The computations that support simple decision-making: A comparison between the diffusion and urgency-gating models

A revised diffusion model for conflict tasks

The recently developed diffusion model for conflict tasks (DMC) Ulrich et al. (Cognitive Psychology, 78, 148-174, 2015) provides a good account of data from all standard conflict tasks (e.g., Stroop, Simon, and flanker tasks) within a common evidence accumulation framework. A central feature of DMC's processing dynamics is that there is an initial phase of rapid accumulation of distractor evidence that is then selectively withdrawn from the decision mechanism as processing continues. We argue that this assumption is potentially troubling because it could be viewed as implying qualitative changes in the representation of distractor information over the time course of processing. These changes suggest more than simple inhibition or suppression of distractor information, as they involve evidence produced by distractor processing "changing sign" over time. In this article, we (a) develop a revised DMC (RDMC) whose dynamics operate strictly within the limits of inhibition/suppression (i.e., evidence strength can change monotonically, but cannot change sign); (b) demonstrate that RDMC can predict the full range of delta plots observed in the literature (i.e., both positive-going and negative-going); and (c) show that the model provides excellent fits to Simon and flanker data used to benchmark the original DMC at both the individual and group level. Our model provides a novel account of processing differences across Simon and flanker tasks. Specifically, that they differ in how distractor information is processed on congruent trials, rather than incongruent trials: congruent trials in the Simon task show relatively slow attention shifting away from distractor information (i.e., location) while complete and rapid attention shifting occurs in the flanker task. Our new model highlights the importance of considering dynamic interactions between top-down goals and bottom-up stimulus effects in conflict processing.

Magnitude-sensitivity: rethinking decision-making

Magnitude-sensitivity refers to the result that performance in decision-making, across domains and organisms, is affected by the total value of the possible alternatives. This simple result offers a window into fundamental issues in decision-making and has led to a reconsideration of ecological decision-making, prominent computational models of decision-making, and optimal decision-making. Moreover, magnitude-sensitivity has inspired the design of new robotic systems that exploit natural solutions and apply optimal decision-making policies. In this article, we review the key theoretical and empirical results about magnitude-sensitivity and highlight the importance that this phenomenon has for the understanding of decision-making. Furthermore, we discuss open questions and ideas for future research.

The importance of urgency in decision making based on dynamic information

A standard view in the literature is that decisions are the result of a process that accumulates evidence in favor of each alternative until such accumulation reaches a threshold and a decision is made. However, this view has been recently questioned by an alternative proposal that suggests that, instead of accumulated, evidence is combined with an urgency signal. Both theories have been mathematically formalized and supported by a variety of decision-making tasks with constant information. However, recently, tasks with changing information have shown to be more effective to study the dynamics of decision making. Recent research using one of such tasks, the tokens task, has shown that decisions are better described by an urgency mechanism than by an accumulation one. However, the results of that study could depend on a task where all fundamental information was noiseless and always present, favoring a mechanism of non-integration, such as the urgency one. Here, we wanted to address whether the same conclusions were also supported by an experimental paradigm in which sensory evidence was removed shortly after it was provided, making working memory necessary to properly perform the task. Here, we show that, under such condition, participants' behavior could be explained by an urgency-gating mechanism that low-pass filters the mnemonic information and combines it with an urgency signal that grows with time but not by an accumulation process that integrates the same mnemonic information. Thus, our study supports the idea that, under certain situations with dynamic sensory information, decisions are better explained by an urgency-gating mechanism than by an accumulation one.

Causal role for the primate superior colliculus in the computation of evidence for perceptual decisions

Trained monkeys performed a two-choice perceptual decision-making task in which they reported the perceived orientation of a dynamic Glass pattern, before and after unilateral, reversible, inactivation of a brainstem area-the superior colliculus (SC)-involved in preparing eye movements. We found that unilateral SC inactivation produced significant decision biases and changes in reaction times consistent with a causal role for the primate SC in perceptual decision-making. Fitting signal detection theory and sequential sampling models to the data showed that SC inactivation produced a decrease in the relative evidence for contralateral decisions, as if adding a constant offset to a time-varying evidence signal for the ipsilateral choice. The results provide causal evidence for an embodied cognition model of perceptual decision-making and provide compelling evidence that the SC of primates (a brainstem structure) plays a causal role in how evidence is computed for decisions-a process usually attributed to the forebrain.

The unknown but knowable relationship between Presaccadic Accumulation of activity and Saccade initiation

The goal of this short review is to call attention to a yawning gap of knowledge that separates two processes essential for saccade production. On the one hand, knowledge about the saccade generation circuitry within the brainstem is detailed and precise - push-pull interactions between gaze-shifting and gaze-holding processes control the time of saccade initiation, which begins when omnipause neurons are inhibited and brainstem burst neurons are excited. On the other hand, knowledge about the cortical and subcortical premotor circuitry accomplishing saccade initiation has crystalized around the concept of stochastic accumulation - the accumulating activity of saccade neurons reaching a fixed value triggers a saccade. Here is the gap: we do not know how the reaching of a threshold by premotor neurons causes the critical pause and burst of brainstem neurons that initiates saccades. Why this problem matters and how it can be addressed will be discussed. Closing the gap would unify two rich but curiously disconnected empirical and theoretical domains.

A flexible framework for simulating and fitting generalized drift-diffusion models

The drift-diffusion model (DDM) is an important decision-making model in cognitive neuroscience. However, innovations in model form have been limited by methodological challenges. Here, we introduce the generalized drift-diffusion model (GDDM) framework for building and fitting DDM extensions, and provide a software package which implements the framework. The GDDM framework augments traditional DDM parameters through arbitrary user-defined functions. Models are solved numerically by directly solving the Fokker-Planck equation using efficient numerical methods, yielding a 100-fold or greater speedup over standard methodology. This speed allows GDDMs to be fit to data using maximum likelihood on the full response time (RT) distribution. We demonstrate fitting of GDDMs within our framework to both animal and human datasets from perceptual decision-making tasks, with better accuracy and fewer parameters than several DDMs implemented using the latest methodology, to test hypothesized decision-making mechanisms. Overall, our framework will allow for decision-making model innovation and novel experimental designs.

Feeling the Beat (and Seeing It, Too): Vibrotactile, Visual, and Bimodal Rate Discrimination

Beats are among the basic units of perceptual experience. Produced by regular, intermittent stimulation, beats are most commonly associated with audition, but the experience of a beat can result from stimulation in other modalities as well. We studied the robustness of visual, vibrotactile, and bimodal signals as sources of beat perception. Subjects attempted to discriminate between pulse trains delivered at 3 Hz or at 6 Hz. To investigate signal robustness, we intentionally degraded signals on two-thirds of the trials using temporal-domain noise. On these trials, inter-pulse intervals (IPIs) were stochastic, perturbed independently from the nominal IPI by random samples from zero-mean Gaussian distributions with different variances. These perturbations produced directional changes in the IPIs, which either increased or decreased the likelihood of confusing the two pulse rates. In addition to affording an assay of signal robustness, this paradigm made it possible to gauge how subjects' judgments were influenced by successive IPIs. Logistic regression revealed a strong primacy effect: subjects' decisions were disproportionately influenced by a trial's initial IPIs. Response times and parameter estimates from drift-diffusion modeling showed that information accumulates more rapidly with bimodal stimulation than with either unimodal stimulus alone. Analysis of error rates within each condition suggested consistently optimal decision making, even with increased IPI variability. Finally, beat information delivered by vibrotactile signals proved just as robust as information conveyed by visual signals, confirming vibrotactile stimulation's potential as a communication channel.

Perceptual Decision-Making in Children: Age-Related Differences and EEG Correlates

Children make faster and more accurate decisions about perceptual information as they get older, but it is unclear how different aspects of the decision-making process change with age. Here, we used hierarchical Bayesian diffusion models to decompose performance in a perceptual task into separate processing components, testing age-related differences in model parameters and links to neural data. We collected behavioural and EEG data from 96 6- to 12-year-old children and 20 adults completing a motion discrimination task. We used a component decomposition technique to identify two response-locked EEG components with ramping activity preceding the response in children and adults: one with activity that was maximal over centro-parietal electrodes and one that was maximal over occipital electrodes. Younger children had lower drift rates (reduced sensitivity), wider boundary separation (increased response caution) and longer non-decision times than older children and adults. Yet, model comparisons suggested that the best model of children's data included age effects only on drift rate and boundary separation (not non-decision time). Next, we extracted the slope of ramping activity in our EEG components and covaried these with drift rate. The slopes of both EEG components related positively to drift rate, but the best model with EEG covariates included only the centro-parietal component. By decomposing performance into distinct components and relating them to neural markers, diffusion models have the potential to identify the reasons why children with developmental conditions perform differently to typically developing children and to uncover processing differences inapparent in the response time and accuracy data alone.

Differentiating between integration and non-integration strategies in perceptual decision making

Many tasks used to study decision-making encourage subjects to integrate evidence over time. Such tasks are useful to understand how the brain operates on multiple samples of information over prolonged timescales, but only if subjects actually integrate evidence to form their decisions. We explored the behavioral observations that corroborate evidence-integration in a number of task-designs. Several commonly accepted signs of integration were also predicted by non-integration strategies. Furthermore, an integration model could fit data generated by non-integration models. We identified the features of non-integration models that allowed them to mimic integration and used these insights to design a motion discrimination task that disentangled the models. In human subjects performing the task, we falsified a non-integration strategy in each and confirmed prolonged integration in all but one subject. The findings illustrate the difficulty of identifying a decision-maker’s strategy and support solutions to achieve this goal.

ChaRTr: An R toolbox for modeling choices and response times in decision-making tasks

BACKGROUND

Decision-making is the process of choosing and performing actions in response to sensory cues to achieve behavioral goals. Many mathematical models have been developed to describe the choice behavior and response time (RT) distributions of observers performing decision-making tasks. However, relatively few researchers use these models because it demands expertise in various numerical, statistical, and software techniques.

NEW METHOD

We present a toolbox - Choices and Response Times in R, or ChaRTr - that provides the user the ability to implement and test a wide variety of decision-making models ranging from classic through to modern versions of the diffusion decision model, to models with urgency signals, or collapsing boundaries.

RESULTS

In three different case studies, we demonstrate how ChaRTr can be used to effortlessly discriminate between multiple models of decision-making behavior. We also provide guidance on how to extend the toolbox to incorporate future developments in decision-making models.

COMPARISON WITH EXISTING METHOD(S)

Existing software packages surmounted some of the numerical issues but have often focused on the classical decision-making model, the diffusion decision model. Recent models that posit roles for urgency, time-varying decision thresholds, noise in various aspects of the decision-formation process or low pass filtering of sensory evidence have proven to be challenging to incorporate in a coherent software framework that permits quantitative evaluation among these competing classes of decision-making models.

CONCLUSION

ChaRTr can be used to make insightful statements about the cognitive processes underlying observed decision-making behavior and ultimately for deeper insights into decision mechanisms.

Accumulators, Neurons, and Response Time

The marriage of cognitive neurophysiology and mathematical psychology to understand decision-making has been exceptionally productive. This interdisciplinary area is based on the proposition that particular neurons or circuits instantiate the accumulation of evidence specified by mathematical models of sequential sampling and stochastic accumulation. This linking proposition has earned widespread endorsement. Here, a brief survey of the history of the proposition precedes a review of multiple conundrums and paradoxes concerning the accuracy, precision, and transparency of that linking proposition. Correctly establishing how abstract models of decision-making are instantiated by particular neural circuits would represent a remarkable accomplishment in mapping mind to brain. Failing would reveal challenging limits for cognitive neuroscience. This is such a vigorous area of research because so much is at stake.

Optimal or not; depends on the task

Decision-making involves a tradeoff between pressures for caution and urgency. Previous research has investigated how well humans optimize this tradeoff, and mostly concluded that people adopt a sub-optimal strategy that over-emphasizes caution. This emphasis reduces how many decisions can be made in a fixed time, which reduces the “reward rate”. However, the strategy that is optimal depends critically on the timing properties of the experiment design: the slower the rate of decision opportunities, the more cautious the optimal strategy. Previous studies have almost uniformly adopted very fast designs, which favor very urgent decision-making. This raises the possibility that previous findings—that humans adopt strategies that are too cautious—could either be ascribed to human caution, or to the experiments’ design. To test this, we used a slowed-down decision-making task in which the optimal strategy was quite cautious. With this task, and in contrast to previous findings, the average strategy adopted across participants was very close to optimal, with about equally many participants adopting too-cautious as too-urgent strategies. Our findings suggest that task design can play a role in inferences about optimality, and that previous conclusions regarding human sub-optimality are conditional on the task settings. This limits claims about human optimality that can be supported by the available evidence.

Optimal models of decision-making in dynamic environments

Nature is in constant flux, so animals must account for changes in their environment when making decisions. How animals learn the timescale of such changes and adapt their decision strategies accordingly is not well understood. Recent psychophysical experiments have shown humans and other animals can achieve near-optimal performance at two alternative forced choice (2AFC) tasks in dynamically changing environments. Characterization of performance requires the derivation and analysis of computational models of optimal decision-making policies on such tasks. We review recent theoretical work in this area, and discuss how models compare with subjects' behavior in tasks where the correct choice or evidence quality changes in dynamic, but predictable, ways.

A method, framework, and tutorial for efficiently simulating models of decision-making

Evidence accumulation models (EAMs) have become the dominant models of rapid decision-making. Several variants of these models have been proposed, ranging from the simple linear ballistic accumulator (LBA) to the more complex leaky-competing accumulator (LCA), and further extensions that include time-varying rates of evidence accumulation or decision thresholds. Although applications of the simpler variants have been widespread, applications of the more complex models have been fewer, largely due to their intractable likelihood function and the computational cost of mass simulation. Here, I present a framework for efficiently fitting complex EAMs, which uses a new, efficient method of simulating these models. I find that the majority of simulation time is taken up by random number generation (RNG) from the normal distribution, needed for the stochastic noise of the differential equation. To reduce this inefficiency, I propose using the well-known concept within computer science of "look-up tables" (LUTs) as an approximation to the inverse cumulative density function (iCDF) method of RNG, which I call "LUT-iCDF". I show that when using an appropriately sized LUT, simulations using LUT-iCDF closely match those from the standard RNG method in R. My framework, which I provide a detailed tutorial on how to implement, includes C code for 12 different variants of EAMs using the LUT-iCDF method, and should make the implementation of complex EAMs easier and faster.

Assessing the practical differences between model selection methods in inferences about choice response time tasks

Evidence accumulations models (EAMs) have become the dominant modeling framework within rapid decision-making, using choice response time distributions to make inferences about the underlying decision process. These models are often applied to empirical data as "measurement tools", with different theoretical accounts being contrasted within the framework of the model. Some method is then needed to decide between these competing theoretical accounts, as only assessing the models on their ability to fit trends in the empirical data ignores model flexibility, and therefore, creates a bias towards more flexible models. However, there is no objectively optimal method to select between models, with methods varying in both their computational tractability and theoretical basis. I provide a systematic comparison between nine different model selection methods using a popular EAM-the linear ballistic accumulator (LBA; Brown & Heathcote, Cognitive Psychology 57(3), 153-178 2008)-in a large-scale simulation study and the empirical data of Dutilh et al. (Psychonomic Bulletin and Review, 1-19 2018). I find that the "predictive accuracy" class of methods (i.e., the Akaike Information Criterion [AIC], the Deviance Information Criterion [DIC], and the Widely Applicable Information Criterion [WAIC]) make different inferences to the "Bayes factor" class of methods (i.e., the Bayesian Information Criterion [BIC], and Bayes factors) in many, but not all, instances, and that the simpler methods (i.e., AIC and BIC) make inferences that are highly consistent with their more complex counterparts. These findings suggest that researchers should be able to use simpler "parameter counting" methods when applying the LBA and be confident in their inferences, but that researchers need to carefully consider and justify the general class of model selection method that they use, as different classes of methods often result in different inferences.

A theoretical analysis of the reward rate optimality of collapsing decision criteria

A standard assumption of most sequential sampling models is that decision-makers rely on a decision criterion that remains constant throughout the decision process. However, several authors have recently suggested that, in order to maximize reward rates in dynamic environments, decision-makers need to rely on a decision criterion that changes over the course of the decision process. We used dynamic programming and simulation methods to quantify the reward rates obtained by constant and dynamic decision criteria in different environments. We further investigated what influence a decision-maker's uncertainty about the stochastic structure of the environment has on reward rates. Our results show that in most dynamic environments, both types of decision criteria yield similar reward rates, across different levels of uncertainty. This suggests that a static decision criterion might provide a robust default setting.

A parameter recovery assessment of time-variant models of decision-making

Evidence accumulation models have been one of the most dominant modeling frameworks used to study rapid decision-making over the past several decades. These models propose that evidence accumulates from the environment until the evidence for one alternative reaches some threshold, typically associated with caution, triggering a response. However, researchers have recently begun to reconsider the fundamental assumptions of how caution varies with time. In the past, it was typically assumed that levels of caution are independent of time. Recent investigations have however suggested the possibility that levels of caution decrease over time and that this strategy provides more efficient performance under certain conditions. Our study provides the first comprehensive assessment of this newer class of models accounting for time-varying caution to determine how robustly their parameters can be estimated. We assess five overall variants of collapsing threshold/urgency signal models based on the diffusion decision model, linear ballistic accumulator model, and urgency gating model frameworks. We find that estimation of parameters, particularly those associated with caution/urgency modulation are most robust for the linearly collapsing threshold diffusion model followed by an urgency-gating model with a leakage process. All other models considered, particularly those with ballistic accumulation or nonlinear thresholds, are unable to recover their own parameters adequately, making their usage in parameter estimation contexts questionable.

Neurodynamic Evidence Supports a Forced-Excursion Model of Decision-Making under Speed/Accuracy Instructions

Evolutionary pressures suggest that choices should be optimized to maximize rewards, by appropriately trading speed for accuracy. This speed-accuracy tradeoff (SAT) is commonly explained by variation in just the baseline-to-boundary distance, i.e., the excursion, of accumulation-to-bound models of perceptual decision-making. However, neural evidence is not consistent with this explanation. A compelling account of speeded choice should explain both overt behavior and the full range of associated brain signatures. Here, we reconcile seemingly contradictory behavioral and neural findings. In two variants of the same experiment, we triangulated upon the neural underpinnings of the SAT in the human brain using both EEG and transcranial magnetic stimulation (TMS). We found that distinct neural signals, namely the event-related potential (ERP) centroparietal positivity (CPP) and a smoothed motor-evoked potential (MEP) signal, which have both previously been shown to relate to decision-related accumulation, revealed qualitatively similar average neurodynamic profiles with only subtle differences between SAT conditions. These signals were then modelled from behavior by either incorporating traditional boundary variation or utilizing a forced excursion. These model variants are mathematically equivalent, in terms of their behavioral predictions, hence providing identical fits to correct and erroneous reaction time distributions. However, the forced-excursion version instantiates SAT via a more global change in parameters and implied neural activity, a process conceptually akin to, but mathematically distinct from, urgency. This variant better captured both ERP and MEP neural profiles, suggesting that the SAT may be implemented via neural gain modulation, and reconciling standard modelling approaches with human neural data.

Modeling the Covariance Structure of Complex Datasets Using Cognitive Models: An Application to Individual Differences and the Heritability of Cognitive Ability

Understanding individual differences in cognitive performance is an important part of understanding how variations in underlying cognitive processes can result in variations in task performance. However, the exploration of individual differences in the components of the decision process-such as cognitive processing speed, response caution, and motor execution speed-in previous research has been limited. Here, we assess the heritability of the components of the decision process, with heritability having been a common aspect of individual differences research within other areas of cognition. Importantly, a limitation of previous work on cognitive heritability is the underlying assumption that variability in response times solely reflects variability in the speed of cognitive processing. This assumption has been problematic in other domains, due to the confounding effects of caution and motor execution speed on observed response times. We extend a cognitive model of decision-making to account for relatedness structure in a twin study paradigm. This approach can separately quantify different contributions to the heritability of response time. Using data from the Human Connectome Project, we find strong evidence for the heritability of response caution, and more ambiguous evidence for the heritability of cognitive processing speed and motor execution speed. Our study suggests that the assumption made in previous studies-that the heritability of cognitive ability is based on cognitive processing speed-may be incorrect. More generally, our methodology provides a useful avenue for future research in complex data that aims to analyze cognitive traits across different sources of related data, whether the relation is between people, tasks, experimental phases, or methods of measurement.