Modeling Speed-Accuracy Tradeoffs
in Recognition
Darryl W. Schneider
John R. Anderson
Carnegie Mellon University
Modeling Behavioral Data With ACT-R
Mean RT and
Error Rate
Speed-Accuracy
Tradeoff Functions
Correct and Error
RT Distributions
Speed-Accuracy Tradeoffs
People can trade speed for accuracy when
performing a task
Speed-accuracy tradeoff functions can be
measured using the response signal procedure
• Typically involves a choice task (e.g., recognition)
• A stimulus is followed at a variable lag by a signal to
respond immediately (e.g., yes/no response as to
whether the stimulus was studied)
• Examine accuracy as a function of lag
Speed-Accuracy Tradeoff Function
Mean Accuracy (d')
4.5
3.5
Asymptote (λ)
2.5
Rate (β)
1.5
Intercept (δ)
0.5
Chance
-0.5
0
700 1400 2100 2800 3500
Lag + Mean Reaction Time (ms)
Shifted exponential function:
𝑑 ′ 𝑡 = 𝜆 1 − 𝑒 −𝛽(𝑡−𝛿)
How can ACT-R produce a
speed-accuracy tradeoff
function?
ACT-R Model: Long Lag
Stimulus
onset
Stimulus
encoding
Response signal
Memory
retrieval
(wait)
Signal
encoding
Lag
Time available for retrieval
Trial time
Response
Response
execution
ACT-R Model: Short Lag
Stimulus Response signal
onset
Stimulus
Memory
Response
encoding
retrieval
Signal
Guess Response
encoding
execution
Lag
Time available for retrieval
Trial time
Modeling the Speed-Accuracy Tradeoff
Accuracy depends on the probability that
retrieval finishes in the time available
• If retrieval finishes, accuracy is perfect
• If retrieval does not finish, accuracy is lowered
due to guessing
Retrieval time
• Calculated with the standard ACT-R equations
• Activation noise produces a time distribution
Modeling the Speed-Accuracy Tradeoff
Probability that retrieval finishes in time:
1 + 𝑡𝑟𝑒𝑡𝑟𝑖𝑒𝑣𝑒 𝑡𝑎𝑣𝑎𝑖𝑙
Time available:
• External deadline (lag)
• Internal deadline
(failure time)
• Shorter deadline
determines the time
available
1 𝑠
1.0
Probability of Retrieval
𝑝𝑟𝑒𝑡𝑟𝑖𝑒𝑣𝑒 =
1
0.8
0.6
0.4
0.2
s = 0.4
0.0
0
400
800
1200
1600
Time Available For Retrieval (ms)
Modeling Fan Effects on SAT Functions
Fan effect: It takes longer to recognize an item
as its associative fan increases
• Associative fan = number of associations with other
items in memory
ACT-R can already model the fan effect
• As fan increases, associative activation from the
probe to items in memory decreases, resulting in
memory retrieval taking longer
Experiments
Wickelgren & Corbett (1977)
• Word pairs and triples
• Briefly studied
• Fan 1 vs. Fan 2
• Associative recognition:
targets vs. rearranged foils
• Response signal procedure
with 8 lags
•
•
•
•
•
Our Experiment
Person-location pairs
Well-learned
Fan 1 vs. Fan 2
Associative recognition:
targets vs. rearranged foils
Response signal procedure
with 8 lags
Modeling Fan Effects on SAT Functions
Our Experiment
Well-learned materials
4.5
5.5
3.5
4.5
2.5
Fan 1 (Data)
Fan 2 (Data)
Fan 1 (ACT-R)
Fan 2 (ACT-R)
Fan 1 (SEF)
Fan 2 (SEF)
1.5
0.5
-0.5
0
900 1800 2700 3600 4500
Lag + Mean Reaction Time (ms)
Mean Accuracy (d')
Mean Accuracy (d')
Wickelgren & Corbett (1977)
Briefly studied materials
3.5
2.5
Fan 1 (Data)
Fan 2 (Data)
Fan 1 (ACT-R)
Fan 2 (ACT-R)
Fan 1 (SEF)
Fan 2 (SEF)
1.5
0.5
-0.5
0
700 1400 2100 2800 3500
Lag + Mean Reaction Time (ms)
Internal deadline shorter than Internal deadline longer than
external deadline
external deadline
Take-Home Message
ACT-R can model speedaccuracy tradeoffs in
response signal data
Current Directions
Modeling nonmonotonic speed-accuracy
tradeoff functions
• Different types of information are retrieved in
series and inform the guessing process
Modeling reaction time distributions
• Free-response procedure
• Guessing is probabilistic and occurs in parallel
with retrieval
For More Information
Schneider, D. W., & Anderson, J. R. (2012).
Modeling fan effects on the time course of
associative recognition. Cognitive Psychology,
64, 127-160.
Available on the ACT-R website