Sequential sampling models with variable boundaries and non-normal noise: A comparison of six models

The temporal profile of self-prioritization

Personal relevance exerts a powerful influence on decisional processing, such that arbitrary stimuli associated with the self are classified more rapidly than identical material linked with other people. Notwithstanding numerous demonstrations of this facilitatory effect, it remains unclear whether self-prioritization is a temporally stable outcome of decision-making. Accordingly, using a shape-label matching task in combination with computational modeling, the current experiment investigated this matter. The results were informative. First, regardless of the target of comparison (i.e., friend or stranger), self-prioritization was a persistent product of decision-making across the testing session. Second, a variant of the standard drift diffusion model in which decisional boundaries collapsed gradually over the course of the task best fit the observed data. Third, whereas the efficiency of stimulus processing increased for other-related stimuli during the task, it decreased for self-related material. Collectively, these findings advance understanding of the temporal profile of self-prioritization.

Mechanically Induced Motor Tremors Disrupt the Perception of Time

Contemporary research has begun to show a strong relationship between movements and the perception of time. More specifically, concurrent movements serve to both bias and enhance time estimates. To explain these effects, we recently proposed a mechanism by which movements provide a secondary channel for estimating duration that is combined optimally with sensory estimates. However, a critical test of this framework is that by introducing "noise" into movements, sensory estimates of time should similarly become noisier. To accomplish this, we had human participants move a robotic arm while estimating intervals of time in either auditory or visual modalities (n = 24, ea.). Crucially, we introduced an artificial "tremor" in the arm while subjects were moving, that varied across three levels of amplitude (1-3 N) or frequency (4-12 Hz). The results of both experiments revealed that increasing the frequency of the tremor led to noisier estimates of duration. Further, the effect of noise varied with the base precision of the interval, such that a naturally less precise timing (i.e., visual) was more influenced by the tremor than a naturally more precise modality (i.e., auditory). To explain these findings, we fit the data with a recently developed drift-diffusion model of perceptual decision-making, in which the momentary, within-trial variance was allowed to vary across conditions. Here, we found that the model could recapitulate the observed findings, further supporting the theory that movements influence perception directly. Overall, our findings support the proposed framework, and demonstrate the utility of inducing motor noise via artificial tremors.

Lévy Flight Model of Gaze Trajectories to Assist in ADHD Diagnoses

The precise mathematical description of gaze patterns remains a topic of ongoing debate, impacting the practical analysis of eye-tracking data. In this context, we present evidence supporting the appropriateness of a Lévy flight description for eye-gaze trajectories, emphasizing its beneficial scale-invariant properties. Our study focuses on utilizing these properties to aid in diagnosing Attention-Deficit and Hyperactivity Disorder (ADHD) in children, in conjunction with standard cognitive tests. Using this method, we found that the distribution of the characteristic exponent of Lévy flights statistically is different in children with ADHD. Furthermore, we observed that these children deviate from a strategy that is considered optimal for searching processes, in contrast to non-ADHD children. We focused on the case where both eye-tracking data and data from a cognitive test are present and show that the study of gaze patterns in children with ADHD can help in identifying this condition. Since eye-tracking data can be gathered during cognitive tests without needing extra time-consuming specific tasks, we argue that it is in a prime position to provide assistance in the arduous task of diagnosing ADHD.

EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters

The investigation of cognitive processes that form the basis of decision-making in paradigms involving continuous outcomes has gained the interest of modeling researchers who aim to develop a dynamic decision theory that accounts for both speed and accuracy. One of the most important of these continuous models is the circular diffusion model (CDM, Smith. Psychological Review, 123(4), 425. 2016), which posits a noisy accumulation process mathematically described as a stochastic two-dimensional Wiener process inside a disk. Despite the considerable benefits of this model, its mathematical intricacy has limited its utilization among scholars. Here, we propose a straightforward and user-friendly method for estimating the CDM parameters and fitting the model to continuous-scale data using simple formulas that can be readily computed and do not require theoretical knowledge of model fitting or extensive programming. Notwithstanding its simplicity, we demonstrate that the aforementioned method performs with a level of accuracy that is comparable to that of the maximum likelihood estimation method. Furthermore, a robust version of the method is presented, which maintains its simplicity while exhibiting a high degree of resistance to contaminant responses. Additionally, we show that the approach is capable of reliably measuring the key parameters of the CDM, even when these values are subject to across-trial variability. Finally, we demonstrate the practical application of the method on experimental data. Specifically, an illustrative example is presented wherein the method is employed along with estimating the probability of guessing. It is hoped that the straightforward methodology presented here will, on the one hand, help narrow the divide between theoretical constructs and empirical observations on continuous response tasks and, on the other hand, inspire cognitive psychology researchers to shift their laboratory investigations towards continuous response paradigms.

Attribute latencies causally shape intertemporal decisions

Intertemporal choices - decisions that play out over time - pervade our life. Thus, how people make intertemporal choices is a fundamental question. Here, we investigate the role of attribute latency (the time between when people start to process different attributes) in shaping intertemporal preferences using five experiments with choices between smaller-sooner and larger-later rewards. In the first experiment, we identify attribute latencies using mouse-trajectories and find that they predict individual differences in choices, response times, and changes across time constraints. In the other four experiments we test the causal link from attribute latencies to choice, staggering the display of the attributes. This changes attribute latencies and intertemporal preferences. Displaying the amount information first makes people more patient, while displaying time information first does the opposite. These findings highlight the importance of intra-choice dynamics in shaping intertemporal choices and suggest that manipulating attribute latency may be a useful technique for nudging.

Are there jumps in evidence accumulation, and what, if anything, do they reflect psychologically? An analysis of Lévy Flights models of decision-making

According to existing theories of simple decision-making, decisions are initiated by continuously sampling and accumulating perceptual evidence until a threshold value has been reached. Many models, such as the diffusion decision model, assume a noisy accumulation process, described mathematically as a stochastic Wiener process with Gaussian distributed noise. Recently, an alternative account of decision-making has been proposed in the Lévy Flights (LF) model, in which accumulation noise is characterized by a heavy-tailed power-law distribution, controlled by a parameter, [Formula: see text]. The LF model produces sudden large "jumps" in evidence accumulation that are not produced by the standard Wiener diffusion model, which some have argued provide better fits to data. It remains unclear, however, whether jumps in evidence accumulation have any real psychological meaning. Here, we investigate the conjecture by Voss et al. (Psychonomic Bulletin & Review, 26(3), 813-832, 2019) that jumps might reflect sudden shifts in the source of evidence people rely on to make decisions. We reason that if jumps are psychologically real, we should observe systematic reductions in jumps as people become more practiced with a task (i.e., as people converge on a stable decision strategy with experience). We fitted five versions of the LF model to behavioral data from a study by Evans and Brown (Psychonomic Bulletin & Review, 24(2), 597-606, 2017), using a five-layer deep inference neural network for parameter estimation. The analysis revealed systematic reductions in jumps as a function of practice, such that the LF model more closely approximated the standard Wiener model over time. This trend could not be attributed to other sources of parameter variability, speaking against the possibility of trade-offs with other model parameters. Our analysis suggests that jumps in the LF model might be capturing strategy instability exhibited by relatively inexperienced observers early on in task performance. We conclude that further investigation of a potential psychological interpretation of jumps in evidence accumulation is warranted.

Age-Related Differences in Decision-Making: Evidence Accumulation is More Gradual in Older Age

Older adults tend to exhibit longer response times than younger adults in choice tasks across cognitive domains, such as perception, attention, and memory. The diffusion model has emerged as a standard model for analyzing age differences in choice behavior. Applications of the diffusion model to choice data from younger and older adults indicate that age-related slowing is driven by a more cautious response style and slower non-decisional processes, rather than by age differences in the rate of information accumulation. The Lévy flight model, a new evidence accumulation model that extends the diffusion model, was recently developed to account for differences in response times for correct and error responses. In the Lévy flight model, larger jumps in evidence accumulation can be accommodated compared to the diffusion model. It is currently unknown whether younger and older adults differ with respect to the jumpiness of evidence accumulation. In the current study, younger and older adults (N = 40 per age group) completed a letter-number-discrimination task. Results indicate that older adults show a more gradual (less "jumpy") pattern of evidence accumulation compared to younger adults. Implications for research on cognitive aging are discussed.

Secondary motor integration as a final arbiter in sensorimotor decision-making

Sensorimotor decision-making is believed to involve a process of accumulating sensory evidence over time. While current theories posit a single accumulation process prior to planning an overt motor response, here, we propose an active role of motor processes in decision formation via a secondary leaky motor accumulation stage. The motor leak adapts the "memory" with which this secondary accumulator reintegrates the primary accumulated sensory evidence, thus adjusting the temporal smoothing in the motor evidence and, correspondingly, the lag between the primary and motor accumulators. We compare this framework against different single accumulator variants using formal model comparison, fitting choice, and response times in a task where human observers made categorical decisions about a noisy sequence of images, under different speed-accuracy trade-off instructions. We show that, rather than boundary adjustments (controlling the amount of evidence accumulated for decision commitment), adjustment of the leak in the secondary motor accumulator provides the better description of behavior across conditions. Importantly, we derive neural correlates of these 2 integration processes from electroencephalography data recorded during the same task and show that these neural correlates adhere to the neural response profiles predicted by the model. This framework thus provides a neurobiologically plausible description of sensorimotor decision-making that captures emerging evidence of the active role of motor processes in choice behavior.

Beyond Drift Diffusion Models: Fitting a Broad Class of Decision and Reinforcement Learning Models with HDDM

Computational modeling has become a central aspect of research in the cognitive neurosciences. As the field matures, it is increasingly important to move beyond standard models to quantitatively assess models with richer dynamics that may better reflect underlying cognitive and neural processes. For example, sequential sampling models (SSMs) are a general class of models of decision-making intended to capture processes jointly giving rise to RT distributions and choice data in n-alternative choice paradigms. A number of model variations are of theoretical interest, but empirical data analysis has historically been tied to a small subset for which likelihood functions are analytically tractable. Advances in methods designed for likelihood-free inference have recently made it computationally feasible to consider a much larger spectrum of SSMs. In addition, recent work has motivated the combination of SSMs with reinforcement learning models, which had historically been considered in separate literatures. Here, we provide a significant addition to the widely used HDDM Python toolbox and include a tutorial for how users can easily fit and assess a (user-extensible) wide variety of SSMs and how they can be combined with reinforcement learning models. The extension comes batteries included, including model visualization tools, posterior predictive checks, and ability to link trial-wise neural signals with model parameters via hierarchical Bayesian regression.

BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks that we call BayesFlow. The method uses simulations to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pretrained in this way can then, without additional training or optimization, infer full posteriors on arbitrarily many real data sets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with handcrafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science, and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.

Transcranial direct current stimulation (tDCS) alters the pattern of information processing in children with ADHD: Evidence from drift diffusion modeling

OBJECTIVE

Performance accuracy and reaction time in cognitive tasks are routinely used to evaluate the efficacy of tDCS to affect cognitive task performance. tDCS alters the excitability of targeted brain areas and thereby alters performance of cognitive tasks. The drift diffusion model (DDM) provides some additional measures to explore information processing style, such as (non)decision time, bias for decision, and speed of information processing. DDM parameters are informative for the study of cognitive impairments in children with ADHD. In the present study, we aimed to evaluate the impact of tDCS on cognitive performance via DDM measures.

METHODS

This study conducted DDM modeling and reanalysis of two exploratory, single-blinded, within-subject design experiments, which were published earlier. In the first experiment, twenty- four children with ADHD performed a Go/ No- Go task during anodal or sham tDCS over the right dlPFC. In the second experiment, twenty- five children with ADHD performed the 1- back working memory task during anodal or sham tDCS over the left dlPFC. We reanalyzed the data after DDM modeling.

RESULTS

The conventional performance measures revealed no significant effect of tDCS on No- Go accuracy in the first experiment and 1-back accuracy in the second experiment. The 1-back reaction time and speed-accuracy tradeoff were however improved under the real stimulation condition. The DDM measures identified increased No-Go- bias and decision time with respect to inhibitory control, and an increased threshold and amount of information required for response in the 1- back test.

CONCLUSION

In children with ADHD, anodal tDCS over the right dlPFC induces more conservative and less impulsive decisions. Furthermore, anodal tDCS over the left dlPFC enhanced efficacy of working memory performance with respect to agility and capacity. The experimental results show that drift diffusion modeling is useful for evaluation of the impact of tDCS on the style of information processing.

Mixing memory and desire: How memory reactivation supports deliberative decision-making

Memories affect nearly every aspect of our mental life. They allow us to both resolve uncertainty in the present and to construct plans for the future. Recently, renewed interest in the role memory plays in adaptive behavior has led to new theoretical advances and empirical observations. We review key findings, with particular emphasis on how the retrieval of many kinds of memories affects deliberative action selection. These results are interpreted in a sequential inference framework, in which reinstatements from memory serve as "samples" of potential action outcomes. The resulting model suggests a central role for the dynamics of memory reactivation in determining the influence of different kinds of memory in decisions. We propose that representation-specific dynamics can implement a bottom-up "product of experts" rule that integrates multiple sets of action-outcome predictions weighted based on their uncertainty. We close by reviewing related findings and identifying areas for further research. This article is categorized under: Psychology > Reasoning and Decision Making Neuroscience > Cognition Neuroscience > Computation.

Age differences in diffusion model parameters: a meta-analysis

Older adults typically show slower response times in basic cognitive tasks than younger adults. A diffusion model analysis allows the clarification of why older adults react more slowly by estimating parameters that map distinct cognitive components of decision making. The main components of the diffusion model are the speed of information uptake (drift rate), the degree of conservatism regarding the decision criterion (boundary separation), and the time taken up by non-decisional processes (i.e., encoding and motoric response execution; non-decision time). While the literature shows consistent results regarding higher boundary separation and longer non-decision time for older adults, results are more complex when it comes to age differences in drift rates. We conducted a multi-level meta-analysis to identify possible sources of this variance. As possible moderators, we included task difficulty and task type. We found that age differences in drift rate are moderated both by task type and task difficulty. Older adults were inferior in drift rate in perceptual and memory tasks, but information accumulation was even increased in lexical decision tasks for the older participants. Additionally, in perceptual and lexical decision tasks, older individuals benefitted from high task difficulty. In the memory tasks, task difficulty did not moderate the negative impact of age on drift. The finding of higher boundary separation and longer non-decision time in older than younger adults generalized over task type and task difficulty. The results of our meta-analysis are consistent with recent findings of a more pronounced age-related decline in memory than in vocabulary performance.

Vision for the blind: visual psychophysics and blinded inference for decision models

Evidence accumulation models like the diffusion model are increasingly used by researchers to identify the contributions of sensory and decisional factors to the speed and accuracy of decision-making. Drift rates, decision criteria, and nondecision times estimated from such models provide meaningful estimates of the quality of evidence in the stimulus, the bias and caution in the decision process, and the duration of nondecision processes. Recently, Dutilh et al. (Psychonomic Bulletin & Review 26, 1051–1069, 2019) carried out a large-scale, blinded validation study of decision models using the random dot motion (RDM) task. They found that the parameters of the diffusion model were generally well recovered, but there was a pervasive failure of selective influence, such that manipulations of evidence quality, decision bias, and caution also affected estimated nondecision times. This failure casts doubt on the psychometric validity of such estimates. Here we argue that the RDM task has unusual perceptual characteristics that may be better described by a model in which drift and diffusion rates increase over time rather than turn on abruptly. We reanalyze the Dutilh et al. data using models with abrupt and continuous-onset drift and diffusion rates and find that the continuous-onset model provides a better overall fit and more meaningful parameter estimates, which accord with the known psychophysical properties of the RDM task. We argue that further selective influence studies that fail to take into account the visual properties of the evidence entering the decision process are likely to be unproductive.