Predicting and Explaining Individual Performance in Complex Tasks

Predicting and Explaining Individual Performance in

Complex Tasks

Marsha Lovett, Lynne Reder, Christian Lebiere, John Rehling, Baris Demiral

This project is sponsored by the Department of the Navy, Office of Naval Research

Multi-Tasking

• A single person can perform multiple tasks.

A single model should be able to capture performance on those multiple tasks.

• A single person brings to bear the same fundamental processing capacities to perform all those tasks.

A single model should be able to predict that person’s performance across tasks from his/her capacities.

A way to keep the multiple-constraint advantage offered by unified theories of cognition while making their development tractable is to do Individual Data Modeling. That is, to gather a large number of empirical/experimental observations on a single subject (or a few subjects analysed individually) using a variety of tasks that exercise multiple abilities (e.g., perception memory, problem solving), and then to use these data to develop a detailed computational model of the subject that is able to learn while performing the tasks.

Gobet & Ritter, 2000

ZERO

PARAMETER

PREDICTIONS!

Basic Goals of Project

• Combine best features of cognitive modeling– Study performance in a dynamic, multi-tasking

situation (albeit less complex than real world)– Explain not only aggregate behavior but variation

(using individual difference variables)– Predict (not fit/postdict) complex performance

• Use cognitive architecture and fixed parameters• Employ off-the-shelf models whenever possible• Plug in individual difference params for each person

How to predict task performance

• Estimate each individual’s processing parameters– Measure individuals’ performance on “standard” tasks – Using models of these tasks, estimate participant’s

corresponding architectural parameters (e.g., working memory capacity, perceptual/motor speed)

• Build/refine model of target task• Select global parameters for model of target task

(e.g., from previously collected data)• Plug into model of target task each individual’s

parameters to predict his/her target task performance

Example: Memory Task Performance

• Fit task A to estimate individuals’ parameters

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

Data

Model

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

Subject 610W = 0.8

Subject 619W = 0.9

Subject 613W = 1.0

Subject 623W = 1.1

Zero-Parameter Predictions

• Plug those parameters into model of task B

0 1 2 3

0.500.550.600.650.700.750.800.850.900.951.00

Memory Load(n-back)

Data

Model

0 1 2 3

0.500.550.600.650.700.750.800.850.900.951.00

Memory Load(n-back)

0 1 2 3

0.500.550.600.650.700.750.800.850.900.951.00

Memory Load(n-back)

0 1 2 3

0.500.550.600.650.700.750.800.850.900.951.00

Memory Load(n-back)

Subject 610W = 0.8

Subject 619W = 0.9

Subject 613W = 1.0

Subject 623W = 1.1

(Lovett, Daily, & Reder, 2000)

Challenges of Complex Tasks

• Modeling the target task is harder

• More than one individual difference variable likely impacting target task

• Possibility of knowledge/strategy differences

What about knowledge differences?

• Develop tasks that reduce their relevance

• Train participants on specific procedures

• Measure skill/knowledge differences in another task and incorporate them in model

• Use model to predict variation in relative use of strategies by way of estimates of individuals’ processing capacities

Individual Differences in ACT-R

• Most ACT-R models don’t account for impact of individual differences on performance, but the potential is there

• There are many parameters with particular interpretations related to individual difference variables

• Most ACT-R modelers set parameters to universal or global values, i.e., defaults or values that fit aggregate data

ACT-R & Individual Differences

M1, M2, M3, …

W1, W2, W3, …

P1, P2, P3, …

Overview of Talk

• Review tasks we are studying

• Illustrate methodology

• Highlight key results– Visual search vs. memory strategies trade off in

final performance => complex task modeling offers best constraint with fine-grained analysis

Modified Digit Span (MODS)

8

f

c

a

j

21st

string

3rdstring

b

i

e

6

recall_ _ _

2ndstring

TIM

E

Modified Digit Span (MODS)

8

f

c

a

j

21st

string

3rdstring

b

i

e

6

recall_ _ _

2ndstring

TIM

E

P/M Tasks

• In our earlier studies, initial training phase of target task was used to collect data on individuals’ perceptual/motor speed.– e.g., Time to find object “A7” and click on it

• In later studies, separate task used to measure perceptual and motor speed.

How to predict task performance

• Estimate each individual’s processing parameters– Measure individuals’ performance on MODS, PercMotor – Using models of these tasks, estimate participant’s

corresponding architectural parameters (e.g., working memory capacity, perceptual/motor speed)

• Build/refine model of target task• Select global parameters for model of target task

(e.g., from previously collected data)• Plug into model of target task each individual’s

parameters to predict his/her target task performance

W affects Performance

• W is the ACT-R parameter for source activation, which impacts the degree to which activation of goal-related facts rises above the sea of other facts’ activations

• Higher W => goal-related facts relatively more activated => faster and more accurately retrieved => better MODS performance

Estimating W• Model of MODS task is fit to individual’s

MODS performance by varying W

• Best fitting value of W is taken as estimate

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

Data

Model

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

3 4 5 6

0.00.10.20.30.40.50.60.70.80.91.0

Memory Set Size

Subject 610W = 0.8

Subject 619W = 0.9

Subject 613W = 1.0

Subject 623W = 1.1

Estimating PM

• For simplicity, we estimated a combined PM parameter directly from each individual’s perceptual/motor task performance.

• This PM parameter was then used to scale the timing of the target task’s perceptual-motor productions.

Joint Distribution of W and P/M

0.40

1.00

1.60

0.40 1.00 1.60

W

Pm

W and P/M are tapping distinct characteristics

ACT-R & Individual Differences

M1, M2, M3, …

W1, W2, W3, …

P1, P2, P3, …

Specifics of our Approach

• Estimate each individual’s processing parameters– Measure individuals’ performance on modified digit span, spatial

span, perceptual/motor speed

– Using models of these tasks, estimate participant’s W, P, M

• Build/refine model of air traffic control task–AMBR

• Select global parameters for AMBR model

• Plug in individuals’ parameters to predict performance across different AMBR scenarios

AMBR: Air Traffic Control Task

• Complex and dynamic task

• Spatial and verbal aspects

• Multi-tasking

• Testbed for cognitive modeling architectures

AMBR TaskAC=aircraft, ATC=air traffice controller

• As ATC, you communicate with AC and other ATC to handle all AC in your airspace

• Six commands with different triggers:• First ACCEPT, then WELCOME incoming AC (these two

separated by short interval)• First TRANSFER, then order a CONTACT message from

outgoing AC (these two separated by short interval)• Decide to OK or REJECT requests for speed increase• When a command is not handled before AC reaches zone

boundary, this is a HOLD (error)

Issuing an AMBR Command

• Text message or radar cues particular action

• Click on Command Button

• Click on Aircraft (in radar screen)

• Click on Air Traffic Controller (if nec’y)

• Click on SEND Button

General Methods

• Empirical Methods– Day 1: Collect MODS and P/M data and train on AMBR

plus AMBR practice– Day 2: Review AMBR instructions, battery of AMBR

scenarios

• Modeling Methods– Use MODS & PM data to estimate W and PM for each

subject– Plug individual W and PM values into AMBR model– Compare individuals’ AMBR performance with model

predictions

Experiments 1 & 2

• AMBR Scenario Design– Experiment 1: alternating 5 easy, 5 hard– Experiment 2: 9 scenarios of varying difficulty

• AMBR Dependent Measures– Total time to handle each command– Number of hold errors

Off-the-shelf ACT-R Model of AMBR

• Scan for something to do: Radar, Left, Right, Bottom text windows

• When an action cue is noticed, determine if it has been handled or not: scan/remember

• If the cue has not been handled, click command, AC, [ATC], SEND

• Resume scanning

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9

Scenario

# Hold Errors

Subject 1Subject 2Subject 3Subject 4LoLo ModelHiHi Model

Model Captures Range of Performance

Model Predictions

• Prediction of whether a subject commits an error in a scenario, based on scenario details and individual’s W & P/M

Subject scenarios with errors

Subject scenarios with no errors

Model scenarios with errors 205 4

Model scenarios with no errors 21 70

Ind’l Diffs’ Impact on Hold Errors

• Hold errors only weakly dependent on W, more strongly on P/M and scenario difficulty

0

5

10

15

20

25

30

35

40

45

50

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

PmW

# Hold Errors

Parameter Value

0

50

100

150

200

250

# aircraft * aircraft speed

Experiment 1Experiment 2

Scenario Difficulty

Scenario

0

2

4

6

8

10

12

14

16

18

Mean # Hold Errors

Experiment 1Experiment 2

Mean Errors by Scenario

Scenario

Be Careful What (DM) you Model

• Error data too coarse to constrain model

• Even total RT/command data insufficient

• Model predicts that scanning strategy plays a large role in performance.

• This is consistent with participant reports who may be doing any combination of visual search or memory retrieval

Observable Behaviors

Subject

T 0.0 Cue: Accept T6?

T 3.6 ACCEPT button

T 5.9 AC “T6”

T 6.7 ATC “EAST”

T 7.7 SEND button

Model

T 0.0 Cue: Accept T6?

T 3.7 ACCEPT button

T 5.7 AC “T6”

T 7.0 ATC “EAST”

T 8.2 SEND button

Stochastic variation on the single-action level is part of subject and model behavior

The Details Are Inside

Model I/OT 0.0 Cue: Accept T6?

T 3.7 ACCEPT button

T 5.7 AC “T6”T 7.0 ATC “EAST”T 8.2 SEND button

Model Trace

T 1.5 Notice cueT 2.5 Subgoal taskT 3.7 Mouse clickT 3.8 Start AC searchT 4.9 Find ACT 5.7 Mouse clickT 7.0 Mouse clickT 8.2 Mouse click

Conclusion thus far…

• Visual search vs. memory strategies trade off in final performance => even when modeling a complex task, coarse dependent measures (accuracy, total RT) hide important details

• Previous AMBR model fit group data well• Only by seeking extra constraint of modeling

individual participants were important gaps in model fidelity revealed

Modifications for Experiment 3

• Use more fine-grained measures: Action RT & Clicks• Modify the ATC task to increase memory demand

– More interesting for our purposes

– More realistic

– Lengthen scenario length so same planes are in play

– Hide AC names until click, then only after delay

• Use model to bracket appropriate difficulty level

Raw Characteristics of Data

Experiment 3

• Action RT 12.1 sec, Holds 3.3 / subject

• Action RT correlates with W (r = -0.314) and Pm (r = 0.485)

• Holds correlates with W (r = -0.444) and Pm (r = 0.508)

Model Modifications

• Search not only can give the answer sought (a specific AC’s location) but an additional rehearsal of that information

• In slack times, possible strategy of studying radar screen to rehearse AC names (called “exploratory clicks”)

Model Predicts Hold Errors

• Predicts errors per subject, r = 0.81

• Hold errors depend more on W (compared to previous version of task) but still mostly dependent on PM and scenario difficulty

• Move to modeling more fine-grained aspects of data…

Model Predicts Number of Clicks

Mean AC Clicks

0

0.5

1

1.5

2

2.5

3

AcceptWelcome Transfer Contact Speed

Command Type

Clicks

Subjects

Model

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Accept Welcome Transfer Contact Speed

Command Type

# AC Clicks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Accept Welcome Transfer Contact Speed

Command Type

# AC Clicks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Accept Welcome Transfer Contact Speed

Command Type

# AC Clicks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Accept Welcome Transfer Contact Speed

Command Type

# AC Clicks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Accept Welcome Transfer Contact Speed

Command Type

# AC Clicks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Accept Welcome Transfer Contact Speed

Command Type

# AC Clicks

W, P/M affect RT click by click

• Set W-P/M parameters in model corresponding to participants (e.g., hi-hi & lo-lo)

• Run model to produce RT predictions click by click (for 2 commands: Accept and Contact)

Hi-Hi Model & Subject

0

2000

4000

6000

8000

10000

12000

14000

Comm AC ATC Send

Click Type

Cumulative RT

data

model

0

2000

4000

6000

8000

10000

12000

14000

Comm AC ATC Send

Click Type

Cumulative RT

data

model

Lo-Lo Model & Subject

W, P/M affect RT click by click

• Set W-P/M parameters in model corresponding to participants

• Run model to produce RT predictions click by click (for 2 commands: Accept and Contact)

0

2000

4000

6000

8000

10000

12000

14000

0 5000 10000 15000 20000

Subject RTs

Model RTs

Conclusion thus far

• Modeling more fine-grained measures required task and model modifications, but this produced individual participant predictions that were very promising.

• Clicking on correct AC the first time ranges from 69% to 96%– Akin to remember vs. scan strategies

– Higher number -> more (accurate) remembering

– This detailed aspect of performance relates to W

Theoretical Interlude:Spatial vs. Verbal WM

• Our working assumption (parsimoniously) posits a single source activation parameter, W

• W modulates the degree to which goal-relevant facts are activated above the sea of unrelated facts

• …regardless of spatial/verbal representation

• This perspective still allows for spatial/verbal distinctions in performance but explains them as a function of differences in spatial/verbal skills etc.

Opportunity to Test in Current Work

• AMBR task has spatial and verbal aspects• Included verbal and spatial working memory tasks

in battery, starting with Experiment 3• Which span task produces W estimates that best

predict individuals’ AMBR performance?• Spatial Span task from Miyake and Shah (1996):

“normal” “normal”“reversed”

Opportunity to Test in Current Work

• Result– Experiments 3 & 4: Spatial Span-based W predicts

AMBR performance better than MODS-based W

• Possible explanations:– Spatial format more relevant for this task?– Spatial Span shows more variability -> more sensitive?– Spatial Span variability taps other sources of variation?

– Are there separate W’s for verbal and spatial WM?

Opportunity to Test in Current Work

• Result– Experiments 3 & 4: Spatial Span-based W predicts

AMBR performance better than MODS-based W

• Possible explanations:– Spatial format more relevant for this task?– Spatial Span shows more variability -> more sensitive?– Spatial Span variability taps other sources of variation?

– Are there separate W’s for verbal and spatial WM?

Spatial Span taps speed as well…• Another study, spawned by this issue, shows

relationship between individuals’ mental rotation speed and Spatial Span

• Pattern of correlations with PM:– MODS: r=.25 Spatial Span: r=.65

• Pattern of correlations with AMBR components:MODS SS PM

SpeedReq-AC -.62 -.55 -.39

Welcome-AC -.20 -.61 -.53

Welcome-Tot -.16 .-56 -.70

Mem+Mouse

Mouse

Mouse

Theoretical Interlude Conclusion

• Studying verbal vs. spatial memory resources in context of AMBR task moves theoretical debate to more realistic arena– This complements work with laboratory tasks

and allows greater potential for generalization of results

Strategic Variation Emerges

• Experiment 4 also revealed several sources of strategic variation, explored further in Experiment 5

• Waiting for AC name: ranges from 42% to 100% – May reflect lack of confidence in memory, utility of

checking one’s memory– Somewhat negatively correlated with W

• Initiating “welcome” and “contact” commands in anticipation of text cue (ranges from 0% to 100%)

• Making exploratory clicks on ACs during slack time (ranges from never to > 5 per scenario)

Experiment 5 Details

• Scenarios designed to have low (6 ACs) vs. high memory load (total 12 ACs)

• Speed requests most common command– Most interesting for model predictions– Least susceptible to snowball effects

• Dependent measures include RTs for individual clicks and strategy use as a function of scenario difficulty and command

EasyScenarios

HardScenarios

Modeling Specific AMBR Components

0

0.2

0.4

0.6

0.8

1

1.2

SPEED REQUEST CONTACT ACCEPT WELCOME Antic

Accuracy of first AC click

Accuracy of first AC click

0

0.2

0.4

0.6

0.8

1

1.2

SPEED REQUEST CONTACT ACCEPT WELCOME Antic

EasyScenarios

HardScenarios

Modeling Specific AMBR Components

RT to Correct AC click

-5000

0

5000

10000

15000

20000

25000

SPEED REQUEST CONTACT ACCEPT WELCOME

RT to Correct AC click

-4000

-2000

0

2000

4000

6000

8000

SPEED REQUEST CONTACT ACCEPT WELCOME

Model Predictions Match Data

• Main effects of scenario difficulty amplified for low W individuals

• Main effects of command type (more/less memory-demanding) amplified for low W

• Wait-for-AC-name strategy varied as a function of command type

• Exploratory clicks strategy varied as a function of scenario difficulty

Summary of Conclusions

• Complex tasks are not a modeling panacaea! Only by seeking extra constraint of modeling individual participants were important gaps in model’s fidelity revealed.

• Studying verbal vs. spatial memory resources in context of AMBR task moves theoretical debate to more realistic arena.

• Variability in performance -- from different use of strategies and/or from differences in processing capacities -- is there for the looking. Studying performance on average offers incomplete understanding.

Features of Our Approach

• Our approach aims to jointly provide– Predictions that are accurate and detailed– At the individual participant level – Generated in real time (or faster)– Based on an interpretable model with variation

in meaningful individual difference parameters– That generalize to variants of the target task

Joint Distribution of W and P/M

W and P/M are tapping distinct characteristics

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Estimated W Value

Estimated PM Value