Modelling transposition latencies: Constraints for theories of serial order memory

Journal ofMemory and

Journal of Memory and Language 51 (2004) 115–135Language

www.elsevier.com/locate/jml

Modelling transposition latencies: Constraints for theoriesof serial order memoryq

Simon Farrella,* and Stephan Lewandowskyb

a Department of Experimental Psychology, University of Bristol, 8 Woodland Road, Clifton, Bristol BS8 ITN, UKb University of Western Australia, Australia

Received 12 December 2003; revision received 23 March 2004

Available online 20 April 2004

Abstract

Several competing theories of short-term memory can explain serial recall performance at a quantitative level.

However, most theories to date have not been applied to the accompanying pattern of response latencies, thus ignoring

a rich and highly diagnostic aspect of performance. This article explores and tests the error latency predictions of four

alternative mechanisms for the representation of serial order. Data from three experiments show that latency is a

negative function of transposition displacement, such that list items that are reported too soon (ahead of their correct

serial position) are recalled more slowly than items that are reported too late. We show by simulation that these data

rule out three of the four representational mechanisms. The data support the notion that serial order is represented by a

primacy gradient that is accompanied by suppression of recalled items.

� 2004 Elsevier Inc. All rights reserved.

Current theories of memory for serial order can ac-

count for recall performance in intricate detail, captur-

ing not only the basic shape of the serial position curve

but also the pattern of different types of errors (e.g.,

Brown, Neath, & Chater, 2004; Brown, Preece, &

Hulme, 2000; Burgess & Hitch, 1999; Farrell & Le-

wandowsky, 2002; Henson, 1998; Page & Norris, 1998).

This theoretical sophistication has been accompanied by

increasingly fine-grained empirical analysis. For exam-

ple, Surprenant, Kelley, Farley, and Neath (in press)

have shown that probabilities of different types of order

errors, when conditionalised on previous order errors in

a trial, place considerable constraints on models of serial

qPreparation of this paper was facilitated by a Large Grant

and a Discovery Grant from the Australian Research Council

to the second author. During writing of the article, the first

author was partly supported by NIMH Grant HD MH44640

and NIA Grant AG17083-01.* Corresponding author.

E-mail address: [email protected] (S. Farrell).

0749-596X/$ - see front matter � 2004 Elsevier Inc. All rights reserv

doi:10.1016/j.jml.2004.03.007

recall. Haberlandt, Thomas, Lawrence, and Krohn (in

press) made a similar point on the basis of the direc-

tionality of individual order errors. Similarly, subtle

differences in the serial position curves obtained with

lists in which phonologically similar and dissimilar items

are intermixed have been taken to differentiate between

alternative theoretical accounts of similarity effects (e.g.,

Henson, Norris, Page, & Baddeley, 1996 vs. Farrell &

Lewandowsky, 2003).

Although such detailed analyses of response prob-

abilities are undoubtedly valuable, we argue here that

analyses of the associated response latencies, in par-

ticular the latencies of errors, can surpass probability

data in their diagnostic value. Specifically, we first

show by simulation that different representational

principles that are indistinguishable on the basis of the

pattern of errors alone make interestingly different

predictions about the latency of transposition errors.

We then report three experiments that test those pre-

dictions. The data consistently confirm the predictions

of models that combine a primacy gradient with re-

sponse suppression.

ed.

mail to: [email protected]

1 We do not consider the representational assumptions of

two models that have not been shown to be capable of

generating the basic transposition gradient; namely ACT-R

(Anderson & Matessa, 1997) and TODAM (Lewandowsky &

Murdock, 1989).

116 S. Farrell, S. Lewandowsky / Journal of Memory and Language 51 (2004) 115–135

Transposition errors and response latencies in serial recall

Most studies of short-term memory involve serial

recall, which requires participants to report list items in

the order of presentation. Because the emphasis is on

memory for order, much interest has focused on trans-

position errors, which arise when a list item is reported

in an incorrect position, for example when the second

item is recalled first. Transposition errors can be divided

into anticipations, which refer to premature recall of an

item (i.e., ahead of its correct position, for example when

C is recalled first from the list A B C D), and post-

ponements, which refer to the delayed report of an item

(e.g., when C is recalled last from the list A B C D).

Another transposition measure is an item�s displace-ment, which we define as the numeric difference between

the item�s output position and its list (input) position.

Under this metric, postponements have positive trans-

position displacements whereas anticipations have neg-

ative displacements. For example, a displacement of )3would involve recalling an item 3 positions too soon

(e.g., anticipating the fifth item at the second output

position), whereas a +2 displacement would be post-

poning recall of an item by 2 positions (e.g., recalling the

second item at the fourth output position). Correct

responses have a displacement of zero.

When the proportion of responses is plotted as a

function of displacement, the resulting transposition

gradient has several prominent and pervasive features.

First, the gradient peaks at displacement zero, as most

responses are correct. Second, as the absolute displace-

ment increases, the proportion of responses declines,

with most responses confined to small distances—this is

referred to as the ‘‘locality constraint’’ (Page & Norris,

1998). Finally, transposition gradients tend to be sym-

metric; that is, response probabilities are not affected by

the sign of the displacement (Healy, 1974; Henson, 1996;

though see Haberlandt et al., in press).

All current models of serial recall are capable of ac-

commodating at least these three features of transposi-

tion gradients (Brown et al., 2000, 2004; Burgess &

Hitch, 1999; Farrell & Lewandowsky, 2002; Henson,

1998; Lewandowsky, 1999; Page & Norris, 1998). It

follows that although transposition gradients provide a

valuable benchmark for models, they cannot differenti-

ate between competing models. However, it turns out

that further differentiation of models becomes possible

through consideration of the latencies of transpositions.

Despite their known empirical diagnosticity (see

Luce, 1986; for a review), serial recall times have been

generally neglected, primarily because models have not

historically made latency predictions. Nonetheless, a

number of studies have recently begun to measure the

time taken to perform ordered recall. Some have con-

sidered only total output time (e.g., Dosher & Ma, 1998;

Hulme, Newton, Cowan, Stuart, & Brown, 1999), which

limits their theoretical impact, whereas other studies

have provided more stringent constraints by reporting

inter-response times for individual serial positions.

Typically, those studies have found that recall of the first

item takes much longer than report of each subsequent

item (Anderson & Matessa, 1997; Anderson, Bothell,

Lebiere, & Matessa, 1998; Cowan, Wood, Wood, Keller,

Nugent, & Keller, 1998; Maybery, Parmentier, & Jones,

2002; Oberauer, 2003; Thomas, Milner, & Haberlandt,

2003), resulting in an approximately flat serial position

curve for all serial positions except the first. Accord-

ingly, the cumulative latency of responses across output

position forms an approximately linear function in most

cases (e.g., Dosher, 1999).

Notably, all research to date has restricted exami-

nation to correct responses only, or does not distinguish

between latency patterns for different types of errors

(Oberauer, 2003), leaving untouched the patterns of

latencies for recall errors, such as transpositions. This

omission is noteworthy because, as we show next by

simulation, different assumptions about the representa-

tion of serial order lead to very different expectations

concerning transposition latencies.

Representational principles in serial recall

The complexity of contemporary models of serial

recall renders their direct comparison difficult. More-

over, most existing models cannot be applied to latency

data without modification. Accordingly, in this article

we do not compare the full instantiations of models.

Instead, we contrast their predictions by comparing four

widely used representational principles within a single

dynamic architecture. Current models represent serial

order either by: (a) temporal or positional item marking,

by (b) a primacy gradient of activation, by (c) use of

response suppression, and by (d) implementing output

interference, or by some combination of those basic

mechanisms.1 We outline these principles before intro-

ducing the dynamic architecture for our simulations.

Item marking

Item marking refers to the association of items with

some independent representation of order, such as time,

temporal context, or ordinal list position. For example, in

the OSCAR model of Brown et al. (2000), each item is

associated with a timing signal that is provided by an

autonomous set of oscillators. Over time, the pattern of

S. Farrell, S. Lewandowsky / Journal of Memory and Language 51 (2004) 115–135 117

activation of the oscillators changes, and thus each item is

associatedwith the unique temporal context current at the

time of its presentation.Recall is achieved by ‘‘rewinding’’

the oscillators to their initial values and allowing them to

once again evolve over time, thus reproducing at recall the

temporal contexts that were present at study. Similar

ideas are implemented in the model of Burgess and Hitch

(1999) and temporal distinctiveness accounts of memory

(e.g., SIMPLE; Brown et al., 2004).

A more abstract variant of the same idea is embodied

in models such as SEM (Henson, 1998), in which items

are associated not to a temporal signal (though see

Henson & Burgess, 1997), but to ‘‘positional’’ markers

that identify each list position. A similar idea is incor-

porated in the order-sensitive variant of the feature

model (e.g., Neath, 1999).

The defining properties of item marking are that: (a)

the order of items is not represented by any property of

the items themselves, (b) items are not associated with

each other, and (c) order information is provided by

some independent structure external to the list.

Primacy gradient

Several models assume that the quality of the en-

coding of items decreases across list presentation (Brown

et al., 2000; Farrell & Lewandowsky, 2002; Henson et al.,

1996; Page & Norris, 1998; see also Grossberg, 1978).

This results in a primacy gradient, such that the first list

item is encoded most strongly, the second list item has

the next-strongest encoding, and so on until the last

presented item, which has the weakest encoding strength.

Some models, such as OSCAR (Brown et al., 2000),

incorporate a primacy gradient in combination with

positional marking. Other models rely entirely on the

primacy gradient to recall a list in order by continually

emitting the strongest item (e.g., Farrell & Lewandow-

sky, 2002; Page & Norris, 1998). If the strength of each

recalled item is attenuated by some mechanism (viz.,

response suppression, see below), this mechanism is

sufficient for simple forward recall.

The defining properties of a primacy gradient are: (a)

encoding strength decreases across serial position and

(b) unless it is assisted by an additional mechanism that

encodes order, a primacy gradient is necessarily ac-

companied by response suppression.

Response suppression

There is much evidence that recall of an item is fol-

lowed by its suppression, which renders it temporarily

unavailable for further report. For example, erroneous

repetitions of items during recall are relatively rare

(Henson, 1996, 1998; Vousden & Brown, 1998), and

people have difficulty reporting both occurrences of a

repeated item (Duncan & Lewandowsky, in press;

Henson, 1998). Recent evidence suggests that this re-

sponse suppression is static (that is, it does not wear off

over time), but that items can be released from response

suppression once an entire list has been recalled (Dun-

can & Lewandowsky, in press).

Accordingly, many models incorporate response

suppression (Brown et al., 2000; Burgess & Hitch, 1999;

Henson, 1998; Lewandowsky &Murdock, 1989; Nairne,

1990), and some use it in conjunction with a primacy

gradient to represent order among items without recourse

to any associative process or positional marking (e.g.,

Farrell & Lewandowsky, 2002; Page & Norris, 1998).

The defining features of response suppression are

that: (a) the representation of an item is attenuated or

eliminated following its recall and (b) suppression lowers

the probability of recalling the item again.

Output interference

The act of recalling an item undoubtedly interferes

with the accessibility of items yet to be recalled (see

Anderson & Neely, 1996; for a review). Accordingly,

when input order and output order are dissociated in

serial recall, output interference can be empirically

identified as a source of primacy effects (Cowan, Saults,

Elliott, & Moreno, 2002; Oberauer, 2003). For example,

Oberauer (2003) randomised the temporal input order,

temporal output order, and spatial order of items by

presenting items randomly (in space and time) in a

spatial array of boxes, and then randomly cueing for

ordered responses by successively probing for the letter

that had appeared in each box. Oberauer found that a

primacy effect only appeared when recall accuracy was

plotted by output position (i.e., it did not appear across

input position or spatial position), suggesting that out-

put interference plays a crucial role in the primacy effect.

Despite its apparent theoretical importance, only two

models of serial recall have explicitly incorporated out-

put interference: Brown et al. (2000) found output in-

terference to be necessary for a full account of list length

effects, and Lewandowsky and Murdock (1989) showed

that their model predicted more realistic serial position

curves when output interference was present (see their

Fig. 29).

The single defining feature of output interference is

that the recall of one item degrades the representation or

accessibility of all remaining list items. The deleterious

effect of recall occurs irrespective of whether or not a

recalled item is suppressed, and irrespective of how or-

der is represented.

Models and principles

Table 1 classifies current models of serial recall on the

basis of which of the preceding architectural principles

they embody. These four principles exhaustively

Table 1

Representational mechanisms of contemporary models of short-term serial order memory

Item

marking

Primacy

gradient

Response

suppression

Output

interference

Feature model (Nairne, 1990; Neath, 1999) r r

Primacy model (Page & Norris, 1998) r r

SEM (Henson, 1998) r r

Burgess and Hitch (1999) r r

OSCAR (Brown et al., 2000) r r r r

SOB (Farrell & Lewandowsky, 2002) r r

SIMPLE (Brown et al., 2004) r

A diamond is shown if a model (rows) incorporates the corresponding representational principle (columns).


characterise all existing models that account for the

benchmark transposition gradients. We next show how

these principles, and by implication the models they

appear in, can be differentiated on the basis of their

predicted transposition latencies.

Fig. 1. Generic lateral inhibition network used to implement

model principles. Nodes, representing items, are fully inter-

connected, with excitatory self-connections, and inhibitory

connections between units. Each node has an associated acti-

vation, with the activation changing in response to input from

outside the network, self-excitation, and weighted inhibitory

input from other nodes.

A common response selection architecture

We created a generic architecture that permitted

implementation of the four preceding principles while

also providing straightforward derivation of latency

predictions. The architecture was based on a lateral in-

hibition network, which has been used previously to

model response competition and choice behaviour (e.g.,

Grossberg, 1976; Usher & McClelland, 2001). Our

model is particularly close in form to Houghton�s (1990)competitive queuing model for speech production, in

which response units (representing phonemes) copy an

activation pattern into a lateral inhibition network,

which then performs a ‘‘winner-take-all’’ response se-

lection to select a single unit for output (see also Burgess

& Hitch, 1999). Houghton�s model also incorporates

response suppression to avoid perseverative responding

with the first phoneme in a sequence.

Fig. 1 shows the structure of the network. Each list

item is represented by a node whose activation value can

be taken as the current ‘‘strength’’ of that item in

memory. Nodes are fully interconnected to each other

and also possess self-connections (i.e., connections

which feed back into the nodes from which they origi-

nate). The connections between nodes are inhibitory,

whereas self-connections are excitatory. Initial explora-

tion of the model suggested that stable performance

could be achieved when inhibitory and excitatory con-

nections were set to )0.1 and +1.1, respectively, and

those values were used throughout. The static nature of

the weights implies that no learning occurs in this net-

work; it simply forms a competitive filter (Houghton,

1990) for taking probabilistic information and giving an

unambiguous response, with an associated recall time.

Retrieval proceeds by first setting the activations to

starting values that are determined by the particular

representational principle being modelled (e.g., by cre-

ating a primacy gradient; see below), and then iteratively

passing activation back through the weights. Iterations

continue until the activation of the strongest node ex-

ceeds a response threshold (set to 0.8 throughout), with

the number of cycles required to determine the response

taken to be the model�s recall latency.The activation of a node aj;t at any time t is the

weighted sum of the inputs from all k nodes:

aj;t ¼Xk

i¼1

wijai;t�1: ð1Þ

Activations are updated in parallel at each time step.

Errors arise because of noise in the iterative updating

(cf. Usher & McClelland, 2001), modelled by slight

Gaussian perturbation (l ¼ 0, r ¼ :04) of the activa-

tions at each iteration.


Implementation of four representational principles

The four representational principles were imple-

mented by different settings of the initial node activations

at each output position. The model therefore entails no

commitment to a specific encoding process because re-

sponse selection is agnostic with regard to the mecha-

nism(s) generating the initial activation values. This

componential approach to modelling follows several di-

rect precedents (e.g., Farrell, 2001; Lewandowsky, 1999)

and is compatible with most current practice: nearly all

models of serial recall distinguish the mechanism for or-

dering from a response selection stage (Brown et al., 2000;

Burgess & Hitch, 1999; Henson, 1998; Houghton, 1990;

Page & Norris, 1998). In those models, probabilistic or

incomplete information from the ordering mechanism is

used as input for the response selection stage, which is

then used to select a response from a number of com-

petitors. The response selection stage is also consonant

with the theoretical notion of redintegration, the process

by which long-term knowledge representations are used

to reconstruct degraded traces in short-term memory (cf.

Brown & Hulme, 1995; Lewandowsky, 1999; Lewan-

dowsky & Farrell, 2000; Schweickert, 1993).

Item marking

Following relevant precedents (e.g., Brown et al.,

2004; Henson, 1998), we chose activation values that

directly represented the confusability of item positions.

Accordingly, the node corresponding to the current

Fig. 2. Example starting activation values for four principles of ser

activations result from: (A) item marking (activations shown are for th

output positions); (C) response suppression (showing the first two item

output interference, showing the increase in noise in the networks ac

output position was maximally activated, with the acti-

vation of neighbouring nodes gradually decreasing, thus

embodying the standard assumption that the proximity

of items maps into the similarity among their positional

markers (see Brown et al., 2000; Burgess & Hitch, 1999;

Henson, 1998). Specifically, the activation of node j atoutput position p was given by:

aj ¼ /jj�pj; ð2Þ

where / was set to 0.65 for the initial simulations. A

typical pattern of starting activations associated with

item marking is shown in Fig. 2A. This panel can be

compared to Fig. 10 of Brown et al. (2000), who plotted

such gradients of item activation for their oscillator-

based context signal (see Farrell, 2001, for examples

from other models).

Primacy gradient

As in other models, the primacy gradient was im-

plemented as a decrease in item activations across input

position (Fig. 2B). The same primacy gradient was es-

tablished at all output positions (before being modified

by suppression of previously emitted responses), and

was determined by:

aj ¼ a1cj�1; ð3Þ

where a1 was set to .65, and was set to .9, for the initial

simulations. The exponential form of this primacy

gradient follows precedent (Brown et al., 2000;

ial recall. Starting at the bottom and moving clockwise, these

e third output position); (B) a primacy gradient (constant across

s suppressed in conjunction with a primacy gradient); and (D)

ross output positions.


Lewandowsky, 1999). (Below, we also explore another

instantiation of the gradient with no qualitative change

in results.)

Response suppression

Response suppression was instantiated as the pro-

portional reduction of the activation of any node after

its recall. Hence, at a given output position, the initial

activation of all items was first determined from the

other principles in operation (e.g., a primacy gradient).

The activation of each item that had already been re-

called was then multiplied by a constant proportion

(0.05 in the initial simulations), to yield actual starting

activations. Fig. 2C shows the pattern of starting acti-

vations at the third output position that would result

from a primacy gradient after suppression of the first

two correctly recalled items.

Output interference

The deleterious effects of output interference were

modelled by assuming that recall of an item generally

made memory noisier. Accordingly, the starting activa-

tions were perturbed with (zero-centred Gaussian) noise

whose standard deviation increased with output position

p and was given by :04� p for the initial simulations (see

Fig. 2D, which shows SD of noise rather than activation

of nodes as the other panels).

Fig. 3. Predicted accuracy serial position curves (A), transposition g

latency serial position curves (D), for four models of serial recall. IT

ference. IT+RS: item marking with response suppression. PR+RS:

Summary of model operation

At each output position the item nodes were acti-

vated according to the principle(s) being modeled.

Activations were then allowed to iterate through the

weights until one item was selected as a response be-

cause its activation exceeded a threshold. This item

was taken as the recalled item at that output position,

with the number of iterations providing the response

latency.

Because we were interested specifically in the la-

tency of order errors, omissions (i.e., ‘‘passes’’) and

extra-list intrusions (recall of items not on the list)

were not allowed—these types of responses are rela-

tively rare in serial recall with closed experimental

vocabularies. Nevertheless, the network could easily be

extended to allow for such responses by, respectively,

incorporating a temporal deadline for omissions

(Farrell & Lewandowsky, 2002), and by allowing

non-list items to enter into response competition

(Brown et al., 2000).

Comparison of models

Fig. 3 shows the predictions of four models built

from these representational principles for the recall of 6-

item lists. The accuracy and latency serial position

radients (B), latency serial position curves (C), and cumulative

: item marking only. IT+OI: item marking with output inter-

primacy gradient with response suppression.

Fig. 4. Predicted latency–displacement functions for four

models of serial recall.

2 Repetition responses (i.e., both occurrences of the errone-

ous repetition of an item) are excluded from all LDF analyses

(both model and data) because, in two of the models, they are

expected to behave differently from the non-repeated postpone-

ments or anticipations that were of interest here. Also, for these

qualitative predictions responses from the first output position

were excluded, as these recalls are associated with extremely

long latencies empirically and were excluded from experimental

analyses (see, e.g., Experiment 1 results).


curves are shown in Figs. 3A and C and the cumulative

latency serial position curves in Fig. 3D. Fig. 3B shows

the predicted transposition gradients. Three of the

models involved item marking, either on its own, in

conjunction with response suppression (analogous to the

model of Burgess & Hitch, 1999), or augmented by

output interference. The fourth model involved the

combination of a primacy gradient and response sup-

pression (analogous to the primacy model; Page &

Norris, 1998; and SOB; Farrell & Lewandowsky, 2002;

see also Grossberg, 1978).

The predictions in Fig. 3 are readily summarised: (a)

All models produce a U-shaped accuracy serial posi-

tion curve, although the pure item-marking model ex-

hibits complete symmetry. Complete symmetry is

absent in the data, with the possible exception of re-

construction tasks (e.g., Nairne, 1992). The symmetry

for the item-marking model is unsurprising because it is

a natural consequence of the directionally na€ıve man-

ner in which starting activations were determined (see

Eq. (2)). (b) All models correctly predict a steeply

peaked transposition gradient that is symmetric (item

marking only) or nearly so (the remaining three mod-

els). This approximately symmetric gradient arises from

combinations with item marking because of the as-

sumed similarity between markers: items at adjacent

positions will tend to get activated together because of

similarity in their positional markers. In the primacy

gradient and response suppression model, by contrast,

anticipations and postponements arise from two dif-

ferent processes. Anticipations arise when a later list

item wins the competitive selection process. Because

activations decrease with list position, only the neigh-

bouring later items are likely to win the competition

with the target. In consequence, anticipations tend to

involve small absolute displacements. Postponements

tend to be localised because of ‘‘fill-in’’ (Henson et al.,

1996; Surprenant et al., in press): if an item has not

been anticipated, and if it is not recalled at the correct

position, then it is very likely to be recalled on the next

few occasions because its strength exceeds that of all

remaining competitors. (c) All models predict that la-

tency is inversely related to accuracy. Accordingly, the

latency serial position curves exhibit some primacy and

recency; however, the extent of bowing in the serial

position curves is insufficient to disrupt the (d) ap-

proximate linearity of the cumulative latency serial

position curves for all models. The linearity of cumu-

lative latency is consistent with the data (e.g., Dosher

& Ma, 1998).

The predictions in Fig. 3 thus confirm that the core

results in serial recall can be obtained by a variety of

very different representational mechanisms. However,

the mechanisms can be differentiated on the basis of

their predicted latency–displacement functions, which

are shown in Fig. 4. In a latency–displacement

function (LDF), mean recall latency of transpositions

is plotted as a function of transposition displacement.

The LDF maps directly onto the transposition gradi-

ent, but plots mean latency rather than proportions for

each response.2 It is clear from the figure that the

models� predicted LDF�s differ considerably from each

other.

In particular, for the item-marking model, the LDF

exhibits perfect symmetry, with the latencies of trans-

positions increasing with absolute displacement. This

mirrors the symmetry of the predicted transposition

gradients and the model therefore consistently maintains

an inverse relationship between the probability of a re-

sponse and its latency. When item marking is augmented

with output interference, the predicted LDF becomes

somewhat asymmetric, with postponements having

shorter latencies than anticipations at the same absolute

displacement. The same partial asymmetry arises when

item marking is augmented with response suppression.

An additional consequence of response suppression is

that it reduces the number of repetition errors, which in

the item-marking model are otherwise overly frequent

(and unrealistic when compared with empirical data;

Henson, 1998).

Finally, the model that combines a primacy gradient

with response suppression predicts a uniquely different


LDF that is monotonically negative and shows no ten-

dency to symmetry. Anticipations are slower than

postponements, and whereas the latency of postpone-

ments decreases with increasing displacement, the la-

tency of anticipations increases as they are displaced

further from the correct position. The reason for this

asymmetry is found in the source of anticipation and

postponement errors described above. If an item is an-

ticipated, it will have had to overcome a number of

stronger items from preceding input positions. These

stronger items will take longer to overcome in order for

an anticipated item to be output. Conversely, post-

ponements are relatively fast in this model because they

will involve a strong item being recalled amongst a

number of weak competitors towards the end of the list.

This strong item will not take long to recall because it

will easily overcome these weaker list items with lateral

inhibition. Finally, note that the model does not predict

postponements at large displacements, due to fill-in—the

longer an item is left unrecalled, the higher the condi-

tional probability that it will be recalled at the next

position.

In summary, Fig. 4 clearly demonstrates that the

competing representational principles make divergent

predictions that can be empirically tested. Whereas all

models produced similar patterns for the conventional

accuracy and latency measures, their predicted LDF�sranged from symmetrically V-shaped to monotonically

decreasing.

3 Much research that has compared temporally grouped and

ungrouped lists has kept the sum of all inter-item intervals

constant between list types (e.g., Henson, 1996; Hitch, Burgess,

Towse, & Culpin, 1996). This approach was not followed here

because inter-item intervals were adjusted during pilot testing to

discourage grouping of ungrouped lists while ensuring that

grouped lists were readily perceived as grouped.

Experiment 1

We now present a series of experiments designed to

collect responses for an empirical examination of LDF�s.All experiments in this article employed visual presen-

tation and keyboard recall.

Experiment 1 used temporally grouped and un-

grouped lists of 6 digits. The grouping manipulation was

introduced because it is associated with a particularly

diagnostic pattern of confusions: items that are trans-

posed between groups tend to maintain their relative

position within the group (Henson, 1999; Ryan, 1969).

These transpositions, known as ‘‘interpositions,’’ have

generally been taken as evidence for positional marking

(Henson, 1999). By implication, given that positional

models—as shown previously—predict an inverse map-

ping between response probabilities and latencies,

grouping should not only increase the frequency of in-

terpositions but should also reduce their response la-

tencies. Conversely, if interpositions were not

accelerated, and if the LDF�s for ungrouped and

grouped lists were to be similar, this would present a

challenge for positional models and would point to

other mechanisms or representations driving serial re-

call.

Method

Participants and apparatus

Nineteen undergraduate and postgraduate students

from the Department of Psychology at the University of

WesternAustraliaparticipatedvoluntarily inexchangefor

course credit or remuneration of A$5/h. All participants

received both temporally grouped and ungrouped lists.

Participants had not previously participated in any

serial recall experiments; this was intended to prevent

the spontaneous grouping of ungrouped lists that is

likely to result from experience with the task. As

grouping is known to affect patterns of transpositions

(e.g., Henson, 1999; Ryan, 1969) we sought to minimise

the possibility that people spontaneously grouped stim-

uli in the ungrouped lists.

The experiment was controlled by a PC that presented

all stimuli and collected and scored all responses. The

same apparatus was used in the remaining experiments.

Materials

Lists contained 6 digits that were randomly sampled

without replacement from the set 0 through 9. Ninety lists

of each type (i.e., grouped vs. ungrouped) were con-

structed subject to two constraints: following Henson

(1996), lists did not contain ascending or descending pairs

of integers (e.g., ‘‘3 4,’’ ‘‘7 6’’). Second, an item could not

appear in the same serial position on consecutive lists.

This constraint also applied to all remaining experiments.

The 90 ungrouped lists always preceded the 90

grouped lists. This order was chosen because subjective

grouping was expected to continue once people had been

presented with grouped lists (Henson, 1999).

Procedure

Each trial commenced with the message ‘‘READY,’’

displayed for 1000ms in the centre of the screen. Fol-

lowing a 1500ms blank interval, digits were presented

singly in the central screen position for 200ms each. Lists

were presented at these fast rates to further discourage

spontaneous grouping, and to ensure a sufficient number

of transposition errors for the LDF analysis. Participants

were instructed to read lists silently.

For temporally grouped lists, items were separated

by 200ms, except for the third and fourth item, which

were separated by an additional 600ms, thus yielding

two temporal groups of three items each. For ungrouped

lists, items were separated by a uniform 100 ms.3


The last item was followed by the message ‘‘Recall

list now!’’, and participants then immediately recalled

the list by typing the digits, one by one, on the number

pad of the keyboard using the index finger of the dom-

inant hand. After recall of the last item, participants

were shown a message giving their total recall time, after

which any key press initiated the next trial. There was a

200ms pause before the next ‘‘READY’’ message.

Participants were instructed to recall the digits in

forward order with an emphasis on accuracy rather than

speed. Participants were instructed to report the first

digit that came to mind if they were uncertain. Omis-

sions were not allowed; participants were to provide a

digit at every output position (to maximise frequency of

order errors). Participants were given five practice trials

and a 30-s break was provided every 18 trials. Experi-

mental sessions lasted about 45min.

Results and discussion

For all analyses in this article, responses in the first

output position with a latency of less than 100 ms were

considered to be ‘‘type-aheads’’ and were omitted from

analyses. Any non-zero latency was acceptable in later

output positions.

Fig. 5. Results of Experiments 1 and 2: serial position curves for ac

curves (C), and cumulative latency serial position curves (D).

Accuracy

All accuracy analyses used strict positional scoring,

such that an item was counted correct only if re-

called in its correct position. Preliminary analysis

identified two participants whose performance was at

ceiling (overall accuracy .98). Given the present em-

phasis on error latencies, these individuals were

therefore removed from consideration (inclusion of

these participants does not qualitatively alter the

conclusions).

The serial position curves for correct-in-position re-

call are shown in Fig. 5A. It is clear from the figure that

the grouping manipulation was successful in that per-

formance on the grouped lists was better overall than

performance on the ungrouped lists. Additionally, the

grouping advantage was greater for later serial positions

than earlier ones, as expected from previous studies (e.g.,

Frankish, 1985).

The pattern was statistically confirmed by a

2 (Grouping)� 6 (Serial Position) ANOVA which

revealed significant main effects of grouping, F ð1; 16Þ ¼26:30, MSE ¼ :023, p < :0001, and serial position, F ð5;80Þ ¼ 35:37, MSE ¼ :005, p < :0001, and the expected

interaction between both variables, F ð5; 80Þ ¼ 6:86,MSE ¼ :003, p < :0001.

curacy (A), transposition gradients (B), latency serial position

4 The small absolute number of transpositions rendered it

difficult to fit the regression models to each list type separately.

In particular, for grouped lists, the average number of �2

displacements per participant was less than 3, with even fewer

observations for greater displacements. We therefore report

only the overall analysis across list types.


Transpositions

The transposition gradients are shown in Fig. 5B.

The pattern of transpositions conforms to standard ex-

pectations, although the high accuracy translated into

few displacements beyond immediately adjacent posi-

tions. This in turn prevented the appearance of the usual

grouping effects on transposition probabilities (Henson,

1996, 1999).

Latency

The average latencies associated with correct re-

sponses at each serial position are shown in the bottom

half of Fig. 5, in two ways. Fig. 5C shows average la-

tencies at each serial position. It is clear from the panel

that the first item took considerably longer to recall than

all subsequent items. This is typical for forward serial

recall (e.g., Anderson & Matessa, 1997; Maybery et al.,

2002; Thomas et al., 2003), and is assumed to reflect the

operation of an initial preparatory stage that precedes

the first response (Farrell & Lewandowsky, 2002;

though see Anderson & Matessa, 1997). Because this

preparatory stage is of little theoretical interest, it is de-

emphasised in Fig. 5D, which shows cumulative mean

latencies.

Immediately evident in both panels is the effect of

grouping. Latencies for grouped lists were generally

faster, although the cumulative curves suggest that this

effect was primarily the result of faster responses for the

first item. In support, separate regression lines fitted to

the cumulative curves for grouped and ungrouped lists

differed considerably in intercept (502.5 and 788ms, re-

spectively) but exhibited fairly similar slopes (326 and

360ms/position, respectively). However, grouping also

introduced a marked discontinuity in recall, with longer

latencies for serial position 4, which represents recall of

the first item of the second group. This again mirrors

previous results (Anderson & Matessa, 1997; Maybery

et al., 2002; Oberauer, 2003).

Statistical confirmation of these patterns was ob-

tained by a 2 (Grouping)� 6 (Serial Position) ANOVA,

which revealed a main effect of grouping, F ð1; 18Þ ¼72:09, MSE ¼ 4748, p < :0001, serial position, F ð5; 80Þ¼ 125:22, MSE ¼ 21; 503, p < :0001, and an interaction

between both variables, F ð5; 80Þ ¼ 28:35, MSE ¼ 4033,

p < :0001.

Hierarchical regression analysis of transposition latencies

The recall latencies were subjected to a hierarchical

regression analysis assessing the relationship between

transposition displacement and transposition latency.

Responses in the first output position were excluded

from the LDF�s for regression analyses because of their

extremely long latencies (order errors at the first output

position can only be anticipations, and inclusion of re-

sponse times from the first output position would thus

artificially inflate response times for anticipations). In

consequence, the furthest anticipations for the LDF�sfor regression were )4, corresponding to the last item

being recalled in the second output position, whereas

postponements could span 5 positions (+5), corre-

sponding to the first list item being recalled last. In order

to compensate for an apparent non-linearity, latencies

collected in all experiments were logarithmically trans-

formed for all LDF analyses.

Log-LDF�s were estimated using a hierarchical re-

gression model (Busing, Meijer, & van der Leeden,

1994). Hierarchical regression permits an aggregate

analysis of data from all participants without con-

founding between- and within-participant variability:

regression coefficients are estimated for each participant

separately, but their statistical significance is assessed by

considering the overall pattern of parameters across in-

dividuals. This avoids several potential pitfalls in situa-

tions in which several individuals contribute multiple

observations each to a regression analysis (see Lorch &

Myers, 1990; for a discussion of those problems).

The regression model examined here included an in-

tercept term plus parameters for the transposition dis-

placement (in the range )4 to 5) and for output position

(ranging from 2 to 6). The latter variable was included in

the regression because transposition displacement is

correlated with output position: anticipations will tend

to occur at the start of recall, while postponements will

tend to occur at the end of recall. Of critical interest was

whether the slope of the function relating recall latencies

to transposition displacement was negative when the

effects of output position were accounted for. Regression

parameters were estimated on the basis of all available

responses (i.e., from grouped and ungrouped lists) si-

multaneously.4

The maximum likelihood estimates of those param-

eters (see Busing et al., 1994; for computational details),

averaged across participants, were 5.75, ).042, and

).013 for intercept, displacement, and output position,

respectively. The negative parameter for displacement

indicates that response get faster with increasing (more

positive) transposition displacements, suggesting post-

ponements are faster than responses.

The effect of displacement is shown graphically in

Fig. 6, which shows average latencies at each displace-

ment separately for ungrouped and grouped lists. To

facilitate graphical presentation, the effects of output

position have been subtracted in Fig. 6 (and Fig. 9 for

Experiment 3) by calculating the mean latency for each

output position for each participant, and then

Fig. 6. Latency–displacement functions for Experiments 1

and 2.


subtracting that mean from each individual response

made at that output position (because this filtering re-

moves output position effects position by position, re-

sponses for the first position were retained in the

figures). This filtering renders some latencies negative,

Fig. 7. Estimated slopes from hierarchical regressions relating recall la

for individual participants for a particular experimental condition. T

panels those for Experiment 2, while the bottom panels correspond t

slope of 0.

preventing the use of logarithmic ordinates. Fig. 6

therefore shows the effects of transposition displacement

on latency, with the effects of output position removed.

The apparent negative relationship between latency

and transposition displacement was given qualified sta-

tistical support by the t values accompanying the pa-

rameter estimates, which were 87.41 (p < :0001), 1.86

(p � :06), and )1.73 (p � :08), for intercept, displace-

ment, and output position, respectively. This shows that

anticipations were slower than postponements, although

the effect failed to reach conventional levels of signifi-

cance. The lack of significance was at least partially due

to the presence of large individual differences. To give an

idea of variability in the LDF slopes, Fig. 7 shows the

observed individual slope estimates for all experiments;

those for Experiment 1 are in the top row. Although the

average slope of the individual LDF�s was negative,

several participants exhibited a positive slope.

A limitation of the transposition latency analysis was

that most participants were extremely accurate. Despite

exclusion of participants at the ceiling, the mean accu-

racy in the remaining sample was .86. This ceiling on

accuracy also prevented grouping effects from emerging,

preventing a detailed examination of the latencies of

tency to transposition displacement. Each panel gives estimates

he top row gives slope estimates for Experiment 1, the middle

o Experiment 3. The full vertical line in each panel indicates a


interpositions. The scarcity of transpositions was ad-

dressed in Experiment 2.

Experiment 2

In an attempt to lower the accuracy of recall per-

formance, and thereby increase the number of transpo-

sitions, the second experiment used a larger

experimental vocabulary (consonants rather than digits)

and included a post-presentation interference task on

some trials. As well as lowering recall, the interference

task was intended to determine the generality of the ef-

fects observed in Experiment 1; in particular, we were

interested in ascertaining whether negative LDF�s wouldbe observed at filled retention intervals longer than the

duration commonly cited for the presumed decay of

traces (i.e., around 2 s; see Brown & Hulme, 1995, for a

discussion).

Method

Participants and materials

Fifteen members of the campus community at the

University of Western Australia participated voluntarily

in exchange for course credit or remuneration of A$5/h.

Lists were drawn from a vocabulary of 16 consonants

(B, C, F, G, H, J, K, L, N, P, Q, R, S, V, X, Z). For each

participant, 140 lists were constructed by randomly

sampling six items without replacement from the vo-

cabulary subject to the constraint that no two adjacent

list items could be alphabetically consecutive.

Procedure

All participants participated in 70 contiguous trials

with or without a post-list distractor task, with the order

of list blocks counterbalanced across participants. Each

trial commenced with the word ‘‘READY’’ centrally

presented for 1000ms, followed by a 1000ms blank

pause. List items were then presented for 400ms, with a

100ms inter-item interval.

If a list was followed by distractors, a pause of 500ms

was inserted between the last list item and presentation

of the distractor(s). The 4 distractor digits, randomly

selected from the set 1 through 9, were presented in the

same manner as list items. Participants were instructed

to read list items and distractors aloud.

The recall phase differed slightly from the previous

study in that responses were entered using a 4� 4 grid

on the main keyboard that maintained alphabetical or-

der among vocabulary items and did not conform to

QWERTY lay-out. As before, participants were to type

the letters one by one using their dominant index finger,

and entered letters remained visible on the screen until

the sixth item had been entered. Omissions could be

recorded in this experiment via space bar, but

extra-vocabulary intrusions were prevented. The last

response was followed by feedback in the form of the

total retrieval time.

There were 30-s breaks after every 35 trials. Sessions

lasted under an hour.


Serial position curves and transposition gradients

One participant�s overall accuracy (.24) was far belowthe mean of the sample, and another participant ap-

peared not to engage with the task on many trials (all

responses consisted of space bar presses). Both partici-

pants were removed from further consideration.

The serial position curves for this experiment are

shown in Fig. 5A.

The obvious deleterious effect of the distractor task

on accuracy was confirmed by the corresponding main

effect in a 2� 6 within-participants ANOVA with

F ð1; 14Þ ¼ 180:70, MSE ¼ :021, p < :0001. The analysis

also showed an effect of serial position, F ð5; 60Þ ¼ 56:99,MSE ¼ :0081, p < :0001, and an interaction between the

two variables, F ð5; 60Þ ¼ 3:40, MSE ¼ :0084, p < :01.The underlying transposition gradients are shown in

Fig. 5B. They confirm the results of the serial position

analysis, with more anticipation and postponement er-

rors for the interference lists.

The latency analysis approximately paralleled the

accuracy results, with a strong effect of serial position,

F ð5; 70Þ ¼ 88:06, MSE¼ 79,508, p < :0001, an interac-

tion between both experimental variables,

F ð5; 70Þ ¼ 3:245, MSE¼ 53,281, p < :05, but no main

effect of distractor task, F ð1; 12Þ ¼ 3:13, p > :10. Re-

gressions using the cumulative latency serial position

curves gave intercepts for the quiet and distractor con-

ditions of 979 and 1385ms, with slopes 1025 and

1059ms/position, respectively (see Figs. 5C and D).

None of these effects were surprising; they merely con-

firm that the distractor manipulation had the expected

effect of reducing accuracy and simultaneously slowing

recall.

Latency–displacement functions

As for Experiment 1, parameters for the latency–

displacement functions were estimated using hierarchical

regression. The increased frequencies of errors in Ex-

periment 2 allowed three analyses to be conducted: one

for each distractor condition separately and one that

combined responses across all trials for each participant.

Table 2 shows regression statistics for the overall anal-

ysis and Fig. 7 the individual parameter estimates.

Replicating Experiment 1, there was a statistically

significant negative relationship between latency and

displacement in the overall analysis. These effects are

illustrated in Fig. 6, which shows the LDF�s for each

condition (subtracting the effect of output position as in

Table 2

Estimated hierarchical regression parameters for Experiment 2

Parameter Estimate SE t p

Combined analysis (all trials)

Intercept 6.80 0.06 105.05 .00

Displacement )0.04 0.01 )4.85 .00

Output position )0.02 0.01 )2.30 .00

Quiet lists

Intercept 6.74 0.06 120.30 .00

Displacement )0.09 0.02 )4.89 .00

Output position 0.00 0.01 )0.41 >.10

Distractor lists

Intercept 6.88 0.09 74.14 .00

Displacement )0.02 0.01 )1.81 .07

Output position )0.04 0.02 )2.63 .01


Experiment 1 to facilitate graphical presentation). In

confirmation of the regression, there was a clear trend

for latencies to decline with transposition displacement,

although that trend was greater for the lists without

interference task. Fig. 7 shows that the displacement

parameter estimates were remarkably stable across in-

dividuals and within individuals across list types. Every

single participant gave rise to a negative displacement

parameter for both list types. This highlights the gen-

erality of the LDF�s found in Experiment 1, not only by

showing their presence using a different experimental

vocabulary, but more importantly, by showing negative

LDF�s at slightly longer retention intervals.

Nonetheless, the size of the displacement effect was

not very large, which may have reflected the restricted

range of possible displacements: transposition distances

in the first two experiments ranged from a minimum of

)5 to a maximum of 5 ()4 to 5 in the hierarchical re-

gression analysis), and there were few transpositions at

large absolute displacements. It follows that a better

assessment of the latency–displacement function can be

obtained by increasing the range of possible displace-

ments and the number of observations at the extremes.

Experiment 3

Experiment 3 differed from the first two studies pri-

marily by using longer lists of 9 digits. The use of longer

lists was motivated by two goals; first, to lower accuracy

of recall and thus increase the frequency of transposition

errors and, second, to replicate the observed negative

LDF�s beyond sub-span list lengths.

Experiment 3 again employed a grouping manipula-

tion—trials in the first half of the experiment involved

ungrouped presentation and the second half involved

grouped lists with pauses after the third and sixth item

(i.e., 3–3–3). It has been suggested that grouping is more

likely in supra-span lists (Henson, 1996), which implies

that the effects of grouping on the LDF�s may be more

apparent with longer lists.

Method

Participants

A new sample of 26 undergraduate and postgraduate

students from the Department of Psychology at the

University of Western Australia participated voluntarily

in exchange for course credit or remuneration of A$5/h.

Materials and procedure

Experiment 3 used the same pool of stimuli and the

same criteria for list construction as Experiment 1, ex-

cept that list length was now 9 items. The remaining

procedural details followed those of Experiment 1, with

three exceptions: first, grouped lists were characterised

by two pauses, inserted after the third and the sixth item,

with all other temporal parameters for both list types

remaining unchanged. Second, there were only 4 prac-

tice trials and, third, each block of 18 trials was followed

by a 30 s break.


Serial position curves and transposition gradients

Fig. 8 shows the serial position curves for both list

types, with accuracy shown in Fig. 8A and latency

(correct responses only) in Figs. 8C and D. The scal-

loped serial position curve for grouped presentation is

typical of experiments involving temporal grouping and

is particularly pronounced for latency. The intercept

estimates for the cumulative latency serial position

curves were 639 and 652ms, respectively, for the un-

grouped and grouped conditions, with slopes 528 and

502ms/position.

The transposition gradients, shown in Fig. 8B, con-

firm that people treated the grouped and ungrouped lists

differently. In particular, the scalloped form of the

transposition gradient for grouped lists, viz. the flat-

tening of the curve at transposition displacement �3 and

the local peak at transposition displacement +6, indi-

cates that when items were exchanged between groups,

they maintained their within-group position (e.g., Ryan,

1969).

Latency–displacement functions

The hierarchical regression models again included an

intercept term plus parameters for the transposition

distance (in the range )7 to 8) and for output position

(ranging from 2 to 9). As for Experiment 2, there were

enough observations at far displacements to fit separate

models to each list type. Table 3 summarises the pa-

rameter estimates (averaged across participants) for each

list type and for an overall analysis that ignored the

grouping manipulation. Irrespective of list type, there

Fig. 8. Results of Experiment 3: serial position curves for accuracy (A), transposition gradients (B), latency serial position curves (C),

and cumulative latency serial position curves (D).


was a strong and statistically significant negative rela-

tionship between latency and displacement, which is

graphically illustrated in Fig. 9. Although Fig. 9 shows

some unique deviations (for example, around transpo-

sition displacement +5), the overall trend is a negative

one; the further a response was erroneously anticipated,

the slower it was, and the further a response was erro-

neously postponed, the faster it was made. To illustrate

the consistency of this effect across participants, Fig. 7

shows the distribution of individual estimates for the

displacement parameter. The figures hows that those

estimates were negative for every participant for

grouped lists, and for all but three participants in the

ungrouped condition.

Table 3

Estimated hierarchical regression parameters for Experiment 3

Parameter Estimate SE t p

Grouped

Intercept 5.92 0.06 105.36 .00

Displacement )0.03 0.01 )3.78 .00

Output position 0.00 0.01 0.47 >.10

Ungrouped

Intercept 5.93 0.07 84.72 .00

Displacement )0.02 0.01 )3.33 .00

Output position 0.02 0.01 1.46 >.10

A final point worth noting about the LDF�s for Ex-periment 3 is that the observed effect of grouping in the

transposition gradients is not apparent in the corre-

sponding latencies in the LDF�s. The interpositions (i.e.,at transposition displacements )6, )3, +3, and +6) were

not accompanied by shorter recall times at the same

displacement distances in the LDF�s; the only effect of

grouping appeared to be a flattening of the LDF. This

Fig. 9. Latency–displacement functions obtained in Experi-

ment 3.


confirms that probability and latency patterns in serial

recall can be dissociated, and it challenges positional

models, which can handle the pattern of interpositions

but not their independence from the associated latencies.

Summary of experiments

The three experiments consistently showed that la-

tency was a monotonic negative function of transposi-

tion displacement. The generality of this finding is

underscored by the fact that it was observed for different

list lengths (6-item lists in Experiments 1 and 2 and

9-item lists in Experiment 3), stimulus materials (digits

in Experiments 1 and 3 and letters in Experiment 2),

temporal arrangements of lists (grouped vs. ungrouped

in Experiments 1 and 3), and distractor conditions

(Experiment 2). In particular, negative trends were wit-

nessed in the LDF�s over time scales beyond the pre-

sumed duration of decaying traces (e.g., Brown &

Hulme, 1995). Moreover, the negative relationship be-

tween latency and displacement persisted despite the fact

that some of those manipulations caused qualitative

changes in other aspects of recall; for example, grouping

clearly altered the serial position curves and transposi-

tion gradients in Experiment 3 but had no systematic

effects on the associated LDF�s.The generality of the negative latency–displacement

relationship is further underscored by its presence in

other experiments not reported here. For example, the

phonological similarity experiments reported by Farrell

and Lewandowsky (2003), a further unpublished ex-

periment in the authors� laboratory, and a study by

Duncan (1996), are all characterised by negative LDF�s.

5 This scaling of the initial activations determines the

amount of information they provide with respect to the noise

resident in the network. The weighting of initial activations will

also determine the distance of each item�s activation from the

output threshold.

Quantitative modelling of observed LDFs

To confirm the impact of the data on the represen-

tational principles examined at the outset, we now re-

port quantitative fits of the models to the data from

Experiment 3. Although the models predicted similar

serial position curves and transposition gradients

(Fig. 3), the predicted LDF�s differed widely (Fig. 4). In

particular, while any involvement of positional marking

resulted in a V-shaped function relating latency to dis-

placement, the combination of a primacy gradient and

response suppression predicted a monotonic decrease in

recall times with increasing (i.e., more positive) dis-

placement of transpositions. Examination of the ob-

tained LDF�s in Figs. 6 and 9 suggests that the data

mirror the pattern predicted by the primacy-gradient

model, although there is some suggestion of a kink in

these curves for correct responses (i.e., displacement 0).

One restriction of the simulations presented at the

outset was that they yielded qualitative predictions

based on parameter values selected to give realistic serial

position curves and transposition gradients. This does

not preclude the possibility that some of the represen-

tational principles might predict more realistic LDF�sunder different parameter values. To examine this pos-

sibility, each of the earlier models was fit to the accuracy

serial position curve and transposition gradient for the

ungrouped condition of Experiment 3 (these fits did not

consider the latency data). The best-fitting parameter

values were then used to obtain latency predictions (se-

rial position curves and LDF�s) for comparison with

those observed in Experiment 3.

Fitting details

Models were fit to the data for individual subjects,

and the model predictions for individual subjects were

then averaged to give overall predictions. The mod-

elling procedure was identical to that used to generate

the predictions at the outset, except that parameter

values were adjusted (using the simplex algorithm of

Nelder & Mead, 1965) to minimise the RMSD be-

tween the data (summed across accuracy serial posi-

tion curve and transposition gradient) and each

model.

The parameters minimised in the fitting routine

differed between the models. For the pure item-mark-

ing model (IT from here on), the two parameters were

the distinctiveness of the positional markers (/), and

the weighting of the initial activation of this informa-

tion.5 When item marking was augmented by output

interference (IT+OI), three parameters were mini-

mised: the distinctiveness of the markers (/), the

weighting of initial activations, and the weighting of

output interference across output positions. The item-

marking plus response suppression model (IT+RS)

likewise had three free parameters, the first two as for

the pure item-marker model, and a third parameter

that governed the extent of response suppression. Fi-

nally, the primacy-gradient model with response sup-

pression (PR+RS) took as its three free parameters the

steepness of the primacy gradient (c), the starting point

of the gradient (a1; effectively the weighting of this

information as for the other models), and the extent of

response suppression.

Fitting results and discussion

Table 4 presents the minimised RMSD for each

model and each participant, with the value of the

Table 4

Minimised RMSD for individual participants’ data

Participant IT IT+OI IT+RS PR+RS

1 0.22 0.11 0.16 0.11

2 0.22 0.09 0.14 0.07

3 0.22 0.13 0.17 0.11

4 0.35 0.18 0.26 0.11

5 0.40 0.17 0.29 0.13

6 0.14 0.14 0.10 0.14

7 0.08 0.08 0.08 0.17

8 0.32 0.09 0.22 0.09

9 0.36 0.19 0.29 0.21

10 0.45 0.23 0.34 0.19

11 0.40 0.24 0.30 0.19

12 0.38 0.17 0.29 0.09

13 0.32 0.14 0.23 0.08

14 0.30 0.14 0.21 0.09

15 0.22 0.14 0.14 0.12

16 0.41 0.18 0.28 0.12

17 0.30 0.11 0.22 0.11

18 0.24 0.12 0.17 0.10

19 0.38 0.21 0.24 0.11

20 0.41 0.18 0.29 0.09

21 0.34 0.17 0.27 0.09

22 0.20 0.14 0.15 0.12

23 0.42 0.21 0.33 0.14

24 0.31 0.18 0.22 0.13

25 0.37 0.21 0.25 0.11

26 0.33 0.17 0.24 0.09

Mean 0.31 0.16 0.23 0.12

Each column gives the RMSDs for a particular model. Bold

numbers show the lowest RMSD for each row, indicating the

best-fitting model for that participant.


best-fitting model (smallest RMSD) bold-faced for each

participant. Although emphasis here was not on good-

ness-of-fit to the accuracy data, a brief examination of

differences in RMSD between models is in order. Given

that it incorporated one less parameter than the other

models, it is perhaps unsurprising that the pure item-

marking model (IT) gave the poorest fit. This poor fit

can be mostly attributed to the symmetry of the pre-

dicted serial position curves (see Fig. 10 for an example).

The other three models fared better to varying extents.

In particular, the PR+RS model gave somewhat better

fits on average than the IT+OI model, and both these

models in turn performed notably better than the

IT+RS model (note that these models all incorporate

three parameters).

Fig. 10 shows the averaged fit of the models to the

aggregate data. The IT+OI and PR+RS models pre-

dicted more realistic serial position curves (compared

with Fig. 8) than the IT and IT+RS models, and both

gave closer accounts of the observed transposition gra-

dient (Fig. 8B).

Figs. 10C and D show the predicted latency serial

position curves (standard on the left and cumulative on

the right). In order to match the appearance of predic-

tions (Fig. 10) and data (Fig. 8), the predictions for the

first output position included time for presumed prepa-

ratory processes—this was set to a constant 40 iterations

for all models. It is clear that the predictions of all

models differ somewhat from the data (e.g., the un-

grouped condition in Fig. 8C), but in interestingly dif-

ferent ways. Unlike the other models, the PR+RS

model predicts a monotonic latency serial position

curve. This handles the observed slowing down of recall

over the majority of serial positions, but it does not

capture the acceleration for the last two serial positions.

The IT, IT+OI, and IT+RS models, by contrast, pre-

dict this saddle point, but they expect it to be much

earlier in the list than is observed in the data. Despite

these differences, all models capture the approximately

linear pattern of the cumulative latency serial position

curve (Figs. 8D and 10D).

Turning to latency–displacement functions, Fig. 11

shows the predictions obtained with the same parameter

settings that underlie Fig. 10. Unlike the qualitative

predictions presented at the outset (Fig. 4), the effect of

output position in these predicted LDF�s was removed

in exactly the same manner as in the empirical LDF�s toprovide comparability with the data. In addition, to

further enhance graphical comparability, the predicted

LDF�s were converted from model iterations to milli-

seconds using two scaling parameters for each model: an

intercept (in milliseconds), and an iteration-to-millisec-

ond slope, obtained by entering the latency serial posi-

tion curve for the ungrouped condition from

Experiment 3 and its predicted counterpart into a re-

gression as dependent and independent variable, re-

spectively.

The predicted LDF�s shown in Fig. 11 do not

qualitatively differ from those shown at the outset

(Fig. 4), suggesting that the predictions that guided our

research represented core properties of the models and

were not tied to particular parameter values. It is also

immediately apparent from Fig. 11 that the IT and

IT+RS models predict a V-shaped LDF, and the

PR+RS model predicts a monotonic negative function

that is flatter for postponements (to the right of

transposition displacement 0) than for anticipations

(left of 0). The IT+OI model also predicts an asym-

metric V-shaped function, though the variability in

latency is much smaller than for the other models (the

underlying V-shaped predictions of this model were

confirmed by estimates for the slope of the LDF

of )3.88 and. 46 for points left and right of 0, re-

spectively).

Comparison of these predictions to the correspond-

ing data in Fig. 9 provides support for the PR+RS

model—the LDF for the ungrouped condition in

Fig. 10. Fits of models to data from the ungrouped condition in Experiment 3. Panels give serial position curves for accuracy (A),

transposition gradients (B), latency serial position curves (C), and cumulative latency serial position curves (D).

Fig. 11. Predicted latency–displacement functions after fitting

models to data from the ungrouped condition of Experiment 3.

The LDF�s have been converted to ms using scaling parameters

calculated from the latency serial position curves (Fig. 8).

6 Mike Page pointed out that the primacy-gradient model we

implemented does not exactly match the primacy model of Page

and Norris (1998). To ensure the specific form of the primacy

gradient did not unduly affect the results,wefit (to the data froma

subset of participants) another version of the PR+RS model in

which the primacy gradient was linear and decayed across output

positions—this more closely corresponds to the assumptions of

the Page and Norris model. We found this form of the PR+RS

model fit the probability data less well than the model we

employed, but gave qualitatively similar predictions for the

latency serial position curves and LDF�s.


Experiment 3 (the probability data from that condition

were used to estimate parameters) shows an overall

monotonically negative trend, with the function being

flatter for postponements than for anticipations.6 The IT

and IT+RS models, by contrast, predict an excessive

extent of non-monotonicity and the IT+OI model

predicts too shallow a function. Note that although the

PR+RS model deviates somewhat from the empirical

LDF, it was the only one of the four models investigated

that qualitatively captured the results. Considering that

the models were not fitted to the LDF�s directly, the

correspondence between the PR+RS predictions and

the data is noteworthy.

Robustness of predictions

Although the fitting exercise ruled out the possibility

that models other than the PR+RS model might give


respectable accounts of the LDF�s when parameters are

estimated from the data, the preceding predictions are

still based on single (best-fitting) sets of parameter

values. Hence, the preceding simulations do not com-

prehensively show that the LDF�s follow from princi-

ples of the models, and indeed, the models might

predict qualitatively different results for different pa-

rameter values.

To confirm the consistency of the predicted LDF

patterns for each model (cf. Li, Lewandowsky, &

DeBrunner, 1996), we ran a further set of simulations

in which the predictions of the models were examined

for a range of parameter combinations. Parameters in

each model were varied independently from 0.05 to

0.95 in steps of 0.1 and crossed factorially, leading to a

set of points (each a parameter vector) on a grid

covering a large portion of the parameter space of each

model. Thus, for the IT+OI, IT+RS, and PR+RS

models, the 10 values for each of the three parameters

were factorially combined to give 1000 (103) parameter

combinations to be examined (the IT model, having

only two free parameters, was run on 100 parameter

combinations). For each grid point, 1000 replications

of performance on 9-item lists were generated for each

model. The dependent variable of interest was the

slope of the LDF for postponements; since the slope of

anticipations is negative for all models, only post-

ponement latencies serve to discriminate between the

models.7

Fig. 12 shows the distributions of LDF slopes for

postponements for each model. It is clear that the IT

model (Fig. 12A), the IT+OI model (B) and the IT+RS

model (C) all predict a majority of steep positive slopes

for postponements; the percentage of simulations that

returned negative slopes was 1.2, 1.9, and 2.6% for the

respective models. In contrast, the PR+RS model pre-

dicts a majority of negative slopes (much of the distri-

bution lies to the left of 0); the percentage of simulations

returning negative slopes was 75.8%. Moreover, when

the PR+RS model does predict positive slopes, they are

generally quite shallow. Overall, these simulations

clearly confirm that the LDF patterns predicted from

the models follow from the key principles under dis-

cussion, and are not specific to particular parameter

values.

7 The predicted LDF�s had the effects of output position

removed in the same manner as the LDF�s generated from best-

fitting parameter values. In some cases LDF slopes could not be

calculated due to perfect or near-perfect performance (which

eliminates postponements). The reported percentages of slope

value were determined only from simulations that returned

LDF�s from which a slope for postponements could be

calculated.

General discussion

The results of the experiments and of the quantitative

modelling provide consistent support for the notion that

serial recall is driven by a primacy gradient of item

strengths that is coupled with suppression of items once

they have been recalled. No other model consistently

predicts a monotonic negative latency–displacement

function, even when parameters are free to vary to ac-

commodate specific results, or are varied arbitrarily

across a wide range. The data consistently show that the

relationship between latency and displacement is indeed

negative, even across manipulations of variables such as

list length, grouping, and type of material.

Implications for primacy-gradient models

Our theoretical analysis lends support to primacy-

gradient models such as the primacy model (Page &

Norris, 1998) and SOB (Farrell & Lewandowsky, 2002),

complementing other independent sources of evidence

for these models (e.g., Duncan & Lewandowsky, in

press; Farrell & Lewandowsky, 2003). Simulations

conducted previously (Farrell, 2001) complement the

present modelling by showing that the predicted LDF of

SOB is very similar to that predicted by the PR+RS

model in the lateral inhibition framework—given this

similarity, SOB simulations are not reported here (see

Farrell, 2001). Unlike the models under discussion, SOB

naturally accounts for the dynamics of recall by imple-

menting these assumptions in a distributed, recurrent

connectionist network (cf. Anderson, Silverstein, Ritz, &

Jones, 1977).

Although primacy-gradient models have been subject

to recent criticism (e.g., Haberlandt et al., in press;

Henson, 1999; Surprenant et al., in press), those cri-

tiques have been limited to showing that a primacy

gradient alone is insufficient to account for all aspects of

serial recall and needs to be supplemented by some other

ordering mechanism (e.g., item marking; see Page &

Norris, 1998). We do not take issue with those conclu-

sions, as pure primacy-gradient models are indeed in-

sufficient to account for effects such as grouping (e.g.,

Farrell, 2001; Henson, 1996; Page & Norris, 1998). In-

stead, we believe that results such as those presented

here identify a necessary role for the primacy gradient

and response suppression in forward serial recall.

Latencies in models of serial recall

We noted at the outset that one major restriction of

most current models is their inability to make latency

predictions. Our results highlight this restriction by

showing the utility of latency data in differentiating be-

tween models. We next examine ways in which current

models might be extended into the latency domain.

Fig. 12. Distributions of slopes of LDF�s for postponements only, across the parameter space of models. See text for details of

simulations. Panels show distributions for IT model (A); IT+OI model (B); IT+RS model (C); and PR+RS model (D). The heavy

vertical line in each panel represents a slope of 0.


Most current models of serial recall distinguish be-

tween the mechanism for representation of order and a

separate mechanism for response selection and output.

We classify models on the basis of their approach to

response selection.

On the one hand, there are models that select a re-

sponse by some form of a ‘‘winner-take-all’’ process. For

example, the primacy model simply chooses the most

active localist node (Page & Norris, 1998), which is

similar to the architecture used here and the model of

Burgess and Hitch (1999). Alternatively, some models

use a matching process in which the output of the or-

dering mechanism is compared to a pool of recallable

items, the most similar of which is selected for output

(Brown et al., 2000; see also Lewandowsky & Murdock,

1989; Neath, 1999). In those models, the process of se-

lecting a specific item for output could be modelled by a

lateral inhibition network as presented here. All that is

required is that the ordering mechanism in a model

provides information that can be converted into a

starting pattern of activations across the units. This

mapping could be trivially achieved in the primacy

model (Page & Norris, 1998; see also Grossberg, 1978),

where order is already represented in the activations of

localist units. This stage could also be implemented in

distributed models such as OSCAR (Brown et al., 2000)

or TODAM (Lewandowsky & Murdock, 1989) by

instituting some mapping (via weights) from distributed

representations in the memory models to localist repre-

sentations in the lateral inhibition output stage. Al-

though distributed attractor models have been shown to

provide successful accounts of response selection in se-

rial recall (e.g., Lewandowsky, 1999; Lewandowsky &

Farrell, 2000), the lateral inhibition network is an easily

implemented alternative, constituting a simple scheme in

which current connectionist models may be given a dy-

namic aspect.

On the other hand, models such as the feature model

(Nairne, 1990) and SIMPLE (Brown et al., 2004) predict

response probabilities based on the Luce–Shepard

choice rule (Luce, 1963; Shepard, 1957; see Nairne,

2002, for use of such matching rules in memory theory).

These models might also be adapted to generate latency

predictions following precedents in the categorisation

literature. Nosofsky and Palmeri (1997) have shown that

an exemplar-based categorisation model that uses the

Luce–Shepard choice rule to provide response proba-

bilities (Nosofsky, 1986) can be extended into the tem-

poral domain by using the output of the model as input

for a random walk process. Nosofsky and Palmeri

(1997) assumed that individual exemplars race (cf. Lo-

gan, 1988) to become evidence entering into a random

walk process. The random walk continues until the ev-

idence for a response passes a criterion, at which time


that response is made, and the duration of the random

walk is taken as the decision time. Similar adjustments

might be made to SIMPLE and the feature model,

taking the distance between each item and the item to be

recalled (in SIMPLE) or the number of matches between

a short-term trace and traces in a long-term store (in the

feature model) as probabilistic evidence entering into a

random walk process. Indeed, given that Usher and

McClelland (2001) argue that their lateral inhibition

model approximates continuous random walk models

(e.g., Ratcliff, 1978), the architecture presented here

might serve as a response selection tool even in models

that rely on the Luce–Shepard choice rule to determine

response probabilities.

In conclusion, we suggest that any contemporary

model of serial recall has the potential for extension to

latency phenomena. We argue that these extensions are

crucial because we have shown that latency data can

readily constrain and differentiate models of serial order

memory.

Acknowledgments

We gratefully acknowledge assistance from Leo

Roberts at all stages of manuscript preparation and

during data collection for Experiments 2 and 3. We also

thank Mike Page and two anonymous reviewers for

their comments.

References

Anderson, J. A., Silverstein, J. W., Ritz, S. A., & Jones, R. S.

(1977). Distinctive features, categorical perception, and

probability learning: Some applications of a neural model.

Psychological Review, 84, 413–451.

Anderson, J. R., & Matessa, M. (1997). A production system

theory of serial memory. Psychological Review, 104, 728–

748.

Anderson, J. R., Bothell, D., Lebiere, C., & Matessa, M. (1998).

An integrated theory of list memory. Journal of Memory and

Language, 38, 341–380.

Anderson, M. C., & Neely, J. H. (1996). Interference and

inhibition in memory retrieval. In E. L. Bjork & R. A. Bjork

(Eds.), Handbook of perception and memory, Vol. 10:

Memory (pp. 237–313). San Diego: Academic Press.

Brown, G. D. A., & Hulme, C. (1995). Modeling item length

effects in memory span: No rehearsal needed? Journal of

Memory and Language, 34, 594–621.

Brown, G. D. A., Neath, I., & Chater, N. (2004). A local

distinctiveness model of scale-invariant memory and per-

ceptual identification. Manuscript submitted for publica-

tion.

Brown, G. D. A., Preece, T., & Hulme, C. (2000). Oscillator-

based memory for serial order. Psychological Review, 107,

127–181.

Burgess, N., & Hitch, G. J. (1999). Memory for serial order: A

network model of the phonological loop and its timing.


Busing, F. M. T. A., Meijer, E., & van der Leeden, R. (1994).

MLA software for multilevel analysis of data with two

levels. User�s guide for version 1.0b [software manual].

Leiden, The Netherlands: Leiden University. Available:

http://www.fsw.leidenuniv.nl/www/w3_ment/medewerkers/

busing/MLA.HTM.

Cowan, N., Saults, J. S., Elliott, E. M., & Moreno, M. V.

(2002). Deconfounding serial recall. Journal of Memory and

Language, 46, 153–177.

Cowan, N., Wood, N. L., Wood, P. K., Keller, T., Nugent, L.

D., & Keller, C. V. (1998). Two separate verbal processing

rates contributing to short-term memory span. Journal of

Experimental Psychology: Learning, Memory, and Cogni-

tion, 127, 141–160.

Dosher, B. A. (1999). Item interference and time delays in

working memory: Immediate serial recall. International

Journal of Psychology, 34, 276–284.

Dosher, B. A., & Ma, J.-J. (1998). Output loss or rehearsal

loop. Output-time versus pronunciation-time limits in

immediate recall for forgetting-matched materials. Journal

of Experimental Psychology: Learning, Memory, and Cog-

nition, 24, 316–335.

Duncan, M. (1996). Recognition and serial reconstruction with

pre-cuing and post-cuing. Unpublished manuscript, Univer-

sity of Toronto.

Duncan, M., & Lewandowsky, S. (in press). The time course of

response suppression: No evidence for a gradual release

from inhibition. Memory.

Farrell, S. (2001). Similarity-sensitive encoding, redintegration,

and response suppression in serial recall. Unpublished

Doctoral thesis, University of Western Australia, Perth.

Farrell, S., & Lewandowsky, S. (2002). An endogenous

distributed model of ordering in serial recall. Psychonomic

Bulletin & Review, 9, 59–79.

Farrell, S., & Lewandowsky, S. (2003). Dissimilar items benefit

from phonological similarity in serial recall. Journal of


tion, 29, 838–849.

Frankish, C. (1985). Modality-specific grouping effects in short-

term memory. Journal of Memory and Language, 24, 200–

209.

Grossberg, S. (1976). Adaptive pattern classification and

universal recoding. Biological Cybernetics, 23, 121–

134.

Grossberg, S. (1978). A theory of human memory: Self-

organization and performance of sensory-motor codes,

maps, and plans. In R. Rosen & F. Snell (Eds.), Progress

in theoretical biology (Vol. 5, pp. 233–374). New York:

Academic Press.

Haberlandt, K., Thomas, J. G., Lawrence, H., & Krohn, T. (in

press). Transposition asymmetry in immediate serial recall.

Memory.

Healy, A. F. (1974). Separating item from order information in

short-term memory. Journal of Verbal Learning and Verbal

Behavior, 13, 644–655.

Henson, R. N. A. (1996). Short-term memory for serial order.

Unpublished doctoral dissertation, Cambridge University,

Cambridge, UK.

http://www.fsw.leidenuniv.nl/www/w3_ment/medewerkers/busing/MLA.HTM

http://www.fsw.leidenuniv.nl/www/w3_ment/medewerkers/busing/MLA.HTM


Henson, R. N. A. (1998). Short-term memory for serial order:

The start-end model. Cognitive Psychology, 36, 73–

137.

Henson, R. N. A. (1999). Positional information in short-term

memory: Relative or absolute? Memory & Cognition, 27,

915–927.

Henson, R. N. A., & Burgess, N. (1997). Representations of

serial order. In J. A. Bullinaria, D. W. Glasspool, & G.

Houghton (Eds.), Proceedings of the fourth neural compu-

tation and psychology workshop: Connectionist representa-

tions (pp. 283–300). London: Springer.

Henson, R. N. A., Norris, D. G., Page, M. P. A., & Baddeley,

A. D. (1996). Unchained memory: Error patterns rule out

chaining models of immediate serial recall. Quarterly

Journal of Experimental Psychology A, 49, 80–115.

Hitch, G., Burgess, N., Towse, J. N., & Culpin, V. (1996).

Temporal grouping effects in immediate recall: A working

memory analysis. The Quarterly Journal of Experimental

Psychology A, 49, 116–139.

Houghton, G. (1990). The problem of serial order: A neural

network model of sequence learning and recall. In R. Dale,

C. Mellish, & M. Zock (Eds.), Current research in natural

language generation (pp. 287–319). London: Academic

Press.

Hulme, C., Newton, P., Cowan, N., Stuart, G., & Brown, G.

(1999). Think before you speak: Pauses, memory search,

and trace redintegration processes in verbal memory span.

Journal of Experimental Psychology: Learning, Memory, and

Cognition, 25, 447–463.

Lewandowsky, S. (1999). Redintegration and response sup-

pression in serial recall: A dynamic network model. Inter-

national Journal of Psychology, 34, 434–446.

Lewandowsky, S., & Farrell, S. (2000). A redintegration

account of the effects of speech rate, lexicality, and word

frequency in immediate serial recall. Psychological Research,

63, 163–173.

Lewandowsky, S., & Murdock, B. B. (1989). Memory for serial

order. Psychological Review, 96, 25–57.

Li, S.-C., Lewandowsky, S., & DeBrunner, V. E. (1996). Using

parameter sensitivity and interdependence to predict model

scope and falsifiability. Journal of Experimental Psychology:

General, 125, 360–369.

Logan, G. D. (1988). Toward an instance theory of automa-

tization. Psychological Review, 95, 492–527.

Lorch, R. F., & Myers, J. L. (1990). Regression analyses of

repeated measures data in cognitive research. Journal of


tion, 16, 149–157.

Luce, R. D. (1963). Detection and recognition. In R. D. Luce,

R. R. Bush, & E. Galanter (Eds.), Handbook of mathemat-

ical psychology (pp. 103–189). New York: Wiley.

Luce, R. D. (1986). Response times. New York: Oxford

University Press.

Maybery, M. T., Parmentier, F. B. R., & Jones, D. M. (2002).

Grouping of list items reflected in the timing of recall:

Implications for models of serial verbal memory. Journal of

Memory and Language, 47, 360–385.

Nairne, J. S. (1990). A feature model of immediate memory.

Memory & Cognition, 18, 251–269.

Nairne, J. S. (1992). The loss of positional certainty in long-

term memory. Psychological Science, 3, 199–202.

Nairne, J. S. (2002). The myth of the encoding-retrieval match.

Memory, 10, 389–395.

Neath, I. (1999). Modelling the disruptive effects of irrelevant

speech on order information. International Journal of

Psychology, 34, 410–418.

Nelder, J. A., & Mead, R. (1965). A simplex method for

function minimization. Computer Journal, 7, 308–313.

Nosofsky, R. M. (1986). Attention, similarity, and the identi-

fication–categorization relationship. Journal of Experimen-

tal Psychology: General, 115, 39–57.

Nosofsky, R. M., & Palmeri, T. J. (1997). An exemplar-based

random walk model of speeded classification. Psychological

Review, 104, 266–300.

Oberauer, K. (2003). Understanding serial position curves in

short-term recognition and recall. Journal of Memory and

Language, 49, 469–483.

Page, M. P. A., & Norris, D. (1998). The primacy model: A new

model of immediate serial recall. Psychological Review, 105,

761–781.

Ratcliff, R. (1978). A theory of memory retrieval. Psychological

Review, 85, 59–108.

Ryan, J. (1969). Grouping and short-term memory: Different

means and patterns of grouping. Quarterly Journal of

Experimental Psychology, 21, 137–147.

Schweickert, R. (1993). A multinomial processing tree model

for degradation and redintegration in immediate recall.

Memory & Cognition, 21, 168–175.

Shepard, R. N. (1957). Stimulus and response generalization: A

stochastic model relating generalization to psychological

space. Psychometrika, 22, 325–345.

Surprenant, A. M., Kelley, M. R., Farley, L. A., & Neath, I. (in

press). Fill-in and infill errors in order memory. Memory.

Thomas, J. G., Milner, H. R., & Haberlandt, K. F. (2003).

Forward and backward recall: Different response time

patterns, same retrieval order. Psychological Science, 14,

169–174.

Usher, M., & McClelland, J. L. (2001). On the time course of

perceptual choice: The leaky competing accumulator model.


Vousden, J. I., & Brown, G. D. A. (1998). To repeat or not to

repeat: The time course of response suppression in sequen-

tial behaviour. In J. A. Bullinaria, D. W. Glasspool, & G.

Houghton (Eds.), Proceedings of the fourth neural compu-

tation and psychology workshop: Connectionist representa-

tions (pp. 301–315). London: Springer-Verlag.

Modelling transposition latencies: Constraints for theories of serial order memory

Documents

Transcript of Modelling transposition latencies: Constraints for theories of serial order memory