Response Times and Their Use in the Cognitive Science of Choice Robin Thomas 1 , Trish Van Zandt 2 , Joe Houpt 3 , Mario Fific 4 , & Joe Johnson 1 1 Miami University, Oxford, OH 2 The Ohio State University, Columbus, OH 3 Wright State University, Dayton, OH 4 Grand Valley State University, MI
46
Embed
Response Times and Their Use in the Cognitive Science of Choice Robin Thomas 1, Trish Van Zandt 2, Joe Houpt 3, Mario Fific 4, & Joe Johnson 1 1 Miami.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Response Times and Their Use in the Cognitive Science of Choice
Robin Thomas1, Trish Van Zandt2, Joe Houpt3, Mario Fific4, & Joe Johnson1
1Miami University, Oxford, OH2The Ohio State University, Columbus, OH
3Wright State University, Dayton, OH4Grand Valley State University, MI
Typical Tasks
• Consider a signal detection experiment: one of two stimuli is presented, a standard (or noise) and a comparison (or signal) that differ in intensity on some dimension. The observer must determine which of two occurred on each trial.
• A decision maker is given two gambles that differ in value and probability of earnings. Gamble A = 40% chance of winning $10, 60 % chance of losing $5. Gamble B = 60 % chance of winning $6, 40 % chance losing $9. Which does he actually play? How long does it take him to decide?
• A participant studies a list of items at time t0. Later, she is presented with another list of items, some old, some new. Her task is to indicate whether each item is old or new.
• A learner trains on examples to discover which objects belong in one of two categories (e.g., friend or foe, poisonous or safe, malignant or benign). New examples are presented to the learner that need to be classified.
• Which city is farther south, Paris or New York? How confident are you (on a scale from 0 – 100%)?
Typical Tasks
In every case, we measure both the choice and the time required to make it.
Typical summary measures
• Mean response times and variance, choice proportions
,
Typical summary measures
• Mean response times and variance, choice proportions
• RT densities and distributions (and functions of)
,
Histogram estimate of density
Empirical cumulative distribution function
- from Van Zandt, 2000
- Ashby, et al. 1993
Overview• Approaches to using response times in cognitive
• Predictions & Statistical analysis issues • Empirical example worked out (Johnson, et al., 2010)
– Micro-process modeling/models of RT and accuracy• Sequential Sampling Basics
– Random walk– Race models– Diffusion– “Easy versions”
• Beyond simple choices multi-option
• Combining approaches • Neural evidence
Mental ArchitecturesSystems Factorial Technology Townsend & Nozawa, 1995) “double-factorial paradigm” based on Sternberg, 1969, see also Schweickert, 1985, Dzhafarov & Schweickert, 1995)
Mental ArchitecturesSystems Factorial Technology Townsend & Nozawa, 1995) “double-factorial paradigm” based on Sternberg, 1969, see also Schweickert, 1985, Dzhafarov & Schweickert, 1995)
Divided attention task: One stimulus presented on a trial, observer asked “Is there an arrow somewhere in the stimulus” = OR gate
(also can use an ‘and’ gate version of task, H&T 2010, 2012)
- from Johnson, et al. (2010)
Mental ArchitecturesDependent Measure: RT from which interaction contrasts are formed. Accuracy is not analyzed (often high) or separately analyzed (Schweickert, 1985).
Mean Interaction Contrast =
– where Rtij refers to the mean response time in the present conditions in which level of factor A is ‘i’ and the other factor ‘j’
– in the global/local arrow search task, the saliency of local level arrow relative to dash is first factor, saliency of global level arrow relative to dash is second factor
Mental ArchitecturesDependent Measure: RT from which interaction contrasts are formed.
Survivor function = S(t) = P( T > t) = 1 – F(t)
where F(t) is the cumulative distribution function.
Survivor Interaction Contrast =
How to calculate the survivor interaction contrast (SIC) function
Some super and near unlimited capacity Most limited capacity
Models of RT and Accuracy
SFT uses only RT of correct responses – a weakness of the approach
Important information is also included in error responses and the probability of each response especially in classification, memory recognition, decision-making.
Predominant approach – sequential sampling• At each moment in time, evidence is accrued
according to an underlying stochastic mechanism until enough to determine a response, or time-limit has expired
Models of RT and Accuracy
Phenomenon: Speed – accuracy tradeoff
26
Sequential sampling models
0 100 200 300 400 500 -2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Deliberation Time
Evi
de
nce
Sta
te
Option A
Option B
Td
27
Sequential sampling models
0 100 200 300 400 500 -2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Deliberation Time
Evi
de
nce
Sta
te
Option A
Option B
Td
Models of RT and Accuracy
Race (Counter) models (e.g., Merkle & Van Zandt, 2006)
- from Merkle & Van Zandt (2006)
Models of RT and Accuracy
Exemplar-based random walk model of classification learning (Nosofsky & Palmeri, 1997)
- from Thomas (2006)
Models of RT and Accuracy
Ratcliff’s Diffusion Model (1978, 2002)
Drift rate distributions, one for each
stimulus category
Models of RT and Accuracy
“Easy” Versions• Offer closed-form solutions for response time and probability predictions
- from Wagenmakers, et al., 2007)
Models of RT and Accuracy
“Easy” Versions• Offer closed-form solutions for response time and probability predictions
- from Brown & Heathcote, 2008)
Linear Ballistic Accumulator
Models of RT and Accuracy
Beyond two-choices: Decision Field Theory of Multi-alternative Decisions (Busemeyer & Townsend, 1993; Johnson & Busemeyer, 2005, 2008)
- Attention shifts at each moment to a particular dimension of the decision problem
- An evaluation of each choice alternative is based on relative values on the focal dimension
- This evaluation is used to update the preference state from the previous moment
- Preference updating continues until an alternative surpasses a decision threshold