Positional and temporal clustering in serial order memory

Transcription

1 Mem Cogn (22) 4:77 9 DOI.3758/s Positionl nd temporl clustering in seril order memory Alec Solwy & Bennet B. Murdock & Michel J. Khn Pulished online: 5 Novemer 2 # Psychonomic Society, Inc. 2 Astrct The well-known finding tht responses in seril recll tend to e clustered round the position of the trget item hs olstered positionl-coding theories of seril order memory. In the present study, we show tht this effect is confounded with nother well-known finding tht responses in seril recll tend to lso e clustered round the position of the prior recll (temporl clustering). The confound cn e llevited y conditioning ech nlysis on the positionl ccurcy of the previously reclled item. The revised nlyses show tht temporl clustering is much more prevlent in seril recll thn is positionl clustering. A simple ssocitive chining model with symmetric neighoring, remote ssocitions, nd primcy grdient cn ccount for these effects. Using the sme prmeter vlues, the model produces resonle seril position curves nd cptures the chnges in item nd order informtion cross study-test trils. In contrst, prominent positionl coding model cnnot ccount for the pttern of clustering uncovered y the new nlyses. Keywords Seril recll. seril order. ssocition. clustering. A. Solwy Princeton University, Princeton, NJ, USA B. B. Murdock University of Toronto, Toronto, ON, Cnd M. J. Khn (*) Deprtment of Psychology, University of Pennsylvni, Phildelphi, PA, USA e-mil: khn@psych.upenn.edu Associtive chining nd positionl coding constitute the two clssic models of seril order memory. Although ssocitive chining ws the implicit theory in Einghus (885/93) seminl studies of seril lerning, erly scholrs lso recognized tht people cn rememer the positions of list items, nd tht this positionl informtion ws often used to id the lerning process (Ldd & Woodworth, 9). During the 95s nd 96s, gret del of reserch ws focused on identifying the functionl stimulus in seril lerning the prior item, s predicted y chining theory, or the item s position, s predicted y positionl coding theory. This work ws generlly inconclusive, with vrious experiments lending prtil support to one or the other ccount (for review, see Young, 968). In recent decdes, s the emphsis shifted from the study of multitril seril lerning to the study of immedite seril recll, theorists hve lrgely rejected the possiility tht chining plys n importnt role in seril-order memory (Burgess & Hitch, 26; Frrell & Lewndowsky, 22; Henson, Norris, Pge & Bddeley, 996.) Insted, most modern ccounts of seril order memory emphsize the importnce of positionl informtion s the mjor retrievl cue. One of the mjor sources of evidence for the positionl coding view is the phenomenon of positionl clustering (lso known s positionl grdients, nd the loclity constrint). While mny reclled list items pper in their correct seril positions, items tht re reclled out of order tend to migrte to neighoring seril positions (e.g., Estes, 972; Lee&Estes,977; Nirne, 992). This phenomenon would e expected if the retrievl cue is memoril representtion of ech item s list position. When the positionl cue fils to correctly retrieve the pproprite item, it ctivtes items from neighoring list positions.

2 78 Mem Cogn (22) 4:77 9 In ddition to positionl clustering, other criticl evidence for position-sed models comes from findings of protrusions (erroneous recll of n item from the sme position in prior list) nd confusions mong phonologiclly similr items occurring in distinct list positions (e.g., Bddeley, 968). Although some experiments hve demonstrted role for ssocitive processes in seril lerning (e.g., Khn, Mollison, & Addis, 2; Serr & Nirne, 2), the striking effects of positionl clustering seen in ll seril recll tsks suggest tht ny contriutions of ssocitive chining re secondry to the more prominent role of positionl informtion. Recent work hs shown tht seril recll lso exhiits high degree of temporl clustering, with responses tending to come from positions ner tht of the just-reclled item (Bhtrh, Wrd, & Tn 26; Klein, Addis, & Khn, 25). Wheres positionl clustering lends support to position-sed models, the temporl clustering effect lends support to chining-sed models. In the present rticle, we exmine the interction etween these effects nd show tht they re confounded. We llevite the confound y exmining suset of responses, nd find tht temporl clustering, rther thn positionl clustering, is more prevlent in seril recll. Moreover, we show tht simple strength-sed chining model provides etter fit to the overll pttern of positionl nd temporl clustering thn does positionl coding model (Burgess & Hitch, 26). Method To reevlute the positionl nd temporl clustering effects in seril recll, we focused on three studies (Golom, Peelle, Addis, Khn, & Wingfield, 28; Khn & Cpln, 22, Experiment 2; Khn et l., 2). All three studies hd prticipnts study nd voclly recll lists of common words. Tle contins summry of these studies. For detils, see the Appendix. Clustering nlyses performed on the two studies tht use longer lists (Khn & Cpln, 22; Khn et l., 2) focused on the middle list items (4 6 for 9-word lists, nd 4 for 3-word lists). Edge items were excluded ecuse they cnnot pper t ll of the distnces tht were nlyzed. However, including ll items produced comprle results. Clustering nlyses performed on the Golom et l. (28) study, which used shorter lists, included ll items. Results Estes (972) reported tht list items re more likely to e reclled in their correct seril position thn in ny other output position. Furthermore, items reclled in the wrong position cluster closely round the correct position. This result my e seen in the top row of Fig., which shows tht the proility of reclling n item decreses s function of its distnce from the correct position. The proility of reclling n item t ech distnce ws conditioned on the numer of times ech distnce ws ville. As n illustrtive exmple, consider list with four items. If prticipnt reclls ll four items in their correct order, the items would ll e t distnce ecuse their output positions would mtch their list positions. On the other hnd, if prticipnt reclls the sequence 2 4, the fourth item would e t distnce ecuse it ppers one position erly. Similrly, if the prticipnt reclls the sequence 3 2, then the second item would e t distnce + ecuse it ppers one position lte. Klein et l. (25) reported tht in seril lerning tsks, prticipnts exhiit strong temporl clustering effect nlogous to the forwrd-symmetric contiguity effect frequently reported in studies of free recll. This cn e seen in the top row of Fig. 2, which shows the degree of temporl clustering round prior reclls. Here, distnce of + mens tht reclled item hd the sme predecessor oth in the recll sequence nd in the list. A distnce of +2 mens tht there ws one item in the list seprting the reclled item from the preceding recll, nd so forth. Negtive distnces correspond to filling in skipped over items. As efore, the proility of reclling n item t ech distnce ws conditioned on the numer of times ech distnce ws ville. The strong temporl clustering effect illustrted in the top row of Fig. 2 hs lso een Tle Summry of the nlyzed studies Presenttion Modlity Response Modlity Numer of Lists List Length Study-Test Trils Golom et l., (28) Visul Spoken,296 Khn nd Cpln (22)[Exp. 2] Spoken Spoken,2 9 Criterion Khn et l., (2) Spoken Spoken 89 3 Criterion Spoken Spoken 89 9 Criterion

3 Mem Cogn (22) 4: c d Conditionl response proility e f g h Distnce from correct position Fig. Proility of reclling n item s function of its distnce from its correct position. Negtive vlues correspond to reclling n item too erly, nd positive vlues correspond to reclling n item too lte. Missing dt points indicte tht the corresponding condition did not occur. Error rs indicte 95% confidence intervls computed using the method of Loftus nd Msson (994). Pnels in the top row were computed sed on ll reclls, while pnels in the ottom row were computed sed only on reclls following the first order error. Ech column is sed on dt from different experiment. nd e Golom et l. (28) nd f Khn nd Cpln (22, Experiment 2) c nd g Khn et l. (2, 3-word lists) d nd h Khn et l. (2, 9-word lists) demonstrted in other seril recll experiments (Bhtrh et l., 26; Bhtrh, Wrd, & Tn, 28; Klein et l., 25). Joint findings of strong positionl nd temporl clustering my seem contrdictory given tht the two phenomen hve een ssocited with very different theoreticl models. However, it is importnt to recognize criticl confound in this comprison. Consider wht hppens fter prticipnt reclls the first two items of four-item list. If the prticipnt reclls Item 3 next, its distnce from the correct output position would e, nd its distnce from the preceding response would e +.If, insted, the prticipnt reclls Item 4 next, its distnce from the correct output position would e, nd its distnce from the preceding response would e +2. In generl, for reclls up to nd including the first-order error, there is one-to-one reltionship etween ech item s distnce from the correct output position nd from the prior recll, given y the function D prior ¼ D pos þ Fortuntely, one cn llevite the confound y restricting the clustering nlyses to items following the first-order error on ech tril. For exmple, in the recll sequence 3 4, Item 4 is included ecuse Item 3 ws reclled erly. Plots of positionl nd temporl clustering for items following the first-order error re displyed in the ottom rows of Figs. nd 2, respectively. Figure shows tht such reclls do not cluster round the correct list position. On some trils, intrusion(s) precede the first order error. Discrding such trils produces comprle results. We cnnot consider items following intrusions ecuse their distnce from the prior recll (the intrusion) is undefined. On the other hnd, Fig. 2 shows tht, lthough ttenuted, the temporl clustering effect is preserved. After committing the first-order error, prticipnts tend to pick up with the list item tht follows the item reclled out of order. Strength-sed ssocitive chining model We next sked whether n ssocitive chining model tht lcks ny direct representtion of positionl informtion cn ccount for this pttern of positionl nd temporl clustering. In previous work, ssocitive chining models (e.g., Lewndowsky & Murdock, 989) hve een successfully pplied to severl key fetures of seril recll nd seril lerning dt, ut hve generlly not een pplied to the positionl clustering effects tht hve een criticl source of evidence for positionl coding theories (lthough see Shiffrin & Cook, 978) To ddress this question, we developed reduced form chining model tht incorportes the two clssic ssumptions of ssocitive chining theory: () tht the strength of ssocition etween items is (exponentilly) decresing function of their distnce, nd () tht forwrd ssocitions (i.e., those etween erlier nd lter items in the chin) re encoded more strongly thn ckwrd ssocitions (Einghus, 885/93; Rskin & Cook, 937). Consistent with other models, we ssume primcy grdient in item encoding strength to simulte prticipnts tendency to llocte greter ttention to erly list items (Brown, Preece, & Hulme, 2; Henson, 998; Jensen, 962; Lewndowsky & Murdock 989; Pge, & Norris, 998). At test, the model simultes recll proilisticlly ccording to Luce choice rule (Luce, 959) nd cn choose

4 8 Mem Cogn (22) 4:77 9 c d Conditionl response proility e f g h Distnce from preceding item Fig. 2 Proility of reclling n item s function of its distnce from the prior recll. Negtive vlues correspond to reclling n erlier item from the list, nd positive vlues correspond to reclling lter item from the list. Error rs indicte 95% confidence intervls computed using the method of Loftus nd Msson (994). Pnels in the top row were computed sed on ll reclls, wheres pnels in the ottom row were computed sed only on reclls following the first order error. Ech column is sed on dt from different experiment, s in Fig. to stop t ny position. As in other strength-sed recll models, we use mtrices to store the strengths of interitem ssocitions (e.g., Kimll, Smith, & Khn, 27; Sirotin, Kimll, & Khn, 25); we do not explicitly model item representtions themselves. In ddition to sking whether our ssocitive chining model cn ccount for the pttern of positionl nd temporl clustering, we sought to exmine whether the model could simultneously ccount for two other criticl spects of seril recll nd lerning dt, specificlly: the multi-tril seril position curves (Wrd, 937) nd the gins nd losses of item nd order informtion cross trils (Addis & Khn, 24). In most modeling studies, different experiments from the literture re used to illustrte different empiricl phenomen. As such, seprte model prmeters re estimted for ech experiment, nd one cnnot e sure whether it is the model s mechnisms or its free prmeters tht re doing the work of fitting the empiricl regulrities. In order to ssess whether the model cn ccount for ech of the findings using single set of prmeter vlues, we fit dt from single experiment (Khn & Cpln, 22, Experiment2). Prticipnts in this experiment lerned ech list to criterion of one perfect recll (see the Appendix). Becuse the numer of study-test trils vried cross lists, we restricted our nlyses to the first three study-test trils nd excluded lists tht were lerned in fewer thn three trils. to ll of the preceding items. The strength of the ssocitions etween nerest neighors hs Gussin distriution with n exponentilly decying men (the primcy grdient; c s controls the gin, d s the decy rte, nd min s the lower ound) nd with vrince s s. The primcy grdient llows the model to mimic the wy in which prticipnts lern lists: Items from the eginning of the list re rememered on the first tril, nd items from lter in the list re progressively dded on susequent trils (Slmeck, 964). The strength of ssocitions etween nondjcent items decys exponentilly s function of distnce. The rte of the decy is Gussin with prmeters m s nd s s (note the incresingly lighter shdes of gry etween nondjcent items in Fig. 3). Remote ssocitions llow the model to skip hed nd lter return to omitted items. Without remote ssocitions, the only type of errors the model would e le to produce re errors of omission. The strengths of ckwrd ssocitions re scled to w times the strengths of forwrd ssocitions, where < w <. In ddition to eing ound to one nother, list items re ound to n dditionl nonlist item tht mrks the eginning of list. During recll, this strt mrker serves Summry of prmeters As n illustrtive exmple of the model s dynmics, consider the list in Fig. 3. During study, ech item is ound Fig. 3 Illustrtion of direct nd remote ssocitions in the chining model

5 Mem Cogn (22) 4: s the initil retrievl cue. Retrievl is proilistic nd follows Luce choice rule with softmx prmeter γ (see Eq. 5). When γ =, the proility of retrieving n item is proportionl to the strength of the ssocition etween the retrievl cue nd the item. As γ pproches, only the item tht is most strongly ssocited with the cue will e reclled (i.e., the winner tkes ll). If list item is successfully retrieved, it then serves s the retrievl cue for the susequent position. Recll my lso terminte t ny list position if second competing nonlist item is selected. The strength of this item is controlled y the prmeter stop nd is independent of the retrievl cue. Tle 2 provides summry of the model s prmeters together with their est-fitting vlues. A forml description of the model cn e found in the Appendix. Modeling positionl nd temporl clustering Figures 4 nd 5 show tht the chining model cn cpture the mjor qulittive fetures of oth positionl nd temporl clustering, computed in the stndrd wy (top rows), nd conditionl on the prior recll eing n order error (ottom rows). Although the model lcks direct representtion of positionl informtion, it cn successfully ccount for the positionl clustering effect ecuse of the confound with the temporl clustering effect. The chining mechnism, together with the prmeter vlues shown in Tle 2, provide simple nd direct ccount of these results. The men rte t which the strength of remote ssocitions decys s function of distnce (m s ) is high throughout the list. On verge, the strength increment etween n item nd nother item more thn two positions wy is very low (<.). Comined with strong forwrd symmetry (w ), these vlues result in strong temporl clustering effect. The model slightly overestimtes the mgnitude of the effect s compred with Tle 2 Model prmeters Prmeter Vlue c s.945 d s.38 min s. s s.645 m s s s 9.93 w.34 stop. γ 9.69 the dt, especilly in lter trils. Becuse the first order error most often involves skipping over single item (see Fig. ), temporl clustering nd positionl clustering re still prtilly confounded, leding the model to lso overestimte the percentge of items reclled one position erly (ottom row of Fig. 4). Modeling seril position curves over trils Seril position curves for the dt re shown in Fig. 6. Vlues for these curves were computed using reltive order scoring (i.e., reclled item ws considered correct if the prior recll ws the item s immedite predecessor in the list). This scoring method is well suited to the experimentl prdigm tht we re modeling. Rther thn eing forced to mke response t ech seril position (e.g. sying pss for seril positions tht cnnot e reclled), prticipnts were free to recll only the words tht cme to mind. Using reltive order scoring llows items from lter seril positions to e mrked correct even if items from erlier seril positions were omitted ( common occurrence for long lists using spoken recll). In contrst, solute, or strict, positionl scoring (i.e., considering n item to e correct only if it is reclled in the sme position in which it ws studied) hevily penlizes recll of midlist nd end-oflist items. As shown in Fig. 6, the chining model cptures the extended primcy effect nd the chnge in oth the level nd shpe of the seril position curve cross trils. The primcy effect is result of: () the inherent interdependencies tht exist etween items, nd () the primcy grdient in encoding strengths. On the first tril, midlist items exhiit low levels of recll ecuse the stop item cts s formidle contender. Although the vlue of the stop prmeter is low (see Tle 2), it hs strong influence, on verge, ecuse the vrince of strength increments (s s ) is reltively high in comprison. This effect is progressively reduced in lter trils s interitem ssocitions re reinforced. Lerning is result of the vriility in encoding strength (s s nd s s ), coupled with closed-loop lerning rule (see the Appendix). The primcy grdient is not necessry to fit the generl shpe of the seril position curve. Becuse successful retrievl of ech item is dependent on the successful retrievl of the previous list item, chining provides nturl ccount of the progressively lower levels of recll seen in lter list positions. We tested this notion y fixing the prmeters c s nd d s to nd fitting the model with the reduced set of prmeters. Although the fits were not quite s good, the model ws still le to cpture the qulittive fetures of the seril position curves nd the pttern of clustering.

6 82 Mem Cogn (22) 4:77 9 Dt Chining Model c Conditionl response proility d e f Distnce from correct position Fig. 4 Proility of reclling n item s function of its distnce from its correct position. Negtive vlues correspond to reclling n item too erly, nd positive vlues correspond to reclling n item too lte. The solid curve ws computed sed on the dt from Khn nd Cpln (22, Experiment 2), nd the dotted curve ws computed sed on dt simulted using the chining model. Model prmeters re given in Tle 2. Error rs indicte 95% confidence intervls computed using the method of Loftus nd Msson (994). The three columns correspond to the first three trils of ech list. c Bsed on ll reclls. d f Bsed only on reclls following the first order error Modeling gins nd losses of item nd order (GLIO) There re two types of informtion prticipnt cn recll out n item: its memership in the list (item informtion) nd its position in the list (order informtion). Ech type of informtion my e gined, lost, or sty the sme etween two consecutive trils (Fig. 7). For exmple, if n item is reclled on the first tril in the wrong seril position (using Dt Chining Model c Conditionl response proility d e f Distnce from preceding item Fig. 5 Proility of reclling n item s function of its distnce from the prior recll. Negtive vlues correspond to reclling n erlier item from the list, nd positive vlues correspond to reclling lter item from the list. The solid curve ws computed sed on the dt from Khn nd Cpln (22, Experiment 2), nd the dotted curve ws computed sed on dt simulted using the chining model. Model prmeters re given in Tle 2. Error rs indicte 95% confidence intervls computed using the method of Loftus nd Msson (994). The three columns correspond to the first three trils of ech list. c Bsed on ll reclls. d f Bsed only on reclls following the first order error

7 Mem Cogn (22) 4: Recll proility.6.2 Tril Tril 2 Tril 3 c Seril position Fig. 6 Seril position curves for Trils 3 of 9 word list (Khn & Cpln, 22, Experiment 2). Error rs indicte 95% confidence intervls computed using the method of Loftus nd Msson (994). Simulted vlues otined using the chining model. Model prmeters re given in Tle 2. c Simulted vlues otined using the Burgess nd Hitch (26) positionl coding model. Only the first tril is modeled reltive order scoring, s in the previous section), it follows trnsition+i from stte none to stte item. If n item is reclled in the correct position, it follows trnsition+io nd ends up in stte item nd order. If item informtion, order informtion, or oth re lost in lter tril, the item trnsitions ck to one of its previous sttes. In ll, there re six trnsitions of interest: +IO Gining item nd order informtion +I Gining item informtion, incorrect order informtion +O Gining order informtion, mintining item informtion -IO Losing item nd order informtion -I Losing item informtion, did not hve order informtion -O Losing order informtion, mintining item informtion Figure 8 shows the proility of gining item nd order informtion together (+IO) t ech seril position on the first three trils. The dt show lrge primcy effect nd smll recency effect on Tril (this is equivlent to the Tril seril position curve shown in Fig. 6). In lter trils, primcy effect is no longer pprent 2 nd insted there is n Fig. 7 Stte digrm representing the possile gins nd losses of item nd order informtion etween consecutive trils. The three sttes correspond to omitting n item, reclling n item out of order, nd reclling n item in the correct order. Items trnsition etween sttes in response to chnges in item nd order informtion. It is lso possile tht no chnge tkes plce, in which cse n item stys in the sme stte (not shown) increse for groups of items from progressively lter in the list. As is shown in Fig. 8, the model is le to cpture the pttern of comined item nd order gins for eginning nd midlist items. The primcy items re lerned first due to the interdependent nture of interitem ssocitions nd the grdient in encoding strength. Further strength increments on lter trils llow the midlist items to e lerned. The proility of gining item nd order informtion seprtely is elow.5 t lmost ll seril positions. We ggregte these results cross seril positions nd summrize them in Tle 3. Here we see trde-off occur over trils, with some items gined out of order in erlier trils nd then supplemented with order informtion in lter trils. As is shown in Tle 3, the model is le to cpture the low levels of seprte item nd order gins compred with the higher levels of comined gins. The proportion of comined gins reltive to seprte gins is controlled y the prmeter w, which determines the likelihood of ckwrd trnsitions, the prmeters m s nd s s, which control the strength of remote ssocitions, nd the prmeter γ, which controls the frequency with which wekly ssocited items re selected for recll. The low vlue of w (see Tle 2) nd the high vlues of m s, s s, nd γ together mke comined gins more frequent. The proility of losing informtion of ny type is elow.5 t ll seril positions. We ggregte these results cross seril positions s well, nd lso summrize them in Tle 3. Once n item is plced in its correct position, tht position is seldom lost. Item informtion y itself is lso seldom lost nd is insted supplemented with order 2 We did not condition on the vilility of trnsitions ecuse it would mke it pper s if more items re gined on lter trils thn on erlier trils. For discussion of this issue, see (Addis nd Khn 24).

8 84 Mem Cogn (22) 4:77 9 Fig. 8 Proility of gining item nd order informtion together t ech seril position on Trils 3 of 9-word list (Khn & Cpln, 22, Experiment 2). Simulted vlues otined using the chining model. Model prmeters re given in Tle 2 Recll proility Seril position 9 2 Tril informtion on lter tril. In the model, the sme prmeters tht mke comined item nd order gins most frequent lso ensure tht there is very little chnce of retrieving remote item or the stop mrker once the ssocitions etween nerest neighors re sufficiently strong. Comprison with positionl coding model We lso exmined whether prominent positionl coding model (Burgess & Hitch, 26) could fit the pttern of positionl nd temporl clustering. The Burgess nd Hitch (26) model fetures neurl network rchitecture in which different contexts, items, nd phonemes re represented in seprte lyers of the network. During study, items ecome ound to slowly vrying list context, with Tle 3 Proilities of gining nd losing item nd order informtion Tril Beh. Dt Simultion +IO I O IO I O proximl items ound to overlpping context signls. At test, the list context is plyed ck nd used s the retrievl cue. Becuse the Burgess nd Hitch (26) model hs not een pplied to multitril seril lerning dt, we restrict our nlysis to the first study-test tril. The seril position curve predicted y the model is shown in Fig. 6c. The model cptures the extensive primcy, the ttenuted recency, nd the overll level of recll seen in the dt. Shown in the top row of Fig. 9, the model is lso le to cpture the mjor qulittive fetures of the trditionl positionl nd temporl clustering effects. The model fils, however, to cpture the pttern of conditionl positionl clustering (Fig. 9c). Insted, it incorrectly predicts tht fter committing n order error, prticipnts re still most likely to recll the item from the proper list position. Although one would not ordinrily expect positionl coding model to predict the conditionl temporl clustering effect, the Burgess nd Hitch (26) model provides very good fit to the dt (Fig. 9d). We cn gin insight into the model s ility to fit this effect y exmining the proility tht the first-order error is given distnce from the correct position (Fig. ). Here, we see tht the first-order error most frequently involves skipping over single list item nd reclling the next item one position erly. Although we did not fit either model to this spect of the dt, oth the chining model nd the Burgess nd Hitch model cn ccount for this effect. With the Burgess nd Hitch model, n error of this kind represents specil cse in which the susequent recll is dependent on the identity of the error item. Consider wht hppens fter the Burgess nd Hitch model reclls the sequence 2 4. After reclling ech item, the model inhiits the corresponding item node. The contextul retrievl cue most strongly mtches the item from the fourth list position, ut tht item ws recently reclled nd inhiited, nd is unlikely to e retrieved gin. Becuse the context signl is utocorrelted, the item to most likely e reclled next is Item 5 (lg +), followed y Item 3 (lg ), nd so on, producing the pttern of temporl clustering shown in Figure 9d. Such depen-

9 Mem Cogn (22) 4: Fig. 9 Proility of reclling n item s function of its distnce from its correct position. The solid curve ws computed sed on the dt from Khn nd Cpln (22, Experiment 2), nd the dshed curve ws computed sed on dt simulted using the model of Burgess & Hitch (26). Error rs indicte 95% confidence intervls computed using the method of Loftus nd Msson (994). Proility of reclling n item s function of its distnce from the prior recll. c d sme s in, respectively, ut sed only on reclls following the first order error Conditionl response proility c Dt B&H (26) Model Distnce from correct position d Distnce from preceding item Distnce from correct position Distnce from preceding item dence etween consecutive reclls is not generl property of the Burgess nd Hitch model. If the model reclled ny item other thn Item 4 in the third output position, Item 4 would not undergo inhiition nd would e the item to most likely e reclled next, regrdless of which item ws reclled in the third output position. In order to exmine the predictions of oth models outside of this specil cse, we repeted the conditionl temporl clustering nlysis, ut this time excluding trils in which the first order error involved skipping over single list item. Figure shows tht while the chining model still correctly predicts the temporl clustering effect, the Burgess nd Hitch (26) model does not. It is possile tht the Burgess nd Hitch model could fit the pttern of results shown in Fig. using nother set of prmeter vlues. In order to test for this possiility, we refit the model, this time including the results of Fig.. The est-fitting prmeter vlues were similr to those of the initil fit, leving the pttern of results shown in Fig. unchnged. Proility of first error.6.2 A -9 9 Distnce from correct position Conditionl response proility.6.2 Dt Chining Model B&H (26) Model Distnce from preceding item Fig. Proility of committing the first-order error s function of distnce from the correct position. Negtive vlues correspond to reclling n item too erly, nd positive vlues correspond to reclling n item too lte. Proility of reclling n item s function of its distnce from the prior recll, sed only on reclls following the firstorder error on trils in which the error did not involve skipping over single item

10 86 Mem Cogn (22) 4:77 9 Generl discussion In reclling sequences of items, people tend to cluster their responses round the correct list position. Items re most likely to e reclled in the correct position nd re progressively less likely to e reclled in positions tht re further wy. This positionl clustering effect hs een well documented in mny recll prdigms nd hs een used to support the positionl coding theory of seril recll. According to positionl coding theory, people ssocite ech list item with positionl mrker nd use those mrkers s cues to guide recll. In contrst to positionl coding theory, the chining theory of seril order memory posits tht people ssocite ech list item with the preceding item or items, nd tht during recll, the items serve s cue for their neighors. Consistent with this ccount of seril-order memory, people show strong temporl clustering, or contiguity, effect. In seril recll, this is seen in the tendency for reclls to e items studied in proximity to the just-reclled item. Becuse positionl informtion does not ply n explicit role in chining theory, it hs generlly een ssumed tht chining models re unle to ccount for the positionl clustering effect (lthough see Shiffrin & Cook, 978). The presence of prominent temporl nd positionl clustering in seril recll would seem to support role for oth chining nd positionl coding. However, the nlyses reported here demonstrte tht positionl nd temporl clustering re highly confounded. Much of the confound is driven y the first severl reclls on ech tril, which oth pper in their correct seril positions (distnce in Figs. nd 4) nd re y definition ech one list position wy from the prior recll (distnce + in Figs. 2 nd 5). A similr miguity exists for the first item on ech tril reclled in the wrong seril position. For these items, it is uncler whether recll is driven primrily y positionl or y temporl informtion. An ssocitive chining model tht mkes no explicit use of positionl informtion cn exhiit significnt positionl clustering (see Figure 4 c), providing good fit to the levels oserved in the dt. Likewise, positionl coding model (Burgess & Hitch, 26) tht mkes no explicit use of temporl informtion cn exhiit significnt temporl clustering (see Fig. 9). Conditioning the positionl nd temporl clustering nlyses on n incorrect prior recll llowed us to llevite the confound. We found tht while the temporl clustering effect persists following n order error, the positionl clustering effect is no longer pprent (see the ottom rows of Figs. nd 2). After mking n order error, prticipnts were most likely to recll the item on the list following the just-reclled item nd not the item from the proper list position. Becuse chining theory posits tht ech recll serves s the susequent retrievl cue, our chining model is lso le to cpture these effects (see Figs. 4d f nd5d f). However, ecuse retrievl in the Burgess nd Hitch (26) model is driven primrily y positionl informtion, their model incorrectly predicts tht reclls following the first order error cluster round the correct list position (see Fig. 9c). Surprisingly, the Burgess nd Hitch (26) model ws le to cpture the conditionl temporl clustering effect (see Fig. 9d). We were le to etter understnd the model s ility to fit this spect of the dt y nlyzing the proility of committing the first-order error s function of its distnce from the correct position (Fig. ). Consistent with the dt, the first-order error most often involves skipping over single list item nd reclling the next list item one position erly. However, ecuse items reclled y the Burgess nd Hitch model re inhiited following recll, n item tht is reclled one position erly is unlikely to e repeted in the next output position, even though it est mtches the positionl retrievl cue. Insted, the next recll depends on the identity of the item tht ws reclled erly, with higher weight given to neighoring items in the list. This type of dependence etween djcent reclls is not generl property of positionl coding models or of the Burgess nd Hitch model in prticulr, ut rther, represents specil cse of the model s ehvior. Repeting the conditionl temporl clustering nlysis while excluding the trils on which this type of order error occurred showed tht the Burgess nd Hitch model cnnot mtch the pttern of temporl clustering eyond this specil cse. Our findings point to contiguity-sed ssocitive mechnism s the primry fctor underlying positionl clustering effects in seril recll. However, these findings do not exclude the possiility tht positionl informtion would ssert itself in other spects of seril order memory, especilly situtions in which interference cused y similrity or item repetitions must e overcome (Bddeley, 968; Chnce & Khn, 997; Henson et l. 996; Khn & Jcos, 2). Furthermore, contiguity-sed ssocitions my e indirect. For exmple, in the temporl context model (Howrd & Khn, 22; Polyn, Normn, & Khn, 29;Sedererg, Howrd, & Khn, 28), list items re ssocited with n overlpping context signl similr to the Burgess nd Hitch (26) model. However, unlike the Burgess nd Hitch model, where contextul drift is independent of the list items tht re experienced (i.e., either studied or recll), in the temporl context model, the context previously ssocited with ech experienced item is incorported into the model s time vrying context signl. In this wy, ech list item ecomes indirectly ound to its predecessors. Future work will need to investigte the potentil of such hyrid models to ridge the gp etween the results tht we hve presented nd previous work suggesting the need for positionl informtion.

11 Mem Cogn (22) 4: Author Note The uthors cknowledge support from Ntionl Institutes of Helth grnt MH55687 nd from the Dn Foundtion. Correspondence concerning this rticle my e ddressed to either Michel J. Khn (khn@psych.upenn.edu) or Alec Solwy (solwy@princeton.edu). Appendix Associtive chining model In this ppendix, we provide concise description of our strength-sed ssocitive chining model of seril recll nd seril lerning. MATLAB computer code used to run the simultions cn e otined from memory.psych.upenn.edu. Study phse Our chining model uses two mtrices to hold the strengths of ssocitions etween items, one for forwrd ssocitions nd one for ckwrd ssocitions. For simplicity, we ssume tht list words re not semnticlly relted nd tht there re no ssocitions cross lists, so we set the initil strengths to zero. Similr to the Lewndowsky nd Murdock (989) model, strt mrker is used to simulte the wy in which prticipnts ccess the eginning of list. The strt mrker cts s list item nd is ssocited with ech susequent item. Following the study of list item i on tril T, we increment the strength of the forwrd ssocition from the immeditely preceding item, i, ccording to the storge eqution: ΔFði ; iþ T ¼ s ½ Fði ; iþ T Š; ðþ where F(i, i) T- is the strength of the ssocition on the previous tril nd s is rndom vrile (Gussin with prmeters m s nd s s ) tht controls the chnge in strength on the current tril. We do not llow the model to unlern previous strength increments, so we clmp negtive vlues of s to zero. We ssume primcy grdient in encoding strength nd reduce the men of s exponentilly cross seril positions to n symptotic minimum of min s : m s ¼ c s e d sði Þ þ min s ; ð2þ where i indexes the seril position of the item. s s in Eq. nd c s, d s,ndmin s in Eq. 2 re model prmeters. Eqution implements closed-loop lerning rule (Lewndowsky & Murdock, 989): The increment in strength is proportionl to the mount of ssocition lredy in memory. The strength of the ckwrd ssocition from item i to item i is computed y scling the forwrd increment y w, prmeter tht rnges from to : ΔBði; i Þ T ¼ w ΔFði ; iþ T ð3þ This llows the model to mimic the forwrd symmetry tht is typicl of seril recll (Bhtrh et l., 26, 28; Golom et l., 28; Klein et l, 25). In ddition to forming ssocitions etween nerest neighors, our model lso forms remote ssocitions y incrementing the strength etween item i nd ech erlier list item, i x, ccording to the more generl storge eqution: ΔFði x; iþ T ¼ s ½ Fði x; iþ T Še sjx j ð4þ Here, s is the sme s ove, nd s is rndom vrile (Gussin with prmeters m s nd s s ) tht determines the strength of remote ssocitions reltive to nerest neighors. The minimum vlue s cn tke is clmped to one. m s nd s s re oth model prmeters. Note tht when x =,this eqution reduces to Eq.. During list study, s is smpled once for ech item nd s is smpled once for ech list. The strength of remote ssocitions is reduced exponentilly s function of the lg, x, which rnges from the previously studied item (x = ) to the strt mrker (x = i). As with nerest neighor ssocitions, we ssume tht remote ssocitions re formed in oth the forwrd nd ckwrd directions, with the ckwrd strength increment scled y w. Test phse At test, the strt mrker serves s the first retrievl cue for ech list. After the first position, ech successfully retrieved item serves s the cue for the next position. Assuming tht the model reclled item i, the next item, j, is chosen y the Luce choice rule (Luce, 959): Pð jjiþ ¼ Sði; jþ g Pk Sði; kþg þ stop g ; ð5þ where S ¼ F þ B, k rnges over ll unreclled items, nd stop sets the proility of retrievl filure. Both stop nd γ re model prmeters. Our ssumption tht items re not repeted does not preclude the use of inhiition or other more relistic repetition suppression mechnisms. We hve purposefully left this spect of our model underspecified in order to focus on the role tht is plyed y the chining mechnism itself. For this sme reson, we hve lso excluded lerning during the test phse. A numericl exmple Consider the ehvior of the model on the first tril of four item list, using the following prmeter vlues: w =.5, min s ¼ :, d s =.55,c s =.6,m s ¼ :2, stop =.2, γ =.. For simplicity, vriility of encoding is omitted. All ssocitions re set to zero t the eginning of the simultion. We egin the study phse y pplying Eq. 2 to

12 88 Mem Cogn (22) 4:77 9 determine the increment in ssocitive strength etween the strt mrker nd the first item: m s ðþ ¼:6 e :55 þ : ¼ :7; Eqution 4 is used to updte the strength mtrix. Since there is no encoding vriility nd no prior lerning, the increment is exctly.7 in the forwrd direction nd.5 in the ckwrd direction (.7 w ). The rest of the list is presentedinsimilrmnner,ndtle4 shows the resulting ssocitive strength mtrices. Here, we comine the forwrd (F, locted in the upper tringle) nd ckwrd (B, locted in the lower tringle) mtrices for ese of presenttion. At test, the proility of retrieving the first item is computed using Eq. 5: Pðj$Þ ¼ :7 :7 þ :34 þ :27 þ :6 þ :2 ¼ :789 The proility of retrieving ech of the remining items is computed in similr fshion, nd n item is selected y smpling from this distriution. If n item is successfully retrieved (i.e., the stop mrker is not smpled), the next recll is selected y smpling from the distriution formed y conditioning the remining items on the first recll. Recll proceeds in this mnner until either the stop mrker is selected or ll of the items re reclled. In the cse of choosing the stop mrker, the study-test cycle is repeted (for mximum of ten trils). If the list is correctly reclled, the strength mtrix is reset to zero nd simultion of the next list egins. Prmeter estimtion ThechiningmodelprmetersshowninTle2 were found y using genetic lgorithm (Mitchell, 996) to minimize the men root-men squred devition (RMSD) etween the dt nd the model for the three spects of the dt descried in the min text (the clustering mesures, the seril position curves, nd the gins nd losses of item nd order informtion). We evolved popultion of 2, initilly rndom prmeter vlues for genertions. We then reduced the size of the popultion to, nd rn the lgorithm for 2 more genertions. The prmeter vlues tht were in the top percent of ech genertion were crried over to the Tle 4 Associtive strengths following the first tril study phse of smple simultion $ $ next, nd new prmeter vlues were computed y smpling from nd perturing the surviving vlues. The est-fitting prmeter vlues re shown in Tle 2, nd the simultions descried in the min text were performed using these vlues. We fit the model of Burgess nd Hitch (26) to the clustering mesures nd to the first tril seril position curve using the sme pproch, vrying ll of the prmeters listed in Tle A of Burgess nd Hitch (26) exceptforn 2 nd α (these two prmeters relte to the grouping of items during presenttion, which we do not consider here). Experiment detils Golom et l. (28). Thirty-six young nd 36 older dult prticipnts performed the experiment over two sessions. Hlf of the prticipnts performed free recll tsk during the first session nd seril recll tsk during the second session, nd the other hlf performed the tsks in the reverse order. We focused our nlysis on the dt from the younger prticipnts performing seril recll. Words were drwn from collection of 846 two-syllle nouns (for detils, see Golom et l., 28). Ech list consisted of words, with ech word ppering on the screen for s. ISIs were either 8 ms,,2 ms, or 2,4 ms, nd were constnt within ech list. At test, prticipnts were given up to min to voclly recll the list in the presented order. Prticipnts received four prctice lists, followed y 36 test lists. The prctice lists were not included in our nlysis. Becuse lists in the Golom et l. (28) study were shorter thn the lists in the other two studies, we included ll items in our nlysis, including edge items, in order to mximize the mount of dt on which ech result is sed. Khn nd Cpln (22), Experiment 2. Sixty prticipnts performed the experiment over the course of five sessions. The first session consisted of one -word, one 5- word, nd two 9-word prctice lists, which were not included in our nlysis. The remining four sessions ech consisted of five 9-word lists. Words were drwn from the Toronto Word Pool (Friendly, Frnklin, Hoffmn, & Ruin, 982) without replcement nd were presented urlly t rte of.5 s. After studying list, prticipnts were sked to voclly recll the list in the presented order. The cycle of study nd test ws repeted for ech list until it ws reclled perfectly. In order to void edge rtifcts, we focused our nlysis on list positions 4 6. Comprisons cross trils (see the section strength-sed ssocitive chining model) were restricted to the first three trils of ech list. Lists tht were lerned in fewer thn three trils (out 7%) were excluded. Khn et l. (2). Forty-two prticipnts performed the experiment over the course of four sessions. Ech list consisted of 7, 3, or 9 words drwn from the Toronto Word Pool (Friendly et l, 982) without replcement nd were presented urlly t rte of s. At test,

13 Mem Cogn (22) 4: prticipnts were given min to voclly recll the list in the presented order, nd the study nd test cycle ws repeted for ech list until it ws reclled perfectly. The experiment consisted of two conditions. In the constnt strt condition, prticipnts studied ech list in the usul mnner, strting t the sme list position. In the spinlist condition, prticipnts studied ech list strting in rndom position on ech tril. We conducted our nlysis on the dt from the constnt strt condition only. The first session of the experiment consisted of prctice lists nd ws not included in our nlysis. Susequent sessions consisted of three lists of ech possile length under one of the two strting conditions (the order of conditions ws counterlnced cross prticipnts). Four sujects were excluded ecuse they filed to lern ny lists within predetermined mximum numer of trils. In order to void edge rtifcts, we focused our nlysis on positions 4 for lists of length 3 nd positions 4 6 for lists of length 9. 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