Modeling Individual Differences in Working Memory Capacity Larry Z. Daily Marsha C. Lovett Lynne M. Reder Carnegie Mellon University This work supported by AFOSR grant F 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

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

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

Articulate Productions 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

Articulate Productions REHEARSE-MEMORY IF the goal is to articulate on a trial and the articulation has been done and there’s a memory of an item in a position THEN rehearse the item and move to the next position

Recall Productions RECALL-SPAN IF 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 recalled THEN recall the item NO-RECALL IF the goal is to recall and there’s no memory of an item in the current 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 R 2 =.99

Experiment 1: Subject Data

Experiment 1: Serial Position

Experiment 2: Aggregate Data Zero free parameters Model parameters: – MP = 2.50 – RT = 0.88 – AN = 0.13 – BLL = 0.50 W fixed at 1.0 R 2 =.99

Experiment 2: Subject Data

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 ›r 2 =.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 articulate vision =char status nil =char> isa character external =string ==> !output! (“Saying ~A” =string) =goal> status done) (p create-memory =goal> isa articulate trial =trial vision =char flag last status done position =position ==> !output! (Memorizing ~A in position ~A incremented to ~A” =char =position =next) =memory> isa memory item = char trial =trial position =position recalled not =goal> vision nil position =next rehearse =position)

( p rehearse-memory =goal> isa articulate trial =trial flag last status done rehearse =position =memory> isa memory trial =trial item =char position =position recalled not =position> isa position previous =next ==> !output! (“Rehearsing ~A in ~A =char =position) =goal> rehearse =next) (p recall-span =goal> isa recall trial =trial item nil position =position =memory isa memory item = item trial =trial position =position recalled not ==> !output! (“Recalling memory position ~A” =position) !eval! (push-last =item *answers*) =memory> recalled done =goal> item =item)