Cognitive models provide profound insights into the psychological processes underlying behavior. However, a significant limitation has constrained their application: the reliance on extensive, repeated-trial data from each participant. The data-hungry nature of cognitive models has largely precluded their application to infrequent but consequential one-shot decisions common in economic, social, and clinical contexts, and has excluded populations unable to complete lengthy experiments. Here, we address this methodological constraint by proposing a conceptual shift: instead of requiring many trials from a few individuals, we leverage few trials from many individuals. By treating between-subject variability as a source of information, we demonstrate that cognitive models can be successfully fit to one-shot data. Through a series of simulations, we first establish that we can recover known parameter values from single-trial data. We then validate the approach empirically by showing that with only a single trial per participant it can replicate canonical findings; namely, the speed-accuracy trade-off, the influence of food quality and expectations on choice, and the task-specificity of linear vs. non-linear numeric representations. This work overcomes a major limitation to the widespread application of cognitive models, opening new frontiers for understanding the cognitive mechanisms of real-world choices.

Diffusion decision models are widely used to characterize the cognitive and neural processes involved in making rapid decisions about objects and events in the environment. These decisions, which are made hundreds of times a day without prolonged deliberation, include recognition of people and things as well as real-time decisions made while walking or driving. Diffusion models assume that the processes involved in making such decisions are noisy and variable and that noisy evidence is accumulated until there is enough for a decision. This volume provides the first comprehensive treatment of the theory, mathematical foundations, numerical methods, and empirical applications of diffusion process models in psychology and neuroscience. In addition to the standard Wiener diffusion model, readers will find a detailed, unified treatment of the cognitive theory and the neural foundations of a variety of dynamic diffusion process models of two-choice, multiple choice, and continuous outcome decisions.

Rosenholtz argues that summary statistics explain attentional phenomena via peripheral vision. While we acknowledge their role, we challenge the claim that they serve as an alternative mechanism. Instead, we argue that summary statistics and selective attention are interdependent, shaping visual perception under limited capacity, as evidenced by perceptual biases in numerosity judgments and mean estimations of shape size, color, and position.

Two leading models of numerosity judgments describe numerical representations as Gaussian distributions on a mental number line. The linear model posits that both numerosity and variability increase linearly with number, while the logarithmic model assumes logarithmic scaling with constant variability. In this study, we use the selective sampling account, which proposes that information is gathered selectively based on goals and available resources, to explore the cognitive processes underlying variations in variability and scaling. In intermingled displays of blue and yellow dots (B/Y task), participants relied on incomplete representations of dots positioned near the center, where spatial resolution is highest, leading to increasing variability with set size. In contrast, spatially separated displays (L/R task) facilitated more comprehensive sampling, resulting in approximately constant variability across set sizes. Behavioral patterns and modeling analyses suggest that linear and logarithmic scaling capture sensitivity differences shaped by the display format and spatial resolution demands. Eye-tracking data further support our account, emphasizing the role of selective attention in forming numerical representations and providing a unified framework for understanding variability and scaling across tasks.

While decision theories have evolved over the past five decades, their focus has largely been on choices among a limited number of discrete options, even though many real-world situations have a continuous-option space. Recently, theories have attempted to address decisions with continuous-option spaces, and several computational models have been proposed within the sequential sampling framework to explain how we make a decision in continuous-option space. This article aims to review the main attempts to understand decisions on continuous-option spaces, give an overview of applications of these types of decisions, and present puzzles to be addressed by future developments.

We present a model-based analysis of aging effects in three symbolic numeracy tasks using three groups of subjects (young adults, 60- to 69-year-olds, and 70- to 90-year-olds). The tasks are number discrimination (is this number greater or less than 50), number memory (was this number in the list of numbers just displayed), and number line (point to where this number is on this number line). The first two tasks were fit by the standard two-choice diffusion model and the last one by the spatially continuous diffusion model (Ratcliff, 2018). Results showed good fits of the models to accuracy (choices) and response time distributions. In the tasks, nondecision time (the time to encode a stimulus and make a response) increased with age, but the amount of evidence needed for a decision (boundary settings) increased in the number discrimination and number memory tasks, but not the number line task. The number discrimination task produced conflicting accuracy and response time results as a function of age, but the model-based analyses resolved these differences. In the number memory task, drift rates (evidence used to drive the decision process) were lower for the older adults than for young adults, but for the other two (easier) tasks, there was no change in drift rate with age. The analyses extracted differences among individuals in model components, some of which were systematic across tasks. In particular, drift rates were correlated across tasks, which shows consistent individual differences across tasks, results that could not have been obtained without model-based analyses.

When considering whether to purchase consumer products, people consider both the items' attractiveness and their brand labels. Brands may affect the decision process through various mechanisms. For example, brand labels may provide direct support for their paired products, or they may indirectly affect choice outcomes by changing the way that people evaluate and compare their options. To examine these possibilities, we combined computational modeling with an eye-tracking experiment in which subjects made clothing choices with brand labels either present or absent. Subjects' choices were consistent with both the attractiveness of the clothing items and, to a smaller extent, the appeal of the brands. In line with the direct support mechanism, subjects who spent more time looking at the brands were more likely to choose the options with the preferred brands. When a clothing item was more attractive, subjects were more likely to look longer at the associated brand label, but not vice versa. In line with indirect mechanisms, in the presence of brand labels subjects exerted more caution and showed marginally less attentional bias in their choices. This research sheds light on the interplay between gaze and choice in decisions involving brand information, indicating that brands have both direct and indirect influences on choice.

We present results from five visual working memory (VWM) experiments in which participants were briefly shown between 2 and 6 colored squares. They were then cued to recall the color of one of the squares and they responded by choosing the color on a continuous color wheel. The experiments provided response proportions and response time (RT) measures as a function of angle for the choices. Current VWM models for this task include discrete models that assume an item is either within working memory or not and resource models that assume that memory strength varies as a function of the number of items. Because these models do not include processes that allow them to account for RT data, we implemented them within the spatially continuous diffusion model (SCDM, Ratcliff, 2018) and use the experimental data to evaluate these combined models. In the SCDM, evidence retrieved from memory is represented as a spatially continuous normal distribution and this drives the decision process until a criterion (represented as a 1-D line) is reached, which produces a decision. Noise in the accumulation process is represented by continuous Gaussian process noise over spatial position. The models that fit best from the discrete and resource-based classes converged on a common model that had a guessing component and that allowed the height of the normal memory-strength distribution to vary with number of items. The guessing component was implemented as a regular decision process driven by a flat evidence distribution, a zero-drift process. The combination of choice and RT data allows models that were not identifiable based on choice data alone to be discriminated.

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).

It has been proposed that evidence accumulation determines not only the speed and accuracy of simple perceptual decisions but also influences performance on tasks assessing higher-order cognitive abilities, such as working memory (WM). Accordingly, estimates of evidence accumulation based on diffusion decision modeling of perceptual decision-making tasks have been found to correlate with WM performance. Here we use diffusion decision modeling in combination with latent factor modeling to test the stronger prediction that practice-induced changes in evidence accumulation correlate with changes in WM performance. Analyses are based on data from the COGITO Study, in which 101 young adults practiced a battery of cognitive tasks, including three simple two-choice reaction-time tasks and three WM tasks, in 100 day-to-day training sessions distributed over six months. In initial analyses, drift rates were found to correlate across the three choice tasks, such that latent factors of evidence accumulation could be established. These latent factors of evidence accumulation were positively correlated with latent factors of practiced and unpracticed WM tasks, both before and after practice. As predicted, individual differences in changes of evidence accumulation correlated positively with changes in WM performance. Our findings support the proposition that decision making and WM both rely on the active maintenance of task-relevant internal representations.

The mnemonic discrimination task (MDT) is a widely used cognitive assessment tool. Performance in this task is believed to indicate an age-related deficit in episodic memory stemming from a decreased ability to pattern-separate among similar experiences. However, cognitive processes other than memory ability might impact task performance. In this study, we investigated whether nonmnemonic decision-making processes contribute to the age-related deficit in the MDT. We applied a hierarchical Bayesian version of the Ratcliff diffusion model to the MDT performance of 26 younger and 31 cognitively normal older adults. It allowed us to decompose decision behavior in the MDT into different underlying cognitive processes, represented by specific model parameters. Model parameters were compared between groups, and differences were evaluated using the Bayes factor. Our results suggest that the age-related decline in MDT performance indicates a predominantly mnemonic deficit rather than differences in nonmnemonic decision-making processes. In addition, this mnemonic deficit might also involve a slowing in processes related to encoding and retrieval strategies, which are relevant for successful memory as well. These findings help to better understand what cognitive processes contribute to the age-related decline in MDT performance and may help to improve the diagnostic value of this popular task.

This article presents a joint modeling framework of ordinal responses and response times (RTs) for the measurement of latent traits. We integrate cognitive theories of decision-making and confidence judgments with psychometric theories to model individual-level measurement processes. The model development starts with the sequential sampling framework which assumes that when an item is presented, a respondent accumulates noisy evidence over time to respond to the item. Several cognitive and psychometric theories are reviewed and integrated, leading us to three psychometric process models with different representations of the cognitive processes underlying the measurement. We provide simulation studies that examine parameter recovery and show the relationships between latent variables and data distributions. We further test the proposed models with empirical data measuring three traits related to motivation. The results show that all three models provide reasonably good descriptions of observed response proportions and RT distributions. Also, different traits favor different process models, which implies that psychological measurement processes may have heterogeneous structures across traits. Our process of model building and examination illustrates how cognitive theories can be incorporated into psychometric model development to shed light on the measurement process, which has had little attention in traditional psychometric models.

I evaluated three models for the representation of numbers in memory. These were integrated with the diffusion decision model to explain accuracy and response time (RT) data from a recognition memory experiment in which the stimuli were two-digit numbers. The integrated models accounted for distance/confusability effects: when a test number was numerically close to a studied number, accuracy was lower and RTs were longer than when a test number was numerically far from a studied number. For two of the models, the representations of numbers are distributed over number (with Gaussian or exponential distributions) and the overlap between the distributions of a studied number and a test number provides the evidence (drift rate) on which a decision is made. For the third, the exponential gradient model, drift rate is an exponential function of the numerical distance between studied and test numbers. The exponential gradient model fit the data slightly better than the two overlap models. Monte Carlo simulations showed that the variability in the important parameter estimates from fitting data collected over 30-40 min is smaller than the variability among individuals, allowing differences among individuals to be studied. A second experiment compared number memory and number discrimination tasks and results showed different distance effects. Number memory had an exponential-like distance-effect and number discrimination had a linear function which shows radically different representations drive the two tasks.

There has been little impact of cognitive psychology and modeling on neuropsychological testing for over 50 years. There is also a disconnect between those tests and the constructs they are said to measure. We discuss studies at the interface between testing and modeling that illustrate the opportunity for advances.

In everyday driving on the road, people are often required to make fast decisions that could compromise the accuracy of choices. We present a diffusion model analysis of the adjustments drivers make to the decision process under speed-stress. Participants operated a PC-based driving simulator while performing one of two decision-making tasks that required a driving action as a response to the stimulus. In a one-choice driving task, participants were asked to drive around a lead car when its brake lights were turned on. A two-choice driving task used a brightness-discrimination task in which participants were asked to drive to the left and back behind a lead car if there were more black than white pixels in a display and to the right and back if there were more white than black pixels. Speed-stress was operationalized by instructing drivers to respond as quickly as possible and by manipulating the distance drivers were required to maintain behind the lead car. Results showed the expected speed-accuracy tradeoff; however, the cost on accuracy in the two-choice task was relatively small. The model-based analysis showed that this was achieved by lowering the decision criteria and speeding up nondecision processes without disrupting components that produce evidence for the decision process. In fact, in the one-choice task, evidence accumulation rate in the speed-stress condition was found to be higher than in the accuracy-stress condition. We concluded that drivers were able to comply with speed-stress demands with relatively safe adjustments that imposed minimal costs on the accuracy of choices.

In this paper, we propose a model-based method to study conditional dependence between response accuracy and response time (RT) with the diffusion IRT model (Tuerlinckx and De Boeck in Psychometrika 70(4):629–650, 2005, https://doi.org/10.1007/s11336-000-0810-3 ; van der Maas et al. in Psychol Rev 118(2):339–356, 2011, https://doi.org/10.1080/20445911.2011.454498 ). We extend the earlier diffusion IRT model by introducing variability across persons and items in cognitive capacity (drift rate in the evidence accumulation process) and variability in the starting point of the decision processes. We show that the extended model can explain the behavioral patterns of conditional dependency found in the previous studies in psychometrics. Variability in cognitive capacity can predict positive and negative conditional dependency and their interaction with the item difficulty. Variability in starting point can account for the early changes in the response accuracy as a function of RT given the person and item effects. By the combination of the two variability components, the extended model can produce the curvilinear conditional accuracy functions that have been observed in psychometric data. We also provide a simulation study to validate the parameter recovery of the proposed model and present two empirical applications to show how to implement the model to study conditional dependency underlying data response accuracy and RTs.

We present a diffusion model analysis of the effect of aging on decision processes during driving. Our goal was to examine the changes in the underlying components as a function of age and both task and environment difficulty. Younger and older adults performed each of three decision-making tasks while operating a computer-based driving simulator in which the task required a driving action. The first task was a one-choice task in which the response to brake lights turning on was to drive around a lead car. The second and third tasks were two-choice brightness-discrimination tasks in which participants were asked to drive the car to the left/right if there were more black/white pixels in an array of black and white pixels. Results showed that older adults were slower in the one-choice task and made more errors in the two-choice tasks than younger adults. The behavioral data were fitted well by one- and two-choice diffusion models, showing lower evidence accumulation rates (drift rates) in older than younger adults. Moreover, in the two-choice tasks under higher environmental demands, older adults showed a lower decision criterion (boundary separation) to compensate for a slower decision process. Together, the differences we found in the decision components between age groups provided an example of a subtle interaction between speed and accuracy in older versus younger adults, and this demonstrates the utility of this modeling approach in studying age effects in driving. (PsycInfo Database Record (c) 2022 APA, all rights reserved).