wuld certainly have difficulties handling many standard results. These include the effects f input rder n utput rder (Andersn, 1972; Kintsch, 1970; Shiffrin, 1970) and the effects f assciability f items presented cntiguusly in the list n the level f recall (Glanzer & Schwartz, 1971). In fact, it is difficult t see hw this hypthesis wuld handle single-trial paired-assciate recall: Why shuld a stimulus cue increase the prbability f recall f the respnse member unless there exists a useful retrieval rute between the tw? Althugh all f the theries prpsed t explain the part-list cuing effect make similar assumptins in rder t explain the lack f a psitive effect, they d differ smewhat in whether they can explain, r in the way they explain, the slight negative effect f cuing and the dependence f the cuing effect n the number f cues presented. Slamecka (1972) prpsed a generatinrecgnitin accunt f categrized recall: He assumed that there is n strengthening at all during study f the categry-name-t-instance assciatins. Therefre, his thery des nt predict an effect f the number f cues prvided t the subject. In fact, it des nt predict a negative effect at all. Althugh this accrds with sme f Slamecka's data (Slamecka, 1968, 1972), Rediger (1974) has shwn that in the majrity f studies there is an increasing negative effect as the number f cues rises. Tw related theries have been prpsed t deal with this phenmenn. First, Rundus (1973) and Rediger (1973, 1974) have suggested that presentatin f the list cues invlves an implicit retrieval f these items. It is assumed that this retrieval results in a higher assciative strength f each retrieved item t the retrieval cue (the categry name). It is further assumed that retrieval invlves a sampling-with-replacement prcess, s that this strengthening f the list cues leads t a lwered prbability f sampling critical items. The mdel als includes the assumptin that in nncued recall, in which the subject first has t search fr the categry names t be used as retrieval cues, the prbability f sampling a particular categry name is prprtinal t the sum f the assciative strengths f the categry exemplars presented in the list t that categry name. Data cnsistent with this latter assumptin have been presented by Parker and Warren (1974) and Rediger (1978). This mdel culd presumably als explain the psitive effects f cuing reprted by Blake and Okada (1973) and Basden (1973) by assuming that in multitrial free-recall learning a subjective hierarchical rganizatin is frmed and that retractive interference leads t a decrease in the prbability f generating the subjective retrieval cues. Secnd, Watkins (1975; see als Mueller & Watkins, 1977; Watkins & Watkins, 1976) has prpsed a cue-verlad interpretatin f part-list cuing. Accrding t this explanatin, recall is mediated by retrieval cues that are subject t verlad: The prbability f recalling any particular item decreases with the number f instances assciated t the retrieval cue. Thus, in this case the part-list cuing effect is attributed t the usual (but in this mdel, unexplained) listlength effect. Watkins (1975) assumes that re-presentatin f the list-cues at the time f testing is functinally equivalent t presentatin f a new categry instance. This

15 SEARCH OF ASSOCIATIVE MEMORY 107 hypthesis is supprted by data f Watkins (1975) and Mueller and Watkins (1977) shwing that recall f the remaining categry instances is decreased nt nly by presentatin f list cues but als by presentatin f extralist cues, categry instances that were nt n the riginal list. Unrelated cues, hwever, have n effect n recall (Mueller & Watkins, 1977, Experiment I). Nte that this explanatin is quite similar t the ne prpsed by Rediger (1973, 1974) and Rundus (1973), if the latter mdel were mdified t incrprate the negative effect f extralist cues. Within the cntext f search theries f either the type represented by SAMS, the type described in Shiffrin (1970), r the general class discussed in Sectin IV, several explanatins shuld be cnsidered at this pint. Since recall depends n the length f the search, it is pssible t predict the partlist cuing effect simply by assuming that the subject searches lnger in the cntrl cnditin than the cue cnditin. One pssibility is t allw the stpping criterin (AT MAX in SAMS) t vary between the tw cnditins. Anther pssibility is t cunt failures in such a way that they accumulate faster in the cue cnditin. Fr example, each sample and recvery f an image frm the list f prvided cues culd be cunted as a search failure, leading t earlier search cessatin in the cue cnditin. Such mechanisms may pssibly cntribute t the bserved effect, but certain evidence makes it seem unlikely that they are perating. The main prblem is that cumulative recall as a functin f time shws a cnsistent advantage fr the cntrl cnditin, even fr times when all subjects in bth cnditins are still searching memry. This is shwn mst persuasively by Rediger et al. (1977), wh instructed subjects t cntinue attempting memry search fr a perid f 10 minutes (by which time very few new items were being retrieved by either grup). On the whle, it seems dubtful that different stpping criteria prvide a general explanatin f the part-list cuing effect. Such pssibilities are explred further within the cntext f the SAMS mdel in the next sectin. Finally, there is ne explanatin that accepts the frmatin f interitem assciatins during study. This is the editing/disruptin hypthesis prpsed by Basden, Basden, and Gallway (1977). They assume that the part-list cues disrupt any intracategry rganizatin that may have taken place during acquisitin. Since the rder in which the items are presented as cues is very unlikely t cincide with the rder in which the subject wuld recall the categry members, part-list cuing may cnstitute an interference paradigm, (p. 104) Nte that this hypthesis is still similar t the ther explanatins, since it is assumed that the interitem assciatins cannt be effectively used in recall. This particular explanatin, hwever, seems t run int difficulties when applied t the psitive cuing effects bserved by Tulving and Pearlstne (1966), wh presented categry names as cues in a randm rder, and Tulving and Osier (1968), wh presented extralist cues fr nncategrized lists. Mrever, n reasns are given why the items shuld nly be recallable in ne particular rder. In summary then, the extant explanatins have certain drawbacks, and mst f the majr explanatins agree with Slamecka's (1968, 1969) riginal cnclusin that the lack f a psitive effect f cuing prves that interitem r hrizntal assciatins play n imprtant rle in free recall. This f curse presents us with a theretical puzzle: What pssible reasn culd there be fr hrizntal assciatins nt being stred? In the next sectin we will present a mdel and an explanatin fr the part-list cuing paradigm that des utilize hrizntal assciatins and thereby eliminates this puzzle. III. Applicatin f SAMS t Part-List Cuing First, SAM will be applied t part-list cuing, with the interitem strength, b (i.e., interwrd similarity), as a variable. Then a number f factrs that d nt affect the basic predictins will be mentined and illustrated. Next we shall endeavr t explain the factrs that d cause ur mdel t predict the effect. We shall then apply the mdel t several additinal findings frm the literature, namely, the effects f number f list cues, the effect f categrized lists, and the

16 108 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN effect f varius pssible types f list cues. Finally, ur explanatins will be cmpared t thers in the literature. Assumptins f the Mdel The mdel prpsed fr part-list cuing is the SAMS mdel already fitted t Rberts' (1972) data, with a few slight changes t enable it t deal with the cued grup. An idealized paradigm is used as a basis fr the theretical develpment in which N wrds are presented fr study and fllwed by arithmetic t clear STS. The cntrl cnditin is nrmal free recall. In the cue cnditin, M wrds randmly chsen frm the list are presented t the subjects at the start f recall. The subjects are tld t utilize the M wrds as cues t help them recall as many f the remaining (N M) wrds as pssible. The mdel fr the cntrl cnditin is the SAMS mdel that was fitted t Rberts' study and has the same parameter values except that STS recall is nt allwed, since the arithmetic task clears STS. The assumptins fr the cue cnditin are identical except fr a few special assumptins that apply at the start f recall t take the list cues int accunt. We are f curse careful nt t make any assumptins that will intrduce an advantage r disadvantage fr the cued grup fr trivial reasns (such as an assumptin that the cued grup used a smaller value f A^MAX t determine when t cease searching). Als, we are careful t treat the list cues in the cue cnditin, which are prvided by the experimenter, in the same way as the self-generated cues in the cntrl cnditin. In particular, it is assumed that the subjects act in accrd with the instructins and utilize the list cues during the search. At the start f recall, each list cue is used in turn as a retrieval cue alng with cntext. Each such cue set is used until Z-MAX failures are reached, and then the next list cue is used, and s frth. During this phase, the subject des nt use any recalled wrds as cues, but instead saves them fr later use. In rder nt t intrduce a disadvantage fr the cue grup, the first successful recvery f the image f any list cue, whether due t selfsampling, cntext sampling, r wrd-pluscntext sampling, is nt cunted as a failure (see Sectin II, Explanatins fr the Part- List Cuing Effect.) Only recveries f the image f a list cue after the first are cunted as failures. This assumptin is cnsistent with the retrieval assumptins fr the cntrl grup, since any wrd's first recvery is a success fr that grup. The usual incrementing and cnditinalizatin assumptins apply during this phase f retrieval fr the cue grup. When the list cues have each been used fr LMAX failures, and if AT M Ax has nt yet been reached, then the subject begins nrmal search, just as at the start f recall in the cntrl cnditin. This cntinues until a criterin f AT MAX ttal failures f any kind is reached, at which time Phase 1 f the search ends fr bth grups. Fllwing the AT MAX stpping pint, bth grups carry ut a final rechecking in which all successfully recvered wrds are used as cues. Thus, recvered list cues are utilized during this phase, but unrecvered list cues are nt. (This last assumptin ensures that the cue grup receives n advantage due t an artificially extended rechecking perid. Alternative rechecking assumptins will be discussed later.) During rechecking, the usual assumptins apply, just as in the mdel described earlier. Predictins f SAMS fr the Part-List Cuing Effect We nw turn t the predictins f the mdel. We assume that using a highly similar list f wrds (as in Slamecka's "butterfly" list) is equivalent in ur mdel t using a high value f the interitem parameter, b. Presumably, semantically similar items are easier t encde tgether. Therefre we derived predictins fr six different cnditins that differed nly in the values assigned t b. These values ranged frm very lw t very high, as shwn in Figure 7. Presentatin time was set t 2 sec per item, list length was set t 30, the number f cues in the cue cnditin was set t 15, and all ther parameters were thse used in the fit t Rberts' data (the residual strength, d, was set in each

17 SEARCH OF ASSOCIATIVE MEMORY 109 cnditin t ne fifth f the value f the interitem strength, b; this was the rati fr the b and d values in the fit t Rberts' data). NSIM was set equal t Figure 7 gives mean critical wrds recalled fr the cuing and cntrl cnditins fr each f the six values f interitem strength. The predictins are interesting in tw respects. First, the cntrl cnditin has a small but systematic advantage ver the cuing cnditin. Secnd, the size f the cntrl grup advantage is fairly cnsistent ver the range f interitem strength values, decreasing slightly with higher values f b. Nte that ttal recall rises frm abut fur t eight items ver this range f values f b withut much altering the part-list cuing effect. Of curse, this pattern f results is very similar t that fund by Slamecka (1968; and see the discussin in Sectin II. f this article). Nte especially that extensive use is made f the assciative pathways between wrds, which is indicated by the fact that predicted recall almst dubles ver the range f interitem strengths in the figure. Certainly, then, the part-list cuing effect cannt be used t argue that interitem assciatins are either nt stred r nt used in retrieval. An imprtant fact abut the mdel that needs t be emphasized and kept in mind thrughut the fllwing sectins is that the cntrl grup advantage in Figure 7 ccurs in spite f a fairly large factr that aids the cue grup. The mdel incrprates a recvery rule which insures that the prbability f recvery fllwing sampling f an image with a wrd-plus-cntext cue set will be higher than when that same image is sampled with a cue set cnsisting f cntext nly. Since the cue cnditin utilizes relatively mre wrd-plus-cntext cue sets and less cntext-nly cue sets, it achieves a cnsiderable advantage, This is seen mst clearly when the recvery prbabilities fr wrdplus-cntext and cntext-nly sets are equated. As a demnstratin, we replaced the recvery equatins in SAMS with a single prbability f recvery,.75, which applied regardless f the cntext set used r the strengths invlved (the usual cnditinalizatin rules abut successive sampling f 111 tr 10 6 s cc. 4 cntrl x * cued INTERITEM STRENGTH PARAMETER Figure 7. Predictins f the part-list cuing effect fr an idealized paradigm as the interitem strength parameter, b, is varied. (List length is 30; number f cues is 15; presentatin time per wrd is 2 sec; d is set t equal.26. Other parameters are as in Figure 4. These values hld fr the fllwing figures, unless indicated differently. Fr each strength value, the cntrl cnditin is slightly superir, a pattern f results similar t thse f Slamecka [1968].) the same image still applied). All ther features f the mdel remained as in Figure 7. When this was dne, the cntrl grup advantage rse by abut.5 items. The imprtant implicatin f this finding is that all the predictins we shall be discussing in the fllwing sectins are ccurring in the presence f a recvery factr aiding the cue grup. Thus even predictins f equality f the cntrl and cue cnditins, which will ccur in several variatins belw, are actually indicating the peratin f substantial factrs favring the cntrl cnditin (since fr equality t ccur, the cue cnditin recvery advantage must be vercme). Factrs That D Nt Explain Part-List Cuing Ineffectiveness f wrd-plus-cntext searching. Cnsider first whether searching with wrd cues plus cntext cues is superir t searching with cntext nly. The answer may be seen mst clearly when rechecking is eliminated frm the mdel. The predictins fr such a case are presented in Figure

18 110 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN UJ : 10 O CC O cntext nly cntext + item INTERITEM STRENGTH PARAMETER Figure 8. Predicted wrds recalled in the cntrl cnditin, withut rechecking, fr nrmal search as a functin f interitem strength (slid line) and fr search with cntext cues nly (dashed line). 8. Fr bth cnditins nrmal free recall is assumed (n list cues are used). The cntextplus-wrd cue curve uses Rberts' parameters and shws hw ttal recall depends n the value f the interitem strength, b. The cntext-nly cnditin assumes that all samples are made with cntext nly. The results shw that the pssibility f wrd-plus-cntext sampling causes recall t be superir at high values f b, but the reverse is true at lw values f b. This is t be expected, since lw values f b will result in wrd cues sampling themselves (since c = a) rather than ther list items. The tw cnditins are abut equal fr b near the value estimated fr Rberts' data. Hwever, this factr evidently has nthing t d with the part-list cuing effect, since the part-list cuing effect is stable and almst equal ver the same range f b values that prduces the large differences in Figure 8 (cmpare with Figure 7). Incrementing. The prcess we have termed incrementing has been prpsed as an explanatin f the part-list cuing effect. It is pssible that the list cues becme strngly assciated t the search cues, particularly cntext cues, during the initial phase f the search. Then the later search tends t sample list cues t the detriment f critical items. Explanatins f this general srt have been prpsed by Rundus (1973), by Rediger (1973, 1974; see als Rediger et al, 1977) and, albeit differently phrased, by Watkins (1975). Since incrementing is built int ur mdel, culd it be accunting fr the effect? Figure 9 shws a set f predictins just like thse in Figure 7, except all the incrementing parameters have been set t zer. Clearly, verall recall is increased when incrementing is eliminated, but the advantage f the cntrl cnditin is unchanged. Thus the SAMS incrementing prcess and the part-list cuing effect are virtually independent within this mdel. The reasn is that incrementing has equally deleterius effects n the cue and cntrl grups. (The effect f incrementing the list cues befre retrieval begins will be discussed later.) It shuld be nted that Crwder (1976) mentins that incrementing is nt needed within a search mdel t explain the partlist cuing effect. This predictin was derived in the cntext f a mdel assuming that all retrievals f list cues (including the first) are cunted as failures an assumptin we d nt make. Withut this assumptin, his line f reasning is invalidated. The chice f stpping rule. Cnsider variatins in ur assumptins abut the stpping rule. In the first variatin, we changed the criterin frm "#MAX ttal failures" t "A^MAX cnsecutive failures." Figure 10 is cmparable t Figure 7, except that the cnsecutive failure rule is used, with K MA % = 10. Clearly, the chice f stp rule has little t d with the part-list cuing effect. Next, fr bth types f stpping rules, varius values f AMAX were tried, since it might be argued that SAMS' predictins nly hld true when UJ tr CO a a: p a. ^_ cntrl x cued _f INTERITEM STRENGTH PARAMETER Figure 9. Recall as a functin f interitem strength. (Predictins use the same mdel as Figure 7, but all incrementing is deleted [e =/= g =.0].)

19 SEARCH OF ASSOCIATIVE MEMORY 111 UJ 10 d g 8. tr «. cntrl x--x cued INTERITEM STRENGTH PARAMETER Figure 10. Recall as a functin f interitem strength. (Predictins use the same mdel as Figure 7, except that the ttal failure stpping rule fr Phase 1 f the search has been changed t a cnsecutive failure stpping rule, with KMA.X = 10 cnsecutive failures.) searching ceases quickly (i.e., t sn). Figure 11 shws the predictins fr varius values f.kmax fr the ttal failure rule, with b set t.10. Clearly the effect and its magnitude are independent f the stpping criterin. (Similar results btain fr the cnsecutive failure rule.) Nte that fr LM\X = 3 and KM AX > 45, all the list cues are used in Phase 1 f the search. The fact that sme are skipped fr AMAX = 30 makes very little difference. Despite the predictins in Figure 11, ne might still be cncerned that stpping criteria are respnsible in sme way fr the effect. Thus in Figure 12 we deleted the stpping rule, and simply graphed cumulative recall fr bth grups as a functin f the ttal number f samples made. (It is assumed that rechecking takes place every 100 samples; withut rechecking, very little additinal recall fr either cnditin wuld take place late in the search, since mst images wuld have been sampled t the cntext cue at least nce.) It is clear that recall increases at a rapidly decreasing rate, even with rechecking. The cntrl grup retains its advantage thrughut, althugh the difference decreases. Rediger et al. (1977) btained results smewhat mre like Figure 11 than Figure 12, which perhaps suggests that their subjects emplyed a stp rule with a large criterin, but it must be admitted that bth figures wuld fit their pattern f results quite well. The chice f prbe cues. It may be nted that the search assumptins fr the tw cnditins differ slightly, since the cntrl grup is assumed t switch cues at nce whenever a new wrd is recalled, whereas the cue grup uses each experimenter-prvided cue until L MAX failures accumulate. In fact, if each time a wrd is recalled, the cue grup is made t mve n at nce t the next list cue, the tw cnditins becme virtually equal. Cnversely, if the cntrl grup is frced t stay with each wrd cue until L MAX failures accumulate, saving all recalled wrds fr later use, whenever AT M AX is reached, then again the tw cnditins becme almst equal. In neither case, hwever, is there a cue grup advantage. Assumptins differing fr the tw grups. Several assumptins can be made that will favr ne cnditin r anther fr the rather bvius reasn that the tw grups are treated differently. Fr example, assuming that all recveries f list cues are failures causes the cued cnditin t reach AMAX mre quickly than the cntrl grup. The advantage f the cntrl grup naturally increases with this assumptin (by abut.15 wrds). Cnsider anther example: If all list cues, whether recvered r nt, are used in rechecking, then the cued grup spends mre UJ <r tr UJ 10 cntrl x cued m STOPPING CRITERION (KMAX) Figure II. Recall as a functin f stpping criterin. (Predictins use the same mdel as Figure 7, but with interitem strength b =.10.)

20 112 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN UJ a: 01 D S NUMBER OF SAMPLES cntrl cued Figure 12. Cumulative critical wrds recalled as a functin f ttal number f samples. (Predictins use the same mdel as Figure 7, but with interitem strength b =.10 and stpping rule deleted. Rechecking ccurs every 100 samples.) time rechecking than the cntrl grup and naturally gets an advantage frm this fact (the cued grup nw gets an advantage f abut.5 wrds). Even withut this assumptin, rechecking tends t favr the cued grup very slightly. When rechecking is eliminated altgether, the cntrl grup advantage increases by abut.40 wrds. The lessn frm the manipulatins that have been tried seems clear: If we remve every pssible simple factr that might favr the cntrl grup, apart frm the basic structure f SAMS itself, but retain factrs that favr the cue grup, such as a recvery advantage when a wrd cue is added t cntext, and a new chance t recver whenever a new cue is used t sample a previusly unrecvered image, at best we bring the cued grup up t the level f the cntrl grup. There are clearly sme fundamental, inherent characteristics f the SAMS mdel that prduce the part-list cuing effect. These are cnsidered next. mystery is remved when it is realized that bth the cntrl and cue cnditins invlve extensive cuing by wrds. Self-generated cues are utilized in the cntrl cnditin, whereas experimenter-prvided cues are utilized first in the cue cnditin. The extensive interitem assciative cuing in bth cnditins tends t make verall perfrmance in the tw cnditins quite cmparable. This reasning suggests that when the ability t generate cues, using cntext, is pr, the cntrl grup will be inferir. Figure 13 shws the predictins as a, the itemt-cntext strength, varies. At very lw values, there is a cnsiderable advantage fr the cued grup (since the cntrl grup can seldm recall anything using cntext alne), but as a increases in value, the usual partlist effect quickly appears and even grws smewhat. One might expect, then, that a cuing advantage culd be experimentally prduced simply by chsing a task in which cntext-t-item strengths are lw at test, that is, a task in which nrmal free recall wuld give very lw perfrmance levels. Such reasning culd well explain the psitive effects f cuing bserved by Blake and Okada (1973) and Basden (1973) in a retractive interference paradigm. The selectin f list cues. In rder fr the part-list cuing effect t be seen, it is extremely imprtant that the subject be given a randm sample f items frm the list as cues. Otherwise, the cues may turn ut t UJ O An Explanatin f the Part-List Cuing Effect By nw, the reader must be wndering which factrs are respnsible fr SAMS' predictin f the part-list cuing effect. Interwrd cuing in the cntrl and cue cnditins. First and fremst, much f the CC O ITEM-TO-CONTEXT STRENGTH PARAMETER Figure 13. Recall as a functin f item-t-cntext strength parameter (a). (Predictins use the same mdel as Figure 7, but interitem strength b =.10 and c = a.)

21 SEARCH OF ASSOCIATIVE MEMORY 113 be extremely useful. It is true in the mdel and has been fund empirically that cues cnsiderably increase the recall f thse wrds that are strngly assciated t the cues it is the ther wrds whse retrieval is harmed (Rediger, 1978). This is nicely illustrated in a study by Twhig (Nte 1). Twhig presented subjects with a list f categries that were each cmpsed f fur pairs f assciated wrds. Subjects in the cued grup were given tw wrds (nt frm the same assciated pair) frm each categry as list cues. There was n psitive effect f cuing, averaging ver all critical items in a categry. Hwever, the cnclusin that the interitem assciatins were ineffective wuld be quite inapprpriate, since the cues did lead t a substantially higher prbability f recall fr the items paired with the cues. This psitive cuing effect was, hwever, cunterbalanced by a negative effect n the recall f the ther categry members. In fact, this reasning suggests that cued recall culd be quite beneficial if the experimenter culd arrange t prvide ne gd cue frm each f the subjective "grupings" that the subject has stred in memry. This is easiest t demnstrate when a categrical structure is built int the list. In this case, cuing with ne wrd frm each categry is very beneficial (due t mre categries' being accessed; see Slamecka, 1972; Tulving & Pearlstne, 1966). This factr can als help explain Allen's (1969) finding that cuing was helpful when the cues cnsisted f ne member f each f a number f wrd pairs judged t be related. Hwever, if the wrd cues are selected randmly (i.e., withut regard t the categrical structure), then there is n increase in recall (Kintsch & Kalk, Nte 2). Such results are a prblem fr thse therists wh use the part-list cuing effect as evidence against the rle f interitem assciatins in recall. Similar reasning applied t these results shuld lead them t the cnclusin that in such experiments hierarchical r vertical assciatins were nt used, an assumptin that prbably nne f them wuld like t embrace. Clearly, then, apprpriate selectin f cues can lead t an advantage r disadvantage, depending n the basis fr selectin. In the studies under cnsideratin, hwever, Figure 14. A. simplified assciative netwrk fr a 12- wrd list stred as fur triads. (The six experimenterprvided cue wrds have images dented by Q. The six remaining critical items are dented by I. The arrws dente assciatins between images. Each image has an assciatin t cntext, which is nt depicted. A cntext sample can access a triad rich in critical items [e.g., the triple-i triad]. The cue-wrd-plus-cntext samples can nly sample triads relatively impverished in critical items, since each such triad must cntain at least ne cue.) randm cue selectin was used. Given that this is the case, an explanatin fr the cuing deficit needs t be established. We turn t this explanatin next. The effect f assciative clustering. The strngest and mst crucial factr favring the cntrl cnditin depends n the nature f sampling frm a subjectively clustered assciative netwrk. It can be shwn that the cntrl grup's sampled clusters will be relatively richer in critical items than the cued grup's sampled clusters (mst f which will cntain at least ne cue wrd). The basic idea is illustrated in simplified frm by the assciative netwrk depicted in Figure 14. It is assumed that the wrds are interassciated in grups f three (triads), with all ther interwrd assciatins being negligible. It is further assumed that sampling f an image frm a triad leads that member and immediately thereafter, bth ther members f that triad t be recalled. During a fixed perid f time, assume that the cntrl and cued grups sample an equal number f different triads (a simplificatin fr the sake f the argument). The cued grup's sampled triads will all cntain a minimum f ne cue wrd and hence a relatively small number f critical wrds. The

22 114 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN O ID O UJ : V) cc. O cntrl x x cued 10 a STRENGTH VALUE Figure 15. Recall as a functin f strength value. (Predictins use the same mdel as Figure 7, but all entries in the test matrix at the start f retrieval are set equal t the same value, which is shwn n the hrizntal axis; thus r, a, b, c, and d are nt used. Nte the sizeable advantage fr the cued cnditin.) cntrl grup's sampled triads, n the ther hand, will ften cntain n cue wrds and hence be relatively rich in critical wrds. Thus the retrieval structure frces the cued grup t retrieve mre list cues than the cntrl grup at the expense f retrieval f critical items, the measure n which the tw grups are cmpared. Keep in mind that fr this simplified example, we assumed that bth grups sample an equal number f different triads and hence recall an equal ttal number f wrds. If instead we assumed that an equal number f triads were sampled, including resamples, then it is clear that mre different triads wuld be sampled and hence mre ttal wrds wuld be recalled in the cntrl cnditin. This factr wuld increase the size f the cntrl grup advantage even further. In general, then, the cuing prcedure leads t a sampling bias fr the cued grup. The cued grup is mre likely t sample list cues than critical items, whereas the cntrl grup is unbiased with respect t the tw types f items. This sampling bias is s strng that it evidently can vercme ther factrs that aid the cue grup, with the net effect that a higher number and prprtin f critical items is recalled by the cntrl grup. Nte that this explanatin des nt require that the subgrups in the structure be nnintersecting. A buffer prcess, fr example, tends t prduce high interwrd strengths in a regin lying athwart the upper left t lwer right diagnal f the strength matrix (Figure 1). This degree f gruping is sufficient fr the present explanatin t cntribute substantially t the part-list cuing effect. In additin t this sampling factr, there are a number f secndary factrs that als cntribute t the cntrl cnditin advantage. One f these is a psitive crrelatin that exists between a wrd's cntext strength and interwrd strengths. Such a crrelatin is prduced by a buffer prcess but seems reasnable fr any sensible strage system. (Nte, hwever, that the SAMS buffer prcess des nt lead t a particularly strng crrelatin.) That the crrelatin des cntribute t the cntrl grup advantage is easy t demnstrate: in each simulatin, after strage and befre retrieval (fr bth cnditins), the set f cntext-t-image strengths in the tp rw f the strength matrix f Figure 1 is randmly permuted. When this is dne, the advantage f the cntrl grup is eliminated, and bth cnditins are abut equal. Nte that bth reasns fr the superirity f the cntrl cnditin depend n the develpment and use f a nnunifrm interwrd retrieval structure. It is rather remarkable that the reasn fr the cue cnditin disadvantage in SAMS is the presence f the very assciatins that previus therists have tried t rule ut. Additinal evidence supprting ur explanatins f the part-list cuing predictin in the mdel may be btained by eliminating the structure in the test matrix. The test matrix was hmgenized by setting all strengths in the matrix equal t each ther. In this case, bth lines f reasning described abve were invalidated, and we expected a cue cnditin advantage due t its higher recvery prbability. In fact a large advantage fr the cue grup appeared, as shwn in Figure 15. Similar results, thugh nt quite as extreme, were btained simply by

23 SEARCH OF ASSOCIATIVE MEMORY 115 raising the residual strength (represented by d) in the basic mdel. As the residual strengths apprach the interwrd strengths, the gruping structure tends t be lst. One final pint shuld be emphasized. Fr the cntrl grup t d well, especially at high interwrd strengths (see Figure 8), it is necessary that an apprpriate mixture f cntext-nly sampling and wrd-plus-cntext sampling be utilized. Cntext-nly sampling may tend t lcate many clusters in memry but will nt tend t retrieve efficiently the members f thse clusters. Furthermre, the sampled wrds will tend t be mre difficult t recver than when wrd cue strengths have been added t the cntext strengths. On the ther hand, reducing cntext sampling t a minimum als reduces perfrmance, since new clusters may nt be fund and inefficient wrd cues may be utilized ver and ver withut success. Althugh the mixture f cue sets used in the mdel may nt ptimize perfrmance fr the cntrl cnditin, it prbably cmes reasnably clse. It ges withut saying that the cue cnditin des nt utilize an ptimal sequence f cue sets. SAMS predicts that much better perfrmance in the cue cnditin culd be prduced if searching went n fr a perid withut cnsidering the prvided cues at all, and then the cues were utilized during a rechecking perid (see Allen, 1969, and An Applicatin f SAMS t Delayed Cuing belw). Applicatins f SAMS t Studies Varying the Number f Cues T btain predictins, we again imagined an idealized situatin in which a 30-wrd list was presented and the number f wrds presented as cues was varied. It is easiest t cmpare the results when they are tabulated in terms f the prbability f critical wrd recall (since ttal critical recall naturally depends n the number f critical wrds in the list). The bjectin might be raised that ^MAX can be reached befre the prvided cues are all utilized and that the number f such unchecked cues will grw with the number f prvided cues. T eliminate this pssibility, LMAX was reduced t 2 and KMAX raised t 50, s that all prvided cues wuld CC Q 1 a: v t CO CO \.43 h \ NUMBER OF CUES Figure 16. Prbability f recall as a functin f number f experimenter-prvided cues. (Predictins use the same mdel as Figure 7, with interitem strength b =.10, MAX = 2, and KMAX = 50.) always be utilized in Phase 1 f the search. The ther parameters were kept the same as in the fit t Rberts' data. Predictins are shwn in Figure 16, which gives the prbability f critical wrd recall as a functin f the number f cues prvided. Clearly, the mdel predicts a slight but almst linear decrease in recall as the number f cues increases. We have nt explred the parameter space, but the magnitude f the decrease can presumably be cntrlled by chices f parameter values. In the research literature, the effect f the number f prvided cues is nt entirely clear when uncategrized lists are used. Slamecka (1968) fund little effect, but Rediger et al. (1977) did shw an increasing deficit fr the cued cnditins as the number f cues increased. It is pssible that subjects d nt always use the prvided cues, and firm instructins t read, study, and use the prvided cues may prduce this effect. An Applicatin f SAMS t Delayed Cuing Allen (1969, Experiment 2) presented pairs f wrds half related, half unrelated. After an initial perid f 5 minutes f r-

24 116 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN dinary free recall, the cued grup was given list cues, ne frm each pair. In the case f related pairs (high interwrd strength), the mdel predicts, and the data shw, a substantial advantage fr cuing. Allen als fund a small cuing advantage fr the unrelated pairs. T simulate this situatin, we ran the uncued free-recall prgram until a criterin f AMAX = 45. Then in the secnd phase, the cued grup used each f the 15 list cues until a criterin f LMAX = 3 was reached; the cntrl grup was simply cntinued free recall until an additinal 45 failures accumulated. N rechecking was used. Fr Rberts' parameters, ttal predicted recall was higher fr the cued grup by.7 wrds, which was similar t Allen's findings fr unrelated wrds. Within SAMS, there are several reasns why delayed cuing shuld be helpful. Fr ne thing, if there are any clusters f wrds nt yet accessed, the list cues might prvide entries t these clusters. Mst imprtant, hwever, are the new chances at recvery that the list cues prvide. Late in any extended search, mst images have been sampled by the cntext cue, and few new wrds are being recalled t serve as new wrd cues. On the ther hand, many f the (delayed) list cues may nt have been recvered yet. When these are used fr sampling, they will prvide new independent chances f recvery fr images that were sampled earlier with ther cues but nt recvered. Allen's study prvided evidence fr this view. The list cues were separated int tw classes: thse that had been recalled in the immediate free-recall perid and thse that had nt. The unrecalled cues were far mre effective. An Applicatin f SAMS t Part- Categry Cuing Many f the studies f part-list cuing have utilized lists f categries f items and have varied the number f wrds presented as cues frm each categry. In additin, sme f the studies have presented ther types f cues. Applying SAMS t such paradigms invlves essentially n new principles; in a sense each categry is treated as a separate list, s mst f the predictins f the preceding sectins hld true. A precise descriptin f the applicatin f SAM t the categry case des invlve a few additinal assumptins, hwever, s these shall be described very briefly. It is assumed that each wrd image stred cntains categry infrmatin and each categry label can be used as a prbe cue (in much the same way, cntext is part f each image and can be used as a prbe cue). In general, a given categry cue will have strng strength values t wrds in that categry and weak residual strengths t wrds in ther categries. In mst studies the subject is tld what categry t recall at a given pint in the search, s we assume that the prbe set will cnsist f the cntext cue, the categry cue, and pssibly a wrd cue, if a wrd has been recalled frm LTS r prvided by the experimenter as a cue. Three kinds f experimenter-prvided cues shuld be distinguished: intralist cues, wrds frm the list in the t-be-recalled categry; extralist cues, wrds nt n the list but frm the t-be-recalled categry; and extracategry cues, wrds that may r may nt have been n the list but are nt frm the t-be-recalled categry. Watkins (1975) and Mueller and Watkins (1977) bserved a negative effect f bth intralist and extralist cues but n effect f extracategry cues. The versin f SAM fr this case was develped and applied by Bruce Williams f Indiana University. It was assumed that the categries are blcked at input and that the usual buffer strage prcess perates, except that wrds frm different categries are nt rehearsed tgether (n interwrd strength is stred when wrds frm different categries share the buffer). Instead, all wrds in different categries were given a cmmn, small, residual strength. Wrds frm the same categry but nt rehearsed tgether were given a (pssibly different) small residual strength. Categry-t-wrd strengths were a linear functin f the time a wrd frm that categry stayed in the buffer, and categry-t-wrd strengths fr wrds in ther categries were set t a small residual value. Finally, extralist cues were assumed t have a small residual strength t the categry label and t list wrds in that categry but negligible strength t wrds in ther cate-

25 SEARCH OF ASSOCIATIVE MEMORY 117 gries. All nnlist wrds were assigned a residual self-strength (which culd be fairly high) and a residual cntext strength. Retrieval f the list items frm a given categry was assumed t perate in essentially the same way as fr a nncategrical list. Bth cntext and categry cues were used fr every sample. If a nncategry wrd was sampled, it culd be recvered but was nt utput, was nt incremented, and was cunted as a failure. In all ther respects retrieval prceeded as fr the nncategrized case, except there was n rechecking (when the mdel was applied with rechecking, n imprtant changes in predictins resulted). Fr the cued cnditins, the retrieval assumptins were again the same as befre, als with the prviss f this paragraph. Since it did nt seem apprpriate t fit the categrized case with the parameters fr Rberts' data, we used the task and data frm Watkins (1975, Experiment 1) and adjusted parameters rughly until a fit was btained. The predictins and data fr the cntrl cnditin, the intralist cue cnditin, and the extralist cue cnditin fr bth tw and fur cues are shwn in Figure 17. Clearly these predictins are quite adequate. One imprtant mispredictin was btained, hwever. The mdel was applied t the extracategry cue cnditin f Mueller and Watkins (1977) and predicted a cntrl cnditin advantage f abut the same size as thse shwn in Figure 17 fr the ther cue cnditins. The data shwed n such deficit, even thugh the prvided cues had been presented n the list in ther categries. We suggest that subjects given wrds frm categries ther than the categry being tested will be very reluctant t use these as cues. Furthermre, we suggest that the predictins f SAMS wuld turn ut t be crrect, if nly the subjects culd smehw be induced t use these extracategry cues. A test f this pssibility must await further research. It is mst interesting t nte that despite the large number f parameters available in this categry case, we culd nt find any cmbinatins f values that wuld allw the predictin f the bserved extracategry finding while simultaneusly predicting the ther findings (unless assumptins are < Q : i n u. 00 < CD O tr Q. I.U n -. 8 NO CUES --C3 OBSERVED PREDICTED ' 9= *~~^9' INTRALIST CUES. v v - EXTRALIST CUES NUMBER OF CUES Figure 17. Predicted and bserved prbabilities f critical wrd recall in a categry fr the cntrl cnditin and fr the intralist and extralist cue cnditins, each with tw r fur cues (data frm Watkins, 1975). (The mdel is described in the text; parameters are list length = 36; wrds per categry = 6; presentatin time per wrd = 3 sec; r = 4; K MAX /categry = 12; L MM = 3; a = c =.38; b =.38; item-categry strength per sec =.38; categry-cue and list-wrd-cue residuals t wrds n list =.1; all increments =.36; residual strength f extralist cues t list items in same categry =.03; and prduct f residual strengths when self-sampling an extralist cue = 2.2.) changed between cnditins). SAMS quite persistently prduced a part-list cuing effect in the extracategry cnditin whenever ne was predicted fr the extralist cnditin. Thus we must nt in this instance cnfuse number f parameters with testability. (Actually, the values f mst f the parameters d nt affect the qualitative predictins.) 1 ' The explanatins in Sectin III fr the cuing deficit clearly d nt apply in the case f extralist cues, since an extralist cue is nt part f any stred cluster. The deficit in the extralist case results frm tw factrs:

26 118 JEROEN O. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN Cnclusins and Cmparisns With Other Mdels SAMS predicts essentially all the phenmena f part-list cuing. It des s rbustly under virtually all cmbinatins f assumptins and parameter values and in fact cannt be made t predict the extracategry cuing result fr this reasn. Mst imprtantly, the basis fr SAMS' predictin f the part-list cuing effect is the presence and utilizatin within a search thery f the very interwrd assciative netwrk that previus therists have argued cannt be present r cannt be utilized. In shrt, it is prpsed that extensive use f wrd cues is made in bth the cntrl and cue cnditins and that the sampling superirity fr the cntrl cnditin utweighs the advantage during recvery f the cue cnditin. The cntrl cnditin superirity is rted in the nature f sampling frm a netwrk f (verlapping) clusters f wrds. When experimenter-presented cues are utilized, there is a tendency t gain access t clusters cntaining mre critical items in the cntrl cnditin than is the case in the cue cnditin. The reader may wnder why we have expended s much effrt in this sectin explring the predictins f the mdel under alternative assumptins. It may seem that we are studying the wrkings f the mdel as much as the wrkings f the subject. There is sme truth in this bservatin. In fact, we have attempted t deal with a prblem that Smith (1978) has termed "the sufficiency/transparency trade-ff." The prblem is that as a mdel becmes mre and mre cmplex and gains pwer t fit the data, it becmes increasingly paque t the external bservers (even the mdel's creatrs). The general principles are lst in the frest f details that such theries cme t cntain. Our present mdel is less cmplex First, an extralist cue has a high prbability f sampling its wn image, since it is nly weakly cnnected t list wrds. Secnd, because the extralist cues are weakly cnnected t list wrds, incrementing will have a disprprtinately large effect, causing later searches t resample with high prbability any wrd recalled earlier. These factrs d nt apply in the usual case f intralist cuing. than many; in fact, SAMS may be written in tw pages f FORTRAN cde. Even s, the basic principles underlying the predictins f the part-list cuing effect wuld be virtually impssible t ascertain, were we t present nly the general mdel and the predictins. Our slutin t the prblem in this instance was an extensive search f the "assumptin space" f the mdel. The fact that SAMS predicts the part-list cuing effect des nt invalidate ther hyptheses that have been prpsed. Even if SAMS is basically crrect, ther factrs might be adding t r subtracting frm the size f the effect. Hwever, it shuld be kept in mind that if a SAM-like apprach is adpted, these ther hyptheses are nt needed t handle the effect. Let us cnsider briefly sme f these alternative prpsals. The pssibility that incrementing f the cntext-t-cue strength takes place when each cue is first used is certainly wrth cnsidering (see Rediger, 1973, 1974; Rundus, 1973). We added this factr t SAMS t see what additinal advantage fr the cntrl grup wuld result. In particular, when each cue was first utilized in a sample, it was given an increment t cntext (the same increment that nrmally applies). Everything else in the mdel remained as befre, and the predicted cntrl grup advantage increased by less than.05 wrds. Thus this factr cntributes relatively little when added t SAMS (thugh it might be mre pwerful if the cue increment were higher than nrmal r in a different type f mdel). There are many fairly trivial ways t prduce a cntrl grup advantage, sme f which are nevertheless plausible and wrth cnsidering even within the cntext f a SAM mdel. Fr example, the cntrl grup might search lnger than the cue grup. This wuld happen if every recvery f a cue, even the first, cunted as a failure. Then the cue cnditin wuld reach K M \x much sner than the cntrl cnditin. One difficulty with this explanatin is the fact that it predicts a strng dependence n the number f cues. Additinal cues d harm recall, but nly t a slight degree (e.g., Rediger, 1974; Slamecka, 1968, 1972; Watkins, 1975). In any event, it is nt knwn what search

27 SEARCH OF ASSOCIATIVE MEMORY 119 strategies subjects adpt; if subjects are induced t search lnger (that is, cntinue despite mre failures) in ne cnditin than anther, ur mdel clearly predicts a crrespnding perfrmance change. If a large value f AMAX is used fr the cued cnditin, the amunt f extra searching needed t significantly raise recall fr the cntrl cnditin can be quite large (since new items are hard t recall after a lng time searching). Thus the differential in the #MAX values might have t be quite large, perhaps t large t justify. Nevertheless, the pssibility f differential stp rules in the different cnditins cannt be ruled ut. We cmment merely that such hyptheses are unnecessary and inelegant. A smewhat different explanatin within the cntext f a search thery wuld pstulate that self-generated wrd cues (in the cntrl cnditin) are mre effective than the experimenter-prvided cues f the cue cnditin fr the fllwing reasn: A retrieved image may cntain wrd plus studycntext infrmatin, whereas a prvided cue may cntain wrd plus test-cntext infrmatin. Therefre the retrieved wrd cues may have higher strengths t the ther wrds in strage than the prvided cues. Higher strengths culd lead t higher prbabilities f recvery fr sampled images. Such a factr culd indeed lead t a cntrl grup superirity. Whether this is an imprtant factr is anther questin. Presumably, the retrieved cue advantage nly ccurs t the extent that the retrieved study cntext prvides infrmatin nt already in the general cntext cue. Hwever, a subject might well accumulate study-cntext infrmatin as the search prceeds and incrprate it int the cntext cue. If s, the difference between a retrieved cue and a prvided cue might be minimal, except pssibly fr the first few lps f the search. In cnclusin, we admit that a difference in cue effectiveness due t cntext retrieval might be cntributing t the part-list cuing effect. Hwever, such an assumptin is nt needed fr SAMS t predict the effect, as we have seen. A prpsed explanatin f part-list cuing that has received cnsiderable interest is the hypthesis that "vertical" r hierarchical, assciatins but nt "hrizntal," r interitem, assciatins are stred in memry (e.g., Rediger, 1973, 1974; Rundus, 1973; Slamecka, 1972). We are nt really sure hw this hypthesis predicts the part-list cuing effect, unless retrieval paths between items n the same level f analysis are nt allwed t traverse ther levels f analysis, a hypthesis easy t rule ut. In any event, there is nthing wrng with vertical r hierarchical assciatins, and they are already part f SAMS, as in the categrized recall situatin. It is the absence f hrizntal, interitem, assciatins that seems unusual. There seems little pint in ruling ut interwrd assciatins, since the success f SAMS shws this hypthesis t be unnecessary. Cnsider, finally, the "cue-verlad" hypthesis (Watkins, 1975), which prpses that the cues act mre r less as additinal list items r categry items, thereby reducing perfrmance fr the same reasn that wrds in lnger lists are recalled mre prly (whatever that reasn is). This effect presumably perates despite the tempral and cntextual separatin f the list cues frm the list. In sme ways this hypthesis is like the cue-incrementing hypthesis discussed abve, since bth extra items and increments fr cues serve t reduce sampling prbabilities fr critical wrds. On the ne hand, SAMS prvides a detailed and accurate accunt f the list length effect (see the fit t Rberts' data); n the ther hand, SAMS des nt need t psit a lengthening f the list r incrementing (see Figure 9) t explain the effects f part-list cuing. Nevertheless, a list length factr culd quite pssibly be cntributing smething t the bserved effect. Why have previus assciative netwrk mdels (e.g., Andersn, 1972; Andersn & Bwer, 1973) had difficulty predicting the part-list cuing effect? Althugh they d include item search alng assciative pathways, they fail t utilize a randm search. Thus, many items in the cntrl cnditin may nt be reached because entry pints t memry are limited. Furthermre, all items that can be reached (within certain limits) frm the list cues will be retrieved, and there is n cst invlved in ding s. There is n build-up f failures nr a stpping rule based n such a build-up. These assumptins are

28 120 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN f curse sensible when a directed, nnrandm search is pstulated, since the search is assumed t prceed serially with n real prvisin fr resampling f previusly fund items. Thus search simply prceeds until all recallable items have been fund. The present thery, n the ther hand, des incrprate the ntin f csts invlved in retrieval. Thus the subjects are given a reasnable basis fr cessatin f search, even thugh ptentially recallable items remain in memry. We have shwn that a sensible stpping rule applied equally t bth cnditins, n matter hw strict the stpping criterin, can give rise t a cue cnditin inferirity. The basis fr SAMS' slutin fr the part-list cuing puzzle is the cmbinatin f an assciative netwrk (as represented in a retrieval structure) with a cue-dependent prbabilistic sampling apprach. Guiding Principles IV. The SAM Thery A number f general cnsideratins are precursrs f the SAM thery. 1. Lng-term memry is effectively permanent, with additins allwed, but nt deletins. As a crllary, frgetting is a result f retrieval failure. 2. Lng-term memry is a richly intercnnected netwrk, with numerus levels, stratificatins, categries, and trees, that cntains varieties f relatinships, schemas, frames, and assciatins. Rughly speaking, all elements f memry are cnnected t all thers, directly r indirectly (thugh perhaps quite weakly). 3. Memry retrieval is cue dependent. What image is elicited frm memry is determined by the prbe cue utilized at that mment (Tulving, 1974). 4. Memry retrieval is nisy and hence prbabilistic. A given set f cues has sme chance f eliciting frm lng-term memry any assciated image (thugh fr many images the prbabilities may be extremely small). Furthermre, successive use f the same prbe cues may well result in the elicitatin frm memry f different images. 5. Tempral-cntextual infrmatin is f fundamental imprtance; its rle in strage and retrieval must be delimited carefully and explicitly. Overview SAM assumes a partitin f memry int unitized images. These images are the bjects in memry that may be sampled during a memry search. Images may be quite cmplex infrmatin structures and may verlap cnsiderably with ne anther. An image is defined by a prperty f unitizatin: At a given stage f the memry search, the infrmatin recverable frm memry is limited t that in sme ne image. The basis fr retrieval is assumed t be the strength f assciative relatinships between prbe cues and memry images. These are described within a retrieval structure that is a matrix f retrieval strengths frm each pssible cue t each pssible image. The strengths determine the tendency fr a given prbe cue t elicit a given image when lngterm memry is prbed with a given set f cues. A retrieval structure is nt a strage structure; it is usually much simpler. Hwever, the retrieval structure is designed t capture thse aspects f the strage structure that are imprtant fr retrieval. Many images, especially thse f imprtance in labratry tasks, are rganized with respect t tempral-cntextual infrmatin. In such tasks, cntextual infrmatin will always be ne f the cues used t prbe memry. Other cues, such as item and categry names, may be used as cues in additin t cntext. A quantitative rati rule is psited in SAM that determines the prbabilities f sampling each image, given any number f cues in the prbe. When an image is sampled, sme f the infrmatin in the image becmes available t the subject fr evaluatin and decisin making. The prprtin f such infrmatin recvered is determined by the retrieval strengths between cues and image. Retrieval is assumed t cnsist f a series f search and recvery peratins rganized by a retrieval plan. The plan may be altered as search prceeds. It is used t determine what cues are utilized at each stage f the search and t make certain decisins, such as when t terminate the search. Retrieval

29 SEARCH OF ASSOCIATIVE MEMORY 121 als includes a rapid initial phase, called sensry cding, that takes place when new infrmatin is presented. This phase is largely autmatic, usually cncludes within several hundred millisecnds, and generally results in the accurate retrieval f features that are representative f the input in any cntext (including lw level cdes and a certain amunt f semantic r type infrmatin). Our main cncern in this article is with memry search fllwing the sensry cding phase. The Units f Lng-Term Memry The cnceptin f lng-term memry as a richly intercnnected system raises immediate prblems fr memry therists. It wuld be impractical and inadvisable t think f memry as a single cmplex bject. On the ther hand, the bundaries f "bjects" in an intercnnected system are bund t be imprecise. It is cmmn, fr example, t think f a wrd as an bject when analyzing traditinal memry paradigms invlving wrd lists. Hwever, such an bject cnsists f a cnstellatin f related cncepts and elements including everything frm shapes, sunds, phnemes, and letters, thrugh parts f speech, synnyms, and meaning, thrugh cdes, sentences, and cnversatins and stries that might have cntained that wrd, t the tempral-cntextual setting in which the wrd was presented and pssibly ther wrds presented at abut the same time. All f these may frm part f the "bject" designated as a wrd. Yet all f the elements that make up an bject will themselves be assciated, t sme degree, t ther elements nt in the bject. In such cnditins, an bject's bundaries are bund t be smewhat fuzzy, at best. A secnd prblem that makes it difficult t partitin memry int bjects is "level." If subjects are presented with and asked t remember letters frm the alphabet, then letters might be the basic level f the infrmatin in each bject. In ther tasks, single bjects culd cmprise wrds, sentences, paragraphs, stries, r pictures. A third prblem depends n the structure f memry. Suppse fr example, that a prtin f memry is rganized as a hierarchical tree. Shuld the entire tree be treated as a single bject, shuld the individual ndes be defined as the bjects, r shuld sme intermediate partitining f the tree be defined as the bject structure? The answer is far frm bvius and may even differ frm ne task t anther. Despite these prblems, it is bth necessary and desirable t partitin memry int bjects; in SAM this is dne thrugh the cncept f utilizatin. It is pssible t distinguish bjects with imprecise bundaries by assuming that intercnnectins between elements will be strnger and mre numerus within ne bject than between bjects. When retrieval frm memry ccurs, a set f elements may be activated, which is thught f as entry int shrt-term stre. Shrt-term stre is limited in capacity (Shiffrin, 1976), and unitized sets f infrmatin presumably require less capacity. Thus it may be easy t maintain elements f ne bject in an active state, but difficult t maintain the same number f elements if they are spread amng several bjects. We assume fr this reasn that retrieval perates n ne bject at a time. The infrmatin recvered frm lng-term stre during ne lp f the search prcess will be a subset f the infrmatin in ne bject. (Hw the bject is selected will be discussed later.) The unitized bjects f lng-term memry are hencefrth termed images (n visual representatin is implied). Hw des unitizatin ccur? The mst imprtant factr is the encding and rehearsal prcess. The infrmatin and structure that are simultaneusly in shrt-term stre underging cding and rehearsal, whether cmpsed mainly f letter, wrd, sentence, r stry infrmatin, tend t be stred as a unitized entity. Of curse, simultaneus presence in a rehearsal buffer is nt sufficient fr a unitized entity t be frmed. The nature and amunt f cding and rehearsal will help t determine whether a unitized image develps. A unitized memry bject will frm mst easily when the inputs t shrt-term strage cnsists f already unitized memry entities. This will be the case with wrds, say, r nursery rhymes. In such cases, nly the present cntext wuld have t be cmbined with the previus im-

30 122 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN ages in rder t prduce a unitized image fr the current situatin. These assumptins imply that there is a gd chance that new images will frm when the same item is repeated in different cntexts r is repeated in a similar cntext but cded in a new way. It shuld be kept in mind that the varius images in memry will, in general, verlap cnsiderably, in the sense that the subcmpnents f ne image may be the subcmpnents f ther images as well. Fr example, sentences might be stred as the images in memry, even thugh the same wrds may appear in mre than ne sentence. In such cases, the images as a whle are quite distinct, even if the subcmpnents are nt. Nte that ne f the mst imprtant subcmpnents that helps t distinguish images frm each ther is the tempral-cntextual infrmatin that is stred within each image. When an image is frmed by the additin f tempral-cntextual infrmatin t preexisting images, it can be described as episdic in Tulving's (1972) terms r as a tken in Andersn and Bwer's (1973) terms. Such images will tend t be retrieved selectively when ne f the cues is an apprpriate cntext cue. Nte that the frmatin f the new image (e.g., hrse + cntext) des nt remve r replace the previus image (hrse) frm memry. Whether that previus image was episdic (hrse + sme previus cntext) r semantic (hrse + n particular cntext), it will still remain in memry. Such reasning is cnsistent with ur general view that new inputs t memry are additive but nt subtractive. Of curse, images can be frmed that have n particular cntextual basis these are usually called semantic images r types. Hw are they frmed? One pssibility arises when the cntextual cding is weak r ineffective. Fr example, in tasks where meaning rather than setting is emphasized, the supplementary infrmatin stred with the wrd in the new image might be semantic in nature rather than time r situatin specific. In additin, features that almst always are present when an input is repeated in different cntexts will tend t becme part f the feature set that is autmatically retrieved during sensry cding. Sensry cding will be discussed later. Are the bjects f memry, nce frmed, fixed and invilable frever? One alternative answer is that bjects are partitined with respect t a given set f prbe cues used in retrieval; different prbe cues culd result in a change in the level and bundaries f the bjects. Fr example, stries might be presented and stred as images, but a later recgnitin test fr individual wrds might lead the subject t desire t tap memry at the wrd level, rather than the stry level. It is pssible that the partitining f memry int bjects depends t sme degree n the chice f prbe cues. Hwever, the tasks and situatins t which we are currently applying SAM (r SAMS) d nt seem t require this assumptin. In any event, selectin f images at different levels culd be accmplished by judicius selectin f cues. It shuld be understd that there may be nly a slight and subtle distinctin between, say, tw wrds plus cntext as a unitized entity and tw wrds, each with cntext, as separate entities cnnected by an assciatin. There are differences, hwever, that are ptentially testable in the cntext f ur sampling and recvery assumptins. After sampling f a unitized tw-wrd image, all f the available infrmatin frm bth wrds wuld be used fr decisin making, with n need fr further search. On the ther hand, when ne f tw separate wrd images is sampled, nly the infrmatin in that image is recvered. Recvery f infrmatin frm the ther image wuld require further searching (perhaps with the first wrd as an additinal cue), which might nt succeed even when the between-image assciatin is quite strng. SAMS assumed fr simplicity that all images were single-wrd units (with apprpriate intercnnectins) and predictins were quite accurate. In ther tasks, the assumptin f multiwrd units might prve necessary. In summary, the intercnnected lng-term system is assumed t be cnstituted f a class f relatively unitized images. These images may be intercnnected in extremely cmplex ways: in netwrks, hierarchies, and with varius types f relatins. Furthermre, a given image will tend t have a cmplex infrastructure. An image has the fllwing imprtant prperty: When sampled in a mem-

31 SEARCH OF ASSOCIATIVE MEMORY 123 ry search, recvery f the available prprtin f its infrmatinal cntent ccurs directly, withut a need fr further memry search with the same prbe cues. Strage Structures Versus Retrieval Structures Because ur main interest lies in the develpment f a retrieval thery, very few assumptins will be stated cncerning the interimage structure. Our aim is t develp an apprach t retrieval that can be used fr as wide a class f strage structures as pssible. T d this, we intrduce the cncept f a retrieval structure cnsisting f retrieval strengths between the pssible cues (images and their subcmpnents) and the images in memry. The strength determines the tendency fr a given cue t sample (i.e., elicit) a given image and shuld be larger the lnger that the cue and image were cded r rehearsed during strage. This strength des nt necessarily have t depend n the type f interimage cnnectin that was cded. Fr example, daisy and rse presented in a list might be cded thrugh the relatin bth are flwers, thrugh visual images f each in a vase, thrugh cnnectin t a superrdinate nde r cntrl element such as flwers in list, r indirectly thrugh a chain f assciatins between intermediate ndes r intermediate list wrds. It is nt necessary that rse as a cue be mre likely t elicit the image f daisy in ne f these cases than the ther. In each case, the retrieval strength (and hence the sampling tendency) wuld be determined by factrs such as the effrt and duratin expended in cding and the type f cding carried ut (e.g., rte rehearsal vs. mnemnics). Fr the purpses f sampling, then, the memry structure need nt be taken int accunt explicitly (see Andersn, 1976, p. 154), as lng as the images and cues t be placed in the retrieval structure are chsen judiciusly (e.g., n the basis f the subject's cding strategies), and the cue-t-image strengths are chsen sensibly (e.g., n the basis f the effrt, type, and duratin f cding). The freging discussin shuld nt be taken t imply that the interimage structure is irrelevant fr retrieval. The interimage retrieval strengths shuld reflect the actual interimage structure clsely, s that even sampling culd be said t cnfrm t the stred structure in this sense. Mre imprtant, the details f the between-image relatins, whether relatins, labeled assciatins, r anything else (see Andersn & Bwer, 1973; Kintsch, 1974; Nrman & Rumelhart, 1975), are part f the infrmatin cntained in each sampled image. This infrmatin, when recvered, will help t determine varius decisins, evaluatins, and recnstructins; the recvered features culd als be used as additinal cues during later stages f the memry search. A gd example was the applicatin f SAMS t categrized free recall: Categry membership was stred in each image, and categry cues were used in the cue sets. Lng-Term Retrieval A SAM retrieval thery is rganized by a retrieval plan that gverns the successive sampling and recvery peratins frm a retrieval structure. Learning during retrieval is termed incrementing, and the initial, rapid retrieval when new infrmatin is input is termed sensry cding. These varius cmpnents are discussed in the fllwing sectins. Except where indicated t the cntrary, it will be assumed fr simplicity that the partitining f lng-term stre int images des nt change with different cues. The retrieval plan. All decisins and cntrl prcesses invlved in retrieval are subsumed in the retrieval plan. The rganizatin f retrieval is an extensin f that prpsed by Shiffrin (1970). Retrieval is a memry search prceeding in series f discrete steps. Each step invlves a prbe f lng-term stre by ne r mre cues, which results in a briefly activated set f infrmatin, which is fllwed by a selectin, r sample, f an image frm that set. The substages within any ne step are depicted in Figure 2. Retrieval begins with sme questin the subject needs t answer regarding the cntents f lng-term stre. This may be as simple as: What is anther wrd n the list mst recently presented? In the mst general case, a retrieval plan is generated t guide the search fr the answer. Initially, the plan may

32 124 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN be smewhat vague by intentin, in the hpe that later phases f the search will be guided by infrmatin lcated in earlier phases. The plan includes such things as an initial decisin whether t search lng-term stre; hw t search (fr instance, in a tempral rder r by an alphabetic strategy); hw t chse prbe cues (fr instance, shuld recalled infrmatin be used as prbe cues?); what cmbinatins f prbe cues shuld be emplyed and with what weights; whether t emply the same prbe cues n successive lps f the search r whether t alter the cues; whether t search first fr preliminary cues t guide later search; and hw lng t search (i.e., hw many lps f the search prcess shuld be carried ut). The retrieval plan itself is cnstructed n the basis f the infrmatin in the test query, the infrmatin currently available in shrt-term memry, and infrmatin retrieved frm lngterm memry; this infrmatin retrieved frm lng-term stre may be cncerned with search plans, previus successful plans in similar situatins, and s frth. Once cnstructed, the retrieval plan is als stred in LTS. We assume in the cntext f the tasks discussed in this article that retrieval f the plan itself is easy and accurate, but there culd be cases where this assumptin is vilated. Simple retrieval plans that might plausibly be used in free-recall tasks were discussed in Sectins I and III. In general, hwever, little is knwn abut retrieval plans, and their explratin may well becme an active research area in the near future. (See Williams, 1978, fr a discussin f retrieval plans.) Next, n the basis f the retrieval plan, the subject assembles prbe cues t be used in retrieval. These cues may include: (a) infrmatin the subject has abut the cntext at the time f study, (b) cntext representative f the mment f test (althugh these cues may nt be useful r desired), (c) infrmatin frm the test questin, (d) infrmatin retrieved earlier in the search, and (e) infrmatin generated during cnstructin f the retrieval plan. After prbing LTS, the cumulative activatin might be utilized as a basis fr a recgnitin decisin. If search des nt stp at this pint, then the infrmatin recvered frm the sampled image is evaluated. The decisins invlved depend n the task but might include the fllwing: Des the image derive frm an item n the presentatin list? What is the name encded in the image? Is the encded name an apprpriate respnse t the cue? Des the encded name match the test cue? Des the encded infrmatin hld the prper relatinship t the prbe infrmatin? Is any f the recvered infrmatin useful fr later phases f the search? At this pint the subject may r may nt decide t emit a respnse. Then a decisin must be made whether t cntinue the memry search. Presumably the decisin t terminate is based n the previus successes r failures up t that pint. Fr example, in free recall a decisin t stp might ccur when m successive searches ccur with n new wrds recalled. If the search cntinues, the search lps back t the retrieval plan where the next prbe set is chsen, and s frth. The changes in prbe cues as the search cntinues are quite imprtant. Althugh sampling is a randm prcess, it is easy t misinterpret such a statement and ascribe mre randmness t the retrieval system than is, in fact, present. The strengths may be such that ne image is far mre likely t be selected than any ther. Even mre imprtant, the subject can cntrl the search by changing the prbe cues as needed. Systematic changes in prbe cues may nt lead t rapid cnclusin f a memry search but may be quite effective nnetheless. Fr example, when a subject is asked t recall a United States city starting with the letter^", 2 ne strategy wuld invlve searching with state-name cues, ne at a time, generated systematically in gegraphic fashin. The retrieval structure. A retrieval structure is a matrix f the strengths between the pssible prbe cues and the varius memry images. It is a generalizatin f the strength matrix shwn in Figure 1. The cues may be labeled Qj,... Q M) the images I,,..., I m, the strengths S(Q,, I,). In thery, all pssible cues and images are cntained in the structure, but in practice, mst f the structure is irrelevant. Typically, therefre, the matrix is restricted t images and cues ' Xenia, Ohi.

33 SEARCH OF ASSOCIATIVE MEMORY 125 that are task specific. In SAMS, fr example, the images and cues were restricted t cntext, list wrds, and categry names. The cues and the images in a retrieval structure are generally quite distinct even when they each encde nminally equivalent infrmatin (e.g., the same wrd). Fr example, suppse hrse has been placed in lng-term memry at the time f study, and then a recgnitin test is given with hrse as the test item. We argue that the image and the test cue are quite distinct, the image cnsisting f hrse at study + study cntext and the test cues cnsisting f hrse at test + test cntext (the encdings f hrse may differ in the tw instances, perhaps rcking vs. running). It is assumed that the lng-term memry image and the prbe cues are separate and identifiable entities, s that if the memry image is sampled, it may be evaluated alne r cmpared with the prbe cues. Hwever, these tw entities will usually be strngly assciated due t their large pl f cmmn infrmatin; it is this fact that makes it likely that the cue hrse will cause the image hrse t be sampled. When an image and cue encde the same nminal infrmatin, the cue is termed a test analgue f the image. Nte that the similarity f an image t its test analgue used as a cue can be greater than is the case in the example abve, if the cue is itself retrieved frm memry during a previus lp f the search. The reasn is clear: The cntext in the cue in this case wuld be mre similar t that at the time f strage, since sme f it wuld have been retrieved. Such a cue might als have higher strengths t ther images in memry. Such reasning suggests that the retrieval structure shuld cntain tw types f cues whenever cues are prvided by the experimenter ne type cnsisting f retrieved cues, the ther, prvided cues. Althugh such reasning is crrect in principle, it may be excessively pedantic in practice. Presumably, a ratinal subject accumulates and utilizes all relevant cntextual infrmatin as he prceeds in the search. As a result, with the pssible exceptin f the first few samples frm memry, the difference between prvided cues and retrieval cues may be small. T generate a retrieval structure fr a particular setting (rather than the theretically infinite-size structure), ne wuld begin by chsing an apprpriate cding mdel t apply during strage. The strage assumptins determine what type f images frm and with what prbabilities. The cues are generally chsen t represent the test analgues f the set f images that have been frmed, alng with the natural subcmpnents f thse images (particularly the cntext cmpnent). Additinal cues are placed in the matrix if they are prvided by the experimenter. Thus, fr example, if sentences are presented, the images will all cntain cntext infrmatin; sme might als cntain sentence cncepts and thers might instead cntain fragments f these, including perhaps single-wrd cncepts. The cues will then cnsist f the test analgues f thse images and their subcmpnents. The strengths in the retrieval structure depend n the assumed strage prcess, n preexisting assciatins and relatins in frce befre strage and at test, and n changes in cntext between strage and test. The strength determines the tendency with which a given cue tends t elicit a given image during sampling (and als determines the amunt f infrmatin recvered frm the infrastructure f a given image). The mre the infrmatin in a cue matches the stred infrmatin in an image, the greater is the strength. Thus the lnger tw wrds are rehearsed tgether, the greater the strength between ne f the wrds when used as a cue and the image f the ther wrd. On the ther hand, as the time between study and test increases, r as the similarity f the cntext at study t that at test decreases, the between-wrd strength shuld decrease. Fr list wrds that were nt rehearsed tgether, the strength (thugh lw) will depend t a greater extent n extra-experimental factrs and shuld be affected less by delay and cntext change. In summary, the retrieval structure is nt meant t be a cpy f the stred memry structure. Rather, the retrieval structure may be thught f as a scaled simplificatin that captures aspects f the strage structure that are relevant fr cue dependent sampling.

34 126 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN The sampling prcess. All SAM retrieval theries assume the same sampling prcess. In wrds, an image has a prbability f being sampled that is determined by the assciative strength relating the set f prbe cues t the image in cmparisn with the strengths relating all ther images t the set f prbe cues. Mre precisely, given a retrieval structure, the prbability f sampling Image i, given cues Q,, Q 2,..., Q m in the prbe set, is given by PsUlQ,, Qa,,. (4) A few wrds f explanatin are useful t aid understanding f Equatin 4. First, nte that this equatin is an extensin f the Luce (1959) rati rule (mst ften applied t chice behavir). This is mst evident when there is nly a single cue and w- 1.0, in which case Equatin 4 becmes S T (Q, I,)/2 S T (Q, I*)- This special case was als * the basis fr the Shiffrin (1970) search thery. In Equatin 4, the Wj are weights representing the saliency f the y'th cue, r the attentin given the jih cue. 3 In SAMS, the Wj were all set t 1.0, regardless f the number f cues (thugh n mre than 3 cues were ever used tgether). Because STS is limited in capacity, there surely is a limit n the number f prbe cues that can be utilized at ne time, and a limit n the amunt f attentin that can be distributed amng the varius cues. Such limitatins culd be captured in any f several restrictins placed n the Wj. One pssibility is a limit, W, n the sum f the weights: fr all m. (5) The SAMS mdel wuld be cnsistent with this restrictin if ff were at least 3. A smewhat different assumptin psits a fixed capacity: =W, fr all m. (6) The pssibilities f Equatin 6 and f the use f nnunitary weights are f mre than academic interest. If weights are always equal t 1.0, then the similarity r verlap amng cues is nt prperly taken int accunt. T see this, cnsider an example f extreme similarity amng tw cues: The cues are identical. Substitutin int Equatin 4 shws that the use f tw identical cues, say A and A, des nt give rise t the same sampling prbabilities as the use f A alne. This lgical difficulty culd be handled by relaxing the assumptin that all weights are unitary. Fr example, the weight given t a cue culd be reduced by a factr representing the cue's verlap with ther cues. Alternatively, the prblem culd be handled by adpting Equatin 6. In this case, A and A tgether wuld give rise t the same sampling prbabilities as A alne. The SAMS simulatin wrked successfully despite letting all weights be unitary. We suspect the reasn lies in the chice f cue sets: They were always made up f dissimilar cues. 4 Aside frm the weights, the sampling rule assumes that the prducts f the strengths f the cues t an image are used in the rati rule. Such a prduct rule allws the search t be fcused n images that are strngly cnnected t all the cues, rather than just ne f the cues. One might think that it wuld generally be advantageus t cmbine as many cues as pssible in each prbe set t fcus the search as narrwly as pssible. Even when the weights are all 1.0, hwever, s that recvery imprves with additinal cues, this is nt necessarily the case. One prblem is the tendency fr sampling ne f the images f the cues themselves; this tendency culd well be disadvantageus in certain recall tasks. Fr example, in the SAMS applicatins t part-list cuing, we saw that ne factr inhibiting free recall (fr bth cnditins) was excessive reliance n wrdplus-cntext cues, cmpared with the cntext cue alne. Furthermre, there are var- 3 Nte that ur use f a multiplicative rule requires the weights t appear as expnents. If they were multiplicative factrs, they wuld simply cancel ut f the sampling equatin. 4 The assumptin f Equatin 6 wuld change the SAMS simulatin. We have nt yet explred this alternative mdel and d nt knw whether the predictins wuld change in imprtant ways.

35 SEARCH OF ASSOCIATIVE MEMORY 127 ius dangers invlved in fcusing a search t narrwly, since a desired image may be missed. Finally, the use f multiple simultaneus cues may be restricted by capacity limitatins such as thse described by Equatins 5 and 6. Mst f the images in lng-term memry have such lw retrieval strengths t the cues that their sampling prbabilities will be vanishingly small. The relatively small set f images with nnnegligible sampling prbabilities is called the search set. It is therefre cnvenient (especially when incrprating the mdel in a cmputer simulatin) t separate the sampling phase int tw parts: first, a restrictin t the search set; secnd, an apprpriate prbabilistic chice frm the search set. The chice f search set is generally determined by task cnsideratins. Fr example, if a subject is asked t recall a just-presented list, the search set might be assumed t cnsist f the images f all the wrds in that list (r perhaps f all the wrds in the sessin, if intrusin predictins are desired). Of curse the mdel shuld always specify a search set cntaining the images that might be sampled. If there is reasn t believe that images are sampled that are nt in the search set specified by the mdel, and relevant predictins are desired, the search set shuld be expanded t include the additinal images. Recvery. When lng-term memry is prbed by a set f cues, a fairly large cllectin f infrmatin in many images is very briefly activated. The ttal amunt f such activatin (and the relative activatin f different images) is determined by the strengths in the retrieval structure fr the cues that are used. The activatin f this infrmatin is equivalent t the placement f the infrmatin int shrt-term stre (STS). Because STS is limited in capacity, it is incapable f retaining very much f the activated infrmatin fr mre than a shrt time, perhaps a few hundred millisecnds. SAM assumes, therefre, that infrmatin frm just a single image is retained lng enugh that the subject can make a detailed evaluatin during that lp f the search prcess. Fr a given set f cues, the recvery assumptins first must determine the amunt and type f initial activatin. Then, when an image is sampled, the recvery assumptins must determine the amunt and type f infrmatin that can be extracted frm that image. The ttal amunt f initial activatin is prbably prprtinal t the denminatr in Equatin 4; it can be viewed as a feeling f familiarity and culd cnceivably be used t make a recgnitin judgment withut further search. Detailed infrmatin is nt available, hwever, until recvery frm a sampled image ccurs. Thus, in tasks such as recall, in which the details f the infrmatin are a prerequisite fr a respnse, nly the recvery frm sampled images is relevant. The prcess f recvery is assumed t be nisy and imperfect, s that nt all f the elements f an image will be activated. In general, the strnger the retrieval strength between the sampled image and the prbe cues, the larger will be the prprtin f image elements that will be recvered and made available t the subject's evaluatin and decisin making mechanisms. In SAMS, the same retrieval strengths that determine sampling prbabilities are used t determine the prprtin f recvered elements. In general, hwever, these strengths might nt be equal; their relatinship will depend n the respnse requirements f the task. Once infrmatin is recvered, it is evaluated and used in decisin making and t generate respnses. In practice, it is ften cnvenient t cmbine the recvery prcess and the subsequent decisins int a single equatin. Cnsider, fr example, a task in which the sampled images are wrds. In such a case we prpse the fllwing equatin t give the prbability that a sampled image, i (that has nt previusly been sampled), can give rise t an accurate prductin f the name f the encded wrd, when Q,,..., Q m are the cues: P R (I,IQ,, Q:, - - -, QJ m = 1 - exp{- 2 H>,S(Q,, I,)}. (7) j-i This equatin was utilized in SAMS, with the Wj all set t 1.0. The frm f this equatin is smewhat arbitrary mathematically, thugh it des capture a number f features we cnsider desirable fr a recvery rule in this case.

36 128 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN First, the strnger the strength is t any ne cue and the strnger the summed strengths are t all cues, the mre likely recall is. Secnd, the larger a cue weight is, the mre the strength t that cue will affect recall. Nte that this prductin rule beys an additive rather than multiplicative rule, s that recall will be high if even ne weighted strength is high. Third, the prbabilities will range frm 0 t 1 as the sum f the strengths ranges frm 0 t. It shuld be nted well that in this system, the recvery prbabilities are determined by strengths frm cues t image, nt by image strength. Image strength per se des nt in fact exist in the system. Undubtedly, the names f cmmn wrds are well encded in numerus images in lng-term memry. Whether the name can be generated in respnse t the cues (including cntext) is the nly relevant questin. Cnsider next hw recvery attempts shuld be related when the same image is sampled several times during a search. Shiffrin (1970) implicitly assumed independence f the infrmatin recvered in successive attempts, but such an assumptin is difficult t defend. We prpse here an alternative view that ver the shrt time span nrmally taken by recall, the infrmatin recverable frm a given image des nt change appreciably when the same cues are used t resample that image. Hwever, if even ne new cue is invlved in the resampling, then substantial amunts f new infrmatin might be recvered. The implicatins f these assumptins fr recall tasks are straightfrward. They were instantiated in the SAMS simulatin in the fllwing manner. It was assumed that successful recall f the wrd encded in an image is always fllwed by successful recall frm that image, regardless f cue set. Failure t recall was assumed t be fllwed by ther failures t recall, unless at least ne new cue fr that image is in the cue set; in this case, a new independent chance at recall ccurs. It will nt escape the reader's attentin that the recall and recvery rule f Equatin 7, which was used in SAMS, makes n use f the fine structure f the assciatin by which a cue and image might be related. Only the strength value is utilized. 5 Such a view can be defended, perhaps, in cnsideratin f the structureless tasks f free recall t which SAMS is applied. Fr tasks such as sentence and paragraph memry, it wuld nt be surprising if the recvery and evaluatin rules required explicit cnsideratin f the type f relatinal infrmatin between cues and images (which is assumed in SAM t be stred in each image). The pint is the fllwing: Althugh SAM des nt take the nature f an assciatin int accunt during sampling (beynd the degree captured by a strength value), there is n prhibitin f recvering and using such infrmatin after sampling. Incrementing. Many results suggest the necessity f a strage prcess that perates during the curse f retrieval (see Sectins I and III and Raaijmakers & Shiffrin, 1980). One type f strage is particularly easy t justify, since we have assumed that strage ccurs when infrmatin is rehearsed tgether in STS. Since infrmatin recvered frm a sampled image enters STS, where it is cnsidered in relatin t the prbe cues already there, it seems likely in this case that the retrieval strength between the prbe cues and the sampled image shuld be increased. In a recall situatin, in which the name is required, it seems likely that the majr increase in strength wuld ccur after successful recall takes place, with little r n increase after a failure t recall. The prcess f increasing cue-t-image strengths during retrieval is called incrementing. Assuming that significant incrementing ccurs nly after successful recvery, it remains t be established hw much incrementing ccurs when the same image is sampled successfully a number f times in a rw with the same cues. It hardly seems likely that incrementing wuld ccur unattenuated after each successive sample f the same image. (Since each increment increases the sampling prbability f that image in the 3 Actually, the use f categry cues in the case f categrized free recall and the assumptin f the recvery f categry infrmatin frm a recalled image were mild cncessins in SAMS t the necessity f taking the type f relatinship int accunt. This des nt alter the basic pint made in the text.

37 SEARCH OF ASSOCIATIVE MEMORY 129 future, the selectin prbability fr sme ne image culd eventually becme almst unity.) We prpse, therefre, that the majr increase in strength ccurs after the first successful recvery, with increases becming smaller thereafter. In SAMS, in fact, the simplifying assumptin was made that incrementing between a given set f prbe cues and a given image ccurs nly after the first successful recvery. These assumptins wuld f curse be altered if the subject were led r instructed t give special attentin and rehearsal t recvered items. Lng-Term Frgetting as Retrieval Failure There are tw basic reasns why an image may be retrieved better at Time A than at Time B. First, the cues utilized at Time A may be mre strngly assciated t that image than thse used at Time B. Secnd, the strength and number f ther images assciated t the cues (even if the cues are the same) may be greater at Time B than at Time A. Everything else being equal, an increase f cue strength t a given image increases bth sampling and recvery prbabilities (see Equatins 4 and 7). On the ther hand, fr fixed cue-t-image strength, an increase in the strengths f cues t ther images will reduce the sampling prbabilities (thugh leaving recvery unaffected). The increase in the strengths f cues t ther images tends t be an inevitable cnsequence f new learning. This new learning will nt necessarily lead t frgetting, hwever. The new infrmatin might be rganized tgether r integrated with the ld image s strngly that a larger image is frmed that cntains bth the new and ld infrmatin. Alternatively, the new infrmatin might frm a new image that is tightly assciated t the ld image. Retrieval f ne f these images culd result in that image's being used as a cue and eliciting the ther image. In this case frgetting is prevented by an apprpriate switch f prbe cues. Cnversely, when the cues are nt changed, frgetting may ccur. This leads t the general principle that frgetting due t new learning ccurs when the same cue is utilized in an attempt t lcate ne image amng an increasing number f ther images. On the ther hand, the subject may change the cue selectin during the search s that each cue is related t a subset f the increasing number f images; in this event frgetting may be lessened r even reversed. The decrease in the strengths f assciatin f cues t image can be the result f several factrs, chief f which is the change f cntext ver time (e.g., see Bwer, 1972; Estes, 1955). The cntext at the time f strage f an image makes the best retrieval cue fr that image. Hwever, the cntext cue used at testing may cnsist largely f the cntext infrmatin available nly at that time. Since the test cntext usually differs frm the strage cntext by a greater amunt as time between strage and test increases, the retrieval strength is reduced. The rle f cntextual factrs in retrieval and frgetting is very imprtant, and it is an essential cmpnent f SAM. The tempralcntextual features include incidental infrmatin frm the sensry envirnment and the subject's lng-term stre that happens t be present in STS at the time f a strage event. They might include the lcatin, the temperature, the time f day, recent events, and the subject's physical state, feelings, emtins, and recent thughts (Bwer, Mnteir, & Gilligan, 1978; Smith, Glenberg, & Bjrk, 1978). In SAM, such cntext features are always ne f the prbe cues, either by intent f the subject r by accident. Presumably, the subject can, thrugh attentin, vary the weight assigned t this cntext cue, but such infrmatin is always present in STS and always plays at least a small rle as a retrieval cue. Whenever pssible, f curse, a knwledgeable subject tries t reinstate in STS as far as pssible the cntextual cues that were present at the time the t-berecalled image was stred (Smith, 1979). The first frgetting factr, in which ne set f cues is cnnected t an increasing number f images, was utilized extensively by Shiffrin (1970) t explain list length effects in free recall. Since that time, list length effects (smetimes called fan effects) have been bserved in many settings. In ur wn research, we have bserved such effects in paired-assciate and recgnitin paradigms, as well as in free-recall studies. Muel-

38 130 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN ler and Watkins (1977) have referred t this frgetting factr as cue verlad. The SAM thery may be said t prvide a theretical basis fr the cue verlad principle. It is interesting t nte that Mueller and Watkins used the cue verlad principle t explain the part-list cuing effect. As described earlier in this article, the SAMS mdel explains the part-list cuing effect withut any recurse t a cue verlad factr. Nevertheless, the cue verlad principle is, in SAM, ne f the fundamental bases f retrieval failure. The secnd basic frgetting principle, cntext change, r mre generally, reductins in cue-t-image retrieval strength, is used t explain the deleterius cnsequences f delay f test and helps explain the difficulties caused by the presentatin f interfering materials during the study-test interval. An expsitin f this principle wuld require a mdel f cntext change and is well beynd the scpe f this article. Sensry Cding When a stimulus is first presented t the subject, it begins underging sensry analysis. Even the very lwest, initial stages f sensry analysis are prperly viewed as invlving retrieval frm lng-term memry. At each stage f analysis, the previusly retrieved features plus cntext already in STS determine the next features t be retrieved. When the stimuli are highly discriminable, these stages f sensry cding are rapid, accurate, and autmatic. At the higher levels f analysis, the meaning f the input is retrieved alng with, perhaps, particular cntextual images cntaining the input. Althugh it is difficult t draw a dividing line at any ne pint in this stream f prcessing, we lump tgether the relatively nncntextual retrievals and call the results sensry cding. These retrieved features are then viewed as the first item cue fr the subsequent memry search. Sensry cding typically cncludes in several hundred millisecnds and is quite autmatic, differing in bth respects frm the subsequent memry search. Nevertheless, it is pssible that the same basic retrieval mechanisms (e.g., Equatins 4 and 7) perate during this initial phase f retrieval. Such a pssibility culd be explred within the cntext f recgnitin and detectin paradigms. Of curse, if the inputs are degraded s that accuracy f cding drps and cnfusins result, the situatin is even clser t that in the memry search dmain. Perhaps threshld detectin culd prve cnsistent with a search mdel psiting a single sample frm memry. Such a pssibility is nt entirely implausible, since ne f the successful mdels fr sensry cnfusins is a mdified Luce chice mdel that is frmally identical t Equatin 4 (Luce, 1959; Luce, Bush, & Galanter, 1963). Applicatins f SAM t Other Paradigms. Althugh it is nt pssible in this article t describe in any detail the applicatin f SAM mdels t ther paradigms (see Raaijmakers & Shiffrin, 1980), a brief discussin is quite useful, especially since very few changes in the SAMS simulatin are needed t fit the results frm certain standard paradigms. Free recall. N changes in the structure f SAMS shuld be necessary t fit the results f standard, verbal, free-recall paradigms. Cumulative respnses as a functin f time and interrespnse times are already inherent in SAMS, since each lp f the search may be assumed t ccupy ne unit f time. Output rates slw dwn, since resampling f previusly sampled images generally increases at the expense f new sampling as search cntinues. The resampling tendency is increased even further by incrementing (ne tends t sample items previusly recalled). It wuld be pssible fr a subject t reduce the resampling tendency cnsiderably by using a systematic strategy t generate and change cues. Fr example, a search based n first letters culd prceed systematically thrugh the alphabet. Apparently subjects seldm use such strategies. Smetimes subjects are asked t recall the same list several times in successin with n new presentatins. Abut the nly additin t SAMS that is required t deal with this situatin is a decisin cncerning whether

39 SEARCH OF ASSOCIATIVE MEMORY 131 additinal incrementing shuld be allwed when the same wrd is recalled during successive retrieval perids. SAMS makes n prvisins fr cnfusins r intrusins in free recall. Intrusins f wrds in the sessin but nt n the current list can be handled by expanding the retrieval structure t include such images (with lw strengths t current list cues, f curse). Intrusins f nnpresented wrds can be handled in part by allwing fr imperfect recvery f presented wrds, that is, cnfusins. Anther pssibility wuld invlve expanding the strength matrix t include images f nnpresented wrds (with very lw strengths t current list cues). Nte that an implicit part f the recvery prcess in SAMS is a judgment that the sampled wrd was in fact n the current list. If false alarms culd ccur, then images f wrds nt n the current list culd be mistaken fr current list wrds, and intrusins wuld ccur (as ppsed t cnfusins). The applicatin f SAMS t categrized free recall has already been described in this article, albeit quite briefly. N imprtant change in the SAMS mdel was required, except fr the inclusin f a categry name cue in the retrieval structure and the assumed use f such a cue during retrieval. Paired-assciate paradigms. Experiments can be carried ut in which items are presented nly nce prir t test but in which the items are gruped at input. Then testing culd be dne by a free-recall technique r by presenting ne r mre members f each grup as cues and requesting recall f the remaining members f the grup. If the gruping is by pairs, and ne member f a pair is prvided as a cue at test, the paradigm may be termed single-list paired-assciate recall. It shuld be clear that SAMS is structured t deal with such a paradigm, since cued testing is already a fundamental part f the mdel and is used extensively in the applicatins described earlier in this article. We have fund that the results f such studies can be predicted quite well by SAMS, even thugh the images are all assumed t cnsist f single wrds plus cntext. One might ask whether there are data requiring multiwrd images t be added t the retrieval structure. We have nt fund this necessary in paired-assciate settings but have fund such assumptins helpful in paradigms invlving three-wrd grupings and cued testing. We suspect that such assumptins might als be useful in studies invlving sentence presentatin. In fact, Jnes (1976) has fitted a variety f such data with a fragment mdel that incrprates a central assumptin that stred units can cnsist f sentence fragments ranging in size up t full sentences. Althugh the SAM thery differs frm the fragment mdel in many respects, an assumptin f multiwrd images in SAM might incrprate many f the same desirable prperties that are captured by fragments in Jnes' mdel. Learning paradigms. There is a vast literature n verbal learning experiments that invlve multiple presentatins f items r lists. A variety f changes wuld take place during learning in such studies accrding t a SAM thery. These include the develpment f the fllwing: multi-item images, a cmplex interitem structure, an elabrate dependence n cntext, and a systematic retrieval strategy. These cmplexities take discussin f such paradigms beynd the scpe f this article. Recgnitin paradigms. Recgnitin pses particular prblems fr search theries. Simple theries require an extended search withut success befre an accurate respnse can be given that a test item is nt n the presentatin list, but if this were crrect, the pssibility f rapid, accurate, n respnses wuld be eliminated. The prblem is nt restricted t stchastic search theries, but this is nt the place t discuss the accuracy f such reasning r the relevant data (see Ratcliff & Murdck, 1976). Instead we prpse ne way in which rapid recgnitin respnses culd be prduced within a SAM framewrk. It is prpsed that the subject has access t the sum f strengths that appears in the denminatr f the sampling equatin (Equatin 4). The details f the activated infrmatin are prbably nt available at this stage. A value prprtinal t the sum f strengths culd be described as a "feeling f familiarity." Within a given task, criteria

40 132 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN culd be set such that a familiarity value abve the upper criterin culd be used as a basis fr a psitive recgnitin respnse, and a familiarity value belw the lwer criterin culd be used as a basis fr a negative recgnitin respnse. A familiarity value between the criteria wuld be ignred, and a nrmal search wuld prceed thereafter. Such a mdel is similar t that f Atkinsn and Jula( 1973). Ignring the pssibility f a recgnitin respnse based n familiarity, recgnitin in a SAM thery prceeds just as in recall settings. The sampling is identical, but the image sught is ne that cntains the prbe cue itself. In additin, after infrmatin is recvered frm a sampled image, several judgments must be made. A match judgment determines whether the infrmatin in the sampled image culd be an encding f the test item. A cntext judgment determines whether the sampled image was n the relevant presentatin list. Nte that these judgments must depend n the quality f the recvered infrmatin; strength alne is nt sufficient. Fr example, a change in cntext reduces the cue-set-t-image strength, and hence less f the infrmatin in the sampled image is recvered. But will a judgment f a match be increased r decreased as a result? Mre detailed knwledge f recvery is needed befre this questin can be answered. Final Cmments We have presented in sme detail the underlying basis fr a new retrieval thery that assumes prbabilistic, cue-dependent sampling frm a retrieval structure representing an assciative netwrk. The strage prcesses, memry representatins, and retrieval mechanisms have all been laid ut, althugh the greatest emphasis has been directed tward the search and retrieval peratins. A specific mdel, SAMS, was develped fr free recall. Parameters were estimated s that the mdel wuld fit free-recall data invlving variatins in list length and presentatin time. SAMS was used, essentially intact, t fit a variety f results frm the part-list cuing paradigm. Althugh the mdel cntains many prcesses and parameters, the predictins f the mdel are largely independent f the prcess assumptins and chices f parameter values. In fact, the predictins graphed were based n parameter values independently generated in fitting Rberts' (1972) free-recall data. The predictins are impressive fr this reasn and because they are based n a mdel making extensive use f interitem assciatins in retrieval a pssibility thught by previus investigatrs t be ruled ut by the data. There are a number f strengths f SAMS and als f the general thery, SAM. One f the mst imprtant is the careful delineatin f the rles f cntrl prcesses and decisin prcesses in retrieval. The applicatin t part-list cuing has illustrated the imprtance f carefully specifying such factrs. The sampling assumptins are anther key element f the present apprach in several different ways. First, the fact that sampling is prbabilistic allws fr a cnsiderable degree f resampling in certain circumstances. Such resampling f previusly sampled images is the basis fr stpping the search and hence an imprtant cntributr t the limitatins n retrieval. Secnd, the sampling equatin (Equatin 4) prvides an explicit basis fr cmbining cues and fr fcusing the search. The recvery equatin (Equatin 7) is als imprtant, because it allws fr imperfect recvery frm sampled images but lets the amunt f recvery depend n the cue-t-image strength. Thus the effects f such variables as presentatin time are easily handled. The use f a retrieval structure is an imprtant part f the SAM thery. The retrieval structure abstracts frm the LTS structure a simple enugh representatin that quantitative calculatins are quite elementary and at the same time abstracts a cmplex enugh representatin that very elabrate situatins can be handled sensibly by the thery. We admit that this apprach hides many f the prblems that arise during mdeling f memry fr highly structured materials by placing details f the interitem relatinships inside the images, where they are dealt with during the recvery prcess. Fr cmplex structures, it might prve necessary t make the recvery prcess a very elabrate system. Nevertheless, the present apprach des prvide a vehicle by which such cmplex situatins culd be handled

41 SEARCH OF ASSOCIATIVE MEMORY 133 within a search thery based n stchastic sampling, which we think is a significant step frward. In cmparisn with theries that fcus n the memry structure rather than the memry prcess, the SAM thery has several advantages. One is the ease with which frgetting phenmena may be handled. In this article, frgetting due t list length (r fanning) effects was predicted by SAMS. Frgetting due t delay is easily handled by mdeling cntext changes. Interference phenmena can presumably be handled by a cmbinatin f these tw factrs, thugh such pssibilities have yet t be explred in detail (but see Shiffrin, 1970, fr ne search mdel fr interference effects). Anther advantage is the emphasis n strategies that allw retrieval t be cntrlled by the subject. Cnversely, the greatest weakness f the SAM thery may be the freedm allwed by the numerus retrieval strategies. It wuld be tempting t predict any new result by arbitrarily assuming a new strategy designed t prduce the bserved effect. Frtunately, strategies may be manipulated experimentally, by instructin and task demand characteristics, s that mdels based n chices f strategies may be evaluated and tested. Ntwithstanding the success f SAMS in fitting free recall and part-list cuing, a general and cmplex mdel such as SAM cannt be judged a success simply n the basis f predicting the results frm ne r tw studies r paradigms. We have therefre embarked n a prgram f evaluatin in which the mdel (in essentially unchanged frm) is applied t as many paradigms and results as pssible. Reprts n these applicatins are frthcming. In particular, fr applicatins t a wide variety f tasks invlving free recall, categrized free recall, cued recall, and paired-assciate recall, see Raaijmakers (1979) and Raaijmakers and Shiffrin (1980). Reference Ntes 1. Twhig, P. T. Facilitatin and inhibitin f list wrds by list cues. Paper presented at the meeting f the Eastern Psychlgical Assciatin, Philadelphia, April 21, Kintsch, W., & Kalk, J. M. Cueing with list items in multitrial free recall. In Studies in mathematical learning thery and psychlinguistics (CLIPR Publicatin N. 6). University f Clrad Cmputer Labratry fr Instructin in Psychlgical Research, April References Allen, M. M. Cueing and retrieval in free recall. Jurnal f Experimental Psychlgy, 1969, 81, Andersn, J. R. FRAN: A simulatin mdel f free recall. In G. H. Bwer (Ed.), The psychlgy f learning and mtivatin: Advances in research and thery (Vl. 5). New Yrk: Academic Press, Andersn, J. R. Language, memry, and thught. Hillsdale, N.J.: Erlbaum, Andersn, J. R., & Bwer, G. H. Human assciative memry. Washingtn, D.C.: Winstn, Atkinsn, R. C., & Jula, J. F. Factrs influencing speed and accuracy f wrd recgnitin. In S. Krnblum (Ed.), Attentin and perfrmance IV. New Yrk: Academic Press, Atkinsn, R. C., & Shiffrin, R. M. Human memry: A prpsed system and its cntrl prcesses. In K. W. Spence & J. T. Spence (Eds.), The psychlgy f learning and mtivatin: Advances in research and thery (Vl. 2). New Yrk: Academic Press, Basden, D. R. Cued and uncued free recall f unrelated wrds fllwing interplated learning. Jurnal f Experimental Psychlgy, 1973, 98, Basden, D. R., Basden, B. H., & Gallway, B. C. Inhibitin with part-list cuing: Sme tests f the item strength hypthesis. Jurnal f Experimental Psychlgy: Human Learning and Memry, 1977, 3, Blake, M., & Okada, R. Intralist cuing fllwing retractive inhibitin f well-learned items. Jurnal f Experimental Psychlgy, 1973, 101, Bwer, G. H. Stimulus-sampling thery f encding variability. In A. W. Meltn & E. Martin (Eds.), Cding prcesses in human memry. Washingtn, D.C.: Winstn, Bwer, G. H., Mnteir, K. P., & Gilligan, S. G. Emtinal md as a cntext fr learning and recall. Jurnal f Verbal Learning and Verbal Behavir, 1978, 17, Buschke, H. Shrt-term retentin, learning, and retrieval frm lng-term memry, hi D. Deutsch & J. A. Deutsch (Eds.), Shrt-term memry. New Yrk: Academic Press, Crwder, R. G. Principles f learning and memry. Hillsdale, N.J.: Erlbaum, Estes, W. K. Statistical thery f spntaneus recvery and regressin. Psychlgical Review, 1955,62, Glanzer, M., & Schwartz, A. Mnemnic structure in free recall: Differential effects n STS and LTS. Jurnal f Verbal Learning and Verbal Behavir, 1971, 10, Hudsn, R. L., & Austin, J. B. Effect f cntext and categry name n the recall f categrized wrd lists. Jurnal f Experimental Psychlgy, 1970, 86, Jnes, G. V. A fragmentatin hypthesis f memry: Cued recall f pictures and f sequential psitin. Jurnal f Experimental Psychlgy: General, 1976, 105, Kintsch, W. Mdels fr free recall and recgnitin. In

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