An ARC-REM Model for Accuracy and Response Time in Recognition and Recall

Transcription

1 Jurnal f Experimental Psychlgy: Learning, Memry, and Cgnitin 2001, l. 27, N. 2, Cpyright 2001 by the American Psychlgical Assciatin, Inc /01/S5.00 DOI: // An ARC-REM Mdel fr Accuracy and Respnse Time in Recgnitin and Recall David E. Diller, Peter A. Nbel, and Richard M. Shiffrin Indiana University Blmingtn This article presents a mdel fr accuracy and respnse time (RT) in recgnitin and cued recall, fitted t free-respnse and signal-t-respnd data frm Experiment 1 f P. A. Nbel and R. M. Shiffrin (2001). The mdel psits that recgnitin perates thrugh parallel activatin in a single retrieval step and cued recall perates as a sequential search. Because the data fr recgnitin shwed that variatins in list length and study time per list had a large effect n accuracy but a small r negligible effect n (a) free-respnse RT distributins and (b) retrieval dynamics in signal-t-respnd, the timing f the recgnitin decisin is based n an assessment f retrieval cmpletin (ARC), rather than n a sufficiency f evidence in favr f 1 f the respnse ptins. By assuming within-trial frgetting, the mdel predicts bth the dissciatin f accuracy and RT and the finding that errrs are slwer than crrect respnses. Fr cued recall, this mdel was incrprated as the 1st step in a search cnsisting f cycles f sampling and recvery. This article presents a mdel fr accuracy and respnse time (RT) in episdic recgnitin and cued-recall tasks. The mdel is fitted t data frm Experiment 1 in the cmpanin article by Nbel and Shiffrin (2001). Nbel and Shiffrin used RTs and retrieval dynamics assessed in signal-t-respnd tasks t cntrast retrieval in recgnitin and cued recall. Three studies demnstrated that retrieval times and retrieval dynamics were cnsiderably slwer in cued recall than in recgnitin. The results are cnsistent with the fllwing prpsals: First, recgnitin is carried ut by cmparing the test item in parallel with episdic memry traces in a "singlestep" retrieval prcess, cmbining the resultant trace activatins int a single measure termed familiarity, and basing a recgnitin decisin n the result. Secnd, cued recall is carried ut with a sequential search cnsisting f a series f cycles, each cmpsed f a sampling f ne trace based n its relative activatin, recvery f infrmatin frm the sampled trace, and decisins abut respnse and search cntinuatin based n the recvered infrmatin. These are, f curse, familiar cncepts that have been used previusly in, fr example, the search f assciative memry (SAM) mdel f Raaijmakers and Shiffrin (1980, 1981) and Gil- David E. Diller, Peter A. Nbel, and Richard M. Shiffrin, Department f Psychlgy, Indiana University Blmingtn. David E. Diller is nw at Blt-Beranek and Newman, Bstn. Peter A. Nbel is nw at Micrsft Crpratin, Seattle, Washingtn, and is nw named Peter A. Kss-Nbel. A prtin f the research in this article was submitted by Peter A. Nbel in partial fulfillment f the requirements fr a PhD in psychlgy at Indiana University Blmingtn. Funding fr this research was prvided by Natinal Institute f Mental Health Grant MH12717, Air Frce Office f Scientific Research Grant , and Natinal Science Fundatin Grant SBR Crrespndence cncerning this article shuld be addressed t Richard M. Shiffrin, Department f Psychlgy, Indiana University Blmingtn, Blmingtn, Indiana Electrnic mail may be sent t shiffrin@indiana.edu. lund and Shiffrin (1984) and the retrieving effectively frm memry (REM) mdel f Shiffrin and Steyvers (1997, 1998). These same ideas frmed the basic structure f the mdel in this article. T prevent redundancy, the reader is referred t Nbel and Shiffrin' s (2001) article fr a full presentatin f the relevant literature, data, and arguments related t this cre cnceptin. Althugh the use f single-step retrieval fr recgnitin and sequential search fr cued recall has rather bvius implicatins fr RT predictins, the SAM and REM mdels have been restricted fr the mst part t accuracy predictins. In this article, we rectify this missin by presenting a jint mdel fr accuracy and RT. Althugh very similar in cnceptin t the SAM mdel, the new mdel is cuched in terms f the Bayesian apprach and vectr representatins f the REM mdel. There are many ways that ne might incrprate RT mechanisms in mdels that fllw the general framewrk we have utlined, r in the SAM and REM mdels in particular. The particular chice that we have adpted fr recgnitin is atypical (as we described in the sectin The ARC Mdel) but was mtivated by recgnitin data frm the studies by Nbel and Shiffrin (2001): Several f their studies varied list length and list study time; these variatins prduced large and reliable accuracy differences but small (r missing) and unreliable RT differences. Althugh the relevant results were reprted by Nbel and Shiffrin, discussin f their imprtance was deferred t this article. We therefre begin this article by summarizing the results cncerning list length and strength (especially fr recgnitin), the relatin f these results t the literature, and the pssible implicatins fr thery. Effects f Length and Strength The experiments f Nbel and Shiffrin (2001) used freerespnse and signal-t-respnd paradigms t track the time curse f retrieval. A given participant tk part in sessins fr each paradigm, with the wrds in 1 sessin being reused in different rders in the next sessin. Each sessin cnsisted f study 414

2 RECOGNITION AND RECALL MODEL 415 f a list f wrd pairs, fllwed by a brief perid f arithmetic t clear shrt-term memry. During the study perid, the participant knew whether testing wuld be by free respnse r by signal-trespnd but nt whether by recgnitin r cued recall (r, in sme studies, by paired recgnitin r by assciative recgnitin). Single-item recgnitin was tested with presentatin f a single test wrd (fr an ld-new respnse), and cued recall was tested with presentatin f a single test wrd (the participant attempted t recall the paired wrd). 1 In free respnse, used in Experiment 1 f Nbel and Shiffrin (2001), participants respnded as quickly and accurately as pssible. In this case, distributins f RTs were cllected fr each cnditin f length and strength, fr each pssible categry: hits, false alarms, crrect rejectins, misses, crrect recalls, recall intrusins, and recall "give-ups." In signal-t-respnd, respnses were withheld until a signal was given, and then respnses were emitted quickly, within a small windw f time. The lags until the signal were varied in 10 steps, chsen randmly acrss trials, ver a range frm 100 ms t 5,000 ms. In this case, respnses and accuracy were measured at each lag. Fr recgnitin, the d' accuracy data (btained frm the hit and false-alarm data at each lag) and, fr cued recall, the prbability f crrect respnse were fitted with expnential functins that start rising frm chance at an intercept value (I), grw expnentially at a rate (G), and level ut at an asymptte (A). Accuracy The effects f length and strength n accuracy are summarized as fllws: Shrtening lists frm 40 pairs t 10 pairs and slwing list presentatin frm 670 ms per pair t 2,000 ms per pair each dramatically increased perfrmance. The free-respnse results are shwn in Table 1: d' fr recgnitin rse 39% fr the shrter lists Table 1 Accuracy Predictins f the ARC-REM Mdel Respnse Cnditin Hits False alarms , , , ,000 Free respnse, recgnitin.68 (.69).82 (.83).67 (.65).78 (.78) Crrects Free respnse, cued recall.18 (.17).42 (.45).10(.ll).32 (.34) Respnse.21 (.21).16 (.14).30 (.31).21 (.25) Intrusins.08 (.10).09 (.08).09 (.06).10 (.08) Nte. Fr the cnditins, the first number (10 r 40) refers t the number f pairs in the list, and the secnd number (670 r 2,000) refers t the length f the list presentatin per pair in millisecnds. Observed values are in parentheses. ARC = assessment f retrieval cmpletin; REM = retrieving effectively frm memry. and 56% fr the strnger lists, and prbability crrect fr recall rse 35% fr the shrter lists and 179% fr the strnger lists. Fr signal-t-respnd, estimated asympttic d' fr recgnitin rse 36% fr the shrter lists and 56% fr the strnger lists, and estimated asympttic prbability crrect fr recall rse 38% fr the shrter lists and 245% fr the strnger lists. All f these accuracy results were highly reliable and highly significant statistically. The list-length effects n accuracy are quite prnunced. In previus research, the questin has been raised whether such effects culd be due t sme cmbinatin f serial psitin effects at study and test and study-test lag (e.g., Murdck & Andersn, 1975). Althugh cgent arguments against this view have been made (e.g., Ohrt & Grnlund, 1999), we adpted a cnservative apprach in the present paradigm: We cntrlled these variables as much as pssible by testing 10 early items r 10 late items in the lnger list. The relevant results are described briefly in Nbel and Shiffrin (2001) and are prvided in detail at the fllwing website: (Appendixes C and D); the results reveal little supprt fr this accunt. There was little difference between tests f the first 10 r last 10 wrds f the 40-wrd list, and thus there is little evidence that serial psitin r lag effects are prducing the list-length differences (see als Grnlund & Elam, 1994). We therefre ascribe list-length effects t extra nise in the retrieval prcess when lnger lists are accessed, a hypthesis cmmn t all the glbal, parallel mdels f recgnitin (e.g., SAM [Gillund & Shiffrin, 1984], MINERA [Hintzman, 1988], the cmpsite hlgraphic assciative recall mdel [Metcalfe Eich, 1982, 1985], and the thery f distributed assciative memry [Murdck, 1982]). The effects f study time n accuracy are als quite prnunced. These effects are presumably due t better strage f infrmatin when study time is lnger, an assumptin cmmn t all mdels. RT RTs did nt exhibit the patterns fund fr accuracy. Fr cued recall, there was, if anything, a small tendency fr the mre accurate cnditins t be slwer, but theretically, the relatin between accuracy and RT in recall tasks is a very cmplex matter (certainly s fr the mdels we cnsider), and we defer discussin f RT fr recall until the end f this article. Recgnitin RTs are ptentially mre interpretable and diagnstic (fr several classes f mdels), and we fcus n these RTs in this sectin. In free respnse, the fur (cnditinal) RT distributins fr hits, false alarms, crrect rejectins, and misses were almst identical acrss the variatins in length and strength. Figure 1 illustrates this claim. Statistical cmparisns f varius measures f central tendency and f the full distributins were carried ut by Nbel and Shiffrin (2001). The length effects and the strength effects were cmpared statistically fr each f the fur measures, giving 8 cmparisns fr each measure f central tendency and 8 fr the full distributins. The means, fr example, shwed significant differences (p <.05) nly fr length fr hits and nly fr 1 Althugh we d nt discuss the data in this article, paired recgnitin was tested with a wrd pair, bth studied tgether r neither studied at all (fr an ld-new respnse); assciative recgnitin was tested with a wrd pair that had been studied r with a rearranged pair, cmpsed f wrds that had each been studied but nt tgether (fr an ld-new respnse).

3 416 DILLER, NOBEL, AND SHIFFRIN.3-- g Q_.3 -- Reactin time (ms) Reactin time (ms) I a False Alarms 10 pairs pairs p =.17 p =.28 H = 1009 IX =990 a =337 a =369 m = 985 m = 946 ' c a. 2 a pairs - p=.24 H =980 =366 m = 924 Misses 40 pairs p =.28 (i =955 a =328 m = False Alarms 670 ms 2000 ms p = a = 386 m = 978 Reactin time (ms) Reactin time (ms)

4 RECOGNITION AND RECALL MODEL 417 strength fr misses. Statistical cmparisn f the full distributins revealed differences fr these tw cases and als fr length fr crrect rejectins. Thus, statistically significant differences fr length and strength variatins were fund fr nly 5 f the 16 cmparisns f the free-respnse data (a result nt ascribable t lack f pwer r sufficient data cllectin). We d nt, f curse, cnclude that there were n RT differences acrss cnditins (which wuld be an impssible utcme), but we d call attentin t the fact that btaining reliable accuracy differences in ur study was far easier than btaining reliable RT differences. Cmpatible with these results is the fact that a cmmn intercept and grwth rate culd nt be rejected fr the signal-t-respnd functins fr the fur length-strength cnditins. We must admit that the signal-t-respnd data were much nisier, and the pwer f the cnclusins that can be drawn frm this result is crrespndingly lwer. Hwever, related findings in signal-t-respnd are nt unknwn: Dsher (1984a) btained a similar result fr study duratin, albeit fr assciative recgnitin. Extraplating frm the high-cnfidence RT data f Ratcliff and Murdck (1976), we had expected significant effects f length and strength n RT n all f ur measures. We shuld als nte that there was a clse relatin acrss length-strength cnditins between accuracy in free respnse and signal-t-respnd. Dsher (1982) dcumented a strng negative crrelatin between asympttic accuracy in signal-t-respnd and free-respnse RTs. Such findings wuld als lead ne t expect effects f length and strength n RT. Thus, ne might ask whether there might be artifactual explanatins fr ur findings. Fr free respnse, ne might prpse that ur participants were just respnding at a certain (albeit highly variable) pace, nt allwing the retrieved infrmatin t affect the RTs. Hwever, this explanatin is nt very likely because the distributins fr incrrect respnses were substantially different frm the distributins fr crrect respnses (i.e., fast respnses were cnsiderably mre accurate than slw respnses). The relative cnstancy f RT as length and strength varied is, at the least, puzzling. It wuld have been trivial fr the participants t make the RTs differ, because they were aware f the length and the strength f the current list and culd have slwed dwn r sped up respnses accrdingly (see Ratcliff, 1978, fr a related discussin). In cntrast, it wuld have been very hard fr participants t prduce the cnstancy strategically even if they had attempted t d s. The individual RTs were quite variable, and the RT feedback was almst certainly nt precise enugh t allw the participants t adjust the times t match as precisely as shwn in the results: The nly RT feedback was the mean crrect RT fr the just-cmpleted blck. Perhaps participants culd remember the mst recent feedback fr the fur cnditins and smehw managed t slw dwn r speed up their respnding when a given cnditin ccurred t bring the cnditins tgether. Hwever, it seems unlikely that participants wuld want t d this r wuld be capable f ding this. One reviewer was cncerned nnetheless that the feedback we prvided culd have allwed the participants t adjust their respnding acrss cnditins t prduce the cnstancy. In part fr this reasn, a study with such feedback eliminated was carried ut in ur labratry by a pstdctral visitr, Rd Smith (Smith & Shiffrin, 1997). This study will be reprted in full elsewhere, but we reprt ne particularly relevant result that bears n the present issue. The study used the same wrds and study cnditins as thse used in Experiment 1 f Nbel and Shiffrin (2001). Hwever, the tests used a variant f signal-t-respnd prcedures intrduced by Meyer, Irwin, Osman, and Kunis (1988): Participants respnded under typical free-respnse instructins emphasizing bth speed and accuracy except when interrupted by a signal; if a signal ccurred befre a respnse had already been made, then a respnse was required within a very shrt time perid after the signal. Signals ccurred nly n a prtin f the ttal test trials; the ther trials were scheduled t have n signals and, therefre, were regular free-respnse trials. This prcedure has been used by Meyer et al. (1988) and Ratcliff (1988) t assess partial infrmatin available befre a free respnse is ready t be emitted. As in these previus studies, we fund that participants indeed had partial infrmatin available en rute t a respnse. Of mre relevance t the present issue, we designed the study s n RT feedback was prvided cncerning the participants' freerespnse RTs. They were given feedback nly cncerning their success in respnding within the time limits n signal trials. We then examined the subset f trials n which n signal was scheduled t ccur. Neither fr variatins in list length nr fr study time did the cnditinal RT distributins differ, replicating the findings frm the study reprted in this article. Althugh accuracy in Smith and Shiffrin's (1997) study was nly slightly (and nnsignificantly) better fr the slw presentatin times, accuracy was significantly better fr the shrter lists. Thus, as in the present experiment, RT distributins did nt change acrss a variatin that did prduce accuracy differences. This result in the Smith and Shiffrin study culd nt have been due t a strategy based n RT feedback because such feedback was nt prvided. The results in bth the present study and the Smith and Shiffrin (1997) study seem at dds with sme previus findings (Murdck & Andersn, 1975; Ratcliff & Murdck, 1976). There are a few differences in apprach and prcedure that culd have led t the differing utcmes. Fr ne thing, ur studies were designed t minimize differential effects f study psitin, test psitin, studytest lag, and, in general, any cntaminatin by recgnitin frm shrt-term memry. We did this by interpsing arithmetic perids after the study phase and befre the test phase f a list and by fixing the number f tests per list t a cnstant regardless f list length. The previus studies generally did nt have such prvisins, which may accunt fr sme f the differences in results. In additin, the previus results were reprted nly fr highcnfidence respnses. Finally, the use f cnfidence ratings may Figure 1. Recgnitin respnse time (RT) distributins cnditinalized fr giving a particular respnse. In Panels A, C, E, and G, the distributins are cmbined acrss study time, whereas in Panels B, D, F, and H, the distributins are cmbined acrss list length, p = prprtin f respnses f that type; ju. = mean RT; a = standard deviatin; m = median RT.

5 418 DILLER, NOBEL, AND SHIFFRIN have induced a strategy f slwing dwn r speeding up f respnses acrss cnditins. Whatever might accunt fr the differences between the present results and thse in earlier studies, we decided it wuld be f value t explre the theretical cnsequences f the present findings. T reiterate, a mdel fit t the present recgnitin data shuld predict at least the fllwing findings: (a) lwered accuracy as list length increases and study time decreases; (b) apprximate cnstancy f cnditinal RT distributins acrss length and strength variatins; (c) incrrect respnses slwer than crrect respnses, and slw respnses less accurate than fast respnses; and (d) similarity f the distributins fr the tw types f crrect respnses (hits and crrect rejectins) and similarity f the distributins fr the tw types f incrrect respnses (false alarms and misses). RT Mdels In lking at previus RT mdels, it seemed t us that the key element they shared, either explicitly r implicitly, was the assumptin that respnses are initiated when enugh evidence has accumulated t justify ne respnse r the ther. Such mdels naturally tend t link accuracy and RT acrss cnditins. Althugh nthing in the present data rules ut this class f mdels in principle (e.g., ne culd simply adjust the quantitative parameterizatin t reduce the magnitude f such a linkage), we decided t explre a relatively new class f mdels in which respnses are initiated nt when enugh differential evidence in favr f ne r anther respnse has been accumulated, but instead when the prcess f retrieval has prceeded far enugh t make it likely that reasnable accuracy is ensured. We nw present a mdel f this type termed assessment f retrieval cmpletin (ARC). The mdel fr recgnitin is an extensin f the REM mdel (Shiffrin & Steyvers, 1997,1998), which was develped t predict recgnitin accuracy. The mdel fr cued recall is an extensin f the REM mdel that in many ways fllws the recall assumptins f the SAM mdel f Raaijmakers and Shiffrin (e.g., 1980, 1981). The recall mdel has a first stage that uses mst f the prcesses f recgnitin, s the expsitin begins with the mdel fr recgnitin. The REM Mdel The ARC-REM Mdel fr Recgnitin Accuracy and Latency A review f the basic cmpnents f the REM mdel prvides a gd starting pint. The features f a given wrd are represented in semantic memry in the lexicn by a vectr f feature values. We set the number f features t the value 20, fllwing Shiffrin and Steyvers (1997) this was an admittedly arbitrary chice chsen fr cmputatinal cnvenience. Psitive integers represent stred infrmatin, with higher numeric values representing features with lwer envirnmental frequencies. In particular, the feature values representing a given wrd are chsen independently, with each value, j, chsen frm a gemetric distributin with parameter g: " 1 (i) Because explratins by Shiffrin and Steyvers (1997) suggested the chice wuld nt be critical, we set g t their value, During study f a pair f wrds, an episdic image vectr f 20 feature values is stred fr each wrd. Because strage takes place in pairs, the episdic images actually cnsist f tw back-t-back 20-lng vectrs, in a vectr 40 psitins lng. This representatin is critical when we later turn t the mdel fr cued recall. Fr the purpses f single-wrd recgnitin, as Shiffrin and Steyvers (1997, 1998) shwed, n duble-wrd vectrs can equivalently be treated as 2n single-wrd vectrs, a cnventin that we fllwed in this article. The episdic vectr is initially filled with zers, with zer representing n infrmatin abut that feature. The prbability f string a nnzer value in a given psitin, termed S r, depends n the study time, t (in ur 'best' fit, S 670 =.516 and S 2, = -955). If a value is stred, it will be a crrect cpy f the studied wrd's value with prbability c (in ur 'best' fit, c =.836); with prbability 1 c, the value stred will be a randm chice frm the gemetric distributin in Equatin 1. Thus, at the end f the study perid fr the list, each wrd will be represented by an incmplete and errr-prne vectr f feature values. As in the riginal versin f the REM mdel used t predict accuracy, the test wrd is assumed t be represented by a cmplete vectr f 20 nnzer values. This vectr is cmpared in parallel with all episdic images in memry (fr simplicity, limited t all images f the study-list wrds, and n ther images). Each image cmparisn prduces a list f the number f features that match (and their values; in Equatin 2, n ijm refers t the number f matching features in image j that have value i) and the number that mismatch (in Equatin 2, the number mismatching in image j is n jq ). (Zers in the image d nt cunt in either categry.) Equatin 2 (derived frm a Bayesian analysis) incrprates these matching cunts and values t give fr each episdic image the likelihd rati fr that image matching versus nt matching the test wrd. The dds that the test wrd is "ld" are determined by summing these likelihd ratis acrss the n episdic images and dividing by n, as in Equatin 3. The default decisin is t respnd "ld" if the dds are greater than 1.0. Aj = (1 - The ARC Mdel c) n * Si- (1 - c)g(\ - gf *(1 - *)'-'! "I nljm The ARC mdel prvides a way t extend the REM mdel t predict RTs and t d s in a way that crrectly predicts the phenmena in the present experiment. We assumed that the features f the prbe d nt all becme active at the same time but instead becme active and take part in cmparisns gradually, ver a highly variable perid f time. The cmparisn f the currently active prbe features with memry is cntinuusly updated, but we assumed that the result f this cmparisn (i.e., the dds value) is nt cntinuusly available t the participant. Instead, we assumed that the participant has access n a mment-t-mment basis nly t the prprtin f the features in the prbe that have thus far becme active. At any time, the participant can interrupt the curse (2) (3)

6 RECOGNITION AND RECALL MODEL 419 f retrieval and read ut the current value f the dds, but this causes the prcess f retrieval t hesitate r stp (fr lng enugh t make it unreasnable t read ut the dds value n mre than ne ccasin during the curse f retrieval). Under these circumstances, it seems clear that a participant will wait until a sufficiently high prprtin f prbe features have becme active and then interrupt the retrieval prcess, read ut the current dds, and respnd accrdingly. The mdel as described thus far dissciates accuracy frm RT because the decisin t stp the curse f retrieval and respnd is based n the ARC and nt n the evidence in favr f "ld" r "new." Because this simple mdel predicts n difference in RTs between errrs and crrect respnses, cntrary t the findings, we added an additinal within-trial "frgetting" assumptin: Features in the episdic images initially start in an active state but gradually becme inactive during the curse f retrieval n a given trial. In particular, we assumed that during each unit f time during retrieval, starting at time t 0 after test-item presentatin, each feature in each episdic image that has nt yet participated in a cmparisn with the prbe becmes inactive with prbability/. (Our units f time were set t 1 ms, and the 'best' fit values fr t 0 and / were 88 ms and.0099, respectively.) A feature that has already participated in cmparisn t the crrespnding prbe feature is prtected and des nt decay. This assumptin ensures that waiting lnger befre interrupting retrieval and respnding cannt lwer mean accuracy. Hwever, the fact that sme features that have nt yet participated in cmparisns cntinue t becme inactive ensures that errrs will be slwer than crrect respnses: When prbe features n a given trial becme active very quickly, little image-feature frgetting will have ccurred when retrieval is interrupted and the dds assessed, s the respnse will be based n a large number f feature cmparisns and hence will be quite accurate. Cnversely, when the prbe features slwly becme active, many image features will have becme inactive by the time their crrespnding prbe features becme active. Therefre, the cmparisn will be based n fewer features, and the respnse will be less accurate. (A cnsequence f these assumptins cncerning frgetting is a lss f the exact equivalence f RT acrss length-strength cnditins, but the departure frm equality is negligible see the sectin The ARC- REM Mdel fr Recgnitin). Under these assumptins, what wuld be the ptimal strategy fr a participant trying t bey the usual free-respnse instructins t respnd as quickly and accurately as pssible? Waiting fr all prbe features t becme active will maximize accuracy but will ccasinally prduce very lng RTs; respnding when nly a few prbe features have becme active will prduce fast RTs but very lw accuracy. We assumed that the participant attempts t balance these factrs by waiting until sme large prprtin, a>, f the prbe features have becme active and then interrupting retrieval, reading ut the dds, and respnding accrdingly (in ur 'best' fit, ).75). In signal-t-respnd cnditins like thse in Experiment 1 f Nbel and Shiffrin (2001), we assumed that the participant simply waits fr the signal and then interrupts retrieval, reads the dds, and respnds. (In the variant f signal-t-respnd intrduced by Meyer et al. [1988] and used by Smith & Shiffrin, 1997, as discussed in the intrductin, regular and signal trials are mixed. Fr this variant, we wuld assume the participant uses the freerespnse strategy until a signal ccurs, at which time retrieval is interrupted and a respnse initiated.) The preceding paragraphs prvide a general descriptin f the ARC versin f the REM mdel; the fllwing paragraphs prvide a few additinal quantitative details. On any given trial, there is a maximum time (which varies acrss trials), f e, by which time all f the prbe features must becme active. At any time t less than f e, the prbability, P A, f any nt-yet-active prbe feature becming active is a functin that increases frm 0 at the time the test item is presented t 1.0 at r e. This functin is given in Equatin 4 and is illustrated in Figure 2A. The distributin acrss trials f the maximum times, /,,, is a start time, f s, plus a time T selected frm an expnential distributin with parameter a given in Equatin 5 (ur 'best' fit values fr a and / s were.0012 and 200 ms, respectively). An example f this distributin is given in Figure 2B. Nte that n mst trials all prbe features are activated quickly; n relatively few trials will activatin prceed slwly. Time Time Figure 2. A: Graph f Equatin 4 fr S = ; prbability density (P) fr the time at which a nt-yet-active prbe feature becmes active (A), fr a fixed time, t e. B: Graph f Equatin 5 fr a =.0012; prbability density (pd) fr the time t e, the maximum time by which all prbe features must becme active. T = maximum time; t s = start time; t e = end time. (4)

7 420 DILLER, NOBEL, AND SHIFFRIN pd{t) = aexp(-a7). (5) Equatins 4 and 5 tgether with the rule fr interrupting retrieval (the value f cu) determine the distributin f prbe cmpletin times, as shwn in Figure 3. If we were fitting nly free-respnse data, this functin (r smething similarly shaped) culd have been used in place f the tw functins shwn in Figure 2. Hwever, mre infrmatin than the functin shwn in Figure 3 is needed t predict the shape f the signal-t-respnd data grwth curves, because we need t knw the state f the system at each time pint en rute t prbe cmpletin. The functins in Equatins 4 and 5 were the simplest we culd find that culd prduce gd fits t bth free-respnse and signal-trespnd data. The mdel predictins fr free respnse. RT is determined by taking a sample f a base time frm a nrmal distributin with a standard deviatin f a and with a mean f /n fr ld respnses and /x n fr new respnses and adding the time at which the prprtin f active features reaches the cutff value <u (the prbe cmpletin time). In the riginal REM frmulatin, it was assumed fr simplicity that an ld respnse wuld be given if the dds exceeded 1.0. We fund that the fit t the present freerespnse data was slightly but significantly imprved when we allwed each f the fur length-strength cnditins t have a separately estimated criterin. The best fitting values were very clse t 1.0, with a slight exceptin fr the 40-pairs/2,000-ms cnditin (see Table 2). The mdel predictins fr signal-t-respnd. In signal-trespnd cnditins, it is assumed that the participant waits until the signal, interrupts the retrieval prcess, reads ut the dds, and respnds. Again, we allwed the respnse criteria n the dds scale t be freely fitted t each f the fur length-strength cnditins, but all fur best fit estimates were very clse t 1.0 (see Table 2). The ARC-REM Mdel fr Cued-Recall Accuracy and Latency The mdel fr cued recall, in cntrast t the recgnitin mdel, is based n a sequential search. The sequential search part f the Table 2 Best Fitting Parameters f the ARC-REM Mdel (Specific t Free Respnse r Signal-t-Respnd) Free parameter Criterin M <x &) MSE Criterin MSE ,000 Free respnse Cnditin Signal-t-respnd , Nte. Fr the cnditins, the first number (10 r 40) refers t the number f pairs in the list, and the secnd number (670 r 2,000) refers t the length f the list presentatin per pair in millisecnds. ARC = assessment f retrieval cmpletin; REM = retrieving effectively frm memry. mdel brrws heavily frm the SAM cued-recall mdel (Raaijmakers & Shiffrin, 1980,1981). The general scheme is utlined in Figure 4. We were led t prpse a sequential search mdel in part because the different shapes f RT distributins in recgnitin and cued recall suggest qualitatively different retrieval prcesses in the tw paradigms. This case is given in Nbel and Shiffrin (2001). An Calculate Likelihd Ratis \ / Sanlple ImEige N N \ / Aceept Ima 3e? I Give-up? Yes N \ Yes Recver & Output Image? \ 1 \ Yes Time (ms) Mtr Respnse Figure 3. Prbability density fr prbe cmpletin times when a> =.75, fr the densities in Figure 2. Figure 4. Flwchart fr the stages f the sequential search prcess that is the basis fr the ARC REM mdel fr cued recall.

8 RECOGNITION AND RECALL MODEL 421 unfrtunate cnsequence f using a search mdel is the many stages and decisins that are lgically and cnceptually necessary (as utlined in Figure 4). These stages and decisins cause the cmplexity f the mdel t increase cnsiderably beynd that required fr recgnitin but are, in ur view, necessary. These stages and assciated decisins are t be distinguished frm the varius quantitative assumptins with which they are implemented (including such things as distributinal shapes). Althugh finding even ne set f quantitative assumptins that crrectly the findings was nntrivial, it is undubtedly true that there must exist numerus alternative quantitative implementatins. We were guided largely by the attempt t find the simplest set that culd d the jb. (These cmments apply als t recgnitin, but the number f required quantitative assumptins was much smaller in that case.) Q. 1.0 e = Give-up decisin. If the image is nt accepted, r if it is accepted and the recvery stage (see the Recvery and utput decisin sectin) fails, then a decisin is made whether t give up. The decisin t give up (in either case) is based n the familiarity f the prbe: If the prbe seems sufficiently unfamiliar, n the basis f the value f the dds, <\>, that the test wrd is ld, then a give-up decisin ccurs. The prbability f giving up, P(G), rises as time appraches the end f the 5-s respnse interval. Equatin 8 gives the prbability f giving up, based n a parameter p. We allwed the give-up prbability t differ fr slw and fast presentatin rates (the idea being that, even fr equivalent dds, partic : 0 0 Time Assumptins Gverning Respnse Accuracy Prbe activatin and likelihd calculatin. Likelihd ratis are first calculated as they are in the recgnitin mdel. The time curse f this stage als fllws the time curse prescribed by the recgnitin mdel, with ne slight change: Fr free respnse in cued recall, the likelihd ratis are calculated when all f the prbe features have becme active. Once the ratis are calculated, they remain fixed thrughut that trial's retrieval perid (i.e., thrughut the rest f the search). Image sampling. The next step is sampling f an image. A duble-wrd image is sampled, based n the larger f the tw likelihd ratis fr that pair. The sampling prbability is prprtinal t a pwer functin f the (larger) likelihd rati fr each pair (with pwer y, fr which the 'best' fit value was.21), accrding t Equatin 6: Image acceptance. The sampled image is nw examined, and a decisin is made as t whether t accept the image as the desired ne (the desired image being the ne cntaining the test wrd). The decisin is based n the value f the likelihd rati fr the sampled image, with the additinal assumptin that the prbability f acceptance increases as time appraches the limit f 5 s fr a respnse. Equatin 7 gives the prbability f acceptance, P(A), fr a scaled likelihd rati f X y, gverned by a parameter e (fr which the 'best' fit value was 6,542). This equatin must be prperly truncated, as illustrated in Figure 5, fr three values f A 7 : (6) P(A) = 1 - (5,000 - t)/ek y. (7) Figure 5. Image acceptance stage f the search. Examples f Equatin 7 fr three values f the scaled likelihd rati (A 1 ) f the sampled image, fr «= 6,542. P(A) = prbability f acceptance. ipants might be mre reluctant t give up had they studied the list lnger). Thus, tw values, p 670 and P2 -O00l were estimated (with 'best' fit values f and.0002, respectively). Equatin 8 must be prperly truncated, as illustrated in Figure 6, fr three values f <j> and the 670-ms cnditin: P(G) = 1 - p4>(5,000 - t). (8) Recvery and utput decisin. The prbability f a successful recvery, P(R), and utput f the respnse wrd in the pair image are based n the prprtin f nnzer feature values in the part f the sampled image crrespnding t the respnse wrd, p r. Equatin 9 gives the recvery prbability, based n a parameter T (fr which the 'best' fit value was.512). Figure 7 depicts P(R) fr three values f r as a functin f the number f nnzer feature values (ut f a pssible maximum f 20). P(R) = p r T. (9) Crrect respnses and intrusins. Finally, the wrd utput might be crrect r might be an intrusin. Intrusins can ccur because the wrd recvered frm the partial infrmatin available is incrrect r because a wrd is recvered crrectly frm the wrng image. Furthermre, the wrng image, in principle, can be either frm the crrect list (the mst recent ne) r frm earlier lists. Hwever, fr simplicity, we restricted the images that are accessed t thse frm the recent list, s that nne f the intrusins in this simplified versin f the mdel are due t sampling images frm prir lists. If the wrng image is sampled, it is assumed an intrusin is made (it is assumed that the prbability f accidental generatin f the crrect respnse is negligible); these intrusins will be episdic in nature. If the crrect image (the image cntaining the prbe wrd and its respnse wrd) is sampled, then the prbability crrect, P(C CS), is given in Equatin 10 (based n the scaled likelihd rati used fr sampling, A v, and a parameter tfi with a 'best' fit value f.86); therwise, an intrusin is made. These intrusins are generally related t the crrect respnse in sme fashin. P(C CS) = 1 - (10)

9 / / / 422 DILLER, NOBEL, AND SHIFFRIN u n. 1 1 p 670 = /... ' / «= 0.5 4>= 1,0 0 = Time Figure 6. Give-up stage f the search. Examples f Equatin 8 fr three values f the dds (< ) fr the presentatin time f the 670-ms cnditin (with p 670 = ). P(G) = prbability f giving up. Assumptins Gverning RT Time f the first step. Fr simplicity, we let the time fr the first step, including prbe cmpletin, image sampling, and the acceptance decisin, be set t the time fr all prbe features t activate, as described fr recgnitin. Times fr stages f the search. All times mentined belw are mean times in millisecnds. On any given step f the search n a given trial, the actual time is selected frm a Gaussian distributin with that mean, with a standard deviatin equal t that mean multiplied by a parameter cr s and truncated at zer if necessary. (The 'best' fit value fr <r s was 105.) Time t resample and accept. This mean time is /x r. (The 'best' fit value fr /t r was 100.) Time t give up. The mean time is ju. g. (The 'best' fit value fr jx g was 264.) Time t recver and utput. This mean time, t K, is allwed t vary in accrd with the scaled likelihd rati, as in Equatin 11, n the basis f tw parameters, f and 0 (the 'best' fit values being 1,973 and.6145, respectively). The higher is the likelihd, the faster is the recvery time. (Althugh the number f target features is nt directly included in this equatin, this number is crrelated with the value f A, primarily thrugh the interactin f variable prbe feature nsets with image-feature frgetting.) mment within the recvery stage, then a give-up respnse is prduced. If the signal ccurs during the recvery stage f the search, and the prprtin f that stage's duratin that has passed by the signal time is pt str, then P(R) as given in Equatin 9 is slightly mdified, as given in Equatin 12: P(R) = (ptjp?. Fitting the Mdel t the Data (12) Acrss recgnitin and cued recall as well as free respnse and signal-t-respnd, there were quite a few data pints t be. Fr recgnitin free respnse, there were tw accuracy values (hit and false-alarm rates) fr each f the fur cnditins f length and strength, giving a ttal f eight values. RTs were cmpiled as the prprtin f respnses in each f 50 bins f duratin 100 ms, cvering the 5-s respnse interval, fr each f the 16 cnditinal distributins. S as nt t drwn the effect f accuracy in these many RTs, the sum f squared errr (SSE) fr the eight accuracy pints was multiplied by 8 befre being added t the summed SSE fr RTs. Fr recgnitin signal-t-respnd, we used hits and false alarms at each f the 10 signal times in each f the fur length-strength cnditins. Fr cued-recall free respnse, we measured prprtins f crrect respnses, intrusins, and give-ups fr each f the fur length-strength cnditins. We multiplied the SSE fr these 12 pints by 4, again t increase the weighting f accuracy in the jint fit. The cued-recall RT distributins were characterized by prprtins f respnses in 50 bins f duratin 100 ms fr the cnditinal distributins fr each f the three types f respnses fr each f the fur length-strength cnditins. Fr cued-recall signal-t-respnd, there were three prprtins f respnses fr each f 10 signal times fr each length-strength cnditin. In ttal, there were 1,620 terms entered int the SSE, with the accuracy terms given sme extra weighting. The cmplete mdel had many parameters t be estimated. These may be categrized as fllws: There were 8 parameters cmmn t free respnse, signal-t-respnd, recgnitin, and cued recall (Table 3). Fr recgnitin, there were 8 parameters specific fr free respnse and 4 fr signal-t-respnd (Table 2). It shuld be f R = exp(-o). (11) Base time. All the ther RT cmpnents, including mtr respnse and perceptin time, are lumped int a base time with a mean ^ (having a 'best' fit value f 856). EC Signal-t-Respnd The pint during the search when the signal ccurs determines whether a respnse is given in signal-t-respnd. The freerespnse mdel previusly described runs until the signal ccurs. If the signal ccurs after the pint in time at which the recvery and utput stage in the search wuld have led t an utput, then the utput wuld be the ne prduced in free respnse. If the signal ccurs when the search is still nging, and the search is nt at that Number f Target Wrd Features Figure 7. Recvery and utput stage f the search. Examples f Equatin 9: prbability f recvery and utput, P(R), as a functin f number f target wrd features (ut f 20), fr three values f T.

10 RECOGNITION AND RECALL MODEL 423 Table 3 Best Fitting Parameters f the ARC-REM Mdel (Cmmn t Free Respnse and Signal-t-Respnd in Bth Recgnitin and Cued Recall) Free parameter alue Nte. ARC = assessment f retrieval cmpletin; REM = retrieving effectively frm memry. nted that 8 f this ttal f 12 were criteria that in all but ne case were very clse t the default value f 1.0; simply setting all 8 parameters t 1.0 prduced a fit almst as gd. Fr cued recall, there were 9 additinal parameters cmmn t bth free respnse and signal-t-respnd (Table 4), and 3 mre applied nly t free respnse (Table 5). Thus, we fitted 32 parameters (althugh 8 f these culd have been set t the default value f 1.0 withut much harm). Finding a set f parameter values that truly minimized the sum f squared deviatins between predictins and data was a task beynd ur capabilities, despite ur limiting the fit t the aggregate data, use f sphisticated parameter estimatin techniques, and parallel utilizatin f 60 netwrked wrkstatins n campus. 2 In additin, the precise frm f the assumptins we listed abve was altered a number f times during the mdel develpment prcess n the basis f partial fits t data and emerging intuitins cncerning the characteristics that an apprpriate mdel must incrprate. The fitting technique thus was a cmbinatin f art and guesswrk: At the highest level, a set f mdel assumptins wuld be explred until it seemed likely that a gd fit culd nt be fund and then the assumptins were adjusted. Fr a given set f assumptins, regins f parameter values were chsen n the basis f an emerging intuitin cncerning the shape f the parameter space, and a variety f quantitative estimatin algrithms were applied t the identified regins in a prcedure that mved back and frth Table 4 Best Fitting Parameters f the ARC-REM Mdel fr Cued Recall (Cmmn t Bth Free Respnse and Signal-t-Respnd) Free parameter T alue , , Nte. ARC = assessment f retrieval cmpletin; REM = retrieving effectively frm memry. Table 5 Best Fitting Parameters f the ARC-REM Mdel fr Cued Recall (Free Respnse) Free parameter P670 P2.0OO alue Nte. ARC = assessment f retrieval cmpletin; REM = retrieving effectively frm memry. between the tw appraches a number f times. We stpped the mdel develpment and the estimatin prcess when a fit was btained mat was clse enugh t demnstrate the value f the mdel. Thus, we use qutatin marks in the phrase 'best' fit t represent the truth f the situatin: It is rather likely that ther sets f parameter values exist that wuld prduce even better fits than thse we reprt. The 'best' parameter values are given in Tables 2, 3, 4, and 5. Predictins f the Mdel Fr free respnse, the predictins fr respnse accuracy in recgnitin (hits and false alarms) and in cued recall (crrect respnses and intrusins; the prbabilities f these plus give-ups summed t 1.0) are given alng with the data in Table 1. The and RT distributins are given in Figures 8A thrugh 8P fr recgnitin and in Figures 9A thrugh 9L fr cued recall. Fr signal-t-respnd, recgnitin predictins are given fr hits and false alarms in Figure 10 and fr d' in Figure 11; cued-recall predictins are given fr crrect respnses, intrusins, and give-ups in Figure 12. It is clear that the mdel captures the essential aspects f the data quite well, ntwithstanding the fact that better fits wuld have been btained had the mdel been fit separately t the recgnitin and cued-recall data and had it been pssible t explre the mdel's parameter space mre thrughly. Hw t judge the success f this mdel-fitting enterprise is smething prbably best left t the individual reader. We nte that accuracy, RTs, and RT distributins are fit fr length and strength variatins, fr bth free-respnse and signal-t-respnd paradigms, and fr bth recgnitin and cued recall. Given these facts, we did nt judge the number f parameters t be verly high: This was especially true fr recgnitin because 8 f the 20 parameters were the criteria n the dds scale fr respnding "ld" and culd have been set t the default value f 1.0 withut greatly harming the quality f the fit. There are a number f cmments that we culd make abut the ARC-REM mdels fr recgnitin and recall separately, but befre turning t these, we discuss alternative mdels fr recgnitin. Alternative Mdels fr Free RTs in Recgnitin Existing mdels had a cnceptual basis that made it seem likely that they wuld predict a relatinship between accuracy and RT 2 T speed up the fitting prcess, we distributed simulatins in parallel acrss a netwrk f 60 UNIX wrkstatins using remte prcedure calling. See Blmer (1992) fr an intrductin t distributed cmputing using remte prcedure calling.

11 (HI) (HI) I -2 + c (FA) (FA) I (CR) (CR) R s (Ml) (Ml) S Q_. 1 Figure 8. Recgnitin respnse time (RT) distributins cnditinalized fr each f the fur cnditins (10 r 40 wrd pairs and 670 r 2,000 ms) and all types f respnses. The parameter values used t prduce the predictins are given in Tables 2 and 3. HI = hits; FA = false alarms; CR = crrect respnses; MI = misses.

12 RECOGNITION AND RECALL MODEL (HI).3 M (HI) (FA).3 - N (FA) Q..1 { (CR).3 O (CR) c =? (Ml) (Ml) I. 1 -, Figure 8. (cntinued)

13 426 DILLER, NOBEL, AND SHIFFRIN (CO) (CO) e (IN) (IN) S S \> I (GU) I.10-- l (GU) Figure 9. Cued-recall respnse time (RT) distributins cnditinalized fr each f the fur cnditins (10 r 40 wrd pairs and 670 r 2,000 ms per pair) and all types f respnses fr list-length variatin and presentatin time variatin. The parameter values used t prduce the predictins are given in Tables 3, 4, and 5. CO = crrect respnses; IN = intrusins; GU = give-ups. acrss ur free-respnse cnditins. Mdels f this srt include the decisin mdel (Hckley & Murdck, 1987) and the diffusin mdel (Ratcliff, 1978). We learned that such mdels culd be fitted t each f ur length-strength cnditins in free respnse if all parameters were fitted separately t each cnditin. Hwever, we culd nt find natural restrictins n the parameters that allwed the data t be. Mrever, even if different parameter values are used acrss cnditins, nthing in these mdels prvided any reasn fr the apprximate equivalence f the RT distributins. These same cmments apply with equal frce t variants f the SAM mdel f Gillund and Shiffrin (1984) and the REM mdel f Shiffrin and Steyvers (1997), in which we tried

14 RECOGNITION AND RECALL MODEL G (CO) c E Q. S Q I (CO) Q a (IN) I I (IN) X- jt\ i (GU) (GU) Figure 9. (cntinued) letting RT be related t the distance f the familiarity measure n a given trial frm the criterin, either directly r indirectly by letting distance determine the rate f a randm walk decisin prcess. Thus, within the cntext f these mdels, we were left with the unsatisfactry cnclusin that the apprximate cnstancy f RT distributins acrss length-strength cnditins was an accident. In this sectin, we briefly describe the tw published RT mdels fr recgnitin and ur attempts at implementatin s as t illustrate these pints. The Decisin Mdel Hckley and Murdck (1987) presented a decisin mdel fr accuracy and respnse latency in recgnitin memry. Althugh this mdel was develped within the framewrk f the thery f distributed assciative memry (Murdck, 1982), it can be applied as well t any mdel that prduces single matching strengths (i.e., familiarity values) t mdel recgnitin perfrmance, such as SAM (Gillund & Shiffrin, 1984), REM (Shiffrin & Steyvers,

15 428 DILLER, NOBEL, AND SHIFFRIN 10 pairs-670 ms - hits v false alarms c O "J v. v 40 pairs ms r > O hits - false alarms - SJ Ttal Prcessing Time (ms) 0 Ttal Prcessing Time (ms) B ( J ) pairs- O 2000 ms5 hits - false alarms - 40 pairs ms O hits false alarms '"' Ttal Prcessing Time (ms) Ttal Prcessing Time (ms) Figure 10. Hits and false alarms fr recgnitin as a functin f signal delay plus respnse time fr each f the fur length-strength cnditins; bservatins are represented by pen symbls, and predictins f the ARC-REM mdel are represented by lines. The parameter values used t prduce the predictins are given in Tables 2 and ), the matrix mdel (Pike, 1984), r MINERA (Hintzman, 1988). On a given trial, the retrieval system prduces a single value (matching strength, familiarity, r activatin). This value is then used in a sequence f decisin steps. At each step in time, a randm sample is taken frm a Gaussian distributin and added t the strength value. If the sum is abve an upper criterin r belw a lwer criterin, an "ld" r a "new" respnse, respectively, is made. If the result falls between the tw criteria, the decisin system cycles t the next step. It is assumed that the tw criteria cme tgether ver time: At each step, the distance between the criteria is reduced by a cnstant fractin (the criteria cnvergence rate). This system by itself fails t prduce sufficient numbers f very lng RTs. T slve this prblem, the number f steps is translated int real time by T k = (k 2 + k + 2)BCT, where k dentes the number f cycles, BCT the base cycle time, and T k the decisin time. Time fr ther stages (JOS; which includes prcesses like encding, cmparisn, and executin) is assumed t fllw a nrmal distributin, and RT is defined as T k + TOS. The familiarity value that is used t "seed" this decisin mdel can cme frm several mdels. We implemented a versin f the SAM mdel (Gillund & Shiffrin, 1984) t generate the familiarity values fr each trial. The SAM mdel assumes strage f assciative strengths between test cues and images f list items (the images are stred separately in memry). It is assumed that the test prbe cnsists f an item cue and a cntext cue. The strengths f these cues t a given image are multiplied, giving an image activatin value. The activatin values are then summed acrss list images t prduce a familiarity value. When the SAM assciative strength parameters were fixed acrss cnditins but all decisin parameters including criteria were allwed t vary acrss cnditins, the resultant mdel prduced quite gd fits t the accuracy and RT data. This fit used a great number f free parameters (i.e., 48). Althugh we culd nt find ways t equate r adjust parameters acrss cnditins that wuld be cnceptually justified and wuld cntinue t prduce a gd fit, ne might wish t argue that the full mdel shuld nt be discunted n the basis f many parameters, because a great deal f data are being. A different cncern abut the decisin mdel lies in general bjectins raised by Grnlund and Ratcliff (1991); sme f these bjectins are well taken, but an analysis ges beynd the scpe f this article. The rather arbitrary quadratic mapping f decisin steps int decisin

16 RECOGNITION AND RECALL MODEL 429 The Resnance-Diffusin Mdel c D. Q B t H Ttal Prcessing Time (ms) 0.0 h- -H 1 0 v 40 pairs -O 670 ms 2000 ms Ttal Prcessing Time (ms) Figure 11. Recgnitin perfrmance (d') as a functin f signal delay plus respnse time fr each f the fur length-strength cnditins; bservatins are represented by pen symbls, and predictins f the ARC- REM mdel are represented by lines. The parameter values used t generate the predictins are given in Tables 2 and 3. time certainly gives the mdel an ad hc flavr that lessens its attractiveness fr many therists. Nne f these bjectins may be as serius as the fllwing: Fr the mdel t fit the data, it was essential that the upper and lwer criteria be adjusted separately fr each length-strength cnditin. In itself, this was n prblem because these criteria culd well be under participants' cntrl, and the length and strength cnditins ccurred in separate lists, allwing the participants t make criteria adjustments. The prblem lies in the fact that there was n bvius way fr the participants t knw in what way t adjust the criteria s as t equate fairly clsely the cnditinal RT distributins acrss length and strength. The participants were nt given feedback f a type that wuld have allwed such adjustment, and the high variance f the distributins f RTs made it mst unlikely that the participants had anything like a precise estimate f the means and variances f these distributins acrss cnditins (and the participants, when asked, prfessed t have n idea f the relative speeds f respnses acrss cnditins). Thus, we were left with the unattractive hypthesis that the criteria were chsen differently fr different cnditins (n sme unknwn basis) and the criteria chices accidentally prduced an apprximate equality f the RT distributins. Ratcliff (1978) prpsed a resnance mdel fr memry retrieval in recgnitin in which item images are stred separately in memry. A test item is encded and then cmpared in parallel with each stred image. Each individual cmparisn is instantiated as a diffusin (randm walk) prcess that accumulates infrmatin ver time and drifts between tw bundaries, ne fr emitting a psitive respnse and ne fr reaching a decisin that the cmparisn is nt a match. The mean rate f drift tward the psitive bundary is higher fr a memry image matching the test item than fr ther memry images, but there is a Gaussian distributin f drift rates with the same variance fr bth kinds f cmparisns. The mdel is described as a resnance mdel because the respnse f each image t the test item is based n the similarity between them. The participant terminates with a psitive respnse when any randm walk reaches the psitive bundary (terminating search) and gives a negative respnse when every randm walk reaches the negative bundary (exhaustive search). T keep the psitive and negative times similar, the negative bundary generally must be placed much clser t the starting psitin than the psitive bundary. There are five basic parameters: the means f drift fr target and distractr traces, the cmmn variance f drift, and the distances f the tw bundaries frm the starting pint. In additin, there is a cnstant time fr encding and respnding. In several instances, Ratcliff (1978) did nt fit the diffusinresnance mdel t the RT distributins themselves but instead t the three-parameter ex-gaussian distributins that best fit each RT distributin (see, e.g., Ratcliff & Murdck, 1976). Fitting the diffusin-resnance mdel either t the raw data r t the ex- Gaussian apprximatins is far frm a trivial prcess. We therefre fitted ur distributins with ex-gaussian distributins and sent them t Rger Ratcliff, wh was kind enugh t fit the diffusin mdel t these distributins, with separate parameters fr each length-strength cnditin. Althugh the resultant fit was nt as gd as the decisin mdel, it was nt unreasnable given that fewer parameters were required. Nnetheless, the same cncerns can be raised as were raised fr the decisin mdel. Even if ne is nt cncerned abut parameter invariance acrss cnditins, the mdel prvides n reasn why the RT distributins shuld have been apprximately equivalent acrss cnditins, and the result is simply left as an accidental utcme. We d nt reject either f these mdels n this basis but rather use this bservatin as a basis fr justifying explratin f an alternative class f RT mdels. This class, instantiated by the ARC-REM mdel, is ne in which respnding is initiated when the retrieval prcess has prceeded sufficiently far t make it likely that respnse accuracy will be clse t the best attainable n that trial. One advantage f such mdels is the fact that they prvide a nnaccidental justificatin fr the apprximate equivalence f RT distributins acrss ur length-strength cnditins. The ARC-REM Mdel fr Recgnitin The ARC-REM recgnitin mdel is cnsistent with and an extensin t the RT dmain f the previusly intrduced REM

17 A v. u 1 1 i 10 pairs ms.. v ms u - v " - u c"- J7 1 1 ] 1 10 pairs ms v -e- IN -v GU H 1 0 Ttal Prcessing Time (ms) 0 - C) Q - Q- ^ r- 1 1 Ttal Prcessing Time (ms) Drtin S l.u - B ^ H 40 pairs ms v 2000 ms 1 - " Ttal Prcessing Time (ms) u - D A i 7 " "! v 1 i i 10 pairs-2000 ms ' ' -O- IN -v GU 1 < I. ^ L " ~l ^H 1 Ttal Prcessing Time (ms) I * v v. y 40 pairs ms -e- IN v- GU 0 Ttal Prcessing Time (ms) v 40 pairs ms -O- IN v GU Ttal Prcessing Time (ms)

18 RECOGNITION AND RECALL MODEL 431 mdel (Shiffrin & Steyvers, 1997, 1998). Hwever, the REM mdel culd have been extended in ther ways that wuld nt have prduced a satisfactry utcme (and, in fact, we tried several f these, such as using the dds value in the REM mdel as input t Hckley and Murdck's [1987] decisin mdel). The ARC-REM mdel is f particular value because it represents an instantiatin f a new class f RT mdels that prbably deserves further explratin and cnsideratin, a class in which the apprximate equality f the RT distributins is a cnsequence rather than an accident. Accrding t the ARC-REM mdel, RT is determined nt by an accumulatin f relevant evidence cncerning the decisin t be made, but instead by an accumulatin f evidence cncerning hw cmplete is the prcess f retrieval. Cmpleteness was defined, mre precisely, as the pint at which the prprtin f activated prbe features reached a criterin value. This apprach separates time and accuracy but des nt predict different times fr crrect and errr respnses. We therefre added an additinal assumptin that features f the images in memry becme unavailable during the curse f a retrieval attempt. The errr-crrect differences then arise because the ARC-REM mdel assumes variability in the time curse f prbe activatin: Trials with slw prbe nsets are assciated with significant frgetting f image features befre they can be cmpared, and hence prer perfrmance is fr these slw trials. Cnversely, trials with fast prbe nsets are assciated with little frgetting, and cmparisns f prbe and image features will almst always take place, imprving perfrmance n these fast trials. Despite this crrelatin f RT and accuracy within any cnditin, different cnditins (e.g., f length and strength) shuld prduce virtually the same RTs. Overall RTs are determined by prbe feature nsets, which are nt affected by cnditin. Furthermre, even when the RTs are separated int crrect and errr cases, the fact that verall accuracy is higher in sme cnditins than thers des nt appreciably affect the relative decline in accuracy assciated with slwer respnding, and hence the cnditinal RT distributins are virtually identical acrss the variables f length and strength. The ARC-REM mdel was, f curse, designed t predict the apprximate dissciatin f accuracy and RT acrss manipulatins f length and strength that was in Experiment 1 (and ther studies) f Nbel and Shiffrin (2001). This feature f the mdel is a cnsiderable asset when the mdel is applied t Nbel and Shiffrin's findings but a debit when the mdel is applied t studies that d shw crrelatins f accuracy with RT acrss cnditins (e.g., Dsher, 1982; Flexser, 1978; Murdck & Andersn, 1975; Ratcliff & Murdck, 1976). Fr this reasn, we are far frm ready t prclaim that the ARC apprach is a better representatin f reality than the traditinal appraches in which RTs are based n the current assessment f the evidence favring ne chice ver anther. Furthermre, even if the ARC apprach prvides the best descriptin f the prcesses taking place in the present studies, we wuld nt want t argue that the apprach necessarily generalizes t ther paradigms. T extend the ARC mdel t paradigms in which RTs crrelate with accuracy acrss cnditins wuld require extra assumptins. In sme cases, such extra assumptins are easy t justify. Fr example, if the cnditins were different in different lists, it might be pssible t argue simply that the criteria fr stpping retrieval differ fr the different lists. Alternatively, if variables were manipulated within lists (as smetimes happens fr study time manipulatins), it wuld nt usually be plausible t argue fr different criteria fr different test items: T adjust criteria n the basis f the test item's study time, ne wuld pretty much have t knw that the test item had been studied, bviating the need t set a criterin. In such cases, it might be pssible t augment an ARC mdel. Fr example, it culd be assumed that the participant waits and interrupts retrieval a secnd time in cases in which the first interruptin des nt prvide a clear answer, it culd be assumed that a recall-like prcess perates in parallel with the familiaritybased prcess f REM, r it culd be assumed that the participant "rechecks" the initial answer with a recall-like prcess r with a secnd retrieval attempt. Such augmentatins f an ARC apprach might be pssible, but the traditinal mdels wuld certainly prvide simpler and mre elegant slutins in such cases. At the least, further research is needed t explre the relative benefits f the tw classes f mdels fr recgnitin RTs. Nnetheless, the present data and the success f the quantitative fits f the mdel t the data prvide a gd case that mdels f RT based n the ARC apprach deserve serius cnsideratin by therists in the field. Pssible Extensins f the ARC-REM Mdel t Pair Recgnitin Nbel and Shiffrin (2001) presented signal-t-respnd data fr the task f pair recgnitin, in which participants study pairs and then try t discriminate studied pairs frm pairs cmpsed f tw wrds neither f which had been studied. Cmpared with singlewrd recgnitin, pair recgnitin has a slightly faster intercept, a slightly slwer grwth rate, and a higher asympttic accuracy. What changes in the mdel might be needed t handle such results? Shiffrin and Steyvers (1998) tk up this questin with respect t the accuracy results at asymptte, when decisins are made in the absence f significant time pressure: The ptimal decisin strategy wuld be t carry ut cmparisns n the basis f all 40 features in bth wrds (treating a pair as a single dublelength wrd). The extra features wuld clearly imprve perfrmance, as (pair d' f 2.2 vs. single d' f 1.7). This apprach des nt wrk, hwever: The parameter values that prduce the gd fits t single-item recgnitin wuld prduce a pair recgnitin d' f abut 2.8, which is much t high. Figure 12. Cued-recall respnse prbabilities as a functin f signal delay plus respnse time fr each f the fur length-strength cnditins; bservatins are represented by pen symbls, and predictins f the ARC- REM mdel are represented by lines. Crrect respnses are presented in Panels A and B; intrusin (IN) and give-up (GU) prbabilities are presented in Panels C, D, E, and F. The parameter values used t prduce the predictins are given in Tables 3 and 4.

19 432 DILLER, NOBEL, AND SHIFFRIN This failure suggests there is sme additinal limitatin acting in the pair task. Shiffrin and Steyvers (1998) reprted tw appraches that wrk abut equally well. In the first (termed the capacity variant), it is assumed that the test prbe f memry des nt have the capacity t hld all the features f tw wrds; randmly chsing features fr the prbe with a prbability f.775 reduced the a" t abut that that was. In the secnd (termed the separate variant), the familiarity (i.e., the dds) f each wrd is cmputed separately; multiplying these dds values tgether and basing the decisin n the prduct als reduced the a" predictin t abut that that was. Extending the single-wrd recgnitin mdel t pair recgnitin in the time dmain is a mre cmplex matter. If bth wrds must be "read" befre retrieval cmparisns begin, then ne might expect the intercept f the signal-t-respnd functin t be larger fr pair than single-wrd recgnitin. Hwever, the results shwed the intercept t be slightly lwer fr pairs (rughly cnsistent with pint estimates f intercept parameters by Grnlund & Ratcliff, 1989), suggesting that cmparisns begin slightly sner fr tw wrds than fr ne wrd. If such results are reliable, they might be dealt with by slightly mdifying the ARC-REM assumptins. The present mdel assumes a fixed minimum time at which prbe features begin t activate. It may be that sme wrds and their features are quicker t be perceived than thers. When tw wrds are presented, there may be a race fr them t be perceived, with the faster f the tw wrds winning r the fastest features winning, thereby starting the prbe feature activatin and cmparisn prcess at an earlier time. The rate f grwth f pair a", cnversely, appeared in ur data t be slightly slwer than that fr single-wrd a" (pint estimates f rate parameters in Grnlund & Ratcliff, 1989, were in the reverse directin). Unfrtunately, fr mst mdel variants, quantitative mdeling wuld be required t determine the rate predictins, partly because a" is nt simply related t the number f features that have participated in cmparisns, and partly because rate is a rather abstract measure nt easy t relate t theretical assumptins. There is ne interesting pssibility that might deserve cnsideratin, hwever. Suppse there is an interactin such that activatin f features f ne test wrd delays activatin f features f the ther (an example is serial activatin f the tw test wrds). Nt nly might this slw the rate f grwth, but it als wuld reduce asympttic accuracy because image-feature frgetting wuld cntinue t ccur during such delays. This pssibility is interesting because it adds anther basis fr explaining why pair perfrmance is nt as much better than single-wrd recgnitin as independence mdels might predict (e.g., Shiffrin & Steyvers, 1998). This hypthesis might be an alternative t the afrementined capacity and separate variants. The ARC-REM Mdel fr Cued Recall Assessing the mdel fr cued recall is a cmplex matter. The relatively gd fit f the mdel t the results prvides an existence prf that a search mdel fr cued recall can be used t predict accuracy and latency fr crrect respnses, intrusins, and giveups fr free respnse and signal-t-respnd. It is a plus that this mdel is cnsistent with, and shares apprpriate parameter values with, the mdel fr recgnitin. In particular, the likelihd ratis fr each episdic memry image frm the recent list are the basis fr bth the recgnitin and cued-recall mdels. Cnsidering nly cued recall, several factrs make it difficult t evaluate the degree t which the fit t the data supprts the mdel. One factr is the large number f parameters t be estimated (i.e., 20, 12 f which were specific t cued recall and nt used fr recgnitin). A mre imprtant factr is the apprach we used t arrive at the present versin f the mdel: We had t tinker at length with the assumptins, prcesses, and particularly their precise frms until a cmbinatin was fund that prduced the present results. At the utset f the mdel develpment prcess, we naively thught that there wuld be many cmbinatins f assumptins that wuld wrk abut equally well in prducing satisfactry predictins. This naive predictin was rted in the fact that a search prcess like that depicted in Figure 4 is cmplex, with many separate steps and many strategic cmpnents assciated with thse steps; assumptins abut all f these stages and steps wuld lgically be required t prduce a cnsistent mdel. It is because many f these necessary assumptins seemed t be smewhat uncnstrained by direct reference t the findings that led us t expect that it ught t be pssible t find many cmbinatins f assumptins that wuld prduce gd fits. In practice, we were surprised t find that it was quite difficult t cme up with even ne cmbinatin f assumptins prducing an adequate fit. Tw hyptheses seem t be plausible candidates t explain this difficulty. First, it is prbable that the large size f the space f pssible mdels makes this space difficult t search; a lw density f gd mdels relative t bad mdels culd be an imprtant inhibitr f the search fr a gd fitting mdel, even if quite a large number f these exist. Secnd, it is certainly the case that the prductin f a gd mdel was highly cnstrained by the fact that many prcesses and parameter values were carried ver frm recgnitin and by the fact that the data set was large, cmplex, and rich. These factrs being duly weighted, it wuld prbably be unwise t place much credence in the detailed frm f any single assumptin f the mdel. It seems likely that a lwering f gdness f fit caused by a change in sme ne detail culd well be redressed by cmpensating changes in the detailed frm f ther assumptins. Hwever, even if the frm f any ne assumptin taken alne is pen t questin, we believe the verall shape f the mdel prvides a reasnable candidate t explain the prcesses f retrieval in cued recall and, at the very least, prvides a starting pint fr further theretical advances. Turning t the assumptins themselves, there are a few that deserve special cmment. The characterizatin f cued recall as a search prcess is, f curse, critical; this characterizatin is rted in the differences in RT distributins between recgnitin and cued recall but is nt discussed in detail here because this issue frms the substance f the cmpanin article by Nbel and Shiffrin (2001). The mdel as stated assumes that the triggering mechanism fr certain decisin stages in the mdel becmes mre liberal as time passes during a given retrieval attempt. At the utset f the mdel explratin prcess, we investigated mdels withut such assumptins. Hwever, it rapidly became clear that the distributins in Figure 9 were skewed t the right relative t the predictins f mdels with time-hmgeneus assumptins. Althugh it may seem ad hc at first glance, we believe it is entirely

20 RECOGNITION AND RECALL MODEL 433 reasnable that participants becme mre and mre willing t cme t a decisin (at any f several stages f the memry search) as the remaining time available fr a respnse drps tward zer. 3 The ARC-REM mdel fr cued recall assumes that the prcess f generating matching values fr the images in memry (i.e., the generatin f likelihd values) takes place ne time during a given search prcess at the utset; the time t generate values ccurs nce, and the values prduced are then "frzen" in place during the remainder f the search. There are several reasns fr this apprach. First, ur attempts t allw the matching prcess t ccur again n every cycle f the search did nt prduce any mdels that seemed gd enugh t pursue. Hwever, the difficulty f searching the space f pssible mdels makes the evidence against the existence f a successful mdel f this srt very weak. Perhaps even mre imprtant are lgical cnsideratins: Given the variability in prbe nset times and the accmpanying variability in respnse accuracy, a new and independent activatin and matching prcess n every cycle f the search wuld tend t lead any extended search t a very high accuracy level. Fr example, in free respnse withut a time limit r in signal-t-respnd with a lng delayed signal, an ptimal strategy wuld invlve a great number f search cycles, using the results nly f thse that take place very quickly. This wuld ensure n frgetting f image features and, hence, the mst accurate pssible matching values. Then by accumulating the results f multiple samples f this kind, ne culd "average ut" the nise prduced by sampling and ensure that the respnse is based n all f the stred infrmatin in the crrect image. In n way wuld such a mdel be able t predict accuracy and RT results in cued recall. This reasning is related t that justifying the decisin t let sampling be based nt n the likelihd ratis, A, but instead n these numbers raised t a pwer, A 7. Because y had an estimated value f.21, the differences in likelihd values were cmpressed, and sampling was much less likely t lcate the crrect image than wuld have been the case with y f 1.0. This turned ut t be a necessary result, t spread ut the pint in time at which the crrect image is sampled. Sme discussin f this and related pints is given in Shiffrin and Steyvers (1998). The central theme f the ARC-REM mdel fr cued recall is, f curse, brrwed frm Shiffrin (1970) and Raaijmakers and Shiffrin (1980, 1981): the idea that retrieval perates thrugh sequential sampling. Why variatins in length and strength f list prduce distributins f cnditinal RTs that verlap greatly is nt easy t intuit. A cmplicating factr is that the pint at which varius decisins are made in the sequential search may vary with length and strength. Beynd this, fr a particular RT distributin, we are selecting ut thse cases in which that particular type f respnse ccurs. Cnsider list length and crrect respnses, fr example. Fr simplicity, cnsider the prbability f giving a crrect respnse n the first sample. Suppse each sample has a prbability f. 1 f lcating the crrect image fr a shrt list and.07 fr a lng list (there are mre images frm which t sample fr the lng list). Suppse the subsequent stages f the first search cycle prduce a crrect utput with prbability Q. The prbability that a crrect respnse ccurs at Time 1 fr the shrt list is AQ divided by the verall prbability crrect fr a shrt list, p s, and fr the lng list is.07q divided by the verall prbability crrect fr the lng list, p L. Because p s is larger than p L, the resultant cnditinal prbabilities can be surprisingly clse. Anther theme invlves the handling f intrusins. We have assumed fr simplicity that episdic intrusins arise frm the sampling f images frm the current list: frm sampling f the crrect image fllwed by incrrect recvery, r by sampling f the wrng image. Our data (see Nbel & Shiffrin, 2001) shw that intrusins als arise frm sampling f images frm earlier lists. Such a prcess wuld nt be hard t add t the mdel by assuming that all images in memry are activated by prbes that include cntext infrmatin, with the cntext ensuring that recent images are preferentially activated abve sme threshld and then sampled (see Shiffrin & Steyvers, 1997, 1998). Such a mdel wuld be cnsiderably mre cmplex than the present versin, and we judged it wuld nt be wrth the extra cmplexity merely t fit extralist intrusins. In summary, the cued-recall data set t which we fitted ur mdel is quite rich, including bth accuracy and RT distributins fr crrect respnses, intrusins, and give-ups, fr lists varying in length and strength, and fr free-respnse and signal-t-respnd cnditins. The reasnably clse quantitative predictins we btained n the ne hand prvide an existence prf that a sequential search mdel is capable f handling the pattern f btained results and n the ther hand prvide a starting pint fr future detailed mdels f perfrmance in cued recall. It is wrthy f additinal nte that despite being a sequential search mdel, this mdel was cnsistent with and shared certain parameter values with the parallel activatin mdel f recgnitin. Pssible Extensins f the ARC-REM Mdel t Assciative Recgnitin and Wickelcall Nbel and Shiffrin (2001) measured retrieval dynamics in signal-t-respnd tasks fr bth assciative recgnitin (discriminating intact studied pairs frm rearranged studied pairs) and wickelcall (similar t assciative recgnitin but with ne member f the test pair presented at the utset f the test perid and the ther presented just prir t the signal-t-respnd). The dynamics in bth cases were quite slw cmpared with either pair r singleitem recgnitin and were similar t thse in cued recall. On the basis f these findings, it may be reasnable t base a mdel f assciative recgnitin and wickelcall n recall prcesses. This apprach differs frm sme extant mdels that treat assciative recgnitin like single-item recgnitin; in these mdels, retrieval ccurs thrugh a single prcess f parallel activatin (e.g., Metcalfe Eich, 1982; Murdck, 1982). Hwever, in additin t the data frm ur present study, ther data shw the need fr an additinal cued-recall-like retrieval prcess in assciative recgnitin (e.g., Clark & Shiffrin, 1992; Dsher, 1984b; Grnlund & Ratcliff, 1989). Fr instance, Grnlund and Ratcliff (1989) fund that discriminatins requiring assciative infrmatin tend t be slwer than discriminatins that can be made n the basis f wrd infrmatin alne. As ne f the pssible mechanisms that cause this delay, they psited the invlvement f recall in recgnitin. In a series f studies n the effect f natural language wrd frequency n varius types f recgnitin and recall, Clark and Shiffrin fund 3 It might be interesting t see data frm a study with n time limit fr respnse, but even in such cases there wuld likely remain a tendency t change criteria as time passes because extended search is aversive.

21 434 DILLER, NOBEL, AND SHIFFRIN patterns f accuracy data that suggest the peratin f recall-like prcesses in assciative recgnitin and, t a lesser extent, in item recgnitin. Perhaps the mst straightfrward way t extend the cued-recall mdel t assciative recgnitin invlves sampling pair images and saying "ld" if ne is fund that matches bth test wrds (bth likelihd ratis lie abve a criterin cr), saying "new" if ne is fund that matches nly ne f the test wrds, r therwise cntinuing the search r terminating the search with a guess. The test prbe n any cycle f the search culd be ne f the tw test wrds (which is chsen as a prbe might be related t the respective familiarity values f the tw wrds), bth wrds, r bth wrds but with the ttal number f features reduced. Likelihd ratis are then calculated n the basis f the parallel match f the test prbe t the memry images (as in recgnitin). A memry image fr a pair is then sampled n the basis f the value f these likelihd ratis. After a pair image is sampled, suppse the test wrds are cmpared with the wrd images in bth rders, with the best rder being used fr subsequent decisins. This prcess thus prduces a pair f likelihd ratis fr each sampled image, ratis that are used in the afrementined decisin prcess. In free respnse, there wuld be search terminatin rules based n factrs like lw familiarity f at least ne f the test wrds and the time spent searching withut success. T arrive at predictins, it wuld be necessary t add assumptins abut the times fr the varius stages f the search. In signal-t-respnd, the search wuld be cntinued either until a decisin is reached r t the time f the signal, at which time a guessing strategy wuld be invked. A sphisticated mdel might allw guessing t be based n the familiarity f the prbe. This wuld prduce a mixed mdel, with respnses based n bth recall and familiarity, and might allw predictin f an initial perid f abve chance perfrmance befre the expnential rising prtin f the signal-t-respnd functin. Hw might a mdel f this srt be extended t wickelcall? Perhaps the simplest and mst straightfrward apprach invlves using the wrd initially presented as a prbe and prceeding as in cued recall. A respnse that is lcated by the time the signal-trespnd ccurs wuld be matched against the secnd wrd presented and a respnse made accrdingly, r else a guessing strategy wuld be invked. This apprach might pssibly help explain the findings by Wickelgren and Crbett (1977) and in Experiment 3 f Nbel and Shiffrin (2001), that wickelcall has cnsiderably lwer (asympttic) accuracy than assciative recgnitin. The pprtunity t use either f tw cues in assciative recgnitin, especially the mre familiar ne, might cnsiderably increase the prbability f sampling the crrect pair image. Cncluding Remark As a cncluding cmment, it is wrth emphasizing that the ARC part f the ARC-REM mdel des nt really apply t cued recall, assciative recgnitin, r wickelcall. A sequential search by its very nature invlves assessment f evidence at each step: The search stps when the evidence prvides a sufficient reasn t d s. Althugh a number f die stpping rules in the cued-recall mdel use criteria that prduce enhanced prbability f stpping as the respnse perid winds dwn, these rules are at best nly slightly reminiscent f the ARC apprach. Thus, the ARC apprach, in which respnding ccurs nt when evidence has reached a level f sufficiency but instead when retrieval has prceeded far enugh, is in the present setting quite specific t the parallel activatin prcess we assume fr recgnitin (and pssibly fr pair recgnitin). Whether this srt f mdel will prve useful fr ther cgnitive tasks in which RTs are measured is a questin that will have t be taken up in future research. References Blmer, J. (1992). 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22 RECOGNITION AND RECALL MODEL 435 systems fr assciative recall and recgnitin. Psychlgical Review, 91, Raaijmakers, J. G. W., & Shiffrin, R. M. (1980). SAM: A thery f prbabilistic search f assciative memry. In G. H. Bwer (Ed.), The psychlgy f learning and mtivatin: Advances in research and thery (l. 14, pp ). New Yrk: Academic Press. Raaijmakers, J. G. W., & Shiffrin, R. M. (1981). Search f assciative memry. Psychlgical Review, 88, Ratcliff, R. (1978). A thery f memry retrieval. Psychlgical Review, 85, Ratcliff, R. (1988). Cntinuus versus discrete infrmatin prcessing: Mdeling accumulatin f partial infrmatin. Psychlgical Review, 95, Ratcliff, R., & Murdck, B. B., Jr. (1976). Retrieval prcesses in recgnitin memry. Psychlgical Review, 83, Shiffrin, R. M. (1970). Memry search. In D. A. Nrman (Ed.), Mdels f human memry (pp ). New Yrk: Academic Press. Shiffrin, R. M., & Steyvers, M. (1997). A mdel fr recgnitin memry: REM retrieving effectively frm memry. Psychnmic Bulletin and Review, 4, Shiffrin, R. M., & Steyvers, M. (1998). The effectiveness f retrieval frm memry. In M. Oaksfrd & N. Chater (Eds.), Ratinal mdels f cgnitin (pp ). Oxfrd, England: Oxfrd University Press. Smith, R. W., & Shiffrin, R. M. (1997). Tempral aspects f recgnitin memry: Reactin time distributins and partial infrmatin. Pster sessin presented at the 38th Annual Meeting f the Psychnmic Sciety, Philadelphia. Wickelgren, W. A., & Crbett, A. T. (1977). Assciative interference and retrieval dynamics in yes-n recall and recgnitin. Jurnal f Experimental Psychlgy: Human Learning and Memry, 3, Received June 15, 1999 Revisin received September 13, 2000 Accepted September 21, 2000 AMERICAN PSYCHOLOGICAL ASSOCIATION SUBSCRIPTION CLAIMS INFORMATION Tday's Date:_ We prvide this frm t assist members, institutins, and nnmember individuals with any subscriptin prblems. With the apprpriate infrmatin we can begin areslutin. If yu use the services f an agent, please d NOT duplicate claims thrugh them and directly t us. PLEASE PRINT CLEARLY AND IN INK IF POSSIBLE. PRINT FULL NAME OR KEY NAME OF INSTITUTION MEMBER OR CUSTOMER NUMBER (MAYBEFOUND ON ANYPAST ISSUE LABEL) DATE YOUR ORDER WAS MAILED (OR PHONED) CITY YOUR NAME AND PHONE NUMBER STATE/COUNTRY _PREPAtt> CHECK CHARGE CHECK/CARD CLEARED DATE:_ (If pssible, send a cpy, frnt and back, f yur cancelled check t belp us in ur research f yur claim.) ISSUES: MISSING DAMAGED TITLE OLUME OR YEAR NUMBER OR MONTH Thank yu. Once a claim is received and reslved, delivery f replacement issues rutinely lakes 4-6 weeks. ^ ^ ^ (TO BE FILLED OUT BY APA STAFF) "^ ^ DATE RECEIED:. ACTION TAKEN: _ STAFF NAME: DATE OF ACTION: _ IN. NO. & DATE: LABEL NO. & DATE:_ Send this frm t APA Subscriptin Claims, 750 First Street, NE, Washingtn, DC PLEASE DO NOT REMOE. A PHOTOCOPY MAY BE USED.