The time course of perceptual choice: the leaky, competing accumulator model

The time course of perceptual choice is discussed in a model of gradual, leaky, stochastic, and competitive information accumulation in nonlinear decision units. Special cases of the model match a classical diffusion process, but leakage and competition work together to address several challenges to existing diffusion, random walk, and accumulator models. The model accounts for data from choice tasks using both time-controlled (e.g., response signal) and standard reaction time paradigms and its adequacy compares favorably with other approaches. A new paradigm that controls the time of arrival of information supporting different choice alternatives provides further support. The model captures choice behavior regardless of the number of alternatives, accounting for the log-linear relation between reaction time and number of alternatives (Hick's law) and explains a complex pattern of visual and contextual priming in visual word identification.     

A comparison of sequential sampling models for two-choice reaction time

The authors evaluated 4 sequential sampling models for 2-choice decisions--the Wiener diffusion, Ornstein-Uhlenbeck (OU) diffusion, accumulator, and Poisson counter models--by fitting them to the response time (RT) distributions and accuracy data from 3 experiments. Each of the models was augmented with assumptions of variability across trials in the rate of accumulation of evidence from stimuli, the values of response criteria, and the value of base RT across trials. Although there was substantial model mimicry, empirical conditions were identified under which the models make discriminably different predictions. The best accounts of the data were provided by the Wiener diffusion model, the OU model with small-to-moderate decay, and the accumulator model with long-tailed (exponential) distributions of criteria, although the last was unable to produce error RTs shorter than correct RTs. The relationship between these models and 3 recent, neurally inspired models was also examined.     

Early evidence affects later decisions: Why evidence accumulation is required to explain response time data

Models of decision making differ in how they treat early evidence as it recedes in time. Standard models, such as the drift diffusion model, assume that evidence is gradually accumulated until it reaches a boundary and a decision is initiated. One recent model, the urgency gating model, has proposed that decision making does not require the accumulation of evidence at all. Instead, accumulation could be replaced by a simple urgency factor that scales with time. To distinguish between these fundamentally different accounts of decision making, we performed an experiment in which we manipulated the presence, duration, and valence of early evidence. We simulated the associated response time and error rate predictions from the drift diffusion model and the urgency gating model, fitting the models to the empirical data. The drift diffusion model predicted that variations in the evidence presented early in the trial would affect decisions later in that same trial. The urgency gating model predicted that none of these variations would have any effect. The behavioral data showed clear effects of early evidence on the subsequent decisions, in a manner consistent with the drift diffusion model. Our results cannot be explained by the urgency gating model, and they provide support for an evidence accumulation account of perceptual decision making.     

A ballistic model of choice response time

Almost all models of response time (RT) use a stochastic accumulation process. To account for the benchmark RT phenomena, researchers have found it necessary to include between-trial variability in the starting point and/or the rate of accumulation, both in linear (R. Ratcliff & J. N. Rouder, 1998) and nonlinear (M. Usher & J. L. McClelland, 2001) models. The authors show that a ballistic (deterministic within-trial) model using a simplified version of M. Usher and J. L. McClelland's (2001) nonlinear accumulation process with between-trial variability in accumulation rate and starting point is capable of accounting for the benchmark behavioral phenomena. The authors successfully fit their model to R. Ratcliff and J. N. Rouder's (1998) data, which exhibit many of the benchmark phenomena.     

The rank hypothesis and lexical decision: a reply to Adelman and Brown (2008)

J. S. Adelman and G. D. A. Brown (2008) provided an extensive analysis of the form of word frequency and contextual diversity effects on lexical decision time. In this reply, the current authors suggest that their analysis provides a valuable tool for the evaluation of models of lexical access and that the results they report are broadly supportive of the rank hypothesis suggested by W. S. Murray and K. I. Forster (2004)--more supportive, in fact, than the originally reported data. However, Adelman and Brown's conclusion that the results of these analyses can be taken as evidence against rank (and thereby serial models of lexical access) and for instance models is rejected. It is shown that at least one instance model makes the wrong predictions and that Adelman and Brown's conclusions rest on the assumption that lexical decision time presents a pure measure of the time involved in lexical access. Results from eye tracking are reported, which also support a rank account, as do results from analyses that show that a log frequency account is clearly inadequate. Finally, it is demonstrated that, unlike other models, the rank account continues to make accurate predictions regarding the form of both reaction time and error rate effects.     

How to say "no" to a nonword: a leaky competing accumulator model of lexical decision

We describe a leaky competing accumulator (LCA) model of the lexical decision task that can be used as a response/decision module for any computational model of word recognition. The LCA model uses evidence for a word, operationalized as some measure of lexical activity, as input to the YES decision node. Input to the NO decision node is simply a constant value minus evidence for a word. In this way, evidence for a nonword is a function of time from stimulus onset (as in standard deadline models) modulated by lexical activity via the competitive dynamics of the LCA. We propose a simple mechanism for determining the value of this constant online during the first trials of a lexical decision experiment, such that the model can rapidly optimize speed and accuracy in discriminating words from nonwords. Further optimization is achieved via trial-by-trial adjustments in response criteria as a function of task demands and list context. We show that the LCA model can simulate mean response times and response distributions for correct and incorrect YES and NO decisions for a number of benchmark experiments that have been shown to be fatal for deadline models of lexical decision. Finally, using lexical activity calculated by a computational model of word recognition as input to the LCA decision module, we provide the first item-level simulation of both word and nonword responses in a large-scale database.     

Optimal decision making in neural inhibition models

In their influential Psychological Review article, Bogacz, Brown, Moehlis, Holmes, and Cohen (2006) discussed optimal decision making as accomplished by the drift diffusion model (DDM). The authors showed that neural inhibition models, such as the leaky competing accumulator model (LCA) and the feedforward inhibition model (FFI), can mimic the DDM and accomplish optimal decision making. Here we show that these conclusions depend on how the models handle negative activation values and (for the LCA) across-trial variability in response conservativeness. Negative neural activations are undesirable for both neurophysiological and mathematical reasons. However, when negative activations are truncated to 0, the equivalence to the DDM is lost. Simulations show that this concern has practical ramifications: the DDM generally outperforms truncated versions of the LCA and the FFI, and the parameter estimates from the neural models can no longer be mapped onto those of the DDM in a simple fashion. We show that for both models, truncation may be avoided by assuming a baseline activity for each accumulator. This solution allows the LCA to approximate the DDM and the FFI to be identical to the DDM.     

Heuristics versus direct calculation,and age-related differences in multiplication: an evidence accumulation account of plausibility decisions in arithmetic

We offer a new theoretical angle for cognitive arithmetic, which is that evidence accumulation may play a role in problem plausibility decisions. We build upon previous studies that have considered such a hypothesis, and here formally evaluate the paradigm. We develop the finding that performance differences, due to variations in strategy use and aging effects, can indeed be reasonably explained through these accumulation-to-bound cognitive models. Results suggest that these models may be effectively used to learn more about the underlying cognitive processes. In this study, we modelled young (18–24) and older (68–82) adults’ solution times in performing arithmetic verification (e.g. whether 8?×?5?=?41 is true/false). The domain-relevant factors in strategy use (problem-verification heuristics) and aging differences (older/younger adult groups) were analyzed by a response process model of the latency data, that is fit by participant and item. Lower thresholds accounted for the faster response times (RTs) for problems solved with heuristics (arithmetic rule-violation checking strategies), as opposed to problems solved by calculation approaches. A more rapid accumulation accounted for faster RTs on problems in which two arithmetic rules were violated (strategy combination) rather than one. Third, higher thresholds (i.e. preferring to have greater certainty before responding) accounted for older adults’ slower speed. These findings are in support of accumulation models being relevant for more complex cognitive tasks, as well as to account for the age-related differences therein.     

Confidence in masked orientation judgments is informed by both evidence and visibility

How do human observers determine their degree of belief that they are correct in a decision about a visual stimulus—that is, their confidence? According to prominent theories of confidence, the quality of stimulation should be positively related to confidence in correct decisions, and negatively to confidence in incorrect decisions. However, in a backward-masked orientation task with a varying stimulus onset asynchrony (SOA), we observed that confidence in incorrect decisions also increased with stimulus quality. Model fitting to our decision and confidence data revealed that the best explanation for the present data was the new weighted evidence-and-visibility model, according to which confidence is determined by evidence about the orientation as well as by the general visibility of the stimulus. Signal detection models, postdecisional accumulation models, two-channel models, and decision-time-based models were all unable to explain the pattern of confidence as a function of SOA and decision correctness. We suggest that the metacognitive system combines several cues related to the correctness of a decision about a visual stimulus in order to calculate decision confidence.     

The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks

In this article, the authors consider optimal decision making in two-alternative forced-choice (TAFC) tasks. They begin by analyzing 6 models of TAFC decision making and show that all but one can be reduced to the drift diffusion model, implementing the statistically optimal algorithm (most accurate for a given speed or fastest for a given accuracy). They prove further that there is always an optimal trade-off between speed and accuracy that maximizes various reward functions, including reward rate (percentage of correct responses per unit time), as well as several other objective functions, including ones weighted for accuracy. They use these findings to address empirical data and make novel predictions about performance under optimality.     

Acquiring a Novel Coordination Skill without Practicing the Correct Motor Commands

There is evidence that experience of the sensory consequences, in the absence of practice of the required motor commands, is sufficient to learn new bimanual coordination patterns. This was shown through improvements of an incongruent group who practiced a desired 30° phase offset between the limbs while 1 limb was weighted such that the desired phase relation was achieved when synchronous motor commands were sent to the limbs (P. Atchy-Delama, P. G. Zanone, C. E. Peper, & P. J. Beek, 2005). In addition to testing a similar incongruent and congruent group (i.e., no weight), the authors extended this experiment by removing visual feedback during practice and by including an auditory modeling and passive guidance group. All groups showed improvement, except for the modeling group. The passive guidance group made more errors in posttests than the congruent and incongruent groups. Only the congruent group increased the amount of time around 30° after practice. Active experience of the sensory consequences combined with practice sending appropriate motor commands is the most effective method for learning, even though strategic improvements can be attained without experience of the latter.     

Showing that the race model inequality is not violated

When participants are asked to respond in the same way to stimuli from different sources (e.g., auditory and visual), responses are often observed to be substantially faster when both stimuli are presented simultaneously (redundancy gain). Different models account for this effect, the two most important being race models and coactivation models. Redundancy gains consistent with the race model have an upper limit, however, which is given by the well-known race model inequality (Miller, 1982). A number of statistical tests have been proposed for testing the race model inequality in single participants and groups of participants. All of these tests use the race model as the null hypothesis, and rejection of the null hypothesis is considered evidence in favor of coactivation. We introduce a statistical test in which the race model prediction is the alternative hypothesis. This test controls the Type I error if a theory predicts that the race model prediction holds in a given experimental condition.     

Updating situation models

The authors examined how situation models are updated during text comprehension. If comprehenders keep track of the evolving situation, they should update their models such that the most current information, the here and now, is more available than outdated information. Contrary to this updating hypothesis, E. J. O'Brien, M. L. Rizzella, J. E. Albrecht, and J. G. Halleran (1998) obtained results suggesting that outdated or incorrect information may still influence the comprehension process. The authors of the current study demonstrate that the nature of E. J. O'Brien et al.'s materials were the likely cause of this pattern of results. Hence, the current authors constructed materials that circumvent identified confounds and in a reading-time experiment obtained evidence supporting the here-and-now hypothesis.     

Reversing Arrows in Mediation Models Does Not Distinguish Plausible Models

Reversing arrows in the classic tri-variate X-M-Y mediation models as a test to check whether one mediation model is superior to another is inadmissible. Presenting evidence that one tri-variate mediation model yields a significant indirect effect, whereas one with some reversed arrows does not, is not proof or even evidence that one model should be preferred. In fact, the significance of the indirect or any other effect can never be used to infer whether one model should be preferred over another, if the models are in the same so-called equivalence class. The practice of running several mediation models with reversed arrows to decide which model to prefer should be abandoned. The only way to choose among equivalent models is through assumptions that are either fulfilled by design features or invoked based on theory. Similar arguments about reversing arrows in mediation models have been made before, but this current work is the first to derive this result analytically for the complete (Markovian) equivalence class of the tri-variate mediation model.     

The impact of anatomical and spatial distance between responses on response conflict

Different features of objects can be associated with different responses, so that their concurrent presence results in conflict. The Simon effect is a prominent example of this type of response conflict. In two experiments, we ask whether it is modulated by the anatomical or spatial relation between responses. Predictions were derived from an extended variant of the leaky, competing accumulator (LCA) model proposed by Usher and McClelland (Psychological Review, 108, 550–592, 2001). The relation between responses was represented by the lateral-inhibition parameter of the model. For the anatomical distance between responses the expectations were largely confirmed, but not for spatial distance. First, the Simon effect was stronger when responses were performed with two fingers of the same hand than with different hands. Second, the Simon effect was larger only for responses with different hands at short reaction times and disappeared at long ones, whereas for responses with fingers of the same hand, the Simon effect was essentially the same for shorter and longer reaction times. This difference resulted in smaller variability of reaction times in noncorresponding than in corresponding conditions. The dependence of decision processes, as modelled by the LCA model, on the anatomical relation between responses supports the broad hypothesis that the accumulation of evidence on the state of the world is intricately linked with the activation of response codes, that is, the selection of the appropriate actions.     

Acquisition of categorical color perception: a perceptual learning approach to the linguistic relativity hypothesis

Color perception can be categorical: Between-category discriminations are more accurate than equivalent within-category discriminations. The effects could be inherited, learned, or both. The authors provide evidence that supports the possibility of learned categorical perception (CP). Experiment 1 demonstrated that observers' color discrimination is flexible and improves through repeated practice. Experiment 2 demonstrated that category learning simulates effects of "natural" color categories on color discrimination. Experiment 3 investigated the time course of acquired CP. Experiment 4 found that CP effects are acquired through hue- and lightness-based category learning and obtained interesting data on the dimensional perception of color. The data are consistent with the possibility that language may shape color perception and suggest a plausible mechanism for the linguistic relativity hypothesis.     

Receiving instrumental support at work: when help is not welcome

Although the role of social support in promoting employees' health and well-being has been studied extensively, the evidence is inconsistent, sometimes even suggesting that social support might have negative effects. The authors examined some psychological processes that might explain such effects. On the basis of the threat-to-self-esteem model, the authors tested the hypothesis that receiving imposed support elicits negative reactions, which are moderated by someone's need for support. The authors distinguished 3 different reactions: (a) self-related, (b) interaction-related, and (c) physiological. The results of an experiment with 48 temporary administrative workers generally confirmed the hypothesis. Imposed support elicited negative reactions, except when there was an unsolvable problem, but even then the effect of imposed support was not positive but neutral.     

From Poisson shot noise to the integrated Ornstein-Uhlenbeck process: Neurally principled models of information accumulation in decision-making and response time

In the diffusion model of decision-making, evidence is accumulated by a Wiener diffusion process. A neurally motivated account of diffusive evidence accumulation is given, in which diffusive accumulation arises from an interaction between neural integration processes operating on short and long time scales. The short time scale process is modeled as a Poisson shot noise process with exponential decay. Stimulus information is coded by excitatory-inhibitory shot noise pairs. The long time scale process is modeled as algebraic integration, possibly implemented as a first-order autoregressive process realized by recurrent connections within a population of neurons. At high intensities, an excitatory-inhibitory shot noise pair converges weakly to an Ornstein-Uhlenbeck (OU) velocity process. The integrated OU process, or OU displacement process, obtained by integrating the velocity process over time, is indistinguishable at long times from the Wiener process. Diffusive information accumulation may therefore be characterized as an integrated OU process whose properties mimic those of the Wiener process.