Variability In Drift Rate Research Articles

Reexamining the effects of speed-accuracy instructions with a diffusion-model-based analysis.

There has been considerable interest in what components of decision-making change when speed or accuracy is stressed. In many early studies, quite strict assumptions were made about parameter invariance across experimental conditions (sometimes called selective influence). Here we fit the standard diffusion model to the data from four large experiments with speed-accuracy instructions (with over a million total responses), allowing all model parameters to vary freely between the speed and accuracy conditions. Results show that most of the observed differences between speed and accuracy conditions appear in the boundary separation parameter, followed by nondecision time, with small effects on drift rates. However, changes in drift rates are accompanied by changes in across-trial variability in drift rate, which cancels out the effect of drift rate on accuracy and response time. Another analysis in which across-trial variance in drift rate was kept the same in fits to speed and accuracy conditions produced no difference in drift rates. Generally, if speed is stressed moderately, then both boundary separation and nondecision time are reduced and any changes in drift rate are compensated for by changes in the across-trial variance in drift rates. If speed is stressed to a high degree (Starns et al., 2012), boundary separation, nondecision time, and drift rates are reduced. This is because (we hypothesize) encoding is restricted leading to a lower degree of perceptual information or match with memory. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Can we dissociate hypervigilance to social threats from altered perceptual decision-making processes in lonely individuals? An exploration with Drift Diffusion Modeling and event-related potentials.

It has been hypothesized that lonely individuals demonstrate hypervigilance toward social threats. However, recent studies have raised doubts about the reliability of tasks commonly used to measure attentional biases toward threats. Two alternative approaches have been suggested to overcome the limitations of traditional analysis of attentional bias. First, the neurophysiological indicators of orienting to threats were shown to have superior psychometric characteristics compared to overt measures of behavioral performance. The second approach involves utilizing computational modeling to isolate latent components corresponding to specific cognitive mechanisms from observable data. To test the usefulness of these approaches in loneliness research, we analyzed behavioral and electroencephalographic (EEG) data from 26 lonely and 26 non-lonely participants who performed a dot-probe task using a computational modeling approach. We applied the Drift Diffusion Model (DDM) and extracted N2pc-an event-related potential that serves as an indicator of spatial attention. No evidence for social threat hypervigilance has been found in DDM parameters nor in N2pc characteristics in the current study. However, we did observe decreased drift rate and increased variability in drift rate between trials within the lonely group, indicating reduced efficiency in perceptual decision-making among lonely individuals. These effects were not detected using standard behavioral measures used in the dot-probe paradigm. Given that DDM indicators were sensitive to differences in perceptual discrimination between the two groups, even when no overt differences were found in standard behavioral measures, it may be postulated that computational approaches offer a more comprehensive understanding of cognitive processes.

"Reliable organisms from unreliable components" revisited: the linear drift, linear infinitesimal variance model of decision making.

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann's (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann's problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann's problem do not address the main theoretical question that historically motivated research in this area.

An adaptive rejection sampler for sampling from the Wiener diffusion model.

The Wiener diffusion model with two absorbing boundaries is one of the most frequently applied models for jointly modeling responses and response latencies in psychological research. We consider four methods for sampling from the model with and without variability in drift rate, starting point, and non-decision time: Inverse transform sampling, rejection sampling, and two new methods based on adaptive rejection sampling (ARS). We implement these four methods in an R package, validate the methods, and compare their sampling speed in different settings. All four implemented methods provide samples that follow the intended distributions. The ARS-based methods, however, outperform the other methods in sampling speed as the requested sample size increases. We provide guidelines for when using ARS is more efficient than using traditional methods and vice versa.

A randomness perspective on intelligence processes

We study intelligence processes using a diffusion IRT model with random variability in cognitive model parameters: variability in drift rate (the trend of information accumulation toward a correct or incorrect response) and variability in starting point (from where the information accumulation starts). The random variation concerns randomness across person-item pairs and cannot be accounted for by individual and inter-item differences. Interestingly, the models explain the conditional dependencies between response accuracy and response time that are found in previous studies on cognitive ability tests, leading us to the formulation of a randomness perspective on intelligence processes. For an empirical test, we have analyzed verbal analogies data and matrix reasoning data using diffusion IRT models with different variability assumptions. The results indicate that 1) models with random variability fit better than models without, with implications for the conditional dependencies in both types of tasks; 2) for verbal analogies, random variation in drift rate seems to exist, which can be explained by person-by-item word knowledge differences; and 3) for both types of tasks, the starting point variation was also established, in line with the inductive nature of the tasks, requiring a sequential hypothesis testing process. Finally, the correlation of individual differences in drift rate and SAT suggests a meta-strategic choice of respondents to focus on accuracy rather than speed when they have a higher cognitive capacity and when the task is one for which investing in time pays off. This seems primarily the case for matrix reasoning and less so for verbal analogies.

A circular diffusion model of continuous-outcome source memory retrieval: Contrasting continuous and threshold accounts.

A circular analogue of the diffusion model adapted for continuous response tasks is applied to a continuous-outcome source memory task. In contrast to existing models of source retrieval that attribute all of the variability in responding to memory, the circular diffusion model decomposes noise into variability arising from memory and from decision processes. We compared three models: (1) a single diffusion process with trial-to-trial variability in drift rate, (2) a mixture of two diffusion processes, one with positive drift that does not vary from trial-to-trial, and a second zero-drift process that represents discrete guessing, and (3) a hybrid model that mixed positive and zero-drift processes with trial-to-trial variability in the positive drift process. Comparison of model fits to joint response error and response-time (RT) data suggest that a memory strength threshold under which no information is retrieved appears to underlie responding in a continuous-report source memory task. Additionally, we also conditioned participants' source responding on their confidence in an old/new recognition task, ruling out the possibility that participant guessing was only due to unrecognized items. Overall, our findings support an all-or-none or some-or none view of source memory retrieval and pose a challenge to continuous models of source memory.

Modeling across-trial variability in the Wald drift rate parameter

The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated.

Internal and external sources of variability in perceptual decision-making.

It is important to identify sources of variability in processing to understand decision-making in perception and cognition. There is a distinction between internal and external variability in processing, and double-pass experiments have been used to estimate their relative contributions. In these and our experiments, exact perceptual stimuli are repeated later in testing, and agreement on the 2 trials is examined to see if it is greater than chance. In recent research in modeling decision processes, some models implement only (internal) variability in the decision process whereas others explicitly represent multiple sources of variability. We describe 5 perceptual double-pass experiments that show greater than chance agreement, which is inconsistent with models that assume internal variability alone. Estimates of total trial-to-trial variability in the evidence accumulation (drift) rate (the decision-relevant stimulus information) were estimated from fits of the standard diffusion decision-making model to the data. The double-pass procedure provided estimates of how much of this total variability was systematic and dependent on the stimulus. These results provide the first behavioral evidence independent of model fits for trial-to-trial variability in drift rate in tasks used in examining perceptual decision-making. (PsycINFO Database Record

A single trial analysis of EEG in recognition memory: Tracking the neural correlates of memory strength

Recent work in perceptual decision-making has shown that although two distinct neural components differentiate experimental conditions (e.g., did you see a face or a car), only one tracked the evidence guiding the decision process. In the memory literature, there is a distinction between a fronto-central evoked potential measured with EEG beginning at 350ms that seems to track familiarity and a late parietal evoked potential that peaks at 600ms that tracks recollection. Here, we applied single-trial regressor analysis (similar to multivariate pattern analysis, MVPA) and diffusion decision modeling to EEG and behavioral data from two recognition memory experiments to test whether these two components contribute to the recognition decision process. The regressor analysis only involved whether an item was studied or not and did not involve any use of the behavioral data. Only late EEG activity distinguishes studied from not studied items that peaks at about 600ms following each test item onset predicted the diffusion model drift rate derived from the behavioral choice and reaction times (but only for studied items). When drift rate was made a linear function of the trial-level regressor values, the estimate for studied items was different than zero. This showed that the later EEG activity indexed the trial-to-trial variability in drift rate for studied items. Our results provide strong evidence that only a single EEG component reflects evidence being used in the recegnition decision process.

Commentary: When the brain takes a break: a model-based analysis of mind wandering.

Commentary: When the brain takes a break: a model-based analysis of mind wandering.

Drifting from slow to “d'oh!”: Working memory capacity and mind wandering predict extreme reaction times and executive control errors.

A combined experimental, individual-differences, and thought-sampling study tested the predictions of executive attention (e.g., Engle & Kane, 2004) and coordinative binding (e.g., Oberauer, Süβ, Wilhelm, & Sander, 2007) theories of working memory capacity (WMC). We assessed 288 subjects' WMC and their performance and mind-wandering rates during a sustained-attention task; subjects completed either a go/no-go version requiring executive control over habit or a vigilance version that did not. We further combined the data with those from McVay and Kane (2009) to (1) gauge the contributions of WMC and attentional lapses to the worst performance rule and the tail, or τ parameter, of reaction time (RT) distributions; (2) assess which parameters from a quantitative evidence-accumulation RT model were predicted by WMC and mind-wandering reports; and (3) consider intrasubject RT patterns--particularly, speeding--as potential objective markers of mind wandering. We found that WMC predicted action and thought control in only some conditions, that attentional lapses (indicated by task-unrelated-thought reports and drift-rate variability in evidence accumulation) contributed to τ, performance accuracy, and WMC's association with them and that mind-wandering experiences were not predicted by trial-to-trial RT changes, and so they cannot always be inferred from objective performance measures.

Simultaneous multifrequency observations of Jovian S bursts

The millisecond component of the Jovian decameter emission has been studied at high resolution, in order to examine the short‐term behavior of the S‐burst drift rates and to define the drift rate spectrum at high frequencies. By using dynamic spectra having 300‐µs and 3.3‐kHz resolution and covering discrete frequency bands in the range 26–33 MHz, large systematic changes in the magnitude of the S‐burst drift rates are observed to take place on a time scale of seconds to minutes. It is noted that the drift rate variability is of sufficient magnitude to prevent reliable evaluation of the drift rate dependence on frequency, unless simultaneous or near‐simultaneous multifrequency measurements are made. In presenting such observations we fail to observe the predicted drift rate turnover in the spectrum, in spite of measurements made at frequencies within 0.6 to 4.4 MHz of the electron gyrofrequency at the Jovian foot of the Io flux tube. This result is interpreted in terms of an ionospheric electron source, rather than within the conventional theoretical framework of trapped particles initially accelerated at Io. Low‐resolution intensity‐time tracings reveal a characteristic organization of S bursts into groups, each of several seconds duration and consisting of tens to hundreds of bursts. Abrupt changes in mean drift rates from group to group suggest that some of the group structuring may be a source‐related rather than a scintillation‐related phenomenon. Finally, some evidence exists for systematic variations in the group‐to‐group mean drift rates, which may be due to predictiable temporal changes in the magnetic field gradient on the Io flux tube. These temporal changes are due to motion of the Io‐associated magnetic flux tube in the Jovian magnetosphere.