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, OH 2The Ohio State University, Columbus, OH 3Wright State University, Dayton, OH 4Grand 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? Typical Tasks • 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%)? 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 Architectures Systems Factorial Technology Townsend & Nozawa, 1995) “doublefactorial paradigm” based on Sternberg, 1969, see also Schweickert, 1985, Dzhafarov & Schweickert, 1995) Mental Architectures Systems Factorial Technology Townsend & Nozawa, 1995) “doublefactorial 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 Architectures Dependent 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 Architectures Dependent 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 = Reaction time histograms LH HHHH Conjunctive-rule classification “AND”” HH HH LH 0.008 0.008 0.006 0.006 LH 0.005 0.005 0.006 0.006 Lips-position 0.004 0.004 HH HL HL LH 0.004 0.004 0.003 0.003 Freq Sharks LL 0.002 0.002 0.002 0.002 0.001 0.001 200. 200. Sharks HL 400. 400. 600. 600. HL HL 0.004 0.004 Freq Jets 200. 200. 800. 800. 1000. 1000. 1200. 1200. 1400. 1400. LL L H 400. 400. 600. 600. 800. 800. 1000. 1200. 1400. 1000. 1200. 1400. LL 0.005 0.005 0.004 0.004 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 Eye- separation 200. 200. 200.200. 400.400. 600.600. 800.800. 1000. 1200. 1400. 1000. 1200. 1400. RT(ms) 400. 400. 600. 600. 800. 800. 1000. 1200. 1200. 1400. 1400. 1000. RT(ms) Reaction time Survivor functions 0.4 0.2 - 0.6 0.4 0.2 - LH 0.8 0.6 0.4 0.2 + LL 0.8 0.6 0.4 0.2 = S IC SIC 0.6 HL 0.8 1 P R O B A B IL IT Y HH 0.8 0.4 1 1 P R O B A B IL IT Y 1 P R O B A B IL IT Y P R O B A B IL IT Y How to calculate the survivor interaction contrast (SIC) function 0.2 0 0.2 50 60 70 80 RT ms 90 100 110 SIC(t) = Shh(t) - 50 60 70 80 RT ms 50 90 100 110 Shl(t) - 60 70 80 RT ms 90 100 110 (Slh(t) 50 60 70 80 RT ms - Sll(t)) 90 100 110 0.4 0 10 20 30 40 RT ms 50 60 70 Mental Architectures Dimensions of a processing model Mental Architectures Serial Processing Parallel Processing Coactive - from Johnson, et al. 2010 Mental Architectures Using the salience factorial conditions 0.4 HL 0.2 SIC (t) LH MIC=0 Lips Serial Self-terminating LL Mean RT (ms) A Architecture flow diagram SIC MIC HH 0 Input Eyes Lips -0.2 Decision OR Response -0.4 LL LH 0 MIC=0 0.4 HL 0.2 SIC (t) Serial Exhaustive Eyes H Lips B Mean RT (ms) L HH 20 40 60 RT (ms) RTbins 10ms 80 0 Input -0.2 Eyes Lips Decision AND Response Decision OR Response Decision AND Response -0.4 Mean RT (ms) 80 SIC (t) 0.2 0 Input Eyes Input Lips Input Eyes Input Lips -0.4 LL H 0 MIC<0 0.4 HL 0.2 LH SIC (t) Eyes 20 40 60 RT (ms) RTbins 10ms 80 0 -0.2 HH -0.4 Eyes LL Coactive 40 60 RT (ms) RTbins 10ms -0.2 HH L E HL 20 0.4 0 H MIC>0 HL LH HH 20 40 60 RT (ms) RTbins 10ms 80 0.4 SIC (t) Mean RT (ms) Parallel Exhaustive MIC>0 LH L D 0 Lips Parallel Self-terminating Mean RT (ms) LL H Lips C Eyes Lips L Input 0.2 Input -0.2 -0.4 L Eyes H Eyes 0 0 20 40 60 RT (ms) RTbins 10ms 80 Lips Joe’s face Decision Response Mental Architectures Capacity Coefficient: • Use presence vs absence factorial conditions • Indicates changes in processing resources due to an increase in workload (# items/channels) Single target conditions • Where integrated hazard function and hazard function • Note that Easy to estimate Mental Architectures Capacity Coefficient: • Measured against a baseline model UCIP with selftermination • 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 Controls Task: 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 Single factor reversal (Townsend & Thomas, 1994) + SIC(t) -> inhibitory parallel Mental Architectures Facilitative 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 Sequential sampling models 2 1.5 Option A Evidence State 1 0.5 0 -0.5 -1 Option B -1.5 -2 0 26 Td 100 200 300 Deliberation Time 400 500 Sequential sampling models 2 1.5 Option A Evidence State 1 0.5 0 -0.5 -1 Option B -1.5 -2 0 27 100 Td 200 300 Deliberation Time 400 500 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 Linear Ballistic Accumulator - from Brown & Heathcote, 2008) Models of RT and Accuracy Beyond two-choices: Decision Field Theory of Multialternative 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 • • • • wFac wRep wSAT wAct 0.40 Ratio 0.30 Reputation 0.20 SAT score 0.10 Activities .923 Adams 1.00 .05 1.00 90 .80 800 .63 50 .834 Buchanan .80 .04 .78 70 .90 900 1.00 80 .732 Coolidge .60 .03 .89 80 1.00 1000 .25 20 Attention shifting Evaluation of relative values Preference updating Decision threshold DFT: Illustration P(t) A θ B A C B t C Multialternative choice Y Z X Alternative space Dimension interpretations Binary choices Additional alternatives Choice pair relations {X,Y} vs. {X,Y,Z} Choice phenomena Y Similarity C Attraction (decoy) S DX = Pr (X|X,C) = Pr (Y|Y,C) Pr (X|X,Y,D) > Pr (Y|X,Y,D) Compromise Pr (X|X,Y) = Pr (Y|X,Y) = 0.5 Pr (X|X,Y,S) < Pr (Y|X,Y,S) Pr (C|X,Y,C) > Pr (X|X,Y,C) = Pr (Y|X,Y,C) DFT: Account for phenomena x Pr (X) Pr (Y) + Pr (S) x Pr (X) Pr (Y) + Pr (D) x Pr (X) Pr (Y) + Pr (C) Y C S DX 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

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