The Ornstein-Uhlenbeck model for decision time in cognitive tasks: An example of control of nonlinear network dynamics

The Ornstein-Uhlenbeck (OU) model for human decision-making has been successfully applied to account for response accuracy and response time (RT) data in recent two-choice decision models. A variant of the OU model is shown to arise from the response dynamics of a nonlinear network consisting of randomly connected neural processing units. When feedback control of the network is effected by the stimulus onset, the average network response is an autocorrelated random signal satisfying the stochastic differential equation for the OU process. An alternative, more general, stimulus detection procedure is proposed which involves the use of an adaptive Kalman filter process to track any temporal change in autoregressive parameters. The predicted decision time distributions suggest that both the OU and the Kalman filter processes can serve as alternative models for RT data in experimental tasks. Received: 15 October 1998 / Accepted: 27 May 1999     

Evidence for Mixed Processes in Normal/Mirror Discrimination of Rotated Letters: A Bayesian Model Comparison Between Single- and Mixed-Distribution Models1

When determining whether a rotated letter is normal or mirrored, an observer mentally rotates the letter to its canonical orientation. To account for patterns of response times (RTs) for the normal/mirror discrimination of rotated letters, previous research formulated a model that postulated a mixture of trials with and without mental rotation. While this model could explain the curvilinear relationship that has been found between averaged RT and letter orientations, the curved RT function is still open to alternative explanations without assuming mixed processes. To address this issue and test the mixed-process hypothesis more directly, we analyzed trial-by-trial RT data instead of averaged RTs by employing a Bayesian model comparison technique. If rotation and non-rotation trials are mixed, trial-by-trial RTs for letters in a particular orientation should not follow a single distribution but a mixed one formed from the superposition of two separate distributions, one for rotation and one for non-rotation trials. In the present study, we compared single- and mixed-distribution models. Bayes-factor analysis showed decisive support for the mixed-distribution model over the single-distribution model. In addition, using the widely applicable information criterion (WAIC), the predictive accuracy of the mixed-distribution model was found to be as high as that of the single-distribution model. These results indicated the involvement of mixed processes in normal/mirror discrimination of rotated letters. The usefulness of statistical modeling in psychological study and necessary precautions to take in the interpretation of the parameters of unconfirmed models are also discussed.     

Concurrent guidance of attention by multiple working memory items: Behavioral and computational evidence

During visual search, task-relevant representations in visual working memory (VWM), known as attentional templates, are assumed to guide attention. A current debate concerns whether only one (Single-Item-Template hypothesis; SIT) or multiple (Multiple-Item-Template hypothesis; MIT) items can serve as attentional templates simultaneously. The current study was designed to test these two hypotheses. Participants memorized two colors, prior to a visual-search task in which the target and the distractor could match or not match the colors held in VWM. Robust attentional guidance was observed when one of the memory colors was presented as the target (reduced response times (RTs) on target-match trials) or the distractor (increased RTs on distractor-match trials). We constructed two drift-diffusion models that implemented the MIT and SIT hypotheses, which are similar in their predictions about overall RTs, but differ in their predictions about RTs on individual trials. Critically, simulated RT distributions and error rates revealed a better match of the MIT hypothesis to the observed data than the SIT hypothesis. Taken together, our findings provide behavioral and computational evidence for the concurrent guidance of attention by multiple items in VWM.

     

A random-walk model of accuracy and reaction time applied to three experiments on pigeon visual discrimination

A random-walk model of visual discrimination is described and applied to reaction time (RT) distributions from three discrete-trial experiments with pigeons. Experiment 1 was a two-choice hue discrimination task with multiple hues. Choice percentages changed with hue discriminability; RTs were shortest for the least and most discriminable stimuli. Experiments 2 and 3 used go/no-go hue discriminations. Blocks of sessions differed in reward probability associated with a variable red stimulus in Experiment 2 and with a constant green stimulus in Experiment 3. Changes in hue had a large effect on response percentage and a small effect on RT; changes in reward shifted RT distributions on the time axis. The "random-walk, pigeon" model applied to these data is closely related to Ratcliff's diffusion model (Ratcliff, 1978; Ratcliff & Rouder, 1998). Simulations showed that stimulus discriminability affected the speed with which evidence accumulated toward a response threshold, in line with comparable effects in human subjects. Reward probability affected bias, modeled as the amount of evidence needed to reach one threshold rather than the other. The effects of reward probability are novel, and their isolation from stimulus effects within the decision process can guide development of a broader model of discrimination.     

Choice and response time processes in the identification and categorization of unidimensional stimuli

Lacouture and Marley (1991, 1995, 2001) have successfully modeled the probabilities of correct responses and the mean correct response times (RTs) in unidimensional absolute identification tasks for various stimulus ranges and stimulus/response set sizes, for individual and group data. These fits include those to a set of phenomena often referred to as end-anchor effects. A revised model, with the independent accumulator decision process replaced by a leaky competing accumulator decision process, fits the probabilities of correct responses and the full distributions of RTs in unidimensional absolute identification. The revised model is also applied successfully to a particular class of unidimensional categorization tasks. We discuss possible extensions for handling sequential effects in unidimensional absolute identification, and other extensions of the given class of categorization tasks that are of potential empirical and theoretical importance as a supplement to the study of multidimensional absolute identification tasks.     

Display size effects in visual search: Analyses of reaction time distributions as mixtures

In a reanalysis of data from Cousineau and Shiffrin (2004) and two new visual search experiments, we used a likelihood ratio test to examine the full distributions of reaction time (RT) for evidence that the display size effect is a mixture-type effect that occurs on only a proportion of trials, leaving RT in the remaining trials unaffected, as is predicted by serial self-terminating search models. Experiment 1 was a reanalysis of Cousineau and Shiffrin's data, for which a mixture effect had previously been established by a bimodal distribution of RTs, and the results confirmed that the likelihood ratio test could also detect this mixture. Experiment 2 applied the likelihood ratio test within a more standard visual search task with a relatively easy target/distractor discrimination, and Experiment 3 applied it within a target identification search task within the same types of stimuli. Neither of these experiments provided any evidence for the mixture-type display size effect predicted by serial self-terminating search models. Overall, these results suggest that serial self-terminating search models may generally be applicable only with relatively difficult target/distractor discriminations, and then only for some participants. In addition, they further illustrate the utility of analysing full RT distributions in addition to mean RT.     

The locus of the benefits of repetition-lag memory training

The current study examined the effects of responses on error-adjacent trials (i.e., those immediately preceding or following errors) on age differences in measures of intraindividual variability and the shape of response time (RT) distributions on a two-back task. Removing error-adjacent responses reduced variability as measured by the coefficient of variation, but did so similarly for younger and older adults. However, older adults’ standard deviations (SDs) were less than those of younger adults with comparable RTs, raising questions regarding the validity of the coefficient of variation. An ex-Gaussian analysis revealed that removing the RTs on error-adjacent trials reduced the length of the tails of distributions and the skewness of the distributions. These properties were reduced more for older adults than for younger adults. These results indicate that the influence of error-adjacent trials should be considered when analyzing intraindividual variability and the shape of RT distributions to test theories of cognitive aging.     

A diffusion model decomposition of the practice effect

When people repeatedly perform the same cognitive task, their mean response times (RTs) invariably decrease. The mathematical function that best describes this decrease has been the subject of intense debate. Here, we seek a deeper understanding of the practice effect by simultaneously taking into account the changes in accuracy and in RT distributions with practice, both for correct and error responses. To this end, we used the Ratcliff diffusion model, a successful model of two-choice RTs that decomposes the effect of practice into its constituent psychological processes. Analyses of data from a 10,000-trial lexical decision task demonstrate that practice not only affects the speed of information processing, but also response caution, response bias, and peripheral processing time. We conclude that the practice effect consists of multiple subcomponents, and that it may be hazardous to abstract the interactive combination of these subcomponents in terms of a single output measure such as mean RT for correct responses. Supplemental materials may be downloaded from http://pbr .psychonomic-journals.org/content/supplemental.     

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.     

Effects of priming, discriminability, and reinforcement on reaction-time components of pigeon visual search

Pigeons searched computer screens for 1 of 4 letter targets among 55 alphanumeric distractors. In Experiment 1, valid-cue trials used distinctive patterns to signal the subsequent appearance of specific targets, whereas ambiguous-cue trials used a signal common to all targets. Search reaction times (RTs) after valid cues were shorter than after the ambiguous cue; increased target discriminability also reduced RT. In Experiment 2, when reinforcement for 2 targets shifted from 10% to 20%, RTs to those targets dropped, whereas RTs to the other 2 targets rose. RT distributions suggested that precues and discriminability both affect the momentary probability of finding a target, as embodied in the decay constant of an underlying exponentially distributed RT component. Reinforcement changes appeared to affect different components of the response process, embodied in changes in the mean of an underlying lognormal distribution.     

Making strides in modeling individual differences: reply to Leite, Ratcliff, and White (2007)

Leite, Ratcliff, and White (2007) claimed that the diffusion model (Ratcliff, 1978) could simulate the molar patterns in response times (RTs) from the multiple tasks observed by Chen, Hale, and Myerson (2007). We present our own simulations to clarify the underlying mechanisms and show that, as is predicted by the difference engine model (Myerson, Hale, Zheng, Jenkins, & Widaman, 2003), correlations across tasks are the key to the molar patterns in individual RTs. Although the diffusion model and other sequential-sampling models may be able to accommodate patterns of RTs across tasks like those studied by Chen et al., the difference engine is the only current model that actually predicts them.     

Selective response activation can begin before stimulus recognition is complete: a psychophysiological and error analysis of continuous flow

In discussions of process models of human information processing, the continuous flow conception (Eriksen and Schultz 1979) plays a prominent role. A central prediction of this conception is that any information in a display associated with a response activates that response as soon as it becomes available in the perceptual system. If it concerns the correct response channel, then response facilitation occurs. If it concerns the incorrect response channel, then response competition occurs. To assess these mechanisms more directly, we used psychophysiological measures as well as reaction time (RT). We used the latency of the P3 component of the event related brain potential (ERP) as an index of stimulus evaluation duration, the onset of lateralized motor activity derived from the ERP as an index of selective central motor activation, and the onset of electromyographic activity as an index of the start of peripheral motor activation. Subjects were required to respond to target letters that were either flanked by letters that signalled the opposite response (incompatible arrays), by the target itself (compatible arrays), by letters not associated with a response (neutral arrays), or by no other letters (targets alone). Our results replicated the basic findings obtained in this paradigm. RTs to targets alone did not differ from RTs to compatible arrays. The latter were faster than RTs to neutral arrays, which were faster than RTs to incompatible arrays. P3 latencies were longer on incompatible than on neutral trials, and longer on compatible than on target alone trials. Incorrect central response activation on incompatible trials and correct central response activation on compatible trials, both began earlier than on target alone trials. Peripheral responding on both trial types, however, began later than on target alone trials. More incompatible but less compatible trials than neutral ones exhibited incorrect peripheral response activation. Peripheral response execution was faster and more accurate on compatible than on target alone trials, while it was slower and less accurate on incompatible than on neutral trials. These results indicate, that the flankers activated their associated response channel while display evaluation was still going on, and that response facilitation and competition occurred. After applying criteria proposed by Miller (1988), it was concluded that the set of stimulus recognition processes and the set of response activation processes cannot be regarded as independent stages of processing.     

Familiarity and categorization processes in memory search

A fundamental distinction in tasks of memory search is whether items receive varied mappings (targets and distractors switch roles across trials) or consistent mappings (targets and distractors never switch roles). The type of mapping often produces markedly different performance patterns, but formal memory-based models that account quantitatively for detailed aspects of the results have not yet been developed and evaluated. Experiments were conducted to test a modern exemplar-retrieval model on its ability to account for memory-search performance involving a wide range of memory-set sizes in both varied-mapping (VM) and consistent-mapping (CM) probe-recognition tasks. The model formalized the idea that both familiarity-based and categorization-based processes operate. The model was required to fit detailed response-time (RT) distributions of individual, highly practiced subjects. A key manipulation involved the repetition of negative probes across trials. This manipulation produced a dramatic dissociation: False-alarm rates increased and correct-rejection RTs got longer in VM, but not in CM. The qualitative pattern of results and modeling analyses provided evidence for a strong form of categorization-based processing in CM, in which observers made use of the membership of negative probes in the “new” category to make old–new recognition decisions.     

Dual payoff band control of reaction time

The location of a S’s simple reaction time (RT) distribution can be controlled by differential reinforcement of RTs that fall within specified temporal limits called a payoff band. Both humans and monkeys can gradually shift the location of a single RT distribution over hundreds of milliseconds in accord with changing payoff band requirements. This study establishes that trained human Ss can also accurately shift theft response latencies back and forth between two different RT distributions when the payoff band is changed from trial to trial. On each trial, the color of the warning stimulus indicated which of two payoff bands would be in effect when the S reacted to a light flashed 1,500 msec later. The RT distributions produced under the condition of random trial-to-trial switching between two payoff bands were the same as the low-variability RT distributions produced when only one payoff band was in effect over a long series of trials.     

A diffusion model analysis of the effects of aging in the lexical-decision task

The effects of aging on response time (RT) are examined in 2 lexical-decision 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 80-100-ms 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).     

Analysis of RT distributions in the remember—know paradigm

Do remembering and knowing differ qualitatively (reflecting distinct underlying processes) or quantitatively (reflecting different levels of strength)? Broadly speaking, models of remember—know judgments based on these alternatives have been tested by examining the proportion of remember and know responses that are made across conditions or levels of confidence. Here, we consider reaction time (RT) data. We replicate Dewhurst and Conway’s (1994) observation that old judgments followed by remember responses are faster, on average, than those followed by know decisions, but show that this effect is largely due to differing distributions of remember and know responses across confidence levels. In addition, fits of ex-Gaussian distributions of hit RTs followed by either remember or know judgments yield similar parameter values when confidence level is controlled. Thus, these RT data do not provide strong support for the idea that remembering and knowing depend on different processes.     

The linear transformation model with frailties for the analysis of item response times

The item response times (RTs) collected from computerized testing represent an underutilized source of information about items and examinees. In addition to knowing the examinees’ responses to each item, we can investigate the amount of time examinees spend on each item. In this paper, we propose a semi‐parametric model for RTs, the linear transformation model with a latent speed covariate, which combines the flexibility of non‐parametric modelling and the brevity as well as interpretability of parametric modelling. In this new model, the RTs, after some non‐parametric monotone transformation, become a linear model with latent speed as covariate plus an error term. The distribution of the error term implicitly defines the relationship between the RT and examinees’ latent speeds; whereas the non‐parametric transformation is able to describe various shapes of RT distributions. The linear transformation model represents a rich family of models that includes the Cox proportional hazards model, the Box–Cox normal model, and many other models as special cases. This new model is embedded in a hierarchical framework so that both RTs and responses are modelled simultaneously. A two‐stage estimation method is proposed. In the first stage, the Markov chain Monte Carlo method is employed to estimate the parametric part of the model. In the second stage, an estimating equation method with a recursive algorithm is adopted to estimate the non‐parametric transformation. Applicability of the new model is demonstrated with a simulation study and a real data application. Finally, methods to evaluate the model fit are suggested.     

Stimulus and response prediction in choice reaction time: Free vs. forced reactions

Verbal predictions were combined in a 1:many mapping in order to analyze the contribution of response preparation to both stimulus and response prediction effects in choice reaction time (RT). Using a three-stimulus, two-response task in which two of the stimuli were mapped 1:1 to separate responses (forced-choice) and the third stimulus was mapped to both responses (free-choice), response frequencies and latencies were compared in two experiments. The results indicated that (1) free-choice response selections were not influenced by forced-choice stimulus predictions; (2) free-choice RTs were reduced only when the free-choice stimulus was correctly predicted; (3) free-choice responses were generally consistent with the response predicted, but RT did not depend on response prediction; (4) on forced-choice trials, the RT difference between correct and incorrect predictions was similar for stimulus and response predictions; and (5) under no-prediction conditions, no difference was found between free and forced RTs. A stimulus anticipation component was the only apparent contribution to the stimulus prediction effect, while the response prediction data suggest some prior response selection with no associated decrease in latency     

Using response time modeling to distinguish memory and decision processes in recognition and source tasks

Receiver operating characteristic (ROC) functions are often used to make inferences about memory processes, such as claiming that memory strength is more variable for studied versus nonstudied items. However, decision processes can produce the ROC patterns that are usually attributed to memory, so independent forms of data are needed to support strong conclusions. The present experiments tested ROC-based claims about the variability of memory evidence by modeling response time (RT) data with the diffusion model. To ensure that the model can correctly discriminate equal- and unequal-variance distributions, Experiment 1 used a numerousity discrimination task that had a direct manipulation of evidence variability. Fits of the model produced correct conclusions about evidence variability in all cases. Experiments 2 and 3 explored the effect of repeated learning trials on evidence variability in recognition and source memory tasks, respectively. Fits of the diffusion model supported the same conclusions about variability as the ROC literature. For recognition, evidence variability was higher for targets than for lures, but it did not differ on the basis of the number of learning trials for target items. For source memory, evidence variability was roughly equal for source 1 and source 2 items, and variability increased for items with additional learning attempts. These results demonstrate that RT modeling can help resolve ambiguities regarding the processes that produce different patterns in ROC data. The results strengthen the evidence that memory strength distributions have unequal variability across item types in recognition and source memory tasks.