Modeling Individual Differences in Working Memory Capacity

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Modeling Individual Differences in Working Memory
Capacity

• Larry Z. Daily
• Marsha C. Lovett
• Lynne M. Reder
• Carnegie Mellon University
• This work supported by AFOSR grantF49620-97-1-045
  5 to Lynne M Reder

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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)

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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

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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

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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

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Model

• Chunks
• Goals
• articulate
• recall
• Memories
• memory
• Productions
• articulate
• read-aloud
• create memory
• rehearse-memory
• recall
• recall-span
• no-recall
• read-item
• next-item

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ArticulateProductions

• READ-ALOUD
• IF the goal is to articulate
• and char is in vision
• and char has not been articulated
• and char has an external representation
• THEN say char
• and note that char has been articulated
• CREATE-MEMORY
• IF the goal is to articulate
• and char is the last character of the string
• and char has been articulated
• THEN create a memory of char in the current
  position on the current trial
• and move to the next position

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ArticulateProductions

• REHEARSE-MEMORY
• IF the goal is to articulate on a trial
• and the articulation has been done
• and theres a memory of an item in a position
• THEN rehearse the item
• and move to the next position

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RecallProductions

• RECALL-SPAN
• IF the goal is to recall a position on the
  current trial
• and theres a memory of an item in that
  position on this trial
• and the item has not been recalled
• THEN recall the item
• NO-RECALL
• IF the goal is to recall
• and theres no memory of an item in
  the current position
• THEN recall blank

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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

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Experiment 1Subject Data
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Experiment 1Serial Position
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Experiment 2Aggregate Data

• Zero free parameters
• Model parameters
• MP 2.50
• RT 0.88
• AN 0.13
• BLL 0.50
• W fixed at 1.0
• R2 .99

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Experiment 2Subject Data
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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

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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

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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

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• (p read-aloud
• goalgt
• isa articulate
• vision char
• status nil
• chargt
• isa character
• external string
• gt
• !output! (Saying A string)
• goalgt
• status done)
• (p create-memory
• goalgt
• isa articulate
• trial trial

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• (p rehearse-memory
• goalgt
• isa articulate
• trial trial
• flag last
• status done
• rehearse position
• memorygt
• isa memory
• trial trial
• item char
• position position
• recalled not
• positiongt
• isa position
• previous next
• gt
• !output! (Rehearsing A in A char position)
• goalgt