Diffusion decision model: Current issues and history

“The most extensively evaluated approach to the problem has been the assumption of trial-to-trial variability in model parameters [2,7,9].”

“Concise introductions to this model, which we will refer to as ‘the diffusion model’ in this review, are available elsewhere [7], as are more general comparative studies of the large class of sequential sampling models (Figure 1).”

“Some investigations have supported nonstationarity but have not generated the critical predictions for correct and error RT distributions ([52,87,111–113], see also [45,86,114]).”

“Initial work on preferential choice was carried out using what is called decision field theory (DFT) [201].”

“A pure (Wiener) diffusion process, with no across-trial variability, can be viewed as a continuous-time log-likelihood ratio accumulator, and is optimal in the same sense [72,73].”

“Many studies have assumed that the decision system accumulates the noisy output of a motion discrimination system, in which the noise arises from variability in the stimulus sequence (following [88,99]).”

“Recent research on value-based decision making has used the attention drift diffusion model [205,206].”

“The stimulus-to-signal time varies from trial to trial [47–50], which means that processing can be assumed to be the same for all signal times up to each specific signal time [2].”

“The assumption that model parameters vary from trial to trial is made by most current models that successfully account for experimental data in psychological applications [1,40].”

“The assumption that model parameters vary from trial to trial is made by most current models that successfully account for experimental data in psychological applications [1,40].”

“Studying such tasks was motivated by the Wald SPRT test [89], which provided an optimality theory for decisions about discrete sequences.”

“An opt-out procedure has been used to examine confidence in animals [146,147].”

“, [62–64]).”

“Qualitative links have been made between neural firing rates and diffusion processes [143,144,173].”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“The standard model that we will discuss was developed by Ratcliff in the 1970s [2] and has only changed in assuming a single diffusion process instead of racing processes [3] and in adding across trial variability in starting point [4,5] and nondecision time [6].”

“An opt-out procedure has been used to examine confidence in animals [146,147].”

“Later, a multialternative version of DFT was used to account for the context effects (similarity, attraction, compromise effects) on choice found by consumer researchers [181].”

“Recent research on value-based decision making has used the attention drift diffusion model [205,206].”

“Other studies in animals and humans have found that accuracy does not increase after some stimulus duration [37,106–110], suggesting a time by which the relevant stimulus information has been constructed.”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“The assumption that drift rate varies from trial to trial [2] has been controversial in some circles [44–46], but across-trial variability in drift rate is no different than variability in signal strength in signal detection theory and, ironically, the latter assumption is almost universally accepted.”

“Other studies in animals and humans have found that accuracy does not increase after some stimulus duration [37,106–110], suggesting a time by which the relevant stimulus information has been constructed.”

“For example, one study [52] reported that the sole source of variability in decision making by human and animal subjects was external noise in the stimulus; they found no effect of internal noise, or leakage, that is, decay of the memory representation of the stimulus sequence with the passage of time.”

“In the diffusion model, sequential effects can be modeled by making the starting point and drift rate functions of prior trials [5].”

“The stimuli have included random dots [44], colored lights [92] and patches [93], line segments [94], sinusoidal gratings [95], clicks and visual pulses [52], and geometric shapes [96], with interelement intervals ranging from a few tens of milliseconds to several hundred milliseconds or longer.”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“cases where it is possible to set different boundaries for each difficulty level, human decision makers seem fairly efficient at setting those many boundaries in an optimal manner [74,75].”

“For example, in motion discrimination tasks that use a brief pulse of motion [105], there is a long-lasting effect (up to 800 ms) on decision-related firing rates in the lateral intraparietal cortex.”

“Other studies that have identified support for nonstationary models have mostly employed unusual decision-making tasks, for example, with very long decision times or slowly changing stimulus properties [85,87].”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“Current diffusion models are the culmination of 50 years of theoretical and empirical research [2,8–11], which has identified the key features of experimental data that a model must explain and the key properties by which a model can do so.”

“, [51–53]).”

“Relationships have been established between diffusion model analyses and behavioral measures such as eye tracking [128,137] and pupil dilation [142].”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“Some investigations have supported nonstationarity but have not generated the critical predictions for correct and error RT distributions ([52,87,111–113], see also [45,86,114]).”

“toward the ‘go’ boundary [65,66].”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“Adaptive regulatory mechanisms to account for trial-by-trial effects have been proposed by a number of investigators [34–36].”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“Fitting packages are available (but subject to misuse if not understood): fast-dm [124], DMAT [125], HDDM [126], as well as alternative fitting methods [127].”

“Some recent investigations have suggested that the effects of this manipulation for both humans and monkeys can be accounted for better by a bias in drift rate, not starting point [27].”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“This and other diffusion models have been used to account for, among other things, value-based decision, social choice, and purchasing decisions [150,152,153,157,207–210].”

“This and other diffusion models have been used to account for, among other things, value-based decision, social choice, and purchasing decisions [150,152,153,157,207–210].”

“Only with feedback does performance of young adults approach reward rate optimal [199].”

“Many studies have assumed that the decision system accumulates the noisy output of a motion discrimination system, in which the noise arises from variability in the stimulus sequence (following [88,99]).”

“However, some of the earliest applications of random walk models [8,22] were to expanded judgment tasks in which a noisy sequence of stimulus elements has to be integrated to make a decision.”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“This and other diffusion models have been used to account for, among other things, value-based decision, social choice, and purchasing decisions [150,152,153,157,207–210].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“The stimulus-to-signal time varies from trial to trial [47–50], which means that processing can be assumed to be the same for all signal times up to each specific signal time [2].”

“This and other diffusion models have been used to account for, among other things, value-based decision, social choice, and purchasing decisions [150,152,153,157,207–210].”

“Relationships have been established between diffusion model analyses and behavioral measures such as eye tracking [128,137] and pupil dilation [142].”

“Two diffusion models have been developed, one that assumes dual stages, and one that assumes that evidence driving the process changed continuously over time as a result of attention gradually focusing on the central target [70,71].”

“Other studies in animals and humans have found that accuracy does not increase after some stimulus duration [37,106–110], suggesting a time by which the relevant stimulus information has been constructed.”

“Another source of support for across-trial variability in drift rate comes from a face/car perceptual discrimination task in which EEG signals are used to sort responses into two groups, those that are more face-like and those that are more car-like ([42], see also [43]).”

“Another assumption with much the same effect is that fixed boundaries are maintained, but an ‘urgency signal’ is added to the accumulated evidence [82,83].”

“Two diffusion models have been developed, one that assumes dual stages, and one that assumes that evidence driving the process changed continuously over time as a result of attention gradually focusing on the central target [70,71].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Other studies that have identified support for nonstationary models have mostly employed unusual decision-making tasks, for example, with very long decision times or slowly changing stimulus properties [85,87].”

“Another source of support for across-trial variability in drift rate comes from a face/car perceptual discrimination task in which EEG signals are used to sort responses into two groups, those that are more face-like and those that are more car-like ([42], see also [43]).”

“Other tasks that have more interdisciplinary relationships include stop signal tasks [137,138], conflict tasks [70,71], reinforcement learning [69,139], preferential choice and value-based decisions (Box 7), and social decisions [140,141] (Box 7).”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Other tasks that have more interdisciplinary relationships include stop signal tasks [137,138], conflict tasks [70,71], reinforcement learning [69,139], preferential choice and value-based decisions (Box 7), and social decisions [140,141] (Box 7).”

“Diffusion model analyses have also been applied to bees and animal swarms [158,159] and even to slime molds [160].”

“An alternative definition of optimality is reward rate maximization [76], defined as maximizing the number of correct decisions (and the associated reward) per unit time [72,77–81].”

“Instead, they were better described by a version of the Vickers accumulator model [98], in which only large stimulus elements are accumulated and small ones are ignored.”

“Fitting packages are available (but subject to misuse if not understood): fast-dm [124], DMAT [125], HDDM [126], as well as alternative fitting methods [127].”

“, [4,13–16]) and much smaller changes in nondecision time [17,18], although instructions that extremely stress speed can reduce drift rates ([19], see also [20]).”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“The conflict conditions were modeled with collapsing decision boundaries that accounted for the shifts in RT distributions [69].”

“In application of the diffusion model to response signal data [17,54,55], there are two response boundaries just as for the usual two-choice task.”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“Overall, error responses are slower than correct responses, not the result found elsewhere [14,16,37,102].”

“Diffusion and related model analyses of tasks in which stimulus information varies from moment to moment provide a theoretical account of change detection [67,68] in which evidence accumulation has to be balanced against changes in the stimulus environment.”

“, [51–53]).”

“Recency weighting has been explained by various mechanisms, including a gain control process [95] and a working memory capacity limitation [97].”

“The stimuli have included random dots [44], colored lights [92] and patches [93], line segments [94], sinusoidal gratings [95], clicks and visual pulses [52], and geometric shapes [96], with interelement intervals ranging from a few tens of milliseconds to several hundred milliseconds or longer.”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Integration time, as assessed by a change in accuracy thresholds as a function of stimulus duration, was shown to be the same (around 400 ms) for high and low coherence stimuli [107].”

“Diffusion model analyses have been used to study manipulations of state such as sleep deprivation [161], hypoglycemia [162], and alcohol [163].”

“Overall, error responses are slower than correct responses, not the result found elsewhere [14,16,37,102].”

“This and other diffusion models have been used to account for, among other things, value-based decision, social choice, and purchasing decisions [150,152,153,157,207–210].”

“Diffusion and related model analyses of tasks in which stimulus information varies from moment to moment provide a theoretical account of change detection [67,68] in which evidence accumulation has to be balanced against changes in the stimulus environment.”

“DFT has also been used to account for puzzling reversals in preference between choice and price of gambles [203] and to explain choice and RTs for intertemporal choice [204].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Changes in starting point and drift rates can also explain sequential effects [21,28–33] in which trial-by-trial variations in RT are partly determined by the prior stimulus and the prior response.”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“The standard model that we will discuss was developed by Ratcliff in the 1970s [2] and has only changed in assuming a single diffusion process instead of racing processes [3] and in adding across trial variability in starting point [4,5] and nondecision time [6].”

“There is no simple generalization of the two-choice diffusion model to multiple alternatives [9,180].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Many studies have established relationships between diffusion models and neurophysiological measures such as single cell recordings in rodents and monkeys [52,88,105,143–148], EEG [42,43,149,150], fMRI [42,43,139,151–155], transcranial magnetic stimulation (TMS) [156], and transcranial alternating current stimulation…”

“Fitting packages are available (but subject to misuse if not understood): fast-dm [124], DMAT [125], HDDM [126], as well as alternative fitting methods [127].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Changes in starting point and drift rates can also explain sequential effects [21,28–33] in which trial-by-trial variations in RT are partly determined by the prior stimulus and the prior response.”

“Response signal studies from the 1980s show that drift rate can change from stimulus-to-signal intervals that are about the mean RTs in the usual procedure (600 ms or less) up to intervals of around 2 s [56–59].”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“There has been a recent resurgence of interest in the application of diffusion and random walk models to expanded judgment tasks, especially in neuroscience, motivated in part by a renewed interest in optimality [76,90,91].”

“Note that there are other ways of producing fast or slow errors (relative to correct responses) such as collapsing bounds (discussed later), but few of these have received extensive testing [41].”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“If the forms of across-trial variability distributions are unconstrained, then Jones and Dzhafarov argued that the diffusion model and other evidence accumulation models can exactly match any data (response probabilities and RT distributions), rendering the models unfalsifiable [197].”

“This and other diffusion models have been used to account for, among other things, value-based decision, social choice, and purchasing decisions [150,152,153,157,207–210].”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“Models with collapsing bounds have been identified with urgency gating signals in some recent theoretical accounts of optimal coding in neural populations and in empirical single cell recording studies [41,78,82–85].”

“Overall, error responses are slower than correct responses, not the result found elsewhere [14,16,37,102].”

“Response signal studies from the 1980s show that drift rate can change from stimulus-to-signal intervals that are about the mean RTs in the usual procedure (600 ms or less) up to intervals of around 2 s [56–59].”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“(E,F) Fits to a dataset that has large differences in the leading edge of the RT distribution, changes too large for a diffusion model with only drift rate changing over conditions to fit (from Experiment 1 [38]).”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“In the standard model, drift rate is normally distributed across trials with standard deviation (SD) h, the starting point is uniformly distributed with range sz (starting point variability is equivalent to variability in the boundaries), and nondecision time is uniformly distributed with range st (Ratcliff examined t…”

“The attractor model developed by Wang assumes two pools of excitatory neurons coupled via a third pool of inhibitory neurons [174,175].”

“cases where it is possible to set different boundaries for each difficulty level, human decision makers seem fairly efficient at setting those many boundaries in an optimal manner [74,75].”

“A pure (Wiener) diffusion process, with no across-trial variability, can be viewed as a continuous-time log-likelihood ratio accumulator, and is optimal in the same sense [72,73].”

“These conditions are weighted most heavily in determining some model parameters and then RTs alone are sufficient to determine drift rates [118,119].”

“For difficult relative to easy blocks, subjects slow down when it is reward rate optimal for them to speed up [200].”

“(B) Shows the mean and plus and minus 1 standard deviation ( 1 SD) average paths from simulations (using the random walk method [171]).”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“Diffusion model analyses have been used to study manipulations of state such as sleep deprivation [161], hypoglycemia [162], and alcohol [163].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“These conditions are weighted most heavily in determining some model parameters and then RTs alone are sufficient to determine drift rates [118,119].”

“Other current sequential sampling models usually offer similar explanations of phenomena in terms of the behavior of model components (parameters) [130,131].”

“If the probability that one alternative is tested is made higher than the other, then the starting point moves toward the higher probability boundary (Figure 2D) [5,22–26].”

“Response signal studies from the 1980s show that drift rate can change from stimulus-to-signal intervals that are about the mean RTs in the usual procedure (600 ms or less) up to intervals of around 2 s [56–59].”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“The stimuli have included random dots [44], colored lights [92] and patches [93], line segments [94], sinusoidal gratings [95], clicks and visual pulses [52], and geometric shapes [96], with interelement intervals ranging from a few tens of milliseconds to several hundred milliseconds or longer.”

“Other tasks that have more interdisciplinary relationships include stop signal tasks [137,138], conflict tasks [70,71], reinforcement learning [69,139], preferential choice and value-based decisions (Box 7), and social decisions [140,141] (Box 7).”

“RT distributions from the dynamic noise task were modeled with a diffusion model with a time-varying drift, in which the growth of the drift rate depended on external noise [100].”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“, [61]).”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“Recency weighting has been explained by various mechanisms, including a gain control process [95] and a working memory capacity limitation [97].”

“A large-scale investigation of data from hundreds of participants in ten different studies, from three different laboratories addressed these questions empirically [86].”

“Some investigations have supported nonstationarity but have not generated the critical predictions for correct and error RT distributions ([52,87,111–113], see also [45,86,114]).”

“When they have been analyzed [94], the decision time distributions were much more variable than those found in single stimulus tasks and could not be predicted by a random walk model with normally distributed increments, which is the discrete time counterpart of the diffusion model with no across-trial variability in…”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“The attractor network model, the Ising Decision Model [177], is based on a stochastic Hopfield network.”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“Below are considerations about this argument [198].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“Diffusive noise in a decision process can be derived from a Poisson shot noise model of stimulus representations [178,179].”

“Diffusion and other models have been applied to many basic perceptual and memory tasks such as item and associative recognition [2,15,121,122,132], lexical decision [121,133], perceptual tasks including brightness, letter, motion, visual search, contrast, orientation discrimination tasks [7,14,16,44,103,104,134,135],…”

“There has been a recent resurgence of interest in the application of diffusion and random walk models to expanded judgment tasks, especially in neuroscience, motivated in part by a renewed interest in optimality [76,90,91].”

“Recent studies have examined models for multialternative decision making that use diffusion processes [24,41,72,79,80,181–189] and a number of algorithms have been used: (i) Independent racing accumulators with termination when one reaches its decision criterion.”

“They have been used to study individual differences in IQ, working memory, and reading measures [120–123], and to examine deficits in populations such as aphasics [164], older adults and children [13,14,121,122], children [165], low literacy adults [166], dyslexics [167], attention deficit hyperactivity disorder (ADHD…”

“Another assumption with much the same effect is that fixed boundaries are maintained, but an ‘urgency signal’ is added to the accumulated evidence [82,83].”

“We compare the reliability of raw DVs (response times and accuracies) to parameters of the DDM, a well-established model that addresses speed–accuracy trade-offs and offers interpretable latent variables (34, 35).”

“However, these raw means reflect the combination of many distinct cognitive parameters, such as encoding, evidence accumulation, response thresholds, and response execution times [143].”

“Participants’ choice behavior was consistent with that observed in previous studies and predicted by prevailing models of evidence accumulation (Pisauro et al., 2017; Polania et al., 2014; Ratcliff et al., 2016): participants chose faster (LMM fixed effect: b = -348.”

“Reprinted from Katz et al. (2016). signal quality, time pressure, and the relative probability or reward value of either response (Bogacz et al., 2006; Ratcliff and Rouder, 1998; Ratcliff et al., 2016).”

“We found that the most extreme response 71 times were typically associated with the disengaged states, which is consistent with previous findings 72 linking accuracy and response times [32, 53, 61].”

“Standard analyses of outcome measures may benefit from computational modeling analyses such as drift diffusion modeling [67,85,101].”

“While these findings have illuminated the mechanistic basis of SAT regulation in non-human primates, time-invariance remains a dominant assumption in the human decision-making literature 10 and recent empirical and model comparison reports have reinforced this stance 15,29–31 .”

“The model is a modification of the original drift diffusion model (Ratcliff, 1978; Ratcliff and McKoon, 2008; Ratcliff et al., 2016) so that it can be used for multiple-choice data from cognitive tests.”

“One of the main reasons why collapsing bounds have not been incorporated in the dominant models is because key behavioural consequences of doing so, such as decreased accuracy for trials with longer reaction times, can be also produced within a drift diffusion model with constant bounds, via an alternative mechanism i…”

“In simple, two-choice perceptual decisions, two bounds represent the two alternatives and the relative strength of evidence for the two choices is the accumulated decision variable (Mazurek et al., 2003; Ratcliff et al., 2016).”

“The diffusion model [80] is a popular model for representing cognitive and neural processes underlying simple two-choice decision making (see [81], Box 2 for a comprehensive summary of the domains of its applications).”

“Over the last 40 years, the DDM has become one of the most popular models for explaining RT and accuracy data from a wide range of domains (Forstmann et al., 2016; Ratcliff & McKoon, 2008; Ratcliff et al., 2016).”

“The drift diffusion model (DDM), first described by Ratcliff and colleagues (Ratcliff, 1978; Ratcliff and McKoon, 2008; Ratcliff et al., 2016), is one example of a broader class of models called evidence accumulation models.”

“Perceptual decisions have often been characterized with models that accumulate (noisy) sensory evidence, such as variants of the drift-diffusion model (Krajbich and Rangel, 2011; Brunton et al., 2013; Ratcliff et al., 2016), and there are neural signatures of this accumulation process (Schall, 2003; Gold and Shadlen,…”

“While the majority of decision-making studies consider only two options [due to both theoretical and experimental tractability (14, 26, 27)], animals moving in real space frequently encounter a greater number than this.”

“In static decision models, such as signal detection theory, the quantity or strength of sensory evidence required for a particular decision is determined by the position of a decision criterion and is equivalent to the starting point of evidence accumulation in dynamic models (Ratcliff et al., 2016).”

“…sensitive (or potentially distinct) measure of this can be gleaned from studying how values that we learn to associate with cues spread or “ generalize ” to other similar cues (50,144) and change the way that evidence is accumulated [as modeled by drift diffusion modeling of reaction times (145)].”

“Decisions susceptible to analysis with such models are made rapidly and typically involve just two alternatives (52).”

“decision-making process to date (Ratcliff et al., 2016), which can provide intuitively and neurally plausible explanations for how information processing may operate (Usher & McClelland, 2001).”

“For example, the diffusion decision model (DDM; Ratcliff, 1978; Ratcliff et al., 2016) conceptualizes decision-making in terms of seven model parameters that represent different cognitive processes, such as encoding of the response stimulus and response caution.”

“, drift diffusion, linear ballistic accumulator (Ratcliff et al., 2016).”

“Further we introduced the computational behavioral model – the diffusion drift model, in order to evaluate the signal-to-noise ratio in the memory system and response conservativeness due to the frontoparietal de/synchronization (Ratcliff, 1978; Ratcliff, Smith, Brown, & McKoon, 2016).”

“According to classic accounts, expectation about a motor response should reduce the amount of evidence needed to trigger a decision (i.e., introduce a response bias; Wald and Wolfowitz, 1949; Green and Swets, 1966; Ratcliff, 1978; Voss et al., 2004; Macmillan and Creelman, 2005; Bogacz et al., 2006; Ratcliff et al., 2…”

“In addition, our paper contributes to a large literature in psychology, neuroeconomics, and neuroscience on response times and process models (e.g., Ratcliff and Rouder 1998; Krajbich, Armel, and Rangel 2010; Krajbich and Rangel 2011; Ratcliff et al. 2016).”

“The two-boundary drift-diffusion model is an optimal strategy to balance the speed-accuracy tradeoff, in that it acheives the fastest decisions for a given level of accuracy (or vice versa) [6, 45].”

“Fixing the barrier separation comes without loss of generality since multiplying the barriers, slope (d), and noise by a fixed constant has no effect on the data that the model generates (Ratcliff & McKoon, 2008; Ratcliff et al., 2016).”

“Sequential sampling models have had a very successful history of fitting data in a variety of decision-making experiments (Bogacz et al., 2006; Ratcliff, 1978; Ratcliff & Smith, 2004; Ratcliff et al., 2016; Smith & Vickers, 1989).”

“Algorithmic models incorporating these features have been highly successful in fitting choice behavior across many domains (Forstmann et al., 2016; Ratcliff et al., 2016; Shadlen and Kiani, 2013).”

“Drift diffusion models (DDMs) of perceptual decision making have enjoyed growing prominence in the cognitive sciences (Ratcliff, Smith, Brown, & McKoon, 2016; see Figure 3).”

“These properties of neuronal activity were in line with the model of decision making that assumed a climbing of neuronal activity to a certain threshold (Wittmann, 2013; Ratcliff et al., 2016).”

“One of the most popular classes of models is the drift diffusion model (DDM [115, 119]), which assumes that decisions are made by continuously accumulating the relative evidence for one of two responses (i.”

“their stated preferences during the initial rating task) are then fitted using drift diffusion models [116,117].”

“There are a number of different frameworks, but most share the fundamental concept that information is accumulated (they are sometimes referred to as accumulator models) until a threshold is reached and a decision is made (Ratcliff, Smith, Brown, & McKoon, 2016; Tsetsos et al., 2012).”

“How might these deficits facilitate suicidal behavior? We view the choice between suicide and its alternatives as a temporally unfolding decision process (30,31).”

“…humans and non-human primates, across a range of laboratory paradigms on especially perceptual decision-making (e.g., discrimination of random dot motion direction) and value-based choice (e.g., between different food items) (Brosnan et al., 2020; Busemeyer et al., 2019; Ratcliff et al., 2016).”

“Many perceptual, memory-based, and reward-based decisions depend on an accumulation of evidence over time ( Brody and Hanks, 2016 ; Gold and Shadlen, 2007 ; Ratcliff et al., 2016 ; Shadlen and Shohamy, 2016 ; Summerfield and Tsetsos, 2012 ).”