psychological review - uvaraaijmakers.edu.fmg.uva.nl/pdfs/raaijmakers and shiffrin... ·...

Psychological ReviewVOLUME 88 NUMBER 2 MARCH 1981

Search of Associative Memory

Jeroen G. W. RaaijmakersUniversity of Nijmegcn

Nijmegen, The Netherlands

Richard M. ShiffrinIndiana University

A general theory of retrieval from long-term memory combines features of as-sociative network models and random search models. It posits cue-dependentprobabilistic sampling and recovery from an associative network, but the networkis specified as a retrieval structure rather than a storage structure. The theoryis labeled SAM, meaning Search of Associative Memory. A quantitative sim-ulation of SAM is developed and applied to the part-list cuing paradigm. Whenfree recall of a list of words is cued by a random subset of words from that list,the probability of recalling one of the remaining words is less than if no cues areprovided at all. SAM predicts this effect in all its variations by making extensiveuse of interword associations in retrieval, a process that previous theorizing hasdismissed.

A cue-dependent probabilistic search the-ory of retrieval has been developed to operatewithin a retrieval structure based on an as-sociative network. This theory, referred toas SAM (Search of Associative Memory),has been applied to the results of studies in-vestigating free recall, paired-associate re-call, and recognition. The theory is capableof fitting the results simultaneously, with noessential change in processes or parameters.Raaijmakers (1979) and Raaijmakers andShiffrin (1980) give early results supportingthese contentions.

In the present article, our goal is the de-lineation of the general theory and a thor-

This research was supported in part by a fellowshipfrom the Netherlands Organization for the Advance-ment of Pure Research to the first author and PublicHealth Service Grant 12717 and National ScienceFoundation Grant BNS-77-00156 to the second author.We gratefully acknowledge the help of Henry RoedigerHI, Edward Roskam, Susan Dumais, David Foyle,Bruce Williams, and Gary Gillund, who assisted us inthe various stages of development of this work.

Requests for reprints should be sent to R. M. Shiffrin,Psychology Department, Indiana University, Blooming-ton, Indiana 47405.

ough exposition of an application to one par-ticular research setting. For expositorypurposes, we begin with a simplified modeland application and then turn to the generaltheory. The first section of the article de-scribes a relatively simple computer simu-lation program for free recall that serves toillustrate the main features of the theory.The power of the approach is then illustratedby applying the simulation model to a puz-zling phenomenon known as the part-listcuing effect (e.g., Slamecka, 1968). SectionII of the paper discusses in detail researchand theory directed toward the part-listcuing effect; Section III explores in depththe way in which the simulation model dealswith this phenomenon. It should be notedthat the model presented in Sections I andIII is a precisely stated, carefully delineated,scaled-down version of the general theoryaimed at a limited set of paradigms. Dis-cussion of the rationale behind many of theassumptions, the ways in which the theoryhandles other types of paradigms, thestrengths and weaknesses of the approach,and comparisons with other theories are re-served for Section IV.

Copyright 1981 by the American Psychological Association, Inc. 0033-295X/81/8802-0093$00.75

93

94 JEROEN G. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN

I. A Simulation Model for Freeand Cued Recall

The general theory will be abbreviated asSAM (Search of Associative Memory); thesimulation model for free recall will be ab-breviated as SAMS (SAM Simulation).

The Paradigms

SAMS is developed to deal with the par-adigms of free verbal recall and free recallwith added cues. In free recall, a list of «words is presented in random order at a rateof t sec per word. Both t and n may be variedbetween lists. In immediate free recall, thesubject is asked to recall as many words aspossible, in any order, immediately followinglist presentation. In this case, the most re-cently presented words are recalled at anenhanced level (the recency effect), presum-ably reflecting the presence of those wordsin a short-term store. In delayed free recall,an interpolated task, usually arithmetic, isinterposed between presentation and test.The interpolated task is presumed to clearshort-term store of the list words so that allrecall is from long-term store. Indeed, therecency effect is eliminated in this case. Thepart-list cuing paradigm will be describedin detail in Section II. In brief, at the timeof testing, some of the list words are pre-sented to the subject, supposedly as helpfulaids to enable recall of the remaining listwords.

The data from such experiments are typ-ically analyzed in terms of the number ofrecalled words or in terms of the probabilityof recall (which is sometimes analyzed interms of the presentation position or the out-put position of particular words). In addi-tion, the rate of output is often analyzed,sometimes in terms of interresponse times,but more often in terms of the cumulativenumber of items recalled as a function ofoutput time.

Short-Term Store and Long-Term Store

SAMS utilizes a two-phase memory sys-tem (Atkinson & Shiffrin, 1968; Shiffrin,1975). Short-term store (STS) is the tem-porary store into which information aboutpresented items is placed and in which con-

trol processes such as coding and rehearsalare carried out. Long-term store (LTS) isthe permanent store, containing all prior in-formation plus new information transferredfrom STS. Retrieval from LTS is quite fal-lible, as described below.

STS is limited in capacity (Shiffrin, 1976),so that only a limited number of items maybe retained, rehearsed, and coded at onetime. In particular, SAMS assumes a bufferrehearsal system operating as follows: Eachpresented word enters STS, joining previouswords there, until the buffer size, r, isreached. Then each new word entering thebuffer replaces one of the r words alreadypresent. The word to be replaced is chosenwith probability l/r.

If immediate testing is used, the r itemscurrently in the buffer are all correctly re-called, and then retrieval from LTS begins.If delayed testing is used, it is assumed thatthe arithmetic clears the buffer at the samerate that would have obtained had the listcontinued. After a long period of arithmetic,the buffer will be empty of list items at test,and retrieval will begin from LTS at once.

Storage in Long-Term Store

What is stored in LTS are associative re-lationships between context and word infor-mation, and between a set of context-plus-word information for one word and a set ofcontext-plus-word information for anotherword. The former is termed word-contextinformation, and the latter is termed word-word information. The amount of word-con-text information stored is assumed to be pro-portional to the total amount of time a givenword remains in the rehearsal buffer. Theamount of word-word information stored isassumed to be proportional to the totalamount of time those two words are simul-taneously present in the rehearsal buffer.

Word information is information that en-ables the subject to produce the name of theencoded word. Context information refers totemporal and situational factors that mightalso be present in STS at a given time, in-cluding environmental details, physical sen-sations, emotional feelings, and all thoughtprocesses not directly relevant to name pro-duction.

SEARCH OF ASSOCIATIVE MEMORY 95

Besides the storage that takes place duringlist presentation, additional storage may oc-cur during the long-term retrieval processitself. The assumptions governing such stor-age are given below. CT

IMAGES

is nS

1T

s(crwls) s(crwns)s(w1T,wnS)

WnT S(WnrWls'

Long-Term Retrieval

LTS retrieval is assumed to be a cue-de-pendent process operating on a retrievalstructure based on an associative memory.At each step of the search process, cues areassembled in STS and used as a probe ofLTS. A localized set of information in LTS,called an image, is sampled. The samplingprobabilities are a function of the strengthof association between the probe cues andthe various images in LTS. The informationin the sampled image is then accessed andevaluated in a process called recovery. Theprobability that enough information is re-covered to enable the name of the encodedword to be recalled is a function of thestrength of association between the probecues and the sampled image.

In SAMS, the only cues considered arethe general context cues, called CT, and thewords from the presented list, termed W,T,W2T, . . . WnT. The subscript T indicates theword at test. A probe set always consists ofCT alone or of CT along with one of the wordcues, for example, (CT, W/T). The imagesthat can be sampled consist of the storedinformation about each of the n words in thepresentation list, including the context atthat time; these are denoted W1S, W2S,. . . WnS. The subscript S indicates the in-formation as it is stored.

The Retrieval Structure

SAMS assumes that relationships be-tween the probe cues and the images maybe completely summarized in a retrievalstructure that gives the strengths of rela-tionship between each possible probe cue andeach possible image. This is illustrated in thematrix of Figure 1. In the figure, S(CT, Ws)represents the strength with which the con-text cue tends to sample the image of Word/; SCW/T, W(s) represents the strength with PS(W/S|CT) =which Cue- word j tends to sample the imageof Word /.

Figure 1. The strength matrix—the matrix of strengthsthat determine the probabilities of selection and recov-ery of list images (horizontal margin) when various cues(vertical margin) are used in the cue set. (Entries in thecells are strengths from individual cues to individualimages; when multiple cues are used in the cue set, thenthe strengths are combined according to Equations 1and 2 in the text. CT refers to the context cue; Wfr andWs refer to the Cue Word i and the image of Word /.)

The strengths in this matrix are assumedin SAMS to be proportional to the amountsof information stored during presentation.Let t, be the time that Word i stays in thebuffer, and let ttj be the time that Words iand j are together in the buffer simulta-neously. Then

S(Cr, W(S) = at,; S(W,r, W,s) = btlf,

S(W/T, Ws) = cth

where a, b, and c are parameters to be es-timated.

It should be noted that many pairs ofwords will never occupy the buffer simul-taneously. In all such cases, a small residualstrength value is assumed. In particular, iftu = 0, S(W,r, Wys) = d, where d is anotherparameter to be estimated (but is presum-ably smaller than a, b, or c).

The Sampling Rule

Equations la and Ib give the quantitativesampling rules:

S(CT, W<s)

2 S(CT, w,s)(la)


Ps(W/s|CT, WCT)

S(Cr. W8)S(WH, W,s)= ~s -

2 S(CT, W,S)S(W,T) W,s)

In Equation 1, Ps indicates the samplingprobability. The left-hand sides of theseequations give the probability of samplingthe image of Word i, given that the probecues consist of CT in Equation la, or CT andW*T in Equation Ib. Equation la is a simpleratio rule for strengths. Equation Ib is a ra-tio rule for the products of strengths. Thisproduct rule has the effect of focusing thesearch so that there is a tendency to sampleimages with high strengths to both cues,rather than images with high strengths toonly one of the cues.

It should be noted that when att is sub-stituted for the strengths in Equation la, thea cancels, and the rule becomes a ratio ofrehearsal times. However, when similar sub-stitutions are made in Equation Ib, the pa-rameters a, b, c, and d do not cancel (exceptfor special combinations of values).

The Recovery Rule

Equations 2a and 2b give the probabilitythat the subject will be able to generate thename of the word encoded in Image /, giventhe cue (or cues) that made up the probe setduring sampling, and given that this recov-ery instance is the first for Image / with thatprobe set. In Equation 2, PR indicates therecovery probability.

PR(W(|CT) = 1 - exp{-S(CT, W,s)} (2a)

PR(W(|CT, Ww) = 1 - exp{-S(CT, Ws)

-S(WOT,W«)} (2b)

These equations essentially say that re-covery probabilities rise as the cue-to-imagestrengths rise. Note that the parameters a,b, and c do not cancel out of these recoveryequations; in fact, these parameters may beviewed as recovery parameters.

SAMS makes special assumptions whenan image that has already been sampled witha given probe set is again sampled with thatsame probe set later in the search. These

"conditionalization" assumptions hold thatthe outcome of the second and subsequentrecovery attempts will match the outcomeof the first recovery attempt. In addition, ifthe context cue and any other word cue to-gether do not lead to recovery of Image /,then it is assumed that any subsequent re-covery attempt for Image i with the contextcue only will also fail. Thus a new indepen-dent recovery chance occurs whenever theprobe set contains a new cue (i.e., one notutilized before for the image sampled).These assumptions represent an assumptionthat successive recovery attempts of thesame image with the same probe set arebased on essentially the same information.

Storage During Retrieval

Whenever a successful recovery occurs,the strengths of the probe set to the re-covered image are increased. This processis termed incrementing and obeys the fol-lowing rules:

S'(CT, Ws) = S(Cr, Ws) + e;

S'(W,T, W,s) = S'(WA, Ws)

-S(Wn,Wjs)+/;

S'(W,T, W«) = S(W,T, W,s) + g. (3)

Here the primes represent the strengths afterincrementing, and e, f, and g are the incre-menting parameters. Two special assump-tions are made concerning incrementing:First, any increment of a context to wordstrength is always linked to an increment ofthe recovered image's self strength. That is,the e and g increments always occur to-gether. Second, only one increment can evertake place for any given cue-to-imagestrength. (See Section IV, Incrementing, forfurther discussion.)

The Search Process

The retrieval process involves an extendedsearch that requires a series of decisions onthe part of the subject concerning what cuesto use during each sampling phase and whento stop searching. The retrieval process inan arbitrary setting is diagrammed in Figure2. The subject makes a plan, chooses a set


of probe cues, samples and tries to recover,decides whether to stop searching, and thenloops back to the retrieval plan to begin thenext phase. This general system will be dis-cussed in Section IV. The specific decisionsand control processes used in SAMS aregiven in the flow chart shown in Figure 3.

The stopping rule. A failure is definedas any sampling and recovery attempt thatdoes not result in recall of a new word. Themain phase of the retrieval process is as-sumed to end whenever the cumulative totalof failures in the search reaches a valuetermed A:MAX.

Selection of probe cues. If cues are notprovided, the subject begins by using contextonly as a cue. This probe set continues to beused until some new word is recalled. When-ever a new word is recalled, the next probeset consists of two cues: the context cue andthe word just recalled. This rule applies evenwhen the previous probe set consisted of con-text plus a different word.

Stopping rule for word cues. LM\x is thestopping criterion for a word cue. If a givencombination of context plus word serves asa probe set for LMAX consecutive loops of thesearch, and no new word is recalled, then thesubject drops the word from the probe setand uses context alone.

Rechecking. When the main search phaseends (when AMAX is reached), then recheck-ing begins. In this phase, each previouslyrecalled word (either from the main phaseor rechecking) is used along with context ina probe set. Each such probe set is utilizeduntil Z-MAX failures accumulate. Any newwords recalled during this period are savedand are used as cues during later rechecking.The rationale for the rechecking process isbased on a certain arbitrariness in the as-sumptions concerning selection of cues forprobe sets. A word may be recalled and usedas a cue. Then it may happen that a newword is recalled on the very next loop of thesearch. Our rules require that the probe setbe changed to use this new word, but it couldbe argued that the previous word cue is stillof value and has not been "used up." Theincorporation of a rechecking process allowsus to argue that all associative retrievalroutes have been checked thoroughly, atleast up to an LMAX stopping criterion.

RETRIEVAL FROM LONG-TERM-STORE

QUESTION

RETRIEVALPLAN

ASSEMBLE PROBECUES IN STS

SE

AR

CH

SEARCH -SETSELECTION

[RESTRICTION TO RELEVANT!L LTS REGION J

i

SAMPLING OF ITEM[ /».OF AGGREGATE OF FEATURES]

*RECOVERYOF CONTEXT AND ITEM FEATURES]

[CONTEXT COMPARISONS]ITEM DECISIONS j

TERMINATION DECISION(NO)

Figure 2. A generalized depiction of the various phasesof retrieval in the theory. (STS = short-term search;LTS = long-term search.)

Parameters

The SAMS model described above isready to be applied to the data from free-recall studies. The parameters are a (con-text-cue-to-image strength), b (word-cue-to-image strength), c (word-cue-to-self-imagestrength), d (residual-word-cue-to-imagestrength), e (context-to-image increment),/ (word-cue-to-image increment), g (word-cue-to-self-image increment), /sfMAx (totalfailure stopping criterion), Z,MAX (stoppingcriterion for a word cue), and r (buffer size).

At first glance, 10 parameters seems quitea high number to fit the results from free-recall studies, especially since Shiffrin (1970)


( START J

( STOP J

sample item iusing context-cue

YES

increase associationto context

sampleand

item j using Itemcontext as cues

i

increase association tocontext and to item i

Figure 3. A flowchart for Phase 1 .of the retrieval process in the computer simulation of SAMS developedfor free recall. (K and L are counters of failures. Old or not recovered refers to a failure to recall a newitem.)

used a much simpler search model with justthree parameters to fit a great deal of free-recall data. This objection is ameliorated bythe following factors. We can show that mostof the present parameters, and their precisevalues, are not essential for the fit of themodel to most of the data. The parametersare listed above for generality, even thoughsome are never varied and others are equatedbefore fits to the data are begun. Some ofthe parameters are given nonzero values andincluded in the fit merely to demonstratethat the presence of the processes they rep-resent will not harm the ability of the modelto predict the data. In fact, we have set manyof these parameters to zero, and no harm tothe model's predictions has resulted. How-ever, each of these parameters representsprocesses that we feel are needed on logical

grounds, or needed to deal with data thatwill not be discussed in detail in this article(see Raaijmakers & Shiffrin, 1980). Theroles played by the various parameters havebeen extensively explored by simulationmeans, as have certain process assumptions,and the results of these explorations will beeither summarized briefly or reported in de-tail in the remainder of the article.

Free-Recall Data

In this section we will apply SAMS tofree-recall data in order to get a set of rea-sonable parameter estimates. A set of dataparticularly well suited for the initial explo-rations of the model was collected by Rob-erts (1972). Four list lengths (10, 20, 30, or40 words) and five presentation rates (.5, 1,


2, 4, or 8 sec per word) were covaried. Nointerpolated arithmetic task was used (soboth short- and long-term components areassumed in recall). Both visual and auditorypresentation modes were utilized, but wehave averaged the results for these twomodes. Our main concern is average recallperformance for each type of list (ratherthan performance as a function of serial pre-sentation position).

The results are given in the upper panelsof Figures 4 and 5. Clearly, mean numberof words recalled is a negatively accelerated

function of total presentation time for a fixedlist length (Figure 4; see also Waugh, 1967).Also, equal total presentation times for dif-ferent list lengths do not yield equal recall;rather, longer lists yield more total wordsrecalled (Figure 4). Finally, as list lengthincreases for fixed presentation time peritem, total recall increases almost linearly,though with a slight hint of negatively ac-celerated growth (Figure 5). The "list lengtheffect" is also implicit in these data: Theprobability of recall of a given word de-creases as list length increases.

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LL=30

LL=40

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LL = 30

LL=40

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ii I i

20 40 60 80 120 160 240 320

TOTAL PRESENTATION TIME (seconds)

Figure 4. Observed data (Roberts, 1972; top panel) and predictions of SAM (lower panel) for meanwords free recalled as a function of presentation time and list length (LL). (The parameters of the modelare r = 4; KMAX = 30; Z-MAX = 3; a = c = .10; 6 = .10; rf = .02; e =/= g = .70. These parameters areused to generate predictions in all the following figures, except where indicated differently.)


25

20 -

55 15

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ci 10oUJ

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25

20

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5 ,0

PT=2.0

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PT = 0.5

PT=

PT=I.O

-* PT = 0.5

20 40 60 80 120 160 240 320

TOTAL PRESENTATION TIME (seconds)

Figure 5. The same data are presented as in Figure 4, except that the label of each curve is presentationtime (PT) per item.

Parameter Estimation

The model has characteristics that makeanalytical derivations infeasible; it is there-fore constructed as a computer simulationprogram. Predictions are derived by MonteCarlo methods—by averaging the results oflarge numbers of "statistical subjects." Pa-rameter estimates are obtained by generat-ing predictions for various combinations ofparameter values and choosing the best com-bination. The number of simulations (NSIM)was 300 for the predictions shown in the fig-ures. Nothing like an exhaustive search wasused to obtain parameter estimates: Someparameters were set on the basis of past data

and models, some were arbitrarily set equalto others, and some were varied over smallregions of values. Surely, then, the fits arenot optimal. They are, however, quite sat-isfactory for our purposes. The parametervalues, methods of estimation, and some gen-eral comments are discussed next.

Parameter r. The buffer size was setequal to 4 on the basis of previous fits toserial position curves and on the basis ofnumerous estimates of short-term capacityas 2.5 (see Crowder, 1976). Typical methodsof estimating short-term capacity, such asthat of Waugh and Norman (1965), producevalues much lower than the buffer size; itcan be shown that our predictions, using a


buffer size of 4, when analyzed accordingto the Waugh and Norman procedure, resultin an estimate of short-term capacity of 2.5.It should be mentioned also that our modelgives an excellent account of the Murdock(1962) serial position data when r is setequal to 4.

Value of #MAX- The criterion for cessa-tion of search was set equal to 30 failures.This value was chosen in part because Shif-frin (1970) fit Murdock's data with an as-sumption of about 36 samples (correspond-ing to about 30 failures). It can be shownthat the choice of stopping rule and the valueof 30 are not crucial for predicting the qual-itative and quantitative effects in the presentdata (nor in much other data, as well). Ofcourse, if the value of XMAX is raised, pre-dicted recall will increase slightly, but theincrease may be counterbalanced by smallchanges in the other parameters.

In general, XMAX is a decision criterion,whose value may be chosen by the subjectand manipulated by instructions.

Value of LMAX- The number of failuresof an item cue before it is discarded andcontext only is utilized as a cue was set equalto 3. The performance changes expected asa result of changes in LMAX are fairly diffi-cult to ascertain, especially since increasesin LMAX extend the period of rechecking.With the help of simulations, the followinggeneral properties have been determined:When interitem strength attains values nearor below those estimated for Roberts' (1972)data, then a word cue's tendency to sampleitself is fairly high, and a context cue alonecan lead to more efficient sampling. (Thisreasoning does not hold if interitem strengthor residual strength is raised.) Since largevalues of LMAX reduce both the number ofcontext cues utilized in the search, and alsothe number of different word cues utilized,increases in LMAX tend to decrease perfor-mance. This effect is counterbalanced some-what by the fact that recovery probabilityfor word-plus-context cue sets is greater thanfor context-only cue sets. The net result isthat, without rechecking, increases in LMAXfrom 1 to 5 have only a small effect, a slightdecrease in performance. However, theamount of search during rechecking in-creases as LMAX increases, so in the model

as it stands, performance turns out to be aweakly inverted-U-shaped function of LMAX»with a maximum near 3. Thus we fortui-tously chose a value of LMAX that maximizesperformance. Also, it certainly is the casethat extensive use of interword associationsis made during the search when LMAX = 3,a desirable property of the model.

The value of LMAX is a choice of the sub-ject and may be manipulated by instruction.

Parameter a. The context-to-imagestrength per second of rehearsal time wasone of the three estimated parameters andattained a value of .10. Sampling probabil-ities are not affected by changes in a (unlessc is set equal to a, in which case word-cuesampling is affected because c changes; seebelow). However, recovery probabilities de-pend directly on a. Thus a strongly influ-ences both the overall level of recall and thedependence of recall on presentation time.

The value of a should depend on the cod-ing or rehearsal technique used, on the na-ture of the words, and on the distinctivenessof the list context.

Parameter b. The interword strengthper second of joint rehearsal time was esti-mated to be . 10. The value of this parameterdirectly influences recovery probabilitieswhenever a word is used as a cue and animage is sampled that had been rehearsedwith the cue word. However, if a word cueis used, b also affects the sampling proba-bilities. The reason for this depends on thethree types of samples: It is possible to self-sample, to sample a word that had not beenrehearsed with the cue word, or to samplea word that had been rehearsed with the cueword. As the value of b rises, the probabilityof the last of these possibilities rises.

The value of b should depend on contextdistinctiveness to a small degree but shoulddepend primarily on the ease with which thelist words may be coded together. For ex-ample, increases in the similarity of the listwords to each other should probably increasethe value of b for that list.

Parameter c. The word's self-samplingstrength per unit of rehearsal time was setequal to the context-to-word strength, a. Theself-sampling strength gives the relative ten-dency for a word to sample its own image,and it seems reasonable that this tendency


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PROBABILITY OF RECALL (Model)

Figure 6. Comparison of the predicted and observedprobabilities of recall, corresponding to each of the 20points in Figures 4 and 5.

should grow with rehearsal time. Setting cequal to a accomplishes this goal, but thereis no real reason to believe these parametersshould be equal (rather than, say, linearlyrelated). If c is raised for fixed a, then self-sampling rises and recall performance drops(though recognition performance would rise).For the recall tasks to which the model hasbeen fit, the value of c does not seem to becrucial. Evidence about the relationship ofc to a can best be obtained from recognitiontasks, but for the present no harm is doneby setting c equal to a.

In general, we expect c and a to vary insimilar ways as the experimental conditionsare changed.

Parameter d. The residual interwordstrength value for words not rehearsed to-gether was set equal to .02. The value waschosen on the basis of applications of themodel to data from paired-associate para-digms (not discussed in this article). Thisvalue is low relative to a, b, and c, as shouldbe the case. In fact, the precise value is notimportant for the present application: Al-most identical predictions of Roberts' dataare obtained when d is set equal to .0, thevalue of a is raised to .12, and the otherparameters are unchanged.

The effect on performance of raising d iscomplex. Sampling will be directed awayfrom words rehearsed with a cue word,which could hurt performance in a cued-re-call or recognition task. However, in thepresent free-recall task, performance is im-proved slightly because more retrieval routesare made likely, because self-sampling is re-duced, and because recovery probability israised.

It is presumed that d reflects preexperi-mental factors and should be higher forwords that are already strongly related, es-"pecially if that relationship was formed ina context similar to the test context. Also,factors that affect the value of b shouldusually affect d similarly.

Parameters e, f, and g. The incrementsin strength following recall were all set equaland then estimated, attaining a value of .70.The particular value chosen is not very im-portant for the present application. How-ever, an increase in these incrementing val-ues does lower overall recall levels, so theymust be estimated jointly with a and b. In-crementing is included in this applicationand set to a fairly high value to achieve con-sistency with applications to other para-digms, in which incrementing is essential topredict the data (see Section I, Discussion).

The amount of incrementing is supposedto reflect the amount of attention given toany word as it is recalled and after it hasbeen recalled.

Predictions for Free Recall

The predictions of SAMS with these pa-rameter values are shown in Figures 4 and5 in the lower panels. Since direct compar-ison of observed and predicted points is dif-ficult in these figures, Figure 6 shows a com-parison of the predicted and observed pointsfor all 20 conditions. Clearly the fit of themodel is quite adequate.

Discussion

Our parameter estimation proceduresmake it clear that this model is far morepowerful than it needs to be to fit free-recalldata. Many of the model's processes and


parameters are included to deal with datafrom other paradigms that we do not havethe space to discuss here. However, we willpresent a brief survey of certain findings thathelp illuminate the roles played by theseprocesses.

First, consider the search stopping crite-rion. One problem with a search model suchas that of Shiffrin (1970) was its dependenceon the number of samples made from mem-ory: The number of samples was equated forall lists. Perhaps such an assumption is de-fensible if the recall period is short and equalfor all lists. However, in almost all studiesthe recall period is set long enough that thesubject ceases attempts to recall before timeexpires. The present model incorporates astopping criterion based on the progress ofretrieval during any given search. Further-more, the criterion is a subject choice thatshould be alterable by the experimenter.Roediger (1978) and Roediger and Thorpe(1978), for example, have examined both thetime course of retrieval and the effect of in-structing subjects to continue recall attemptsbeyond the point at which retrieval normallyceases. In both cases, our model predicts thedata with no changes in assumptions andonly minor changes in parameter values. Itis worth noting that our assumption of^MAX = 30 causes recall to cease during aperiod when new recalls are occurring at avery slow rate relative to the rate occurringearlier in the search. This comment is sup-ported by the observation that an alternativestopping rule, in which search ceases when12 consecutive failures occur, produces pre-dictions almost identical to those obtainedfor a rule of 30 total failures.

Consider next the purpose of recheckingand the effects of this process on the pre-dictions. Rechecking was included initiallyso that it could be argued that the subjecthad exhausted all available retrieval routes.Rechecking is not essential to predict Rob-erts' (1972) data; the elimination of recheck-ing can be handled without difficulty by in-creasing the value of AMAX or raising thevalues of a and b. Rechecking does play animportant role in other situations, however.For example, without rechecking, cumula-tive recall functions can be predicted to grow

to asymptote too sharply; rechecking pro-vides new retrieval routes that allow totalrecall to continue to grow (albeit slowly) forlong periods of time (Buschke, 1975, Roe-diger & Thorpe, 1978).

Consider incrementing next. Although notreally crucial for predicting Roberts' data,this process is essential for predicting a num-ber of effects from other paradigms. For ex-ample, two consecutive tests of the same listmay be given, one by the technique of freerecall and one by some sort of cued recall(e.g., category cues or part-list cues), in ei-ther order. Quite large order effects havebeen found in our own research, and thesecan be explained quite well by the effects ofincrementing. A somewhat smaller effect isthat of test order of categories in cued recallof categorized word lists. Slight drops in re-call are found for categories that are delayedin testing (e.g., Roediger, 1973; Smith,1971). This effect also is well predicted byincrementing. The reason why incrementingexplains these effects is straightforward:Recall leads to incrementing that increasesthe sampling probability for the items al-ready recalled.

Interword associations and their use inretrieval are a cornerstone of SAMS, buteven these are not needed to predict Roberts'data. Such associative routes are needed,however, to predict many results, includingthose concerning paired-associate paradigmsand the effects of variations in interwordassociation values. Perhaps most intriguingis the manner in which such interword re-trieval routes explain the part-list cuing ef-fect, which is discussed in the next two sec-tions.

Finally, consider the residual strengthsbetween list words not rehearsed together.We include such retrieval routes in part be-cause it seems logical that they should bepresent. However, many results show theneed for such routes. For example, if a listof word pairs is studied, with instructions toform codes for each pair, and one memberof a pair is presented at test, recall proba-bility depends strongly on list length (Raa-ijmakers & Shiffrin, 1980). This effect isdue within the model to the assumption thatthe cue word is associated not just to the


response word but also, residually, to eachword on the list.

We realize, of course, that no serious sup-port for our present model can be obtainedfrom our fit to Roberts' free-recall data.However, the applications to part-list cuingdiscussed in the next two sections help showthe value of the present approach.

II. Part-List Cuing

A Survey of the Literature

One of the more intriguing results ob-tained in the free-recall paradigm is the so-called "part-list cuing" effect, first reportedby Slamecka (1968). The effect is importantbecause it is counterintuitive and seeminglyinconsistent with many theories of humanmemory.

In the prototypical part-list cuing exper-iment, subjects are given a list of words forstudy and are later tested for recall of theseitems in one of two ways: One group of sub-jects, the control group, simply recalls asmany items as possible; that is, this groupis given the usual free-recall instructions. Asecond group is given a randomly chosensubset of the list items as cues, supposedlyto aid retrieval of the remaining items. Therecall by this latter, part-list cued group ofthe remaining or critical items (also calledtarget items) is then compared with the per-formance of the control group on the sameitems. This paradigm was devised by Sla-mecka (1968) as a rather direct test of therole of interitem associations in recall. Sla-mecka reasoned that any theory that as-sumes that interitem associations are usedin recall should predict that at least some ofthese cues would facilitate recall of itemsthat would otherwise not have been recalled.Failure to find recall facilitation should (ac-cording to Slamecka) lead to the conclusionthat interitem associations are not formedduring study or not used during recall.

The result that is obtained quite reliablyin this paradigm and in a number of variantsshows that recall of the critical items is notbetter for the cued group than for the controlgroup (even when short-term memory ef-fects are controlled). In fact, there is usuallya slight negative effect, with the control

group showing superior recall (Roediger,Stellon, & Tulving, 1977; Slamecka, 1969).What is surprising about this result is notso much the small superiority of the controlgroup, but the fact that no reliable cuingfacilitation is found.

Most conventional theories assume thatduring study of a list of words a network ofinteritem associations is formed. A modelpostulating that the list cues simply give anumber of additional entry points into thenetwork should predict a large advantage forthe cued group. For example, Anderson'sFRAN model, which makes exactly this as-sumption, predicts much better critical wordrecall by the cued group than by the controlgroup (Anderson, 1972, p. 362).

In the early experiments on part-list cuing(Slamecka, 1968), a rather large advantagewas found for the control group. However,Slamecka (1968, Experiments V and VI)showed that this was because the controlgroup had the advantage of being able toreport the items still in short-term store,whereas the cued group had to process thelist cues. When this artifact was eliminated,no significant differences were observed be-tween the two conditions. Moreover, the lackof a positive cuing effect did not seem todepend on the interitem associative strength.For example, in one of Slamecka's experi-ments (Slamecka, 1968, Experiment VI),three types of lists were used: a list of 30rare words, a list of 30 common words, anda list composed of the word butterfly and 29of its most frequently named associates. Themean number of target items recalled by thecontrol group was 5.58 for the rare word list,7.04 for the common word list, and 8.50 forthe butterfly list. For the cued group thesemeans were 4.70, 6.79, and 8.97, respec-tively. The difference between the cued andthe noncued conditions was not significant(F < 1), nor was the interaction between thiscuing factor and the type of list (F < 1). Thedifferences between the three lists were,however, highly significant.

Thus, the part-list cuing effect does notseem to depend very much on the interitemstrength. Although the control group advan-tage does seem to diminish somewhat oreven reverse slightly with higher interitemstrength, no large positive effect of cuing


appears, even when the variation in interitemstrengths between conditions is enough tomake total recall differ by a factor of nearlytwo. Such a result has been thought by pre-vious investigators to be at odds with thetypical associative network theories^

Similar results have been reported by anumber of other researchers. Roediger et al.(1977) reported a control group advantagethat increased slightly with the number ofcues provided. They also observed that theadvantage of the noncued over the cued con-dition did not disappear or reverse even whenvery long recall periods were used (up to 10minutes).

Slight positive effects of cuing (often notsignificant) have been reported, but only inspecial conditions. Anderson (1972) andWood (1969) reported a very slight positiveeffect after multitrial free-recall learning. Ina similar experiment, Slamecka (1969) ob-served a slight negative effect of cuing. Allen(1969) presented subjects with a list com-posed of contiguous pairs of items, whichwere judged to be either related or unrelated.After an initial recall for both groups, hecued the subjects in one group with onemember of each word pair and found greaterrecall for the cue group, especially with re-lated pairs. Note, however, that this proce-dure is quite different from the normal pro-cedure, in which a random subset of wordsis given as cues. The only paradigms in whicha reasonably large advantage appears for thecued condition are retroactive interferenceparadigms. Blake and Okada (1973) re-ported an experiment in which subjects weregiven 10 study-test trials on a 6-item list,followed by 10 study-test trials on a second,interpolated list. Following this interpolatedlearning they were tested on the first list. Inthis experiment, cuing on the final test trialdid have a positive effect. Similar resultswere reported by Basden (1973).

Roediger (1974) has summarized a num-ber of experiments with categorized listsin which the number of cues per categoryvaried. In these paradigms, cuing may helpin retrieving categories when there are toomany categories in the list to be retrievedunaided, but cuing has no beneficial effectat all on within-category recall, that is, onthe number of words recalled per category

of which at least one member was recalled.In fact, a slight negative effect is consistentlyfound in within-category recall. Results con-sistent with this generalization have beenreported by Hudson and Austin (1970),Mueller and Watkins (1977), Roediger(1973, 1974), Rundus (1973), Slamecka(1972), and Watkins (1975).

Moreover, it is usually found that the neg-ative effect of cuing on within-category re-call increases slightly with the number ofcues provided (Mueller & Watkins, 1977;Roediger, 1973, 1974; Watkins, 1975). Roe-diger (1974, Table 1) summarized a numberof experiments that show that the higher theproportion of items from a particular cate-gory that are given as recall cues, the lowerthe probability of recalling the remainingitems from that category. For example, Run-dus (1973) obtained recall probabilities forthe remaining category members of .36, .34,.29, and .28 for cuing with 1, 2, 3, and 4category instances, respectively.

Explanations for the Part-List CuingEffect

The basic part-list cuing result—the lackof an advantage for the cued group—is in-terpreted by researchers in this area as ev-idence against the role of interitem associ-ations in free recall. Slamecka (1972),Rundus (1973), Roediger (1974) and Wat-kins (1975) assume only vertical or hierar-chical associations. Thus, Slamecka (1972)writes:A truly associative theory of learning, one which iden-tities learning with the active elaboration and strength-ening of interitem linkages, cannot, in our opinion, con-vincingly incorporate these findings without abandoninga central feature of the term "association." The uniqueforce of the proposition that A and B are associated isthat presence of A has the power to elicit B; that A can"pull out" B. (p. 331)

This conclusion is shared by most other re-searchers in the area:It should be noted that the results . . . contradict pre-dictions of theories postulating direct associations be-tween items. If items were directly interlinked in mem-ory, it should be the case that presentation of some itemsas cues would increase the likelihood of other items beingrecalled. (Roediger, 1974, p. 265)

However, we will show in the next sectionthat this reasoning is quite incorrect. DespiteSlamecka's contention that the part-list cuing


effect shows that interitem associations arenot used in recall, the effect is completelyconsistent with a model that relies heavilyon the use of interitem retrieval routes. Infact, we shall see that the effect is virtu-ally an inevitable consequence of modelslike SAM.

First, let us consider the explanations thathave been developed by theorists who havedecided to abandon the role of interitem as-sociations. These explanations have tendedto postulate hierarchical, or "vertical," as-sociations in place of interitem, or "horizon-tal," associations. Such theories have notbeen worked out in detail, so it is not clearhow they propose to handle the part-listcuing effect. One hypothesis would assumethat a retrieval path from an item to a nodeat another level and then back to anotheritem at the initial level is either difficult orimpossible to follow: Thus a word cue at onelevel will not effectively cue another wordat the same level. Whatever the merits ofthis hypothesis for part-list cuing, it wouldcertainly have difficulties handling manystandard results. These include the effectsof input order on output order (Anderson,1972; Kintsch, 1970; Shiffrin, 1970) and theeffects of associability of items presentedcontiguously in the list on the level of recall(Glanzer & Schwartz, 1971). In fact, it isdifficult to see how this hypothesis wouldhandle single-trial paired-associate recall:Why should a stimulus cue increase theprobability of recall of the response memberunless there exists a useful retrieval routebetween the two?

Although all of the theories proposed toexplain the part-list cuing effect make sim-ilar assumptions in order to explain the lackof a positive effect, they do differ somewhatin whether they can explain, or in the waythey explain, the slight negative effect ofcuing and the dependence of the cuing effecton the number of cues presented.

Slamecka (1972) proposed a generation-recognition account of categorized recall: Heassumed that there is no strengthening at allduring study of the category-name-to-in-stance associations. Therefore, his theorydoes not predict an effect of the number ofcues provided to the subject. In fact, it does

not predict a negative effect at all. Althoughthis accords with some of Slamecka's data(Slamecka, 1968, 1972), Roediger (1974)has shown that in the majority of studiesthere is an increasing negative effect as thenumber of cues rises. Two related theorieshave been proposed to deal with this phe-nomenon.

First, Rundus (1973) and Roediger (1973,1974) have suggested that presentation ofthe list cues involves an implicit retrieval ofthese items. It is assumed that this retrievalresults in a higher associative strength ofeach retrieved item to the retrieval cue (thecategory name). It is further assumed thatretrieval involves a sampling-with-replace-ment process, so that this strengthening ofthe list cues leads to a lowered probabilityof sampling critical items. The model alsoincludes the assumption that in noncued re-call, in which the subject first has to searchfor the category names to be used as retrievalcues, the probability of sampling a particularcategory name is proportional to the sum ofthe associative strengths of the category ex-emplars presented in the list to that categoryname. Data consistent with this latter as-sumption have been presented by Parker andWarren (1974) and Roediger (1978). Thismodel could presumably also explain thepositive effects of cuing reported by Blakeand Okada (1973) and Basden (1973) byassuming that in multitrial free-recall learn-ing a subjective hierarchical organization isformed and that retroactive interferenceleads to a decrease in the probability of gen-erating the subjective retrieval cues.

Second, Watkins (1975; see also Mueller& Watkins, 1977; Watkins & Watkins,1976) has proposed a cue-overload interpre-tation of part-list cuing. According to thisexplanation, recall is mediated by retrievalcues that are subject to overload: The prob-ability of recalling any particular item de-creases with the number of instances asso-ciated to the retrieval cue. Thus, in this casethe part-list cuing effect is attributed to theusual (but in this model, unexplained) list-length effect. Watkins (1975) assumes thatre-presentation of the list-cues at the timeof testing is functionally equivalent to pre-sentation of a new category instance. This


hypothesis is supported by data of Watkins(1975) and Mueller and Watkins (1977)showing that recall of the remaining cate-gory instances is decreased not only by pre-sentation of list cues but also by presentationof extralist cues, category instances thatwere not on the original list. Unrelated cues,however, have no effect on recall (Mueller& Watkins, 1977, Experiment I). Note thatthis explanation is quite similar to the oneproposed by Roediger (1973, 1974) andRundus (1973), if the latter model weremodified to incorporate the negative effectof extralist cues.

Within the context of search theories ofeither the type represented by SAMS, thetype described in Shiffrin (1970), or the gen-eral class discussed in Section IV, severalexplanations should be considered at thispoint. Since recall depends on the length ofthe search, it is possible to predict the part-list cuing effect simply by assuming that thesubject searches longer in the control con-dition than the cue condition. One possibilityis to allow the stopping criterion (ATMAX inSAMS) to vary between the two conditions.Another possibility is to count failures insuch a way that they accumulate faster inthe cue condition. For example, each sampleand recovery of an image from the list ofprovided cues could be counted as a searchfailure, leading to earlier search cessation inthe cue condition. Such mechanisms maypossibly contribute to the observed effect,but certain evidence makes it seem unlikelythat they are operating. The main problemis that cumulative recall as a function of timeshows a consistent advantage for the controlcondition, even for times when all subjectsin both conditions are still searching mem-ory. This is shown most persuasively by Roe-diger et al. (1977), who instructed subjectsto continue attempting memory search fora period of 10 minutes (by which time veryfew new items were being retrieved by eithergroup). On the whole, it seems doubtful thatdifferent stopping criteria provide a generalexplanation of the part-list cuing effect.Such possibilities are explored further withinthe context of the SAMS model in the nextsection.

Finally, there is one explanation that ac-

cepts the formation of interitem associationsduring study. This is the editing/disruptionhypothesis proposed by Basden, Basden, andGalloway (1977). They assume that

the part-list cues disrupt any intracategory organizationthat may have taken place during acquisition. Since theorder in which the items are presented as cues is veryunlikely to coincide with the order in which the subjectwould recall the category members, part-list cuing mayconstitute an interference paradigm, (p. 104)

Note that this hypothesis is still similar tothe other explanations, since it is assumedthat the interitem associations cannot be ef-fectively used in recall. This particular ex-planation, however, seems to run into diffi-culties when applied to the positive cuingeffects observed by Tulving and Pearlstone(1966), who presented category names ascues in a random order, and Tulving andOsier (1968), who presented extralist cuesfor noncategorized lists. Moreover, no rea-sons are given why the items should only berecallable in one particular order.

In summary then, the extant explanationshave certain drawbacks, and most of themajor explanations agree with Slamecka's(1968, 1969) original conclusion that thelack of a positive effect of cuing proves thatinteritem or horizontal associations play noimportant role in free recall. This of coursepresents us with a theoretical puzzle: Whatpossible reason could there be for horizontalassociations not being stored? In the nextsection we will present a model and an ex-planation for the part-list cuing paradigmthat does utilize horizontal associations andthereby eliminates this puzzle.

III. Application of SAMSto Part-List Cuing

First, SAM will be applied to part-listcuing, with the interitem strength, b (i.e.,interword similarity), as a variable. Then anumber of factors that do not affect the basicpredictions will be mentioned and illus-trated. Next we shall endeavor to explain thefactors that do cause our model to predictthe effect. We shall then apply the model toseveral additional findings from the litera-ture, namely, the effects of number of listcues, the effect of categorized lists, and the


effect of various possible types of list cues.Finally, our explanations will be comparedto others in the literature.

Assumptions of the Model

The model proposed for part-list cuing isthe SAMS model already fitted to Roberts'(1972) data, with a few slight changes toenable it to deal with the cued group. Anidealized paradigm is used as a basis for thetheoretical development in which N wordsare presented for study and followed byarithmetic to clear STS. The control con-dition is normal free recall. In the cue con-dition, M words randomly chosen from thelist are presented to the subjects at the startof recall. The subjects are told to utilize theM words as cues to help them recall as manyof the remaining (N—M) words as possible.

The model for the control condition is theSAMS model that was fitted to Roberts'study and has the same parameter valuesexcept that STS recall is not allowed, sincethe arithmetic task clears STS.

The assumptions for the cue condition areidentical except for a few special assump-tions that apply at the start of recall to takethe list cues into account. We are of coursecareful not to make any assumptions thatwill introduce an advantage or disadvantagefor the cued group for trivial reasons (suchas an assumption that the cued group useda smaller value of A^MAX to determine whento cease searching). Also, we are careful totreat the list cues in the cue condition, whichare provided by the experimenter, in thesame way as the self-generated cues in thecontrol condition.

In particular, it is assumed that the sub-jects act in accord with the instructions andutilize the list cues during the search. At thestart of recall, each list cue is used in turnas a retrieval cue along with context. Eachsuch cue set is used until Z-MAX failures arereached, and then the next list cue is used,and so forth. During this phase, the subjectdoes not use any recalled words as cues, butinstead saves them for later use. In order notto introduce a disadvantage for the cuegroup, the first successful recovery of theimage of any list cue, whether due to self-

sampling, context sampling, or word-plus-context sampling, is not counted as a failure(see Section II, Explanations for the Part-List Cuing Effect.) Only recoveries of theimage of a list cue after the first are countedas failures. This assumption is consistentwith the retrieval assumptions for the controlgroup, since any word's first recovery is asuccess for that group. The usual incre-menting and conditionalization assumptionsapply during this phase of retrieval for thecue group.

When the list cues have each been usedfor LMAX failures, and if ATMAx has not yetbeen reached, then the subject begins normalsearch, just as at the start of recall in thecontrol condition. This continues until a cri-terion of ATMAX total failures of any kind isreached, at which time Phase 1 of the searchends for both groups.

Following the ATMAX stopping point, bothgroups carry out a final rechecking in whichall successfully recovered words are used ascues. Thus, recovered list cues are utilizedduring this phase, but unrecovered list cuesare not. (This last assumption ensures thatthe cue group receives no advantage due toan artificially extended rechecking period.Alternative rechecking assumptions will bediscussed later.) During rechecking, theusual assumptions apply, just as in the modeldescribed earlier.

Predictions of SAMS for the Part-ListCuing Effect

We now turn to the predictions of themodel. We assume that using a highly sim-ilar list of words (as in Slamecka's "butter-fly" list) is equivalent in our model to usinga high value of the interitem parameter, b.Presumably, semantically similar items areeasier to encode together. Therefore we de-rived predictions for six different conditionsthat differed only in the values assigned tob. These values ranged from very low to veryhigh, as shown in Figure 7. Presentation timewas set to 2 sec per item, list length was setto 30, the number of cues in the cue con-dition was set to 15, and all other parameterswere those used in the fit to Roberts' data(the residual strength, d, was set in each


condition to one fifth of the value of the in-teritem strength, b; this was the ratio for theb and d values in the fit to Roberts' data).NSIM was set equal to 1000.

Figure 7 gives mean critical words re-called for the cuing and control conditionsfor each of the six values of interitemstrength. The predictions are interesting intwo respects. First, the control condition hasa small but systematic advantage over thecuing condition. Second, the size of the con-trol group advantage is fairly consistent overthe range of interitem strength values, de-creasing slightly with higher values of b.Note that total recall rises from about fourto eight items over this range of values ofb without much altering the part-list cuingeffect. Of course, this pattern of results isvery similar to that found by Slamecka(1968; and see the discussion in Section II.of this article).

Note especially that extensive use is madeof the associative pathways between words,which is indicated by the fact that predictedrecall almost doubles over the range of in-teritem strengths in the figure. Certainly,then, the part-list cuing effect cannot be usedto argue that interitem associations are ei-ther not stored or not used in retrieval.

An important fact about the model thatneeds to be emphasized and kept in mindthroughout the following sections is that thecontrol group advantage in Figure 7 occursin spite of a fairly large factor that aids thecue group. The model incorporates a recov-ery rule which insures that the probabilityof recovery following sampling of an imagewith a word-plus-context cue set will behigher than when that same image is sam-pled with a cue set consisting of context only.Since the cue condition utilizes relativelymore word-plus-context cue sets and lesscontext-only cue sets, it achieves a consid-erable advantage, This is seen most clearlywhen the recovery probabilities for word-plus-context and context-only sets areequated. As a demonstration, we replacedthe recovery equations in SAMS with a sin-gle probability of recovery, .75, which ap-plied regardless of the context set used orthe strengths involved (the usual condition-alization rules about successive sampling of

o

tro

10

o1116

scc.o£ 4

•——• controlx—* cued

0.2 0.6 1.0

INTERITEM STRENGTH PARAMETER

Figure 7. Predictions of the part-list cuing effect for anidealized paradigm as the interitem strength parameter,b, is varied. (List length is 30; number of cues is 15;presentation time per word is 2 sec; d is set to equal.26. Other parameters are as in Figure 4. These valueshold for the following figures, unless indicated differ-ently. For each strength value, the control condition isslightly superior, a pattern of results similar to those ofSlamecka [1968].)

the same image still applied). All other fea-tures of the model remained as in Figure 7.When this was done, the control group ad-vantage rose by about .5 items.

The important implication of this findingis that all the predictions we shall be dis-cussing in the following sections are occur-ring in the presence of a recovery factor aid-ing the cue group. Thus even predictions ofequality of the control and cue conditions,which will occur in several variations below,are actually indicating the operation of sub-stantial factors favoring the control condi-tion (since for equality to occur, the cuecondition recovery advantage must beovercome).

Factors That Do Not Explain Part-ListCuing

Ineffectiveness of word-plus-contextsearching. Consider first whether searchingwith word cues plus context cues is superiorto searching with context only. The answermay be seen most clearly when recheckingis eliminated from the model. The predic-tions for such a case are presented in Figure


oUJo: 10

OCCO context only

• • context + item

0.2 0.4 0.6 0.8 1.0


Figure 8. Predicted words recalled in the control con-dition, without rechecking, for normal search as a func-tion of interitem strength (solid line) and for search withcontext cues only (dashed line).

8. For both conditions normal free recall isassumed (no list cues are used). The context-plus-word cue curve uses Roberts' parame-ters and shows how total recall depends onthe value of the interitem strength, b. Thecontext-only condition assumes that all sam-ples are made with context only. The resultsshow that the possibility of word-plus-con-text sampling causes recall to be superior athigh values of b, but the reverse is true atlow values of b. This is to be expected, sincelow values of b will result in word cues sam-pling themselves (since c = a) rather thanother list items. The two conditions are aboutequal for b near the value estimated forRoberts' data. However, this factor evidentlyhas nothing to do with the part-list cuingeffect, since the part-list cuing effect is sta-ble and almost equal over the same rangeof b values that produces the large differ-ences in Figure 8 (compare with Figure 7).

Incrementing. The process we havetermed incrementing has been proposed asan explanation of the part-list cuing effect.It is possible that the list cues becomestrongly associated to the search cues, par-ticularly context cues, during the initialphase of the search. Then the later searchtends to sample list cues to the detriment ofcritical items. Explanations of this generalsort have been proposed by Rundus (1973),by Roediger (1973, 1974; see also Roedigeret al, 1977) and, albeit differently phrased,by Watkins (1975). Since incrementing is

built into our model, could it be accountingfor the effect? Figure 9 shows a set of pre-dictions just like those in Figure 7, exceptall the incrementing parameters have beenset to zero. Clearly, overall recall is increasedwhen incrementing is eliminated, but theadvantage of the control condition is un-changed. Thus the SAMS incrementing pro-cess and the part-list cuing effect are vir-tually independent within this model. Thereason is that incrementing has equally del-eterious effects on the cue and controlgroups. (The effect of incrementing the listcues before retrieval begins will be discussedlater.)

It should be noted that Crowder (1976)mentions that incrementing is not neededwithin a search model to explain the part-list cuing effect. This prediction was derivedin the context of a model assuming that allretrievals of list cues (including the first) arecounted as failures—an assumption we donot make. Without this assumption, his lineof reasoning is invalidated.

The choice of stopping rule. Considervariations in our assumptions about the stop-ping rule. In the first variation, we changedthe criterion from "#MAX total failures" to"A^MAX consecutive failures." Figure 10 iscomparable to Figure 7, except that the con-secutive failure rule is used, with KMA% = 10.Clearly, the choice of stop rule has little todo with the part-list cuing effect. Next, forboth types of stopping rules, various valuesof AMAX were tried, since it might be arguedthat SAMS' predictions only hold true when

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p ^_a.o

—• control—x cued

_ f0.2 0.4 0.6 0.8 1.0


Figure 9. Recall as a function of interitem strength.(Predictions use the same model as Figure 7, but allincrementing is deleted [e =/= g = .0].)


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dog 8

.o

tro

«—. controlx--x cued

0.2 0.4 0.6 0.8 1.0


Figure 10. Recall as a function of interitem strength.(Predictions use the same model as Figure 7, except thatthe total failure stopping rule for Phase 1 of the searchhas been changed to a consecutive failure stopping rule,with KMA.X = 10 consecutive failures.)

searching ceases quickly (i.e., too soon). Fig-ure 11 shows the predictions for various val-ues of .KMAX for the total failure rule, withb set to .10. Clearly the effect and its mag-nitude are independent of the stopping cri-terion. (Similar results obtain for the con-secutive failure rule.) Note that forLM\X = 3 and KM AX > 45, all the list cuesare used in Phase 1 of the search. The factthat some are skipped for AMAX = 30 makesvery little difference.

Despite the predictions in Figure 11, onemight still be concerned that stopping cri-teria are responsible in some way for theeffect. Thus in Figure 12 we deleted the stop-ping rule, and simply graphed cumulativerecall for both groups as a function of thetotal number of samples made. (It is as-sumed that rechecking takes place every 100samples; without rechecking, very little ad-ditional recall for either condition wouldtake place late in the search, since most im-ages would have been sampled to the contextcue at least once.) It is clear that recall in-creases at a rapidly decreasing rate, evenwith rechecking. The control group retainsits advantage throughout, although the dif-ference decreases. Roediger et al. (1977)obtained results somewhat more like Figure11 than Figure 12, which perhaps suggeststhat their subjects employed a stop rule witha large criterion, but it must be admitted

that both figures would fit their pattern ofresults quite well.

The choice of probe cues. It may benoted that the search assumptions for thetwo conditions differ slightly, since the con-trol group is assumed to switch cues at oncewhenever a new word is recalled, whereasthe cue group uses each experimenter-pro-vided cue until LMAX failures accumulate. Infact, if each time a word is recalled, the cuegroup is made to move on at once to the nextlist cue, the two conditions become virtuallyequal. Conversely, if the control group isforced to stay with each word cue until LMAXfailures accumulate, saving all recalled wordsfor later use, whenever ATMAX is reached, thenagain the two conditions become almostequal. In neither case, however, is there acue group advantage.

Assumptions differing for the twogroups. Several assumptions can be madethat will favor one condition or another forthe rather obvious reason that the two groupsare treated differently. For example, assum-ing that all recoveries of list cues are failurescauses the cued condition to reach AMAXmore quickly than the control group. Theadvantage of the control group naturally in-creases with this assumption (by about .15words). Consider another example: If all listcues, whether recovered or not, are used inrechecking, then the cued group spends more

10

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control—x cued

5 10 30 50 70 90

STOPPING CRITERION (KMAX)

Figure I I . Recall as a function of stopping criterion.(Predictions use the same model as Figure 7, but withinteritem strength b = .10.)


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01

DS

controlcued

NUMBER OF SAMPLES

Figure 12. Cumulative critical words recalled as a func-tion of total number of samples. (Predictions use thesame model as Figure 7, but with interitem strengthb = .10 and stopping rule deleted. Rechecking occursevery 100 samples.)

time rechecking than the control group andnaturally gets an advantage from this fact(the cued group now gets an advantage ofabout .5 words). Even without this assump-tion, rechecking tends to favor the cuedgroup very slightly. When rechecking iseliminated altogether, the control group ad-vantage increases by about .40 words.

The lesson from the manipulations thathave been tried seems clear: If we removeevery possible simple factor that might favorthe control group, apart from the basic struc-ture of SAMS itself, but retain factors thatfavor the cue group, such as a recovery ad-vantage when a word cue is added to context,and a new chance to recover whenever a newcue is used to sample a previously unrecov-ered image, at best we bring the cued groupup to the level of the control group. Thereare clearly some fundamental, inherentcharacteristics of the SAMS model that pro-duce the part-list cuing effect. These areconsidered next.

An Explanation of the Part-List CuingEffect

By now, the reader must be wonderingwhich factors are responsible for SAMS'prediction of the part-list cuing effect.

Interword cuing in the control and cueconditions. First and foremost, much of the

mystery is removed when it is realized thatboth the control and cue conditions involveextensive cuing by words. Self-generatedcues are utilized in the control condition,whereas experimenter-provided cues areutilized first in the cue condition. The ex-tensive interitem associative cuing in bothconditions tends to make overall perfor-mance in the two conditions quite compa-rable.

This reasoning suggests that when theability to generate cues, using context, ispoor, the control group will be inferior. Fig-ure 13 shows the predictions as a, the item-to-context strength, varies. At very low val-ues, there is a considerable advantage for thecued group (since the control group can sel-dom recall anything using context alone),but as a increases in value, the usual part-list effect quickly appears and even growssomewhat. One might expect, then, that acuing advantage could be experimentallyproduced simply by choosing a task in whichcontext-to-item strengths are low at test,that is, a task in which normal free recallwould give very low performance levels.Such reasoning could well explain the pos-itive effects of cuing observed by Blake andOkada (1973) and Basden (1973) in a ret-roactive interference paradigm.

The selection of list cues. In order forthe part-list cuing effect to be seen, it is ex-tremely important that the subject be givena random sample of items from the list ascues. Otherwise, the cues may turn out to

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Figure 13. Recall as a function of item-to-contextstrength parameter (a). (Predictions use the same modelas Figure 7, but interitem strength b = .10 and c = a.)


be extremely useful. It is true in the modeland has been found empirically that cuesconsiderably increase the recall of thosewords that are strongly associated to thecues—it is the other words whose retrievalis harmed (Roediger, 1978). This is nicelyillustrated in a study by Twohig (Note 1).Twohig presented subjects with a list of cat-egories that were each composed of fourpairs of associated words. Subjects in thecued group were given two words (not fromthe same associated pair) from each cate-gory as list cues. There was no positive effectof cuing, averaging over all critical items ina category. However, the conclusion that theinteritem associations were ineffective wouldbe quite inappropriate, since the cues didlead to a substantially higher probability ofrecall for the items paired with the cues. Thispositive cuing effect was, however, counter-balanced by a negative effect on the recallof the other category members.

In fact, this reasoning suggests that cuedrecall could be quite beneficial if the exper-imenter could arrange to provide one goodcue from each of the subjective "groupings"that the subject has stored in memory. Thisis easiest to demonstrate when a categoricalstructure is built into the list. In this case,cuing with one word from each category isvery beneficial (due to more categories'being accessed; see Slamecka, 1972; Tulving& Pearlstone, 1966). This factor can alsohelp explain Allen's (1969) finding thatcuing was helpful when the cues consistedof one member of each of a number of wordpairs judged to be related. However, if theword cues are selected randomly (i.e., with-out regard to the categorical structure), thenthere is no increase in recall (Kintsch &Kalk, Note 2). Such results are a problemfor those theorists who use the part-list cuingeffect as evidence against the role of inter-item associations in recall. Similar reasoningapplied to these results should lead them tothe conclusion that in such experiments hi-erarchical or vertical associations were notused, an assumption that probably none ofthem would like to embrace.

Clearly, then, appropriate selection ofcues can lead to an advantage or disadvan-tage, depending on the basis for selection.In the studies under consideration, however,

Figure 14. A. simplified associative network for a 12-word list stored as four triads. (The six experimenter-provided cue words have images denoted by Q. The sixremaining critical items are denoted by I. The arrowsdenote associations between images. Each image has anassociation to context, which is not depicted. A contextsample can access a triad rich in critical items [e.g., thetriple-I triad]. The cue-word-plus-context samples canonly sample triads relatively impoverished in criticalitems, since each such triad must contain at least onecue.)

random cue selection was used. Given thatthis is the case, an explanation for the cuingdeficit needs to be established. We turn tothis explanation next.

The effect of associative clustering. Thestrongest and most crucial factor favoringthe control condition depends on the natureof sampling from a subjectively clusteredassociative network. It can be shown that thecontrol group's sampled clusters will be rel-atively richer in critical items than the cuedgroup's sampled clusters (most of which willcontain at least one cue word).

The basic idea is illustrated in simplifiedform by the associative network depicted inFigure 14. It is assumed that the words areinterassociated in groups of three (triads),with all other interword associations beingnegligible. It is further assumed that sam-pling of an image from a triad leads thatmember—and immediately thereafter, bothother members of that triad—to be recalled.During a fixed period of time, assume thatthe control and cued groups sample an equalnumber of different triads (a simplificationfor the sake of the argument). The cuedgroup's sampled triads will all contain aminimum of one cue word and hence a rel-atively small number of critical words. The


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Figure 15. Recall as a function of strength value. (Pre-dictions use the same model as Figure 7, but all entriesin the test matrix at the start of retrieval are set equalto the same value, which is shown on the horizontal axis;thus r, a, b, c, and d are not used. Note the sizeableadvantage for the cued condition.)

control group's sampled triads, on the otherhand, will often contain no cue words andhence be relatively rich in critical words.Thus the retrieval structure forces the cuedgroup to retrieve more list cues than the con-trol group at the expense of retrieval of crit-ical items, the measure on which the twogroups are compared.

Keep in mind that for this simplified ex-ample, we assumed that both groups samplean equal number of different triads andhence recall an equal total number of words.If instead we assumed that an equal numberof triads were sampled, including resamples,then it is clear that more different triadswould be sampled and hence more totalwords would be recalled in the control con-dition. This factor would increase the sizeof the control group advantage even further.

In general, then, the cuing procedure leadsto a sampling bias for the cued group. Thecued group is more likely to sample list cuesthan critical items, whereas the controlgroup is unbiased with respect to the twotypes of items. This sampling bias is sostrong that it evidently can overcome otherfactors that aid the cue group, with the neteffect that a higher number and proportion

of critical items is recalled by the controlgroup.

Note that this explanation does not re-quire that the subgroups in the structure benonintersecting. A buffer process, for ex-ample, tends to produce high interwordstrengths in a region lying athwart the upperleft to lower right diagonal of the strengthmatrix (Figure 1). This degree of groupingis sufficient for the present explanation tocontribute substantially to the part-list cuingeffect.

In addition to this sampling factor, thereare a number of secondary factors that alsocontribute to the control condition advan-tage. One of these is a positive correlationthat exists between a word's context strengthand interword strengths. Such a correlationis produced by a buffer process but seemsreasonable for any sensible storage system.(Note, however, that the SAMS buffer pro-cess does not lead to a particularly strongcorrelation.) That the correlation does con-tribute to the control group advantage is easyto demonstrate: in each simulation, afterstorage and before retrieval (for both con-ditions), the set of context-to-image strengthsin the top row of the strength matrix of Fig-ure 1 is randomly permuted. When this isdone, the advantage of the control group iseliminated, and both conditions are aboutequal.

Note that both reasons for the superiorityof the control condition depend on the de-velopment and use of a nonuniform inter-word retrieval structure. It is rather re-markable that the reason for the cuecondition disadvantage in SAMS is the pres-ence of the very associations that previoustheorists have tried to rule out.

Additional evidence supporting our expla-nations of the part-list cuing prediction inthe model may be obtained by eliminatingthe structure in the test matrix. The testmatrix was homogenized by setting allstrengths in the matrix equal to each other.In this case, both lines of reasoning describedabove were invalidated, and we expected acue condition advantage due to its higherrecovery probability. In fact a large advan-tage for the cue group appeared, as shownin Figure 15. Similar results, though notquite as extreme, were obtained simply by


raising the residual strength (represented byd) in the basic model. As the residualstrengths approach the interword strengths,the grouping structure tends to be lost.

One final point should be emphasized. Forthe control group to do well, especially athigh interword strengths (see Figure 8), itis necessary that an appropriate mixture ofcontext-only sampling and word-plus-con-text sampling be utilized. Context-only sam-pling may tend to locate many clusters inmemory but will not tend to retrieve effi-ciently the members of those clusters. Fur-thermore, the sampled words will tend to bemore difficult to recover than when word cuestrengths have been added to the contextstrengths. On the other hand, reducing con-text sampling to a minimum also reducesperformance, since new clusters may not befound and inefficient word cues may be uti-lized over and over without success. Al-though the mixture of cue sets used in themodel may not optimize performance for thecontrol condition, it probably comes reason-ably close. It goes without saying that thecue condition does not utilize an optimal se-quence of cue sets. SAMS predicts thatmuch better performance in the cue condi-tion could be produced if searching went onfor a period without considering the providedcues at all, and then the cues were utilizedduring a rechecking period (see Allen, 1969,and An Application of SAMS to DelayedCuing below).

Applications of SAMS to Studies Varyingthe Number of Cues

To obtain predictions, we again imaginedan idealized situation in which a 30-word listwas presented and the number of words pre-sented as cues was varied. It is easiest tocompare the results when they are tabulatedin terms of the probability of critical wordrecall (since total critical recall naturallydepends on the number of critical words inthe list). The objection might be raised that^MAX can be reached before the providedcues are all utilized and that the number ofsuch unchecked cues will grow with the num-ber of provided cues. To eliminate this pos-sibility, LMAX was reduced to 2 and KMAXraised to 50, so that all provided cues would

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always be utilized in Phase 1 of the search.The other parameters were kept the sameas in the fit to Roberts' data. Predictions areshown in Figure 16, which gives the prob-ability of critical word recall as a functionof the number of cues provided. Clearly, themodel predicts a slight but almost lineardecrease in recall as the number of cues in-creases. We have not explored the parameterspace, but the magnitude of the decrease canpresumably be controlled by choices of pa-rameter values.

In the research literature, the effect of thenumber of provided cues is not entirely clearwhen uncategorized lists are used. Slamecka(1968) found little effect, but Roediger etal. (1977) did show an increasing deficit forthe cued conditions as the number of cuesincreased. It is possible that subjects do notalways use the provided cues, and firm in-structions to read, study, and use the pro-vided cues may produce this effect.

An Application of SAMS to DelayedCuing

Allen (1969, Experiment 2) presentedpairs of words—half related, half unrelated.After an initial period of 5 minutes of or-


dinary free recall, the cued group was givenlist cues, one from each pair. In the case ofrelated pairs (high interword strength), themodel predicts, and the data show, a sub-stantial advantage for cuing. Allen alsofound a small cuing advantage for the un-related pairs. To simulate this situation, weran the uncued free-recall program until acriterion of AMAX = 45. Then in the secondphase, the cued group used each of the 15list cues until a criterion of LMAX = 3 wasreached; the control group was simply con-tinued free recall until an additional 45 fail-ures accumulated. No rechecking was used.For Roberts' parameters, total predicted re-call was higher for the cued group by .7words, which was similar to Allen's findingsfor unrelated words.

Within SAMS, there are several reasonswhy delayed cuing should be helpful. Forone thing, if there are any clusters of wordsnot yet accessed, the list cues might provideentries to these clusters. Most important,however, are the new chances at recoverythat the list cues provide. Late in any ex-tended search, most images have been sam-pled by the context cue, and few new wordsare being recalled to serve as new word cues.On the other hand, many of the (delayed)list cues may not have been recovered yet.When these are used for sampling, they willprovide new independent chances of recoveryfor images that were sampled earlier withother cues but not recovered. Allen's studyprovided evidence for this view. The list cueswere separated into two classes: those thathad been recalled in the immediate free-re-call period and those that had not. The un-recalled cues were far more effective.

An Application of SAMS to Part-Category Cuing

Many of the studies of part-list cuing haveutilized lists of categories of items and havevaried the number of words presented as cuesfrom each category. In addition, some of thestudies have presented other types of cues.Applying SAMS to such paradigms involvesessentially no new principles; in a sense eachcategory is treated as a separate list, so mostof the predictions of the preceding sectionshold true.

A precise description of the application ofSAM to the category case does involve a fewadditional assumptions, however, so theseshall be described very briefly. It is assumedthat each word image stored contains cate-gory information and each category labelcan be used as a probe cue (in much thesame way, context is part of each image andcan be used as a probe cue). In general, agiven category cue will have strong strengthvalues to words in that category and weakresidual strengths to words in other cate-gories.

In most studies the subject is told whatcategory to recall at a given point in thesearch, so we assume that the probe set willconsist of the context cue, the category cue,and possibly a word cue, if a word has beenrecalled from LTS or provided by the ex-perimenter as a cue. Three kinds of experi-menter-provided cues should be distin-guished: intralist cues, words from the listin the to-be-recalled category; extralist cues,words not on the list but from the to-be-re-called category; and extracategory cues,words that may or may not have been on thelist but are not from the to-be-recalled cat-egory. Watkins (1975) and Mueller andWatkins (1977) observed a negative effectof both intralist and extralist cues but noeffect of extracategory cues.

The version of SAM for this case was de-veloped and applied by Bruce Williams ofIndiana University. It was assumed that thecategories are blocked at input and that theusual buffer storage process operates, exceptthat words from different categories are notrehearsed together (no interword strength isstored when words from different categoriesshare the buffer). Instead, all words in dif-ferent categories were given a common,small, residual strength. Words from thesame category but not rehearsed togetherwere given a (possibly different) small re-sidual strength. Category-to-word strengthswere a linear function of the time a wordfrom that category stayed in the buffer, andcategory-to-word strengths for words in othercategories were set to a small residual value.Finally, extralist cues were assumed to havea small residual strength to the category la-bel and to list words in that category butnegligible strength to words in other cate-


gories. All nonlist words were assigned a re-sidual self-strength (which could be fairlyhigh) and a residual context strength.

Retrieval of the list items from a givencategory was assumed to operate in essen-tially the same way as for a noncategoricallist. Both context and category cues wereused for every sample. If a noncategory wordwas sampled, it could be recovered but wasnot output, was not incremented, and wascounted as a failure. In all other respectsretrieval proceeded as for the noncategorizedcase, except there was no rechecking (whenthe model was applied with rechecking, noimportant changes in predictions resulted).For the cued conditions, the retrieval as-sumptions were again the same as before,also with the provisos of this paragraph.

Since it did not seem appropriate to fit thecategorized case with the parameters forRoberts' data, we used the task and datafrom Watkins (1975, Experiment 1) andadjusted parameters roughly until a fit wasobtained. The predictions and data for thecontrol condition, the intralist cue condition,and the extralist cue condition for both twoand four cues are shown in Figure 17.Clearly these predictions are quite adequate.One important misprediction was obtained,however. The model was applied to the ex-tracategory cue condition of Mueller andWatkins (1977) and predicted a control con-dition advantage of about the same size asthose shown in Figure 17 for the other cueconditions. The data showed no such deficit,even though the provided cues had been pre-sented on the list in other categories.

We suggest that subjects given words fromcategories other than the category beingtested will be very reluctant to use these ascues. Furthermore, we suggest that the pre-dictions of SAMS would turn out to be cor-rect, if only the subjects could somehow beinduced to use these extracategory cues. Atest of this possibility must await furtherresearch.

It is most interesting to note that despitethe large number of parameters available inthis category case, we could not find anycombinations of values that would allow theprediction of the observed extracategoryfinding while simultaneously predicting theother findings (unless assumptions are

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Figure 17. Predicted and observed probabilities of crit-ical word recall in a category for the control conditionand for the intralist and extralist cue conditions, eachwith two or four cues (data from Watkins, 1975). (Themodel is described in the text; parameters are listlength = 36; words per category = 6; presentation timeper word = 3 sec; r = 4; KMAX/category = 12; LMM =3; a = c = .38; b = .38; item-category strength per sec =.38; category-cue and list-word-cue residuals to wordson list = .1; all increments = .36; residual strength ofextralist cues to list items in same category = .03; andproduct of residual strengths when self-sampling an ex-tralist cue = 2.2.)

changed between conditions). SAMS quitepersistently produced a part-list cuing effectin the extracategory condition whenever onewas predicted for the extralist condition.Thus we must not in this instance confusenumber of parameters with testability. (Ac-tually, the values of most of the parametersdo not affect the qualitative predictions.)1

' The explanations in Section III for the cuing deficitclearly do not apply in the case of extralist cues, sincean extralist cue is not part of any stored cluster. Thedeficit in the extralist case results from two factors:

118 JEROEN O. W. RAAIJMAKERS AND RICHARD M. SHIFFRIN

Conclusions and Comparisons With OtherModels

SAMS predicts essentially all the phe-nomena of part-list cuing. It does so robustlyunder virtually all combinations of assump-tions and parameter values and in fact can-not be made to predict the extracategorycuing result for this reason.

Most importantly, the basis for SAMS'prediction of the part-list cuing effect is thepresence and utilization within a search the-ory of the very interword associative networkthat previous theorists have argued cannotbe present or cannot be utilized. In short, itis proposed that extensive use of word cuesis made in both the control and cue condi-tions and that the sampling superiority forthe control condition outweighs the advan-tage during recovery of the cue condition.The control condition superiority is rootedin the nature of sampling from a network of(overlapping) clusters of words. When ex-perimenter-presented cues are utilized, thereis a tendency to gain access to clusters con-taining more critical items in the controlcondition than is the case in the cue condi-tion.

The reader may wonder why we have ex-pended so much effort in this section ex-ploring the predictions of the model underalternative assumptions. It may seem thatwe are studying the workings of the modelas much as the workings of the subject.There is some truth in this observation. Infact, we have attempted to deal with a prob-lem that Smith (1978) has termed "the suf-ficiency/transparency trade-off." The prob-lem is that as a model becomes more andmore complex and gains power to fit thedata, it becomes increasingly opaque to theexternal observers (even the model's cre-ators). The general principles are lost in theforest of details that such theories come tocontain. Our present model is less complex

First, an extralist cue has a high probability of samplingits own image, since it is only weakly connected to listwords. Second, because the extralist cues are weaklyconnected to list words, incrementing will have a dis-proportionately large effect, causing later searches toresample with high probability any word recalled earlier.These factors do not apply in the usual case of intralistcuing.

than many; in fact, SAMS may be writtenin two pages of FORTRAN code. Even so,the basic principles underlying the predic-tions of the part-list cuing effect would bevirtually impossible to ascertain, were we topresent only the general model and the pre-dictions. Our solution to the problem in thisinstance was an extensive search of the "as-sumption space" of the model.

The fact that SAMS predicts the part-listcuing effect does not invalidate other hy-potheses that have been proposed. Even ifSAMS is basically correct, other factorsmight be adding to or subtracting from thesize of the effect. However, it should be keptin mind that if a SAM-like approach isadopted, these other hypotheses are notneeded to handle the effect.

Let us consider briefly some of these al-ternative proposals. The possibility that in-crementing of the context-to-cue strengthtakes place when each cue is first used iscertainly worth considering (see Roediger,1973, 1974; Rundus, 1973). We added thisfactor to SAMS to see what additional ad-vantage for the control group would result.In particular, when each cue was first uti-lized in a sample, it was given an incrementto context (the same increment that nor-mally applies). Everything else in the modelremained as before, and the predicted con-trol group advantage increased by less than.05 words. Thus this factor contributes rel-atively little when added to SAMS (thoughit might be more powerful if the cue incre-ment were higher than normal or in a dif-ferent type of model).

There are many fairly trivial ways to pro-duce a control group advantage, some ofwhich are nevertheless plausible and worthconsidering even within the context of aSAM model. For example, the control groupmight search longer than the cue group. Thiswould happen if every recovery of a cue, eventhe first, counted as a failure. Then the cuecondition would reach KM\x much soonerthan the control condition. One difficultywith this explanation is the fact that it pre-dicts a strong dependence on the number ofcues. Additional cues do harm recall, butonly to a slight degree (e.g., Roediger, 1974;Slamecka, 1968, 1972; Watkins, 1975).

In any event, it is not known what search


strategies subjects adopt; if subjects are in-duced to search longer (that is, continue de-spite more failures) in one condition thananother, our model clearly predicts a cor-responding performance change. If a largevalue of AMAX is used for the cued condition,the amount of extra searching needed to sig-nificantly raise recall for the control condi-tion can be quite large (since new items arehard to recall after a long time searching).Thus the differential in the #MAX valuesmight have to be quite large, perhaps toolarge to justify. Nevertheless, the possibilityof differential stop rules in the different con-ditions cannot be ruled out. We commentmerely that such hypotheses are unnecessaryand inelegant.

A somewhat different explanation withinthe context of a search theory would pos-tulate that self-generated word cues (in thecontrol condition) are more effective thanthe experimenter-provided cues of the cuecondition for the following reason: A re-trieved image may contain word plus study-context information, whereas a provided cuemay contain word plus test-context infor-mation. Therefore the retrieved word cuesmay have higher strengths to the other wordsin storage than the provided cues. Higherstrengths could lead to higher probabilitiesof recovery for sampled images. Such a fac-tor could indeed lead to a control group su-periority. Whether this is an important fac-tor is another question. Presumably, theretrieved cue advantage only occurs to theextent that the retrieved study context pro-vides information not already in the generalcontext cue. However, a subject might wellaccumulate study-context information as thesearch proceeds and incorporate it into thecontext cue. If so, the difference between aretrieved cue and a provided cue might beminimal, except possibly for the first fewloops of the search. In conclusion, we admitthat a difference in cue effectiveness due tocontext retrieval might be contributing tothe part-list cuing effect. However, such anassumption is not needed for SAMS to pre-dict the effect, as we have seen.

A proposed explanation of part-list cuingthat has received considerable interest is thehypothesis that "vertical" or hierarchical,associations but not "horizontal," or interi-

tem, associations are stored in memory (e.g.,Roediger, 1973, 1974; Rundus, 1973; Sla-mecka, 1972). We are not really sure howthis hypothesis predicts the part-list cuingeffect, unless retrieval paths between itemson the same level of analysis are not allowedto traverse other levels of analysis, a hy-pothesis easy to rule out. In any event, thereis nothing wrong with vertical or hierarchicalassociations, and they are already part ofSAMS, as in the categorized recall situation.It is the absence of horizontal, interitem,associations that seems unusual. There seemslittle point in ruling out interword associa-tions, since the success of SAMS shows thishypothesis to be unnecessary.

Consider, finally, the "cue-overload" hy-pothesis (Watkins, 1975), which proposesthat the cues act more or less as additionallist items or category items, thereby reducingperformance for the same reason that wordsin longer lists are recalled more poorly(whatever that reason is). This effect pre-sumably operates despite the temporal andcontextual separation of the list cues fromthe list. In some ways this hypothesis is likethe cue-incrementing hypothesis discussedabove, since both extra items and incrementsfor cues serve to reduce sampling probabil-ities for critical words. On the one hand,SAMS provides a detailed and accurate ac-count of the list length effect (see the fit toRoberts' data); on the other hand, SAMSdoes not need to posit a lengthening of thelist or incrementing (see Figure 9) to explainthe effects of part-list cuing. Nevertheless,a list length factor could quite possibly becontributing something to the observed ef-fect.

Why have previous associative networkmodels (e.g., Anderson, 1972; Anderson &Bower, 1973) had difficulty predicting thepart-list cuing effect? Although they do in-clude item search along associative path-ways, they fail to utilize a random search.Thus, many items in the control conditionmay not be reached because entry points tomemory are limited. Furthermore, all itemsthat can be reached (within certain limits)from the list cues will be retrieved, and thereis no cost involved in doing so. There is nobuild-up of failures nor a stopping rule basedon such a build-up. These assumptions are


of course sensible when a directed, nonran-dom search is postulated, since the searchis assumed to proceed serially with no realprovision for resampling of previously founditems. Thus search simply proceeds until allrecallable items have been found.

The present theory, on the other hand,does incorporate the notion of costs involvedin retrieval. Thus the subjects are given areasonable basis for cessation of search, eventhough potentially recallable items remainin memory. We have shown that a sensiblestopping rule applied equally to both con-ditions, no matter how strict the stoppingcriterion, can give rise to a cue conditioninferiority. The basis for SAMS' solution forthe part-list cuing puzzle is the combinationof an associative network (as represented ina retrieval structure) with a cue-dependentprobabilistic sampling approach.

IV. The SAM Theory

Guiding Principles

A number of general considerations areprecursors of the SAM theory.

1. Long-term memory is effectively per-manent, with additions allowed, but not dele-tions. As a corollary, forgetting is a resultof retrieval failure.

2. Long-term memory is a richly inter-connected network, with numerous levels,stratifications, categories, and trees, thatcontains varieties of relationships, schemas,frames, and associations. Roughly speaking,all elements of memory are connected to allothers, directly or indirectly (though perhapsquite weakly).

3. Memory retrieval is cue dependent.What image is elicited from memory is de-termined by the probe cue utilized at thatmoment (Tulving, 1974).

4. Memory retrieval is noisy and henceprobabilistic. A given set of cues has somechance of eliciting from long-term memoryany associated image (though for many im-ages the probabilities may be extremelysmall). Furthermore, successive use of thesame probe cues may well result in the elic-itation from memory of different images.

5. Temporal-contextual information is offundamental importance; its role in storage

and retrieval must be delimited carefully andexplicitly.

Overview

SAM assumes a partition of memory intounitized images. These images are the ob-jects in memory that may be sampled duringa memory search. Images may be quite com-plex information structures and may overlapconsiderably with one another. An image isdefined by a property of unitization: At agiven stage of the memory search, the in-formation recoverable from memory is lim-ited to that in some one image.

The basis for retrieval is assumed to bethe strength of associative relationships be-tween probe cues and memory images. Theseare described within a retrieval structurethat is a matrix of retrieval strengths fromeach possible cue to each possible image. Thestrengths determine the tendency for a givenprobe cue to elicit a given image when long-term memory is probed with a given set ofcues. A retrieval structure is not a storagestructure; it is usually much simpler. How-ever, the retrieval structure is designed tocapture those aspects of the storage structurethat are important for retrieval.

Many images, especially those of impor-tance in laboratory tasks, are organized withrespect to temporal-contextual information.In such tasks, contextual information willalways be one of the cues used to probememory. Other cues, such as item and cat-egory names, may be used as cues in additionto context. A quantitative ratio rule is pos-ited in SAM that determines the probabil-ities of sampling each image, given any num-ber of cues in the probe.

When an image is sampled, some of theinformation in the image becomes availableto the subject for evaluation and decisionmaking. The proportion of such informationrecovered is determined by the retrievalstrengths between cues and image.

Retrieval is assumed to consist of a seriesof search and recovery operations organizedby a retrieval plan. The plan may be alteredas search proceeds. It is used to determinewhat cues are utilized at each stage of thesearch and to make certain decisions, suchas when to terminate the search. Retrieval


also includes a rapid initial phase, called sen-sory coding, that takes place when new in-formation is presented. This phase is largelyautomatic, usually concludes within severalhundred milliseconds, and generally resultsin the accurate retrieval of features that arerepresentative of the input in any context(including low level codes and a certainamount of semantic or type information).Our main concern in this article is withmemory search following the sensory codingphase.

The Units of Long-Term Memory

The conception of long-term memory asa richly interconnected system raises im-mediate problems for memory theorists. Itwould be impractical and inadvisable tothink of memory as a single complex object.On the other hand, the boundaries of "ob-jects" in an interconnected system are boundto be imprecise. It is common, for example,to think of a word as an object when ana-lyzing traditional memory paradigms in-volving word lists. However, such an objectconsists of a constellation of related conceptsand elements including everything fromshapes, sounds, phonemes, and letters,through parts of speech, synonyms, andmeaning, through codes, sentences, and con-versations and stories that might have con-tained that word, to the temporal-contextualsetting in which the word was presented andpossibly other words presented at about thesame time. All of these may form part of the"object" designated as a word. Yet all of theelements that make up an object will them-selves be associated, to some degree, to otherelements not in the object. In such condi-tions, an object's boundaries are bound tobe somewhat fuzzy, at best.

A second problem that makes it difficultto partition memory into objects is "level."If subjects are presented with and asked toremember letters from the alphabet, thenletters might be the basic level of the infor-mation in each object. In other tasks, singleobjects could comprise words, sentences,paragraphs, stories, or pictures.

A third problem depends on the structureof memory. Suppose for example, that a por-tion of memory is organized as a hierarchical

tree. Should the entire tree be treated as asingle object, should the individual nodes bedefined as the objects, or should some inter-mediate partitioning of the tree be definedas the object structure? The answer is farfrom obvious and may even differ from onetask to another.

Despite these problems, it is both neces-sary and desirable to partition memory intoobjects; in SAM this is done through theconcept of utilization. It is possible to dis-tinguish objects with imprecise boundariesby assuming that interconnections betweenelements will be stronger and more numer-ous within one object than between objects.When retrieval from memory occurs, a setof elements may be activated, which isthought of as entry into short-term store.Short-term store is limited in capacity (Shif-frin, 1976), and unitized sets of informationpresumably require less capacity. Thus itmay be easy to maintain elements of oneobject in an active state, but difficult tomaintain the same number of elements ifthey are spread among several objects. Weassume for this reason that retrieval operateson one object at a time. The informationrecovered from long-term store during oneloop of the search process will be a subsetof the information in one object. (How theobject is selected will be discussed later.) Theunitized objects of long-term memory arehenceforth termed images (no visual repre-sentation is implied).

How does unitization occur? The mostimportant factor is the encoding and re-hearsal process. The information and struc-ture that are simultaneously in short-termstore undergoing coding and rehearsal,whether composed mainly of letter, word,sentence, or story information, tend to bestored as a unitized entity. Of course, si-multaneous presence in a rehearsal bufferis not sufficient for a unitized entity to beformed. The nature and amount of codingand rehearsal will help to determine whethera unitized image develops. A unitized mem-ory object will form most easily when theinputs to short-term storage consists of al-ready unitized memory entities. This will bethe case with words, say, or nursery rhymes.In such cases, only the present context wouldhave to be combined with the previous im-


ages in order to produce a unitized imagefor the current situation. These assumptionsimply that there is a good chance that newimages will form when the same item is re-peated in different contexts or is repeatedin a similar context but coded in a new way.

It should be kept in mind that the variousimages in memory will, in general, overlapconsiderably, in the sense that the subcom-ponents of one image may be the subcom-ponents of other images as well. For exam-ple, sentences might be stored as the imagesin memory, even though the same words mayappear in more than one sentence. In suchcases, the images as a whole are quite dis-tinct, even if the subcomponents are not.Note that one of the most important sub-components that helps to distinguish imagesfrom each other is the temporal-contextualinformation that is stored within each image.

When an image is formed by the additionof temporal-contextual information to pre-existing images, it can be described as epi-sodic in Tulving's (1972) terms or as a tokenin Anderson and Bower's (1973) terms. Suchimages will tend to be retrieved selectivelywhen one of the cues is an appropriate con-text cue. Note that the formation of the newimage (e.g., horse + context) does not re-move or replace the previous image (horse)from memory. Whether that previous imagewas episodic (horse + some previous con-text) or semantic (horse + no particularcontext), it will still remain in memory. Suchreasoning is consistent with our general viewthat new inputs to memory are additive butnot subtractive.

Of course, images can be formed that haveno particular contextual basis—these areusually called semantic images or types.How are they formed? One possibility ariseswhen the contextual coding is weak or in-effective. For example, in tasks where mean-ing rather than setting is emphasized, thesupplementary information stored with theword in the new image might be semanticin nature rather than time or situation spe-cific. In addition, features that almost alwaysare present when an input is repeated in dif-ferent contexts will tend to become part ofthe feature set that is automatically retrievedduring sensory coding. Sensory coding willbe discussed later.

Are the objects of memory, once formed,fixed and inviolable forever? One alternativeanswer is that objects are partitioned withrespect to a given set of probe cues used inretrieval; different probe cues could resultin a change in the level and boundaries ofthe objects. For example, stories might bepresented and stored as images, but a laterrecognition test for individual words mightlead the subject to desire to tap memory atthe word level, rather than the story level.It is possible that the partitioning of memoryinto objects depends to some degree on thechoice of probe cues. However, the tasks andsituations to which we are currently applyingSAM (or SAMS) do not seem to require thisassumption. In any event, selection of imagesat different levels could be accomplished byjudicious selection of cues.

It should be understood that there may beonly a slight and subtle distinction between,say, two words plus context as a unitizedentity and two words, each with context, asseparate entities connected by an associa-tion. There are differences, however, that arepotentially testable in the context of oursampling and recovery assumptions. Aftersampling of a unitized two-word image, allof the available information from both wordswould be used for decision making, with noneed for further search. On the other hand,when one of two separate word images issampled, only the information in that imageis recovered. Recovery of information fromthe other image would require furthersearching (perhaps with the first word as anadditional cue), which might not succeedeven when the between-image association isquite strong. SAMS assumed for simplicitythat all images were single-word units (withappropriate interconnections) and predic-tions were quite accurate. In other tasks, theassumption of multiword units might provenecessary.

In summary, the interconnected long-termsystem is assumed to be constituted of a classof relatively unitized images. These imagesmay be interconnected in extremely complexways: in networks, hierarchies, and with var-ious types of relations. Furthermore, a givenimage will tend to have a complex infra-structure. An image has the following im-portant property: When sampled in a mem-


ory search, recovery of the availableproportion of its informational content oc-curs directly, without a need for furthermemory search with the same probe cues.

Storage Structures Versus RetrievalStructures

Because our main interest lies in the de-velopment of a retrieval theory, very fewassumptions will be stated concerning theinterimage structure. Our aim is to developan approach to retrieval that can be used foras wide a class of storage structures as pos-sible. To do this, we introduce the conceptof a retrieval structure consisting of retrievalstrengths between the possible cues (imagesand their subcomponents) and the imagesin memory. The strength determines the ten-dency for a given cue to sample (i.e., elicit)a given image and should be larger thelonger that the cue and image were codedor rehearsed during storage. This strengthdoes not necessarily have to depend on thetype of interimage connection that wascoded. For example, daisy and rose pre-sented in a list might be coded through therelation both are flowers, through visual im-ages of each in a vase, through connectionto a superordinate node or control elementsuch as flowers in list, or indirectly througha chain of associations between intermediatenodes or intermediate list words. It is notnecessary that rose as a cue be more likelyto elicit the image of daisy in one of thesecases than the other. In each case, the re-trieval strength (and hence the sampling ten-dency) would be determined by factors suchas the effort and duration expended in cod-ing and the type of coding carried out (e.g.,rote rehearsal vs. mnemonics). For the pur-poses of sampling, then, the memory struc-ture need not be taken into account explicitly(see Anderson, 1976, p. 154), as long as theimages and cues to be placed in the retrievalstructure are chosen judiciously (e.g., on thebasis of the subject's coding strategies), andthe cue-to-image strengths are chosen sen-sibly (e.g., on the basis of the effort, type,and duration of coding).

The foregoing discussion should not betaken to imply that the interimage structureis irrelevant for retrieval. The interimage

retrieval strengths should reflect the actualinterimage structure closely, so that evensampling could be said to conform to thestored structure in this sense. More impor-tant, the details of the between-image rela-tions, whether relations, labeled associations,or anything else (see Anderson & Bower,1973; Kintsch, 1974; Norman & Rumelhart,1975), are part of the information containedin each sampled image. This information,when recovered, will help to determine var-ious decisions, evaluations, and reconstruc-tions; the recovered features could also beused as additional cues during later stagesof the memory search. A good example wasthe application of SAMS to categorized freerecall: Category membership was stored ineach image, and category cues were used inthe cue sets.

Long-Term Retrieval

A SAM retrieval theory is organized bya retrieval plan that governs the successivesampling and recovery operations from aretrieval structure. Learning during retrievalis termed incrementing, and the initial, rapidretrieval when new information is input istermed sensory coding. These various com-ponents are discussed in the following sec-tions. Except where indicated to the con-trary, it will be assumed for simplicity thatthe partitioning of long-term store into im-ages does not change with different cues.

The retrieval plan. All decisions and con-trol processes involved in retrieval are sub-sumed in the retrieval plan. The organizationof retrieval is an extension of that proposedby Shiffrin (1970). Retrieval is a memorysearch proceeding in series of discrete steps.Each step involves a probe of long-term storeby one or more cues, which results in abriefly activated set of information, whichis followed by a selection, or sample, of animage from that set. The substages withinany one step are depicted in Figure 2. Re-trieval begins with some question the subjectneeds to answer regarding the contents oflong-term store. This may be as simple as:What is another word on the list most re-cently presented? In the most general case,a retrieval plan is generated to guide thesearch for the answer. Initially, the plan may


be somewhat vague by intention, in the hopethat later phases of the search will be guidedby information located in earlier phases. Theplan includes such things as an initial deci-sion whether to search long-term store; howto search (for instance, in a temporal orderor by an alphabetic strategy); how to chooseprobe cues (for instance, should recalled in-formation be used as probe cues?); whatcombinations of probe cues should be em-ployed and with what weights; whether toemploy the same probe cues on successiveloops of the search or whether to alter thecues; whether to search first for preliminarycues to guide later search; and how long tosearch (i.e., how many loops of the searchprocess should be carried out). The retrievalplan itself is constructed on the basis of theinformation in the test query, the informa-tion currently available in short-term mem-ory, and information retrieved from long-term memory; this information retrievedfrom long-term store may be concerned withsearch plans, previous successful plans insimilar situations, and so forth. Once con-structed, the retrieval plan is also stored inLTS. We assume in the context of the tasksdiscussed in this article that retrieval of theplan itself is easy and accurate, but therecould be cases where this assumption is vi-olated. Simple retrieval plans that mightplausibly be used in free-recall tasks werediscussed in Sections I and III. In general,however, little is known about retrievalplans, and their exploration may well be-come an active research area in the near fu-ture. (See Williams, 1978, for a discussionof retrieval plans.)

Next, on the basis of the retrieval plan,the subject assembles probe cues to be usedin retrieval. These cues may include: (a) in-formation the subject has about the contextat the time of study, (b) context represen-tative of the moment of test (although thesecues may not be useful or desired), (c) in-formation from the test question, (d) infor-mation retrieved earlier in the search, and(e) information generated during construc-tion of the retrieval plan.

After probing LTS, the cumulative acti-vation might be utilized as a basis for a rec-ognition decision. If search does not stop atthis point, then the information recovered

from the sampled image is evaluated. Thedecisions involved depend on the task butmight include the following: Does the imagederive from an item on the presentation list?What is the name encoded in the image? Isthe encoded name an appropriate responseto the cue? Does the encoded name matchthe test cue? Does the encoded informationhold the proper relationship to the probe in-formation? Is any of the recovered infor-mation useful for later phases of the search?

At this point the subject may or may notdecide to emit a response. Then a decisionmust be made whether to continue the mem-ory search. Presumably the decision to ter-minate is based on the previous successes orfailures up to that point. For example, in freerecall a decision to stop might occur whenm successive searches occur with no newwords recalled. If the search continues, thesearch loops back to the retrieval plan wherethe next probe set is chosen, and so forth.

The changes in probe cues as the searchcontinues are quite important. Althoughsampling is a random process, it is easy tomisinterpret such a statement and ascribemore randomness to the retrieval systemthan is, in fact, present. The strengths maybe such that one image is far more likely tobe selected than any other. Even more im-portant, the subject can control the searchby changing the probe cues as needed. Sys-tematic changes in probe cues may not leadto rapid conclusion of a memory search butmay be quite effective nonetheless. For ex-ample, when a subject is asked to recall aUnited States city starting with the letter^",2

one strategy would involve searching withstate-name cues, one at a time, generatedsystematically in geographic fashion.

The retrieval structure. A retrievalstructure is a matrix of the strengths be-tween the possible probe cues and the variousmemory images. It is a generalization of thestrength matrix shown in Figure 1. The cuesmay be labeled Qj, . . . QM) the images I,,. . . , Im, the strengths S(Q,, I,). In theory,all possible cues and images are containedin the structure, but in practice, most of thestructure is irrelevant. Typically, therefore,the matrix is restricted to images and cues

' Xenia, Ohio.


that are task specific. In SAMS, for exam-ple, the images and cues were restricted tocontext, list words, and category names.

The cues and the images in a retrievalstructure are generally quite distinct evenwhen they each encode nominally equivalentinformation (e.g., the same word). For ex-ample, suppose horse has been placed inlong-term memory at the time of study, andthen a recognition test is given with horseas the test item. We argue that the imageand the test cue are quite distinct, the imageconsisting of horse at study + study contextand the test cues consisting of horse attest + test context (the encodings of horsemay differ in the two instances, perhapsrocking vs. running). It is assumed that thelong-term memory image and the probe cuesare separate and identifiable entities, so thatif the memory image is sampled, it may beevaluated alone or compared with the probecues. However, these two entities will usuallybe strongly associated due to their large poolof common information; it is this fact thatmakes it likely that the cue horse will causethe image horse to be sampled. When animage and cue encode the same nominal in-formation, the cue is termed a test analogueof the image.

Note that the similarity of an image to itstest analogue used as a cue can be greaterthan is the case in the example above, if thecue is itself retrieved from memory duringa previous loop of the search. The reason isclear: The context in the cue in this casewould be more similar to that at the timeof storage, since some of it would have beenretrieved. Such a cue might also have higherstrengths to other images in memory.

Such reasoning suggests that the retrievalstructure should contain two types of cueswhenever cues are provided by the experi-menter—one type consisting of retrievedcues, the other, provided cues. Althoughsuch reasoning is correct in principle, it maybe excessively pedantic in practice. Presum-ably, a rational subject accumulates andutilizes all relevant contextual informationas he proceeds in the search. As a result,with the possible exception of the first fewsamples from memory, the difference be-tween provided cues and retrieval cues maybe small.

To generate a retrieval structure for aparticular setting (rather than the theoreti-cally infinite-size structure), one would beginby choosing an appropriate coding model toapply during storage. The storage assump-tions determine what type of images formand with what probabilities. The cues aregenerally chosen to represent the test ana-logues of the set of images that have beenformed, along with the natural subcompo-nents of those images (particularly the con-text component). Additional cues are placedin the matrix if they are provided by theexperimenter. Thus, for example, if sen-tences are presented, the images will all con-tain context information; some might alsocontain sentence concepts and others mightinstead contain fragments of these, includingperhaps single-word concepts. The cues willthen consist of the test analogues of thoseimages and their subcomponents.

The strengths in the retrieval structuredepend on the assumed storage process, onpreexisting associations and relations in forcebefore storage and at test, and on changesin context between storage and test. Thestrength determines the tendency with whicha given cue tends to elicit a given image dur-ing sampling (and also determines theamount of information recovered from theinfrastructure of a given image). The morethe information in a cue matches the storedinformation in an image, the greater is thestrength. Thus the longer two words are re-hearsed together, the greater the strengthbetween one of the words when used as a cueand the image of the other word. On theother hand, as the time between study andtest increases, or as the similarity of the con-text at study to that at test decreases, thebetween-word strength should decrease. Forlist words that were not rehearsed together,the strength (though low) will depend to agreater extent on extra-experimental factorsand should be affected less by delay and con-text change.

In summary, the retrieval structure is notmeant to be a copy of the stored memorystructure. Rather, the retrieval structuremay be thought of as a scaled simplificationthat captures aspects of the storage structurethat are relevant for cue dependent sam-pling.


The sampling process. All SAM re-trieval theories assume the same samplingprocess. In words, an image has a probabilityof being sampled that is determined by theassociative strength relating the set of probecues to the image in comparison with thestrengths relating all other images to the setof probe cues. More precisely, given a re-trieval structure, the probability of samplingImage i, given cues Q,, Q2, . . . , Qm in theprobe set, is given by

PsUlQ,, Qa, • • • ,

. (4)

A few words of explanation are useful toaid understanding of Equation 4. First, notethat this equation is an extension of the Luce(1959) ratio rule (most often applied tochoice behavior). This is most evident whenthere is only a single cue and w- 1.0, inwhich case Equation 4 becomes ST(Q,I,)/2 ST(Q, I*)- This special case was also

*the basis for the Shiffrin (1970) searchtheory.

In Equation 4, the Wj are weights repre-senting the saliency of the y'th cue, or theattention given the jih cue.3 In SAMS, theWj were all set to 1 .0, regardless of the num-ber of cues (though no more than 3 cueswere ever used together). Because STS islimited in capacity, there surely is a limit onthe number of probe cues that can be utilizedat one time, and a limit on the amount ofattention that can be distributed among thevarious cues. Such limitations could be cap-tured in any of several restrictions placed onthe Wj. One possibility is a limit, W, on thesum of the weights:

for all m. (5)

The SAMS model would be consistent withthis restriction if ff were at least 3. A some-what different assumption posits a fixed ca-pacity:

The possibilities of Equation 6 and of theuse of nonunitary weights are of more thanacademic interest. If weights are alwaysequal to 1.0, then the similarity or overlapamong cues is not properly taken into ac-count. To see this, consider an example ofextreme similarity among two cues: The cuesare identical. Substitution into Equation 4shows that the use of two identical cues, sayA and A, does not give rise to the same sam-pling probabilities as the use of A alone. Thislogical difficulty could be handled by relax-ing the assumption that all weights are uni-tary. For example, the weight given to a cuecould be reduced by a factor representingthe cue's overlap with other cues. Alterna-tively, the problem could be handled byadopting Equation 6. In this case, A and Atogether would give rise to the same sam-pling probabilities as A alone. The SAMSsimulation worked successfully despite let-ting all weights be unitary. We suspect thereason lies in the choice of cue sets: Theywere always made up of dissimilar cues.4

Aside from the weights, the sampling ruleassumes that the products of the strengthsof the cues to an image are used in the ratiorule. Such a product rule allows the searchto be focused on images that are stronglyconnected to all the cues, rather than justone of the cues. One might think that itwould generally be advantageous to combineas many cues as possible in each probe setto focus the search as narrowly as possible.Even when the weights are all 1.0, however,so that recovery improves with additionalcues, this is not necessarily the case. Oneproblem is the tendency for sampling one ofthe images of the cues themselves; this ten-dency could well be disadvantageous in cer-tain recall tasks. For example, in the SAMSapplications to part-list cuing, we saw thatone factor inhibiting free recall (for bothconditions) was excessive reliance on word-plus-context cues, compared with the con-text cue alone. Furthermore, there are var-

=W, for all m. (6)

3 Note that our use of a multiplicative rule requiresthe weights to appear as exponents. If they were mul-tiplicative factors, they would simply cancel out of thesampling equation.

4 The assumption of Equation 6 would change theSAMS simulation. We have not yet explored this al-ternative model and do not know whether the predictionswould change in important ways.


ious dangers involved in focusing a searchtoo narrowly, since a desired image may bemissed. Finally, the use of multiple simul-taneous cues may be restricted by capacitylimitations such as those described by Equa-tions 5 and 6.

Most of the images in long-term memoryhave such low retrieval strengths to the cuesthat their sampling probabilities will be van-ishingly small. The relatively small set ofimages with nonnegligible sampling proba-bilities is called the search set. It is thereforeconvenient (especially when incorporatingthe model in a computer simulation) to sep-arate the sampling phase into two parts:first, a restriction to the search set; second,an appropriate probabilistic choice from thesearch set. The choice of search set is gen-erally determined by task considerations.For example, if a subject is asked to recalla just-presented list, the search set might beassumed to consist of the images of all thewords in that list (or perhaps of all the wordsin the session, if intrusion predictions aredesired). Of course the model should alwaysspecify a search set containing the imagesthat might be sampled. If there is reason tobelieve that images are sampled that are notin the search set specified by the model, andrelevant predictions are desired, the searchset should be expanded to include the ad-ditional images.

Recovery. When long-term memory isprobed by a set of cues, a fairly large col-lection of information in many images is verybriefly activated. The total amount of suchactivation (and the relative activation of dif-ferent images) is determined by the strengthsin the retrieval structure for the cues thatare used. The activation of this informationis equivalent to the placement of the infor-mation into short-term store (STS). BecauseSTS is limited in capacity, it is incapable ofretaining very much of the activated infor-mation for more than a short time, perhapsa few hundred milliseconds. SAM assumes,therefore, that information from just a singleimage is retained long enough that the sub-ject can make a detailed evaluation duringthat loop of the search process.

For a given set of cues, the recovery as-sumptions first must determine the amountand type of initial activation. Then, when animage is sampled, the recovery assumptions

must determine the amount and type of in-formation that can be extracted from thatimage. The total amount of initial activationis probably proportional to the denominatorin Equation 4; it can be viewed as a feelingof familiarity and could conceivably be usedto make a recognition judgment without fur-ther search. Detailed information is notavailable, however, until recovery from asampled image occurs. Thus, in tasks suchas recall, in which the details of the infor-mation are a prerequisite for a response, onlythe recovery from sampled images is rele-vant.

The process of recovery is assumed to benoisy and imperfect, so that not all of theelements of an image will be activated. Ingeneral, the stronger the retrieval strengthbetween the sampled image and the probecues, the larger will be the proportion of im-age elements that will be recovered andmade available to the subject's evaluationand decision making mechanisms. In SAMS,the same retrieval strengths that determinesampling probabilities are used to determinethe proportion of recovered elements. In gen-eral, however, these strengths might not beequal; their relationship will depend on theresponse requirements of the task.

Once information is recovered, it is eval-uated and used in decision making and togenerate responses. In practice, it is oftenconvenient to combine the recovery processand the subsequent decisions into a singleequation. Consider, for example, a task inwhich the sampled images are words. In sucha case we propose the following equation togive the probability that a sampled image,i (that has not previously been sampled), cangive rise to an accurate production of thename of the encoded word, when Q,, . . .,Qm are the cues:

PR(I,IQ,, Q:, - - - , QJm

= 1 - exp{- 2 H>,S(Q,, I,)}. (7)j-i

This equation was utilized in SAMS, withthe Wj all set to 1.0.

The form of this equation is somewhatarbitrary mathematically, though it doescapture a number of features we considerdesirable for a recovery rule in this case.


First, the stronger the strength is to any onecue and the stronger the summed strengthsare to all cues, the more likely recall is. Sec-ond, the larger a cue weight is, the more thestrength to that cue will affect recall. Notethat this production rule obeys an additiverather than multiplicative rule, so that recallwill be high if even one weighted strengthis high. Third, the probabilities will rangefrom 0 to 1 as the sum of the strengths rangesfrom 0 to oo.

It should be noted well that in this system,the recovery probabilities are determined bystrengths from cues to image, not by imagestrength. Image strength per se does not infact exist in the system. Undoubtedly, thenames of common words are well encodedin numerous images in long-term memory.Whether the name can be generated in re-sponse to the cues (including context) is theonly relevant question.

Consider next how recovery attemptsshould be related when the same image issampled several times during a search. Shif-frin (1970) implicitly assumed independenceof the information recovered in successiveattempts, but such an assumption is difficultto defend. We propose here an alternativeview—that over the short time span nor-mally taken by recall, the information re-coverable from a given image does notchange appreciably when the same cues areused to resample that image. However, ifeven one new cue is involved in the resam-pling, then substantial amounts of new in-formation might be recovered.

The implications of these assumptions forrecall tasks are straightforward. They wereinstantiated in the SAMS simulation in thefollowing manner. It was assumed that suc-cessful recall of the word encoded in an im-age is always followed by successful recallfrom that image, regardless of cue set. Fail-ure to recall was assumed to be followed byother failures to recall, unless at least onenew cue for that image is in the cue set; inthis case, a new independent chance at recalloccurs.

It will not escape the reader's attentionthat the recall and recovery rule of Equation7, which was used in SAMS, makes no useof the fine structure of the association bywhich a cue and image might be related.

Only the strength value is utilized.5 Such aview can be defended, perhaps, in consid-eration of the structureless tasks of free re-call to which SAMS is applied. For taskssuch as sentence and paragraph memory, itwould not be surprising if the recovery andevaluation rules required explicit consider-ation of the type of relational informationbetween cues and images (which is assumedin SAM to be stored in each image). Thepoint is the following: Although SAM doesnot take the nature of an association intoaccount during sampling (beyond the degreecaptured by a strength value), there is noprohibition of recovering and using such in-formation after sampling.

Incrementing. Many results suggest thenecessity of a storage process that operatesduring the course of retrieval (see SectionsI and III and Raaijmakers & Shiffrin,1980). One type of storage is particularlyeasy to justify, since we have assumed thatstorage occurs when information is re-hearsed together in STS. Since informationrecovered from a sampled image enters STS,where it is considered in relation to the probecues already there, it seems likely in this casethat the retrieval strength between the probecues and the sampled image should be in-creased. In a recall situation, in which thename is required, it seems likely that themajor increase in strength would occur aftersuccessful recall takes place, with little orno increase after a failure to recall.

The process of increasing cue-to-imagestrengths during retrieval is called incre-menting. Assuming that significant incre-menting occurs only after successful recov-ery, it remains to be established how muchincrementing occurs when the same imageis sampled successfully a number of timesin a row with the same cues. It hardly seemslikely that incrementing would occur unat-tenuated after each successive sample of thesame image. (Since each increment increasesthe sampling probability of that image in the

3 Actually, the use of category cues in the case ofcategorized free recall and the assumption of the re-covery of category information from a recalled imagewere mild concessions in SAMS to the necessity of tak-ing the type of relationship into account. This does notalter the basic point made in the text.


future, the selection probability for some oneimage could eventually become almost unity.)We propose, therefore, that the major in-crease in strength occurs after the first suc-cessful recovery, with increases becomingsmaller thereafter. In SAMS, in fact, thesimplifying assumption was made that in-crementing between a given set of probe cuesand a given image occurs only after the firstsuccessful recovery. These assumptions wouldof course be altered if the subject were ledor instructed to give special attention andrehearsal to recovered items.

Long-Term Forgetting as RetrievalFailure

There are two basic reasons why an imagemay be retrieved better at Time A than atTime B. First, the cues utilized at Time Amay be more strongly associated to that im-age than those used at Time B. Second, thestrength and number of other images asso-ciated to the cues (even if the cues are thesame) may be greater at Time B than atTime A. Everything else being equal, an in-crease of cue strength to a given image in-creases both sampling and recovery proba-bilities (see Equations 4 and 7). On the otherhand, for fixed cue-to-image strength, an in-crease in the strengths of cues to other im-ages will reduce the sampling probabilities(though leaving recovery unaffected).

The increase in the strengths of cues toother images tends to be an inevitable con-sequence of new learning. This new learningwill not necessarily lead to forgetting, how-ever. The new information might be orga-nized together or integrated with the old im-age so strongly that a larger image is formedthat contains both the new and old infor-mation. Alternatively, the new informationmight form a new image that is tightly as-sociated to the old image. Retrieval of oneof these images could result in that image'sbeing used as a cue and eliciting the otherimage. In this case forgetting is preventedby an appropriate switch of probe cues. Con-versely, when the cues are not changed, for-getting may occur. This leads to the generalprinciple that forgetting due to new learningoccurs when the same cue is utilized in anattempt to locate one image among an in-

creasing number of other images. On theother hand, the subject may change the cueselection during the search so that each cueis related to a subset of the increasing num-ber of images; in this event forgetting maybe lessened or even reversed.

The decrease in the strengths of associa-tion of cues to image can be the result ofseveral factors, chief of which is the changeof context over time (e.g., see Bower, 1972;Estes, 1955). The context at the time of stor-age of an image makes the best retrieval cuefor that image. However, the context cueused at testing may consist largely of thecontext information available only at thattime. Since the test context usually differsfrom the storage context by a greater amountas time between storage and test increases,the retrieval strength is reduced.

The role of contextual factors in retrievaland forgetting is very important, and it is anessential component of SAM. The temporal-contextual features include incidental infor-mation from the sensory environment andthe subject's long-term store that happensto be present in STS at the time of a storageevent. They might include the location, thetemperature, the time of day, recent events,and the subject's physical state, feelings,emotions, and recent thoughts (Bower, Mon-teiro, & Gilligan, 1978; Smith, Glenberg,& Bjork, 1978). In SAM, such context fea-tures are always one of the probe cues, eitherby intent of the subject or by accident. Pre-sumably, the subject can, through attention,vary the weight assigned to this context cue,but such information is always present inSTS and always plays at least a small roleas a retrieval cue. Whenever possible, ofcourse, a knowledgeable subject tries to rein-state in STS as far as possible the contextualcues that were present at the time the to-be-recalled image was stored (Smith, 1979).

The first forgetting factor, in which oneset of cues is connected to an increasingnumber of images, was utilized extensivelyby Shiffrin (1970) to explain list length ef-fects in free recall. Since that time, listlength effects (sometimes called fan effects)have been observed in many settings. In ourown research, we have observed such effectsin paired-associate and recognition para-digms, as well as in free-recall studies. Muel-


ler and Watkins (1977) have referred to thisforgetting factor as cue overload. The SAMtheory may be said to provide a theoreticalbasis for the cue overload principle. It is in-teresting to note that Mueller and Watkinsused the cue overload principle to explainthe part-list cuing effect. As described ear-lier in this article, the SAMS model explainsthe part-list cuing effect without any re-course to a cue overload factor. Neverthe-less, the cue overload principle is, in SAM,one of the fundamental bases of retrievalfailure.

The second basic forgetting principle, con-text change, or more generally, reductionsin cue-to-image retrieval strength, is used toexplain the deleterious consequences of de-lay of test and helps explain the difficultiescaused by the presentation of interferingmaterials during the study-test interval. Anexposition of this principle would require amodel of context change and is well beyondthe scope of this article.

Sensory Coding

When a stimulus is first presented to thesubject, it begins undergoing sensory anal-ysis. Even the very lowest, initial stages ofsensory analysis are properly viewed as in-volving retrieval from long-term memory. Ateach stage of analysis, the previously re-trieved features plus context already in STSdetermine the next features to be retrieved.When the stimuli are highly discriminable,these stages of sensory coding are rapid, ac-curate, and automatic. At the higher levelsof analysis, the meaning of the input is re-trieved along with, perhaps, particular con-textual images containing the input. Al-though it is difficult to draw a dividing lineat any one point in this stream of processing,we lump together the relatively noncontex-tual retrievals and call the results sensorycoding. These retrieved features are thenviewed as the first item cue for the subse-quent memory search.

Sensory coding typically concludes in sev-eral hundred milliseconds and is quite au-tomatic, differing in both respects from thesubsequent memory search. Nevertheless, itis possible that the same basic retrieval

mechanisms (e.g., Equations 4 and 7) op-erate during this initial phase of retrieval.Such a possibility could be explored withinthe context of recognition and detection par-adigms. Of course, if the inputs are degradedso that accuracy of coding drops and con-fusions result, the situation is even closer tothat in the memory search domain. Perhapsthreshold detection could prove consistentwith a search model positing a single samplefrom memory. Such a possibility is not en-tirely implausible, since one of the successfulmodels for sensory confusions is a modifiedLuce choice model that is formally identicalto Equation 4 (Luce, 1959; Luce, Bush, &Galanter, 1963).

Applications of SAM to Other Paradigms.

Although it is not possible in this articleto describe in any detail the application ofSAM models to other paradigms (see Raa-ijmakers & Shiffrin, 1980), a brief discus-sion is quite useful, especially since very fewchanges in the SAMS simulation are neededto fit the results from certain standard par-adigms.

Free recall. No changes in the structureof SAMS should be necessary to fit the re-sults of standard, verbal, free-recall para-digms. Cumulative responses as a functionof time and interresponse times are alreadyinherent in SAMS, since each loop of thesearch may be assumed to occupy one unitof time. Output rates slow down, since re-sampling of previously sampled images gen-erally increases at the expense of new sam-pling as search continues. The resamplingtendency is increased even further by incre-menting (one tends to sample items previ-ously recalled). It would be possible for asubject to reduce the resampling tendencyconsiderably by using a systematic strategyto generate and change cues. For example,a search based on first letters could proceedsystematically through the alphabet. Appar-ently subjects seldom use such strategies.

Sometimes subjects are asked to recall thesame list several times in succession with nonew presentations. About the only additionto SAMS that is required to deal with thissituation is a decision concerning whether


additional incrementing should be allowedwhen the same word is recalled during suc-cessive retrieval periods.

SAMS makes no provisions for confusionsor intrusions in free recall. Intrusions ofwords in the session but not on the currentlist can be handled by expanding the re-trieval structure to include such images(with low strengths to current list cues, ofcourse). Intrusions of nonpresented wordscan be handled in part by allowing for im-perfect recovery of presented words, that is,confusions. Another possibility would in-volve expanding the strength matrix to in-clude images of nonpresented words (withvery low strengths to current list cues). Notethat an implicit part of the recovery processin SAMS is a judgment that the sampledword was in fact on the current list. If falsealarms could occur, then images of wordsnot on the current list could be mistaken forcurrent list words, and intrusions would oc-cur (as opposed to confusions).

The application of SAMS to categorizedfree recall has already been described in thisarticle, albeit quite briefly. No importantchange in the SAMS model was required,except for the inclusion of a category namecue in the retrieval structure and the as-sumed use of such a cue during retrieval.

Paired-associate paradigms. Experi-ments can be carried out in which items arepresented only once prior to test but in whichthe items are grouped at input. Then testingcould be done by a free-recall technique orby presenting one or more members of eachgroup as cues and requesting recall of theremaining members of the group. If thegrouping is by pairs, and one member of apair is provided as a cue at test, the paradigmmay be termed single-list paired-associaterecall. It should be clear that SAMS is struc-tured to deal with such a paradigm, sincecued testing is already a fundamental partof the model and is used extensively in theapplications described earlier in this article.

We have found that the results of suchstudies can be predicted quite well by SAMS,even though the images are all assumed toconsist of single words plus context. Onemight ask whether there are data requiringmultiword images to be added to the re-

trieval structure. We have not found thisnecessary in paired-associate settings buthave found such assumptions helpful in par-adigms involving three-word groupings andcued testing. We suspect that such assump-tions might also be useful in studies involvingsentence presentation. In fact, Jones (1976)has fitted a variety of such data with a frag-ment model that incorporates a central as-sumption that stored units can consist of sen-tence fragments ranging in size up to fullsentences. Although the SAM theory differsfrom the fragment model in many respects,an assumption of multiword images in SAMmight incorporate many of the same desir-able properties that are captured by frag-ments in Jones' model.

Learning paradigms. There is a vast lit-erature on verbal learning experiments thatinvolve multiple presentations of items orlists. A variety of changes would take placeduring learning in such studies according toa SAM theory. These include the develop-ment of the following: multi-item images, acomplex interitem structure, an elaboratedependence on context, and a systematic re-trieval strategy. These complexities take dis-cussion of such paradigms beyond the scopeof this article.

Recognition paradigms. Recognitionposes particular problems for search theo-ries. Simple theories require an extendedsearch without success before an accurateresponse can be given that a test item is noton the presentation list, but if this were cor-rect, the possibility of rapid, accurate, noresponses would be eliminated. The problemis not restricted to stochastic search theories,but this is not the place to discuss the ac-curacy of such reasoning or the relevant data(see Ratcliff & Murdock, 1976). Instead wepropose one way in which rapid recognitionresponses could be produced within a SAMframework.

It is proposed that the subject has accessto the sum of strengths that appears in thedenominator of the sampling equation(Equation 4). The details of the activatedinformation are probably not available atthis stage. A value proportional to the sumof strengths could be described as a "feelingof familiarity." Within a given task, criteria


could be set such that a familiarity valueabove the upper criterion could be used asa basis for a positive recognition response,and a familiarity value below the lower cri-terion could be used as a basis for a negativerecognition response. A familiarity valuebetween the criteria would be ignored, anda normal search would proceed thereafter.Such a model is similar to that of Atkinsonand Juola( 1973).

Ignoring the possibility of a recognitionresponse based on familiarity, recognition ina SAM theory proceeds just as in recall set-tings. The sampling is identical, but the im-age sought is one that contains the probe cueitself. In addition, after information is re-covered from a sampled image, several judg-ments must be made. A match judgmentdetermines whether the information in thesampled image could be an encoding of thetest item. A context judgment determineswhether the sampled image was on the rel-evant presentation list. Note that these judg-ments must depend on the quality of the re-covered information; strength alone is notsufficient. For example, a change in contextreduces the cue-set-to-image strength, andhence less of the information in the sampledimage is recovered. But will a judgment ofa match be increased or decreased as a re-sult? More detailed knowledge of recoveryis needed before this question can be an-swered.

Final CommentsWe have presented in some detail the un-

derlying basis for a new retrieval theory thatassumes probabilistic, cue-dependent sam-pling from a retrieval structure representingan associative network. The storage pro-cesses, memory representations, and re-trieval mechanisms have all been laid out,although the greatest emphasis has been di-rected toward the search and retrieval op-erations.

A specific model, SAMS, was developedfor free recall. Parameters were estimatedso that the model would fit free-recall datainvolving variations in list length and pre-sentation time. SAMS was used, essentiallyintact, to fit a variety of results from thepart-list cuing paradigm. Although the modelcontains many processes and parameters, thepredictions of the model are largely inde-

pendent of the process assumptions andchoices of parameter values. In fact, the pre-dictions graphed were based on parametervalues independently generated in fittingRoberts' (1972) free-recall data. The pre-dictions are impressive for this reason andbecause they are based on a model makingextensive use of interitem associations in re-trieval—a possibility thought by previousinvestigators to be ruled out by the data.

There are a number of strengths of SAMSand also of the general theory, SAM. Oneof the most important is the careful deline-ation of the roles of control processes anddecision processes in retrieval. The appli-cation to part-list cuing has illustrated theimportance of carefully specifying such fac-tors. The sampling assumptions are anotherkey element of the present approach in sev-eral different ways. First, the fact that sam-pling is probabilistic allows for a consider-able degree of resampling in certaincircumstances. Such resampling of previ-ously sampled images is the basis for stop-ping the search and hence an important con-tributor to the limitations on retrieval.Second, the sampling equation (Equation 4)provides an explicit basis for combining cuesand for focusing the search. The recoveryequation (Equation 7) is also important, be-cause it allows for imperfect recovery fromsampled images but lets the amount of re-covery depend on the cue-to-image strength.Thus the effects of such variables as presen-tation time are easily handled.

The use of a retrieval structure is an im-portant part of the SAM theory. The re-trieval structure abstracts from the LTSstructure a simple enough representationthat quantitative calculations are quite ele-mentary and at the same time abstracts acomplex enough representation that veryelaborate situations can be handled sensiblyby the theory. We admit that this approachhides many of the problems that arise duringmodeling of memory for highly structuredmaterials by placing details of the interitemrelationships inside the images, where theyare dealt with during the recovery process.For complex structures, it might prove nec-essary to make the recovery process a veryelaborate system. Nevertheless, the presentapproach does provide a vehicle by whichsuch complex situations could be handled


within a search theory based on stochasticsampling, which we think is a significant stepforward.

In comparison with theories that focus onthe memory structure rather than the mem-ory process, the SAM theory has severaladvantages. One is the ease with which for-getting phenomena may be handled. In thisarticle, forgetting due to list length (or fan-ning) effects was predicted by SAMS. For-getting due to delay is easily handled bymodeling context changes. Interference phe-nomena can presumably be handled by acombination of these two factors, thoughsuch possibilities have yet to be explored indetail (but see Shiffrin, 1970, for one searchmodel for interference effects). Another ad-vantage is the emphasis on strategies thatallow retrieval to be controlled by the sub-ject.

Conversely, the greatest weakness of theSAM theory may be the freedom allowedby the numerous retrieval strategies. Itwould be tempting to predict any new resultby arbitrarily assuming a new strategy de-signed to produce the observed effect. For-tunately, strategies may be manipulated ex-perimentally, by instruction and task demandcharacteristics, so that models based onchoices of strategies may be evaluated andtested.

Notwithstanding the success of SAMS infitting free recall and part-list cuing, a gen-eral and complex model such as SAM cannotbe judged a success simply on the basis ofpredicting the results from one or two studiesor paradigms. We have therefore embarkedon a program of evaluation in which themodel (in essentially unchanged form) isapplied to as many paradigms and resultsas possible. Reports on these applications areforthcoming. In particular, for applicationsto a wide variety of tasks involving free re-call, categorized free recall, cued recall, andpaired-associate recall, see Raaijmakers(1979) and Raaijmakers and Shiffrin (1980).

Reference Notes1. Twohig, P. T. Facilitation and inhibition of list

words by list cues. Paper presented at the meetingof the Eastern Psychological Association, Philadel-phia, April 21, 1979.

2. Kintsch, W., & Kalk, J. M. Cueing with list itemsin multitrial free recall. In Studies in mathematicallearning theory and psycholinguistics (CLIPR Pub-

lication No. 6). University of Colorado ComputerLaboratory for Instruction in Psychological Re-search, April 1972.

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Received September 27, 1979Revision received April 20, 1980

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