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197
The physics of optimal decision making: A formal analysis of models of performance in twoalternative forced choice tasks
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The Diffusion Decision Model: Theory and Data for TwoChoice Decision Tasks
, 2008
"... The diffusion decision model allows detailed explanations of behavior in twochoice discrimination tasks. In this article, the model is reviewed to show how it translates behavioral data—accuracy, mean response times, and response time distributions—into components of cognitive processing. Three exp ..."
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Cited by 203 (25 self)
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The diffusion decision model allows detailed explanations of behavior in twochoice discrimination tasks. In this article, the model is reviewed to show how it translates behavioral data—accuracy, mean response times, and response time distributions—into components of cognitive processing. Three experiments are used to illustrate experimental manipulations of three components: stimulus difficulty affects the quality of information on which a decision is based; instructions emphasizing either speed or accuracy affect the criterial amounts of information that a subject requires before initiating a response; and the relative proportions of the two stimuli affect biases in drift rate and starting point. The experiments also illustrate the strong constraints that ensure the model is empirically testable and potentially falsifiable. The broad range of applications of the model is also reviewed, including research in the domains of aging and neurophysiology.
The effect of stimulus strength on the speed and accuracy of a perceptual decision
 Journal of Vision
, 2005
"... Both the speed and the accuracy of a perceptual judgment depend on the strength of the sensory stimulation. When stimulus strength is high, accuracy is high and response time is fast; when stimulus strength is low, accuracy is low and response time is slow. Although the psychometric function is well ..."
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Cited by 71 (5 self)
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Both the speed and the accuracy of a perceptual judgment depend on the strength of the sensory stimulation. When stimulus strength is high, accuracy is high and response time is fast; when stimulus strength is low, accuracy is low and response time is slow. Although the psychometric function is well established as a tool for analyzing the relationship between accuracy and stimulus strength, the corresponding chronometric function for the relationship between response time and stimulus strength has not received as much consideration. In this article, we describe a theory of perceptual decision making based on a diffusion model. In it, a decision is based on the additive accumulation of sensory evidence over time to a bound. Combined with simple scaling assumptions, the proportionalrate and powerrate diffusion models predict simple analytic expressions for both the chronometric and psychometric functions. In a series of psychophysical experiments, we show that this theory accounts for response time and accuracy as a function of both stimulus strength and speedaccuracy instructions. In particular, the results demonstrate a close coupling between response time and accuracy. The theory is also shown to subsume the predictions of Piéron’s Law, a power function dependence of response time on stimulus strength. The theory’s analytic chronometric function allows one to extend theories of accuracy to response time.
A Ballistic Model of Choice Response Time
"... Almost all models of simple and choice response time (RT) employ a stochastic (i.e., variable within trial) accumulation decision process. In order to account for the relationship between correct and error choice RT, it has been found necessary to also include between trial variability in the st ..."
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Cited by 59 (10 self)
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Almost all models of simple and choice response time (RT) employ a stochastic (i.e., variable within trial) accumulation decision process. In order to account for the relationship between correct and error choice RT, it has been found necessary to also include between trial variability in the starting point and/or the rate of accumulation, both in linear (Ratcliff & Rouder, 1998) and nonlinear (Usher & McClelland, 2001) stochastic models. We show that a ballistic (i.e., deterministic within trial) model using a simplified version of Usher and McClellands nonlinear accumulation process, and assuming only between trial variability in the rate and starting point of accumulation, is not only capable of accounting for the relationship between error and correct RT, but can also model other benchmark behavioural phenomena, such as RT distribution and speedaccuracy trade off. We successfully fit our ballistic model to Ratcliff and Rouders data, which exhibit many of the benchmark phenomena. Even for fast and easy decisions, a simple summation of sensory and motor transduction delays and conduction times in the nervous system cannot account for the duration and variability of reaction times. (Hanes & Schall, 1996, p.427). The slowness and variability of response time (RT) has been almost universally explained by decision processes involving stochastic accumulation of information. Stochastic models assume that the accumulated information varies randomly from moment to moment during the decision process. RT is relatively slow because a criterion amount of information must be accumulated before a response is made, and RT ...
A diffusion model analysis of the effects of aging in the lexicaldecision task
 Psychology and Aging
, 2004
"... The effects of aging on response time (RT) are examined in 2 lexicaldecision experiments with young and older subjects (age 60–75). The results show that the older subjects were slower than the young subjects, but more accurate. R. Ratcliff’s (1978) diffusion model provided a good account of RTs, t ..."
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Cited by 57 (25 self)
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The effects of aging on response time (RT) are examined in 2 lexicaldecision experiments with young and older subjects (age 60–75). The results show that the older subjects were slower than the young subjects, but more accurate. R. Ratcliff’s (1978) diffusion model provided a good account of RTs, their distributions, and response accuracy. The fits show an 80–100ms slowing of the nondecision components of RT for older subjects relative to young subjects and more conservative decision criterion settings for older subjects than for young subjects. The rates of accumulation of evidence were not significantly different for older compared with young subjects (less than 2 % and 5 % higher for older subjects relative to young subjects in the 2 experiments). Across a wide variety of cognitive tasks, research has shown that processing slows with age. For some tasks, especially those like letter discrimination that depend heavily on peripheral processes, this is not surprising (e.g., Thapar, Ratcliff, & McKoon, 2003). However, for other tasks it might be expected that performance would improve with age. One such task is lexical decision, the task of interest in this article. Over a lifetime of 60 to 70 years, the number of encounters with many words must greatly exceed the number of encounters in the first 20 years. Yet despite so many years of practice, lexicaldecision response times (RTs) increase with age. For example, Allen, Madden, and Crozier (1991) found average RTs of 800 ms for older adults compared with 500 ms for young adults. Word frequency effects, longer RTs with lower frequency words, are also larger for older adults (see Allen et al.,
The dynamics of choice among multiple alternatives
 Journal of Mathematical Psychology
, 2006
"... We consider neurallybased models for decisionmaking in the presence of noisy incoming data. The twoalternative forcedchoice task has been extensively studied, and in that case it is known that mutuallyinhibited leaky integrators in which leakage and inhibition balance can closely approximate a ..."
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Cited by 56 (8 self)
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We consider neurallybased models for decisionmaking in the presence of noisy incoming data. The twoalternative forcedchoice task has been extensively studied, and in that case it is known that mutuallyinhibited leaky integrators in which leakage and inhibition balance can closely approximate a driftdiffusion process that is the continuum limit of the optimal sequential probability ratio test (SPRT). Here we study the performance of neural integrators in n ≥ 2 alternative choice tasks and relate them to a multihypothesis sequential probability ratio test (MSPRT) that is asymptotically optimal in the limit of vanishing error rates. While a simple race model can implement this ‘maxvsnext ’ MSPRT, it requires an additional computational layer, while absolute threshold crossing tests do not require such a layer. Race models with absolute thresholds perform relatively poorly, but we show that a balanced leaky accumulator model with an absolute crossing criterion can approximate a ‘maxvsave ’ test that is intermediate in performance between the absolute and maxvsnext tests. We consider free and fixed time response protocols, and show that the resulting mean reaction times under the former and decision times for fixed accuracy under the latter obey versions of Hick’s law in the low error rate range, and we interpret this in terms of information gained. Specifically, we derive relationships of the forms log(n − 1), log(n), or log(n + 1) depending on error rates, signaltonoise ratio, and the test itself. We focus on linearized models, but also consider nonlinear effects of neural activities (firing rates) that are bounded below and show how they modify Hick’s law. KEYWORDS: leaky accumulator, driftdiffusion model, neural network, Hick’s law, multihypothesis sequential test, sequential ratio test.
Quantum dynamics of human decisionmaking
, 2006
"... A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics descri ..."
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Cited by 48 (11 self)
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A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics describe the evolution of complex valued probability amplitudes over time, whereas Markov models describe the evolution of real valued probabilities over time. Quantum dynamics generate interference effects, which are not possible with Markov models. An interference effect occurs when the probability of the union of two possible paths is smaller than each individual path alone. The choice probabilities and distribution of choice response time for the quantum model are derived, and the predictions are contrasted with the Markov model.
A Model of the Go/NoGo Task
"... In this article, the first explicit, theorybased comparison of 2choice and go/nogo variants of 3 experimental tasks is presented. Prior research has questioned whether the underlying coreinformation processing is different for the 2 variants of a task or whether they differ mostly in response de ..."
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Cited by 41 (11 self)
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In this article, the first explicit, theorybased comparison of 2choice and go/nogo variants of 3 experimental tasks is presented. Prior research has questioned whether the underlying coreinformation processing is different for the 2 variants of a task or whether they differ mostly in response demands. The authors examined 4 different diffusion models for the go/nogo variant of each task along with a standard diffusion model for the 2choice variant (R. Ratcliff, 1978). The 2choice and the go/nogo models were fit to data from 4 lexical decision experiments, 1 numerosity discrimination experiment, and 1 recognition memory experiment, each with 2choice and go/nogo variants. The models that assumed an implicit decision criterion for nogo responses produced better fits than models that did not. The best model was one in which only response criteria and the nondecisional components of processing changed between the 2 variants, supporting the view that the core information on which decisions are based is not different between them.
An integrated theory of attention and decision making in visual signal detection
 Psychological Review
, 2009
"... The simplest attentional task, detecting a cued stimulus in an otherwise empty visual field, produces complex patterns of performance. Attentional cues interact with backward masks and with spatial uncertainty, and there is a dissociation in the effects of these variables on accuracy and on response ..."
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Cited by 39 (7 self)
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The simplest attentional task, detecting a cued stimulus in an otherwise empty visual field, produces complex patterns of performance. Attentional cues interact with backward masks and with spatial uncertainty, and there is a dissociation in the effects of these variables on accuracy and on response time. A computational theory of performance in this task is described. The theory links visual encoding, masking, spatial attention, visual shortterm memory (VSTM), and perceptual decision making in an integrated dynamic framework. The theory assumes that decisions are made by a diffusion process driven by a neurally plausible, shunting VSTM. The VSTM trace encodes the transient outputs of early visual filters in a durable form that is preserved for the time needed to make a decision. Attention increases the efficiency of VSTM encoding, either by increasing the rate of trace formation or by reducing the delay before trace formation begins. The theory provides a detailed, quantitative account of attentional effects in spatial cuing tasks at the level of response accuracy and the response time distributions.