source memory ROCs indicate recollection is a ... - CiteSeerX

MEMORY, 2010, 18 (1), 2739

‘‘Remember’’ source memory ROCs indicate recollection is a continuous process

Downloaded By: [Boston College] At: 17:56 18 January 2010

Scott D. Slotnick Boston College, Chestnut Hill, MA, USA The dual process model assumes memory is based on recollection (retrieval with specific detail) or familiarity (retrieval without specific detail). A current debate is whether recollection is a threshold process or, like familiarity, is a continuous process. In the present study two continuous models and two threshold models of recollection were evaluated using receiver operating characteristic (ROC) analysis. These models included the continuous signal detection unequal variance model and the threshold dual process model. In the study phase of three experiments, objects were presented to the right or left of fixation. At test, participants made either rememberknow responses or item confidence responses followed by source memory (spatial location) confidence ratings. Recollection-based ROCs were generated from source memory confidence ratings associated with ‘‘remember’’ responses (in Experiments 12) or the highest item confidence responses (in Experiment 3). Neither threshold model adequately fit any of the recollection-based ROCs. By contrast, one or both of the continuous models adequately fit all of the recollection-based ROCs. The present results indicate recollection and familiarity are both continuous processes.

Keywords: Dual process; Signal detection; Source memory.

Memories can be based on either specific recollection or non-specific familiarity. In the common instantiation of this dual process model (Parks & Yonelinas, 2009; Yonelinas, 1999; Yonelinas & Parks, 2007) recollection is assumed to be a threshold process (i.e., previously presented information is either remembered or forgotten) whereas familiarity is assumed to be a continuous process (i.e., memory for previously presented information is graded, ranging in strength from very weak to very strong). Recently it has been proposed that recollection and familiarity are both continuous processes (Mickes, Wais, & Wixted, 2009; Wixted, 2007; Wixted & Stretch, 2004) that can be described by classic signal detection theory (Green & Swets, 1966; Macmillan & Creelman, 2005). Consequently an

issue of current debate is whether recollection is a continuous process or a threshold process. While continuous models and threshold models of memory have been compared using other approaches (Mickes et al., 2009; Parks & Yonelinas, 2009; Wixted, 2007; Yonelinas, 2002), some of the most convincing evidence has come from analysis of the receiver operating characteristic (ROC), a plot of hit rates versus false alarm rates, and the z-transformed ROC (zROC; see Macmillan & Creelman, 2005). Specifically, each model’s predicted ROC is tested against an empirically derived ROC to assess the adequacy of the model. Critically, under conditions in which memory is largely based on recollection such as in standard source memory paradigms, the continuous and threshold models make completely

Address correspondence to: Scott D. Slotnick, Department of Psychology, McGuinn Hall, Boston College, Chestnut Hill, MA 02467, USA. E-mail: [email protected] I thank Lauren Moo for invaluable comments and Julie Grimes for data collection.

# 2009 Psychology Press, an imprint of the Taylor & Francis Group, an Informa business http://www.psypress.com/memory DOI:10.1080/09658210903390061


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distinct predictions with regard to the shape of the source memory ROC and zROC. In the present study two continuous models and two threshold models of source memory were evaluated. Each source memory model can be described by its underlying probability distributions in decision space (Macmillan & Creelman, 2005). The continuous unequal variance (UEV) model, the standard signal-detection model, is defined by two overlapping Gaussian distributions in decision space, where the distance between distribution means, d?, is a measure of source memory strength, and the distributions can have unequal variance (Figure 1A). The source memory ROC is generated by plotting the hit rate versus the false alarm rate, computed from confidence rating probabilities (see Slotnick & Dodson, 2005). The UEV model source memory ROC always has negative curvature and the zROC is always linear (the ratio of source distribution standard deviations, ss1/ss2, is equal to the slope of the zROC). Evidence from a number of ROC/zROC studies has supported the UEV model of source memory (Dodson, Bawa, & Slotnick, 2007; Glanzer, Hilford, & Kim, 2004; Hilford, Glanzer, Kim, & DeCarlo, 2002; Qin, Raye, Johnson, & Mitchell, 2001; Slotnick & Dodson, 2005; Slotnick, Klein, Dodson, & Shimamura, 2000). We recently modified the UEV model to account for source misattributions (UEVSM), where an item from one source is misattributed to the other source (Dodson et al., 2007). In decision space, this corresponds to a proportion of misattributed items (z) from each source centred at the mean of the other source distribution (Figure 1B). If z is equal to 0, the UEVSM model is equivalent to the UEV model, illustrating that these models are nested. The UEVSM model source memory ROC always has negative curvature and, if there is an appreciable degree of source misattribution, the zROC also has negative curvature. The threshold source memory models include the two-high threshold (2HT) model and the threshold dual process (DPT) model. The 2HT model is an extension of the multinomial model (Batchelder & Riefer, 1990; Riefer, Hu, & Batchelder, 1994) where source memory is assumed to be a two-high threshold process (Bayen, Murnane, & Erdfelder, 1996; Yu & Bellezza, 2000). This model dictates that there are two thresholds in decision space, beyond which only one distribution exists and threshold recollection occurs (Figure 1C). The 2HT model

source memory ROC is always linear while the zROC always has positive curvature. Evidence from one source memory study has supported the 2HT model (Yonelinas, 1999) which was taken to support the DPT model, as this model has been assumed to primarily rely on threshold recollection when the familiarity of each source is relatively equal which limits familiarity-based source discrimination (Diana, Yonelinas, & Ranganath, 2008; Yonelinas, 1999; see also Parks & Yonelinas, 2009; Quamme, Yonelinas, & Norman, 2007; Yonelinas, Kroll, Dobbins, & Soltani, 1999). Of relevance, all of the experiments in the present study were designed to have sources with relatively equal familiarity so that both threshold models predict linear or near linear source memory ROCs (and zROCs with positive curvature). Still, the DPT model, including both threshold recollection and familiarity, was fitted to the present source memory ROCs in case there was an unanticipated but substantial proportion of familiarity-based responding (although, again, such effects have only been reported under experimental conditions that supported familiarity-based responses; i.e., imposing a 4-day delay between the encoding of two source lists or unitised encoding; Diana et al., 2008; Parks & Yonelinas, 2007; Yonelinas, 1999). The DPT model (Figure 1D) is a hybrid between an equal variance signal detection model, corresponding to source familiarity, and a 2HT model, corresponding to threshold recollection. It is worth mentioning that the cognitive process of source familiarity (used for source discrimination) is distinct from the process of item familiarity (used for item identification). The DPT model source memory ROC is linear (if based solely on threshold recollection) or has some degree of negative curvature (if based on both threshold recollection and familiarity), while the source memory zROC always has positive curvature. We previously attempted to increase the relative contribution of recollection by analysing conditional source memory ROCs generated from the highest item confidence ratings; these conditional source memory ROCs were curved in support of a continuous rather than threshold retrieval process (Slotnick & Dodson, 2005; Slotnick et al., 2000). This analysis was based on evidence that recollection-based responses map onto the highest confidence ratings, while familiarity-based responses map onto relatively lower confidence ratings (Tulving, 1985; Yonelinas, 2001; Yonelinas, Dobbins, Szymanski, Dhaliwal, &

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CONTINUOUS VS THRESHOLD RECOLLECTION

Figure 1. Source memory decision space (left column) with source 1 (S1) and source 2 (S2) distributions, corresponding ROC (centre column), and zROC (right column) for (AB) continuous models and (CD) threshold models. Only threshold models have thresholds (T1 and T2) in decision space, demarcated by grey arrows, beyond which only one distribution exists.

King, 1996). However, Parks and Yonelinas (2007) pointed out that our conditional source memory ROCs might have been based on familiarity, which could have produced the curved conditional source memory ROCs observed in our previous study. The aim of the present study was to

construct ROCs and zROCs that were more convincingly based on recollection, and evaluate the models described above to assess whether recollection is a continuous or threshold process. Three procedures were used with the aim of maximising the process of recollection: (1) Only


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source memory responses were analysed, under conditions where the familiarity of each source was relatively equal, which have typically been assumed to reflect recollection (e.g., Diana et al., 2008; Kahn, Davachi, & Wagner, 2004; Vilberg & Rugg, 2009; Yonelinas, 1999). (2) Only ‘‘remember’’ responses corresponding to retrieval of specific detail were included in the analysis, given that these responses have been assumed to directly reflect recollection (Gardiner, 1988; Gardiner, Ramponi, & RichardsonKlavehn, 2002; Yonelinas, 2001, 2002; Yonelinas et al., 1996; Yonelinas, Otten, Shaw, & Rugg, 2005). Of importance, while signal detection accounts suggest ‘‘remember’’ and ‘‘know’’ judgements do not necessarily disentangle recollection and familiarity (Wixted, 2007; Wixted & Stretch, 2004), ‘‘remember’’ judgements have still been assumed to be based primarily on recollection (Wais, Mickes, & Wixted, 2008). (3) Short lists of visual objects were used, as shorter versus longer list lengths have been associated with a higher proportion of recalled items (Murdock, 1962; Ward, 2002) and a higher proportion of ‘‘remember’’ responses (Cary & Reder, 2003; see also Tulving, 1985), and visual items are remembered better than words (which should also translate into a relatively high proportion of recollected items; see Hockley, 2008). It is notable that while the latter manipulations might also increase familiarity-based retrieval, as indexed by ‘‘know’’ responses (Yonelinas, 2001, 2002; Yonelinas et al., 1996), these data were not used to generate the present recollection-based ROCs. While previous studies have analysed either source memory ROCs (Dodson et al., 2007; Glanzer et al., 2004; Hilford et al., 2002; Qin et al., 2001; Slotnick & Dodson, 2005; Slotnick et al., 2000; Yonelinas, 1999) or ‘‘remember’’ ROCs (Rotello, Macmillan, & Reeder, 2004; Rotello, Macmillan, Reeder, & Wong, 2005; Yonelinas, 2001), the current study is the first to analyse ‘‘remember’’ source memory ROCs, which should reflect the highest degree of recollection of any investigation to date. Consequently the present paper presents a methodological advance that holds the promise of offering a definitive resolution to the debate over the nature of recollection, as the current recollection-based ROCs should be particularly sensitive in evaluating the disparate predictions of the continuous and threshold models of recollection. As mentioned above, each model will be evaluated by comparing the predicted ROC with the empirically derived recollection-based ROC. In addi-

tion, zROC shape will be considered given that the continuous models predict the zROC will be linear or have negative curvature while the threshold models predict the zROC will have positive curvature (Figure 1).

METHOD Three experiments were conducted using the same protocol, unless otherwise noted. Participants were recruited from the Boston College undergraduate student population and received course credit or remuneration. The protocol was approved by the Boston College Institutional Review Board and informed consent was obtained from each participant before the experiment commenced. A total of 15 participants completed Experiment 1, 18 participants completed Experiment 2, and 15 participants completed Experiment 3 (each experiment had a different set of participants). The experiments were conducted using E-Prime (Psychology Software Tools, Inc., Pittsburgh, PA). Stimuli consisted of line drawings drawn from a pool of 520 objects (International Picture Naming Project at the UCSD Center for Research in Language). Selected objects had at least a 96% valid response rate, at least a 90% name agreement, and a name with one or two syllables. Each participant completed seven studytest sessions. During each study session, objects were sequentially presented for 3.5 seconds to the right (10 objects) or left (10 objects) of a red fixation cross, with a 0.5-second period of fixation between trials (Figure 2A). Each object was contained within a bounding box 7.5 8 of visual angle along each side, with the nearest edge 3 8 of visual angle from fixation. Spatial location was randomly determined with the constraint that no more than three objects were sequentially presented on the same side of the screen. Participants were instructed to maintain central fixation and remember each object and its spatial location. They were also encouraged to remember the entire display (i.e., the object and fixation cross), rather than use non-visual strategies. During each test session in Experiment 1, studied (old) and new objects were randomly intermixed and presented at fixation (Figure 2B) with the constraint that no more than three items of a given type (old-right, old-left, or new) were presented sequentially. For each object,


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6moderately sure ‘‘right’’, and 7very sure ‘‘right’’. Rememberknownew instructions were adapted from Eldridge, Sarfatti, and Knowlton (2002), where participants were instructed ‘‘when we remember something, we consciously recollect and become aware of aspects of its occurrence’’ and ‘‘at other times, we simply know that something has occurred before, but without being able to consciously recollect what was experienced at the time of its occurrence’’ (Eldridge et al., 2002, p. 140). The test session for Experiment 2 was modified to better isolate recollection of source (spatial location), given that ‘‘remember’’ responses in Experiment 1 could refer to recollection of any item or source detail. Only old items were presented and participants made an initial ‘‘remember’’, ‘‘know’’, or ‘‘guess’’ response (Eldridge et al., 2002). Instructions included the same descriptions of ‘‘remember’’ and ‘‘know’’ responses used in Experiment 1, but they were extended such that ‘‘remember’’ responses referred specifically to the memorial experience associated with retrieval of object spatial location. Specifically, the remember instructions included the following addition: We are particularly interested in your memory for an object’s previous spatial location. As such, a remember response signifies that the object evokes a specific memory of how it looked on the screen (specifically, you remember seeing the object on one side of the screen).

Figure 2. (A) During study, objects were presented to the left or right of fixation. (B) During test, objects were presented at fixation (object type is labelled to the right).

participants were instructed to respond ‘‘remember’’, ‘‘know’’, or ‘‘new’’ followed by a source confidence rating where 1very sure ‘‘left’’, 2moderately sure ‘‘left’’, 3less sure ‘‘left’’, 4don’t know (or ‘‘new’’), 5less sure ‘‘right’’,

The test session for Experiment 3 was identical to Experiment 1 except that participants first made an item confidence response (ranging from 1very sure ‘‘new’’ to 7very sure ‘‘old’’) rather than a rememberknownew response. This experiment was conducted in an effort to avoid potential ceiling effects by implementing this response manipulation (that we have found reduces source memory strength). Previous studies that acquired both item confidence responses and rememberknow responses have shown that the highest item confidence response was associated with a much higher proportion of ‘‘remember’’ than ‘‘know’’ responses (Tulving, 1985; Rotello et al., 2005; Yonelinas, 2001). It follows that the highest item confidence rating in the present study primarily reflects ‘‘remember’’ responses as well. To confirm this, the proportion of ‘‘remember’’ responses at a given item confidence level in Experiment 3 was


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estimated based on the ‘‘remember’’ and ‘‘know’’ response distributions from Experiment 1 (as these experimental protocols were identical except for the rememberknownew versus item confidence responses). Specifically, linear combinations of Experiment 1 ‘‘remember’’ and ‘‘know’’ probability distributions were compared to a given Experiment 3 item confidence probability distribution, generated from the corresponding rows in Table 1, and the combination that minimised the sum-of-squares error was selected (‘‘remember’’ distribution weight ranged from 01 and ‘‘know’’ distribution weight ranged from 1 ‘‘remember’’ distribution weight, as these responses are mutually exclusive). For all three experiments, each response at test was self-paced with accuracy stressed as being of primary importance (response speed was also stressed as important as long as it did not reduce accuracy). Although participants were encouraged to use the entire range of confidence rating responses, they were instructed to always respond in a way that accurately reflected their source confidence. The object types (old-right, old-left, and new, for Experiment 1 and Experiment 3; old-right and old-left for Experiment 2) comprising each of the seven studytest lists were selected to have similar values of reaction time (mean values 893, 896, 899 ms), object visual complexity (mean values 16746, 16718, 16730), and log of frequency (mean values 3.04, 3.04, 3.07). Objects were counterbalanced across participants using a Latin Square design. Source memory accuracy was computed separately for ‘‘remember’’ and ‘‘know’’ responses in Experiment 1 and Experiment 2 to assess whether the present data replicated previous findings (Hicks, Marsh, & Ritschel, 2002; Wais et al., 2008; one participant with an absence of ‘‘know’’ responses was excluded from the analysis). Specifically, for a given response type (‘‘remember’’ or ‘‘know’’), percent correct was computed from the number of responses in the three highest/accurate source confidence ratings plus half the number of responses in the middle/guess source confidence rating (given that guess responses would have been equally distributed if there were only two source response options), divided by the total number responses. For example, ‘‘remember’’ source accuracy corresponding to Experiment 1 left source response ratings (Table 1) was computed from the three accurate/‘‘left’’ source confidence ratings (682 9356) plus half the middle/guess source

TABLE 1 Response matrices

1

2

1 ‘‘Left’’ ‘‘Right’’ 0 3 4 5 6

7

a

Experiment 1 ‘‘Remember’’ ‘‘Know’’ ‘‘New’’ a

Right source 17 14 17 0 6 14 0 0 1 17 20 32

33 43 60 136

59 17 1 77

103 30 1 134

626 869 8 118 0 63 634 1050

‘‘Remember’’ ‘‘Know’’ ‘‘New’’ a

Left source 682 93 56 6 11 22 1 2 1 689 106 79

30 42 43 115

20 9 0 29

14 6 0 20

9 904 3 99 0 47 12 1050

‘‘Remember’’ ‘‘Know’’ ‘‘New’’ a

New 2 0 0 2

4 5 0 9

10 57 941 1008

4 7 2 13

3 2 0 5

1 26 1 81 0 943 2 1050

‘‘Remember’’ ‘‘Know’’ ‘‘Guess’’ a

Right source 12 3 3 1 16 24 0 0 2 13 19 29

2 10 100 112

8 51 1 60

41 82 0 123

895 964 9 193 0 103 904 1260

‘‘Remember’’ ‘‘Know’’ ‘‘Guess’’ a

Left source 887 31 13 11 73 51 0 0 1 898 104 65

2 5 113 120

4 28 0 32

7 19 0 26

13 957 2 189 0 114 15 1260

2 9 0 11

Experiment 2

Experiment 3 7 6 ‘‘Old’’ 5 ‘‘New’’ 4 ¡3 2 1 a

Right source 26 9 7 1 2 4 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 28 11 15

17 5 13 9 6 12 50 112

24 13 8 0 0 0 0 45

42 18 1 1 0 0 0 62

770 895 4 47 0 27 0 10 0 6 1 13 2 52 777 1050

7 6 ‘‘Old’’ 5 ‘‘New’’ 4 ¡3 2 1 a

Left source 736 61 22 5 17 6 0 2 4 0 0 0 0 1 0 0 0 1 9 0 1 750 81 34

13 3 8 12 12 8 53 109

8 6 4 0 0 0 0 18

16 3 1 0 0 0 1 21

37 893 0 40 0 19 0 12 0 13 0 9 0 64 37 1050

7 6 ‘‘Old’’ 5 ‘‘New’’ 4 ¡3 2 1 a

New 3 0 0 0 1 0 2 6

2 0 4 17 25 80 891 1019

0 2 1 0 0 0 0 3

2 1 0 0 0 0 0 3

6 16 0 3 0 11 0 17 0 26 0 81 1 896 7 1050

2 0 3 0 0 1 1 7

1 0 3 0 0 0 1 5


confidence rating (30/2), divided by the total number of responses (904). Recollection-based ROCs and zROCs were generated from source response ratings preceded by ‘‘remember’’ responses in Experiment 1 and Experiment 2 and from source response ratings at the highest item confidence rating in Experiment 3 (Table 1, right source and left source, top rows). Each model was fitted to the recollection-based ROC by adjusting model parameters using maximum likelihood estimation. Log-likelihood chi-square was used to assess the adequacy of each model, with lower chi-square values reflecting a better fit ( p.05 indicated an adequate fit).


TABLE 2 Probability of ‘‘remember’’ and ‘‘know’’ responses as a function of item confidence p(‘‘Remember’’)

The source response matrices are shown in Table 1. A large majority of source items were associated with ‘‘remember’’ responses in Experiment 1 (84.43%) and Experiment 2 (76.23%), and the highest item confidence rating responses in Experiment 3 (85.14%). These proportions were relatively higher than those observed under standard source memory conditions (e.g., the highest item confidence response proportions in Slotnick et al., 2000, ranged from 47.67% to 64.92%), which indicated the present experimental manipulations aimed at increasing the proportion of recollectionbased responses had the desired effect. Replicating previous findings (Hicks et al., 2002; Wais et al., 2008), source memory accuracy was significantly greater than chance (50% correct) for both ‘‘remember’’ responses, Experiment 1, 92.829 0.010% correct, t (14)43.78, pB.001; Experiment 2, 97.8190.006% correct, t (17)80.32, pB.001, and ‘‘know’’ responses, Experiment 1, 62.3190.048% correct, t (13)2.55, pB.05; Experiment 2, 77.0090.038% correct, t (17)7.04, pB.001; mean91 SE. Table 2 (top) shows the estimated proportion of ‘‘remember’’ and ‘‘know’’ responses at the three highest item confidence levels in Experi-

p(‘‘Know’’)

Present Experiment 3 Highest item confidence 2nd highest item confidence 3rd highest item confidence

1.00 .18 .00

.00 .82 1.00

Tulving (1985) Highest item confidence 2nd highest item confidence 3rd highest item confidence

.80 .39 .26

.20 .61 .74

Rotello et al. (2005) Highest item confidence 2nd highest item confidence 3rd highest item confidence

RESULTS

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.88 .54 .38

.12 .46 .62

ment 3. These estimates indicate that the highest item confidence rating corresponded to ‘‘remember’’ responses, the second highest item confidence rating corresponded to both ‘‘remember’’ and ‘‘know’’ responses (18% and 82%, respectively), and the third highest item confidence rating corresponded to ‘‘know’’ responses. This pattern of activity is consistent with previous findings (Table 2; Rotello et al., 2005; Tulving, 1985; see also Yonelinas, 2001), and indicates the highest item confidence rating in Experiment 3 corresponded to ‘‘remember’’ responses and thus can be assumed to primarily reflect recollection (Gardiner, 1988; Gardiner et al., 2002; Yonelinas, 2001, 2002; Yonelinas et al., 1996, 2005). Best fit model parameters are illustrated in Table 3. As expected, recollection-based responses were associated with very high memory strength, as illustrated by the 2HT model R values ranging from 0.78 to 0.96 (which have an upper limit of 1) and the UEV model d? values ranging from 2.34 to 2.97. The recollection-based ROCs/zROCs (generated from ‘‘remember’’ source responses in Experiments 12 and the highest item confidence responses in Experiment

TABLE 3 Recollection-based ROC model parameters UEV

Exp. 1 Exp. 2 Exp. 3

UEVSM

2HT

DPT

d?

ss1/ss2

d?

ss1/ss2

z

R1

R2

d?

R1

R2

2.84 2.97 2.34

1.05 1.29 1.24

2.84 5.09 2.66

1.05 0.92 1.19

0.000 0.014 0.018

0.84 0.96 0.89

0.78 0.92 0.79

2.90 3.52 2.50

0.01 0.27 0.28

0.05 0.26 0.30


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3) and best fit continuous and threshold models are shown in Figure 3. By direct inspection, the recollection-based zROC curvature of Experiment 1 was close to zero or slightly negative and the recollection-based zROC curvatures of Experiment 2 and Experiment 3 were negative, which provides some support for the continuous models and is in opposition to the positive zROC curvature predicted by the threshold models. Chi-square analysis results are shown in Table 4. The UEV model adequately fit the recollection-based ROC of Experiment 1; however, this model did not adequately fit the recollection-based ROC of the other two experiments. The UEVSM model adequately fit the recollection-based ROC of all three experiments. Consistent with these findings, the UEVSM model did not produce a significantly better fit than the UEV model for Experiment 1 ( p.20), but did produce a significantly better fit for the other two experiments (both psB.001). This suggests there was a substantial degree of source misattribution in Experiment 2 and Experiment 3. Evidence of source misattribution in this experiment can also be observed in Table 1 as an increase towards the highest incorrect source confidence rating (e.g., in Experiment 2 the ‘‘remember-right’’ confidence ratings for the left source increased from 4 to 13, reflecting source misattribution, while in Experiment 1 the same responses decreased from 20 to 9). In contrast to the continuous models, which fit one or both recollection-based ROCs in all the experiments, neither the 2HT model nor the DPT model adequately fit the recollection-based ROCs in any of the experiments. It could be argued that ceiling effects may have influenced the preceding results, particularly in Experiment 2 (Figure 3B) where source memory strength was very high. However, it should be TABLE 4 Chi-square analysis results for all experiments Recollection-based ROC/zROC UEV x2(4) Exp. 1 Exp. 2 Exp. 3

UEVSM p

4.76 .313 23.65 .000 20.79 .000

x2(3) 4.76 0.56 1.47

p

2HT x2(4)

DPT p

x2(3)

p

.191 142.81 .000 7.91 .048 .906 34.38 .000 25.24 .000 .688 20.64 .000 20.64 .000

Bold p values indicate adequate fit ( p.05).

underscored that even at high source memory strength the ROC shape predicted by each model is still maintained (e.g., the UEV model still predicts a curved ROC and the 2HT model still predicts a linear ROC), and at extremely high source memory strength (i.e., at ceiling) the ROCs predicted by all four models would track the left and upper ROC axes. Therefore ceiling effects would have been manifested by an adequate fit by all of the models, rather than the differential model-fitting results observed (as continuous models provided adequate fits and the threshold models provided inadequate fits). Still, this issue was further addressed by conducting a simulation to determine the source memory strength at which ceiling effects might have occurred under the present experimental conditions. An UEV model ROC was generated adopting the d? and ss1/ss2 parameter values from Experiment 1 (Table 3), and then simulated UEV ROC points were generated at the same false alarm rate (by selecting the appropriate criteria) and hit rate (by adding the difference between the empirical and simulated ROC to estimate variability). In this way the simulated UEV ROC using these parameter values was identical to the empirically defined UEV ROC in Experiment 1. A family of simulated UEV model ROCs were then generated by varying source memory strength starting with a d? of 2.8 in increments of 0.1, and the UEV model and the 2HT model were fitted to each ROC (holding the Experiment 1 UEV ratio ss1/ss2 constant). Simulated 2HT model ROCs were also generated by varying source memory strength such that the area under each ROC precisely matched the area under the corresponding UEV model ROC (holding the Experiment 1 2HT ratio R1/R2 constant, and linearly scaling the hit rate variability such that the chi-square value matched the corresponding Experiment 1 UEV chi-square value). As mentioned above, when source memory strength is below ceiling differential effects should be observed, but when source memory strength approaches ceiling both models should adequately fit the ROC. The simulation results (Table 5, Figure 4) show, as expected, that simulated UEV ROCs were always adequately fit by the UEV model and simulated 2HT ROCs were always adequately fit by the 2HT model. Of particular relevance, the simulated UEV ROCs were not adequately fit by the 2HT model at lower d? values, but the quality of the 2HT model

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Figure 3. (A) Experiment 1, (B) Experiment 2, and (C) Experiment 3 recollection-based ROCs and zROCs (black circles) with best fit continuous and threshold models (legend in upper left panel). For Experiment 1, the UEV model and UEVSM model fits were identical.

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TABLE 5 Simulation to identify source memory strength (d?) at which ceiling effects might occur Simulated UEV ROCs UEV Fit

Simulated 2HT ROCs 2HT Fit

2

d?

x

2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6

4.42 3.52 2.85 3.27 3.88 3.87 0.50 0.35 2.80

2

UEV Fit 2

p

x

p

x

.491 .621 .723 .658 .567 .568 .992 .997 .731

152.98 125.43 103.55 83.41 58.85 42.62 24.99 6.69 1.94

.000 .000 .000 .000 .000 .000 .000 .245 .858

104.93 72.08 45.39 64.28 39.46 18.44 27.19 16.86 3.59

p .000 .000 .000 .000 .000 .002 .000 .005 .610

2HT Fit x2

p

4.14 5.31 4.61 5.03 5.21 4.44 5.61 6.14 5.58

.530 .379 .465 .413 .391 .489 .347 .292 .349


Bold p values indicate adequate fit ( p.05).

fit systematically improved as d? values increased until the fit was adequate at a d? of 3.5 (as illustrated in Figure 4, left, where the uppermost simulated UEV model ROC was proximal to both of the best-fitting models). The same pattern of results occurred for the simulated 2HT ROCs, where the fit of the UEV model was not adequate at lower d? values, but the fit systematically improved until it was adequate at a d? of 3.6 (Figure 4, right). These simulation results indicate that appreciable ceiling effects would not be expected until the UEV model d? was 3.5 or greater. This is well above the UEV model d? values of the present experiments (that ranged from 2.34 to 2.97) and, coupled with the differential model-fitting results observed, indicate ceiling effects did not significantly influence the present results.

DISCUSSION In the present study the 2HT model did not adequately fit the recollection-based ROC of either experiment, which can be taken as evidence against the DPT model, given that this model has long been assumed to reduce to the 2HT model when the familiarity of each source is relatively equal (Diana et al., 2008; Yonelinas, 1999). Moreover, the DPT model failed to adequately fit either recollection-based ROC. By contrast, the UEV model fit the recollectionbased ROC in Experiment 1 and the UEVSM model fit all of the recollection-based ROCs. One possible criticism of the present results is that the recollection-based ROCs were generated

from a subset of the data (e.g., ‘‘remember’’ responses), as ROCs are typically produced from collapsed data (e.g., the bottom rows of the source response matrices in Table 1). However, collapsed ROCs are necessarily based on both recollection and familiarity. For instance, a substantial proportion of source confidence responses were associated with familiarity-based ‘‘know’’ responses (Table 1). As the aim of the present study was to evaluate whether recollection is a continuous process or a threshold process, the ROCs in the present study were intentionally generated from ‘‘remember’’ responses in Experiments 12 or highest item confidence responses in Experiment 3 (which correspond to ‘‘remember’’ responses; Table 2), as only these responses directly reflect recollection (Gardiner, 1988; Gardiner et al., 2002; Yonelinas, 2001, 2002; Yonelinas et al., 1996, 2005). It is also notable that the present study only employed group analysis, as there were an insufficient number of responses in each confidence rating bin to conduct a meaningful individual participant analysis. Of relevance, every source memory ROC study that has conducted both group analysis and individual participant analysis has reported the identical pattern of results (Dodson et al., 2007; Glanzer et al., 2004; Hilford et al., 2002; Slotnick & Dodson, 2005; Slotnick et al., 2000; Yonelinas, 1999), and there is no reason why this would not pertain to the present study as well. Moreover, the present group analysis does not seem problematic, as linear ROCs cannot be averaged into the non-linear ROCs observed, and zROCs with positive curvature cannot be averaged into the zROCs with negative curvature observed. Still, although the results do not appear susceptible to an explanation based on averaging artefacts, this is a limitation of the present study that may warrant further investigation. Parks and Yonelinas (2007) have argued that a parameter corresponding to the proportion of attended items at encoding (l which has been used to modify the UEV model (DeCarlo, 2003; Hilford et al., 2002) reflects a threshold process similar to the DPT threshold recollection parameters (R1 and R2). In the present study this modified UEV model is equivalent to the standard UEV model, as all ‘‘remembered’’ source items can be assumed to have been attended at encoding. It could similarly be argued that the UEVSM model parameter z reflects a threshold process, like the threshold recollection parameters. However, the DPT parameters R1 and R2 estimate the probability



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Figure 4. Simulated UEV model ROCs (left) and 2HT model ROCs (right) at increasing levels of memory strength (legend in left panel), each with best fit UEV model and 2HT model.

of threshold recollection (Figure 1D) while the parameter z estimates the probability that an item will be attributed to the alternate continuous source distribution (Figure 1B). That is, the UEVSM model is not associated with any thresholds in decision space, so z reflects a continuous process (the same logic applies to the l parameter described above). Given that the UEVSM z parameter values were very small (0% for Experiment 1, 1.4% for Experiment 2, and 1.8% for Experiment 3) it could be argued that this parameter was not necessary. However, only the UEVSM model adequately fit the recollection-based ROCs of Experiment 2 and Experiment 3, indicating that source misattribution occurred in these experiments. A significant degree of source misattribution may have stemmed in part from the high source memory strength in these experiments, which could have biased participants to make high confidence source responses even when a response was attributed to the incorrect source. Future research will be necessary to delineate the experimental conditions under which source misattribution occurs. Furthermore, Dodson et al. (2007) observed source misattribution in older adults at a very high rate (e.g., in one experiment source misattribution was over 20%). Therefore, the UEVSM model appears to be necessary to adequately represent memory for a large range of experimental conditions and participant populations. While the threshold dual-process account commonly assumes that ‘‘remember’’ judgements

reflect recollection and ‘‘know’’ judgements index familiarity (Yonelinas, 2001, 2002; Yonelinas et al., 1996, 2005), signal detection accounts, including the dual-process version of signal detection theory (Wixted, 2007; Wixted & Stretch, 2004), assume that ‘‘remember’’ judgements reflect strong memory and ‘‘know’’ judgements reflect weak memory. Critically, even evidence supporting signal detection theory indicates that ‘‘remember’’ judgements are primarily based on recollection (Wais et al., 2008). If ‘‘remember’’ judgements reflect recollection, and the threshold dual-process model is also correct, then ‘‘remember’’ source memory ROCs must be linear or nearly linear (under the present experimental conditions that do not support familiarity-based responding; Diana et al., 2008; Yonelinas, 1999). Since the ‘‘remember’’ source memory ROCs deviated largely from linearity, either ‘‘remember’’ judgements do not reflect recollection or the threshold dual-process model is incorrect. As ‘‘remember’’ judgements can be assumed to reflect recollection (by both the threshold dual-process and signal detection accounts), the problem likely resides with the threshold dualprocess model (which assumes recollection is a threshold process). Still, it could be argued that ‘‘remember’’ responses in the current study reflected familiarity rather than recollection. The present findings were inconsistent with the threshold models of recollection, but supported the continuous models of recollection that can be described by a classic signal detection model (Green & Swets, 1966; Macmillan & Creelman,

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SLOTNICK

2005) or a modified signal detection model (Dodson et al., 2007). A definitive resolution to the debate over the nature of recollection must await further research that analyses individual participant ROCs and avoids ceiling effects (it is hoped that the present investigation will stimulate work along these lines). Still, the current results are suggestive, providing support for a continuous dual process model of memory where both familiarity and recollection range in strength from very weak to very strong (Mickes et al., 2009; Wixted, 2007; Wixted & Stretch, 2004).


Manuscript received 25 April 2009 Manuscript accepted 24 September 2009 First published online 20 November 2009

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