response times and their use in the cognitive science of choice robin thomas 1, trish van zandt 2,...

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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DecisionJ oe’sface

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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 50

Buchanan

.04 70 900 80

Coolidge .03 80 1000 20

wFac wRep wSAT wAct

0.40 0.30 0.20 0.10Ratio Reputatio

nSAT score Activities

Adams 1.00 1.00 .80 .63

Buchanan

.80 .78 .90 1.00

Coolidge .60 .89 1.00 .25

.923

.834

.732

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)

Y

X

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SD

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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Pr (X)Pr (Y)Pr (D)

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Pr (X)Pr (Y)Pr (C)+

x Y

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Combining Approaches

Thomas (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