Modeling Individual Differences in Working

Memory Capacity

Larry Z. DailyMarsha C. LovettLynne M. Reder

Carnegie Mellon University

This work supported by AFOSR grantF49620-97-1-0455 to Lynne M Reder

Working Memory

• provides the resources needed to retrieve and maintain information during cognitive processing

• as the working memory demands of a task increase, performance on the task decreases– Anderson & Jeffries (1985)– Anderson, Reder, & Lebiere (1996)– Burgess & Hitch (1992)– Salthouse (1992)

Working Memory in ACT-R

• Limit on working memory is a limit on source activation

• This limit affects chunk activation

• Chunk activation affects the likelihood and speed of retrieval

W jwj constant

iA iB jw jisj

Goals

• To continue the work of Lovett, Reder, & Lebiere (in press) and model working memory differences at the level of the individual subject.

• To further that work by showing that we can model subject performance at a fine grain

• To show that estimates of W from one task correlate with performance on a qualitatively different task

The Oakhill Task

• Developed by Oakhill and her colleagues (e.g., Yuill, Oakhill, & Parkin, A., 1989)

• Modified span task– Subjects read all characters– Recall only digits

. . .

. . ....

..

....

..

.

a

f

. . . 8

. . .

. . ....

..

....

..

.

j

d

. . . 5

1st string

2nd string

<remaining strings>

Model

• Chunks– Goals

• articulate• recall

– Memories• memory

• Productions– articulate

• read-aloud• create memory• rehearse-memory

– recall• recall-span• no-recall• read-item• next-item

ArticulateProductions

READ-ALOUDIF the goal is to articulateand char is in visionand char has not been articulatedand char has an external representationTHEN say charand note that char has been articulated

CREATE-MEMORYIF the goal is to articulateand char is the last character of the stringand char has been articulatedTHEN create a memory of char in the current position on the current trialand move to the next position

ArticulateProductions

REHEARSE-MEMORYIF the goal is to articulate on a trial

and the articulation has been doneand there’s a memory of an item in a

positionTHEN rehearse the item

and move to the next position

RecallProductions

RECALL-SPANIF the goal is to recall a position on the current trial

and there’s a memory of an item in that position on this trial

and the item has not been recalledTHEN recall the item

NO-RECALLIF the goal is to recall

and there’s no memory of an item in thecurrent position

THEN recall blank

Experiment 1: Aggregate Results

• Model parameters:– MP = 2.50– RT = 0.88– AN = 0.13– BLL = 0.50

• W fixed at 1.0• R2 = .99

BB

B

B

J

J

J

J

3 4 5 60.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Memory Set Size

B Data

J Model

Experiment 1:Subject Data

B B B BJ J J J

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 100W = 1.5

BB

B

B

JJ

JJ

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 104W = 0.9

B B

B

B

JJ

JJ

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 105W = 1.0

B

B

B

B

J

J

JJ

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 107W = 0.8

Experiment 1:Serial Position

B BB B B BJ J J J

JJ

1 2 3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Serial Position

B Data

J Model

Subject 100W = 1.5

B

B

B

B

B

BJ JJ

JJ

J

1 2 3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Serial Position

B Data

J Model

Subject 104W = 0.9

B B B

B

B BJ J

JJ J

J

1 2 3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Serial Position

B Data

J Model

Subject 105W = 1.0

B B

B B B

B

JJ

JJ J

J

1 2 3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Serial Position

B Data

J Model

Subject 107W = 0.8

Experiment 2:Aggregate Data

B

B

BB

J

J

JJ

3 4 5 60.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Memory Set Size

B Data

J Model

•Zero free parameters •Model parameters:

– MP = 2.50– RT = 0.88– AN = 0.13– BLL = 0.50

•W fixed at 1.0 •R2 = .99

Experiment 2:Subject Data

B

BB B

J

JJ J

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 201W = 0.7

B

BB

B

J

J

JJ

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 211W = 1.0

B

B

BB

J

J

JJ

3 4 5 60.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 216W = 1.2

B

B

B B

J

J

J J3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

B Data

J Model

Subject 241W = 0.8

CAM Sub-test• Pencil & paper adaptation of CAM battery

item (Kyllonen, 1993, 1994, 1995)

• 9 items of varying difficulty

• Scores on original version correlate with performance on a WM dependent task (Reder & Schunn, in press)

• Example item:

W / CAM Correlation

• Estimates of W were strongly correlated with CAM scores› r = .55› r2 = .3025

› n = 29› W varied from 0.6 to 1.6› CAM varied from 3 to 9

Conclusions

• Varying W captures individual differences in performance on a WM task

• Correlation with CAM supports the use of W as a model for WM capacity

• ACT-R can accurately model performance at the individual subject level

(p read-aloud=goal>

isa articulatevision =charstatus nil

=char>isa characterexternal =string

==>!output! (“Saying ~A” =string)=goal>

status done)

(p create-memory=goal>

isa articulatetrial =trialvision =charflag laststatus doneposition =position

==>!output! (Memorizing ~A in position ~A

incremented to ~A” =char =position =next)=memory>

isa memoryitem = chartrial =trialposition =positionrecalled not

=goal>vision nilposition =nextrehearse =position)

(p rehearse-memory=goal>

isa articulatetrial =trialflag laststatus donerehearse =position

=memory>isa memorytrial =trialitem =charposition =positionrecalled not

=position>isa positionprevious =next

==>!output! (“Rehearsing ~A in ~A =char =position)=goal>

rehearse =next)

(p recall-span=goal>

isa recalltrial =trialitem nilposition =position

=memoryisa memoryitem = itemtrial =trialposition =positionrecalled not

==>!output! (“Recalling memory position ~A” =position)!eval! (push-last =item *answers*)=memory>

recalled done=goal>

item =item)