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 science
– Macro-process modeling/Mental architectures• Basic SFT paradigm & data variables • Dimensions of a Processing System
– Architectures – Stopping Rules– Capacity – Dependence
• 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
Reaction time histograms
Reaction time Survivor functions
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SIC(t) = Shh(t) - Shl(t) - (Slh(t) - Sll(t))
Mental ArchitecturesDimensions of a processing model
Mental Architectures
Serial Processing
Parallel Processing
Coactive
- from Johnson, et al. 2010
Mental Architectures
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MIC SIC Architecture flowdiagram
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Eyes Lips DecisionAND ResponseInput
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Using the salience factorial conditions
Mental ArchitecturesCapacity Coefficient:
• Use presence vs absence factorial conditions• Indicates changes in processing resources due to an
increase in workload (# items/channels)
• Where
• Note that
Single target conditions
Easy to estimate
hazard functionand
integrated hazard
function
Mental Architectures
Capacity Coefficient:
• Measured against a baseline model UCIP with self-termination
• Unlimited Capacity: No change in resources available for individual items due to increased overall workload
• Independent: Stochastic independence• Parallel: Simultaneous processing of inputs• Self-terminating: stops at first opportunity
• C(t) = 1 unlimited capacity, • C(t) > 1 supercapacity• C(t) < 1 limited capacity
Mental Architectures
Statistical Issues:
Mean interaction contrast (MIC) which can be assessed via standard factorial ANOVA test of interaction
Survivor interaction contrast (Houpt & Townsend, 2010)
Capacity coefficient (Houpt & Townsend, 2012)
Above are Fisherian. Houpt promises Bayesian approaches forthcoming ….
Mental Architectures
Empirical Example: Global – local processing in autism (Johnson, et al., 2010)
Participants: 10 ASD, 11 ControlsTask: indicate if arrow present
Measured response time and accuracy, RT analyses only
All MIC, SIC, and capacity analyses performed on individual participants
In normal visual processing, global precedes and may interfere with local
Mental ArchitecturesSingle factor reversal (Townsend & Thomas, 1994) + SIC(t) ->
inhibitory parallelFacilitative parallel exhaustive
Mental Architectures
Coactive or facilitative parallel
Inhibitory parallel
Mental Architectures
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
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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
DFT Example: College choice
• Attention shifting• Evaluation of relative values• Preference updating• Decision threshold
Ratio Reputation
SAT score Activities
Adams .05 90 800 50Buchana
n.04 70 900 80
Coolidge .03 80 1000 20
wFac wRep wSAT wAct
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Adams 1.00 1.00 .80 .63Buchana
n.80 .78 .90 1.00
Coolidge .60 .89 1.00 .25
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DFT: Illustration
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Multialternative choice Alternative space Dimension interpretations Binary choices Additional alternatives Choice pair relations
{X,Y} vs. {X,Y,Z}
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Choice phenomena Similarity
Pr (X|X,Y,S) <Pr (Y|X,Y,S)
Attraction (decoy) Pr (X|X,Y,D) >
Pr (Y|X,Y,D) Compromise
Pr (C|X,Y,C) >Pr (X|X,Y,C) =Pr (Y|X,Y,C)
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Pr (X|X,Y) = Pr (Y|X,Y) = 0.5
= Pr (X|X,C) = Pr (Y|Y,C)
DFT: Account for phenomena
Pr (X)Pr (Y)Pr (S)
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Combining ApproachesThomas (2006) simulated diffusion models and random walk models of choice (e.g., EBRW) in a factorial task to derive MIC predictions
• characterized optimal responding in random walks and diffusion models in additive factor paradigms
• provided a reinterpretation of previously paradoxical findings regarding the effects of stimulus probability on choice RT
Combining Approaches
Combining Approaches
- Fific, et al., 2010
Combining Approaches- Townsend, et al., 2012, “General recognition theory extended to include response times:
Predictions for a class of parallel systems”, JMP
Neural Evidence
- Smith & Ratcliff (2004)
Neural Evidence
Neural Evidence
- from Purcell, et al. 20120
Summary & Conclusions
• Two major approaches to understanding response times in choice• Axiomatic analysis of mental architecture in factorial
paradigms• Parameter free, class-wide applicability• Accuracy information not generally taken into account
(exception, Schweickert’s work)• Micro-process models of both accuracy and decision
time – sequential sampling• Computationally complex – though some ‘EZ’ versions• Parametric• Some efforts to incorporate macro axiomatic logic into
microprocess models• Neural evidence for information accumulation to a
threshold assumption