Scott D. Brown

The simplest complete model of choice response time: Linear ballistic accumulation

We propose a linear ballistic accumulator (LBA) model of decision making and reaction time. The LBA is simpler than other models of choice response time, with independent accumulators that race towards a common response threshold. Activity in the accumulators increases in a linear and deterministic manner. The simplicity of the model allows complete analytic solutions for choices between any number of alternatives. These solutions (and freely-available computer code) make the model easy to apply to both binary and multiple choice situations. Using data from five previously published experiments, we demonstrate that the LBA model successfully accommodates empirical phenomena from binary and multiple choice tasks that have proven difficult for other theoretical accounts. Our results are encouraging in a field beset by the tradeoff between complexity and completeness.

The power law repealed: the case for an exponential law of practice

The power function is treated as the law relating response time to practice trials. However, the evidence for a power law is flawed, because it is based on averaged data. We report a survey that assessed the form of the practice function for individual learners and learning conditions in paradigms that have shaped theories of skill acquisition. We fit power and exponential functions to 40 sets of data representing 7,910 learning series from 475 subjects in 24 experiments. The exponential function fit better than the power function in all the unaveraged data sets. Averaging produced a bias in favor of the power function. A new practice function based on the exponential, the APEX function, fit better than a power function with an extra, preexperimental practice parameter. Clearly, the best candidate for the law of practice is the exponential or APEX function, not the generally accepted power function. The theoretical implications are discussed.

Striatum and pre-SMA facilitate decision-making under time pressure

Human decision-making almost always takes place under time pressure. When people are engaged in activities such as shopping, driving, or playing chess, they have to continually balance the demands for fast decisions against the demands for accurate decisions. In the cognitive sciences, this balance is thought to be modulated by a response threshold, the neural substrate of which is currently subject to speculation. In a speed decision-making experiment, we presented participants with cues that indicated different requirements for response speed. Application of a mathematical model for the behavioral data confirmed that cueing for speed lowered the response threshold. Functional neuroimaging showed that cueing for speed activates the striatum and the pre-supplementary motor area (pre-SMA), brain structures that are part of a closed-loop motor circuit involved in the preparation of voluntary action plans. Moreover, activation in the striatum is known to release the motor system from global inhibition, thereby facilitating faster but possibly premature actions. Finally, the data show that individual variation in the activation of striatum and pre-SMA is selectively associated with individual variation in the amplitude of the adjustments in the response threshold estimated by the mathematical model. These results demonstrate that when people have to make decisions under time pressure their striatum and pre-SMA show increased levels of activation.

Cortico-striatal connections predict control over speed and accuracy in perceptual decision making

When people make decisions they often face opposing demands for response speed and response accuracy, a process likely mediated by response thresholds. According to the striatal hypothesis, people decrease response thresholds by increasing activation from cortex to striatum, releasing the brain from inhibition. According to the STN hypothesis, people decrease response thresholds by decreasing activation from cortex to subthalamic nucleus (STN); a decrease in STN activity is likewise thought to release the brain from inhibition and result in responses that are fast but error-prone. To test these hypotheses—both of which may be true—we conducted two experiments on perceptual decision making in which we used cues to vary the demands for speed vs. accuracy. In both experiments, behavioral data and mathematical model analyses confirmed that instruction from the cue selectively affected the setting of response thresholds. In the first experiment we used ultra-high-resolution 7T structural MRI to locate the STN precisely. We then used 3T structural MRI and probabilistic tractography to quantify the connectivity between the relevant brain areas. The results showed that participants who flexibly change response thresholds (as quantified by the mathematical model) have strong structural connections between presupplementary motor area and striatum. This result was confirmed in an independent second experiment. In general, these findings show that individual differences in elementary cognitive tasks are partly driven by structural differences in brain connectivity. Specifically, these findings support a cortico-striatal control account of how the brain implements adaptive switches between cautious and risky behavior.

On the linear relation between the mean and the standard deviation of a response time distribution

Although it is generally accepted that the spread of a response time (RT) distribution increases with the mean, the precise nature of this relation remains relatively unexplored. The authors show that in several descriptive RT distributions, the standard deviation increases linearly with the mean. Results from a wide range of tasks from different experimental paradigms support a linear relation between RT mean and RT standard deviation. Both R. Ratcliffs (1978) diffusion model and G. D. Logans (1988) instance theory of automatization provide explanations for this linear relation. The authors identify and discuss 3 specific boundary conditions for the linear law to hold. The law constrains RT models and supports the use of the coefficient of variation to (a) compare variability while controlling for differences in baseline speed of processing and (b) assess whether changes in performance with practice are due to quantitative speedup or qualitative reorganization.

Quantile maximum likelihood estimation of response time distributions

Queen’s University, Kingston, Ontario, Canada We introduce and evaluate via a Monte Carlo study a robust new estimation technique that fits distribution functions to grouped response time (RT) data, where the grouping is determined by sample quantiles. The new estimator, quantile maximum likelihood (QML), is more efficient and less biased than the best alternative estimation technique when fitting the commonly used ex-Gaussian distribution. Limitations of the Monte Carlo results are discussed and guidance provided for the practical application of the new technique. Because QML estimation can be computationally costly, we make fast open source code for fitting available that can be easily modified

A Ballistic Model of Choice Response Time.

Almost all models of response time (RT) use a stochastic accumulation process. To account for the benchmark RT phenomena, researchers have found it necessary to include between-trial variability in the starting point and/or the rate of accumulation, both in linear (R. Ratcliff & J. N. Rouder, 1998) and nonlinear (M. Usher & J. L. McClelland, 2001) models. The authors show that a ballistic (deterministic within-trial) model using a simplified version of M. Usher and J. L. McClellands (2001) nonlinear accumulation process with between-trial variability in accumulation rate and starting point is capable of accounting for the benchmark behavioral phenomena. The authors successfully fit their model to R. Ratcliff and J. N. Rouders (1998) data, which exhibit many of the benchmark phenomena.

Domain General Mechanisms of Perceptual Decision Making in Human Cortex

To successfully interact with objects in the environment, sensory evidence must be continuously acquired, interpreted, and used to guide appropriate motor responses. For example, when driving, a red light should motivate a motor command to depress the brake pedal. Single-unit recording studies have established that simple sensorimotor transformations are mediated by the same neurons that ultimately guide the behavioral response. However, it is also possible that these sensorimotor regions are the recipients of a modality-independent decision signal that is computed elsewhere. Here, we used functional magnetic resonance imaging and human observers to show that the time course of activation in a subregion of the right insula is consistent with a role in accumulating sensory evidence independently from the required motor response modality (saccade vs manual). Furthermore, a combination of computational modeling and simulations of the blood oxygenation level-dependent response suggests that this region is not simply recruited by general arousal or by the tonic maintenance of attention during the decision process. Our data thus raise the possibility that a modality-independent representation of sensory evidence may guide activity in effector-specific cortical areas before the initiation of a behavioral response.

Diffusion Decision Model: Current Issues and History

There is growing interest in diffusion models to represent the cognitive and neural processes of speeded decision making. Sequential-sampling models like the diffusion model have a long history in psychology. They view decision making as a process of noisy accumulation of evidence from a stimulus. The standard model assumes that evidence accumulates at a constant rate during the second or two it takes to make a decision. This process can be linked to the behaviors of populations of neurons and to theories of optimality. Diffusion models have been used successfully in a range of cognitive tasks and as psychometric tools in clinical research to examine individual differences. In this review, we relate the models to both earlier and more recent research in psychology.

Minimalist models for protein folding and design

Protein folding research during the past decade has emphasized the dominant role of native state topology in determining the speed and mechanism of folding for small proteins; this has been illustrated by simulations using minimalist protein models. The advantages of minimalist protein models lie in their ability to rapidly collect meaningful statistics about folding pathways and kinetics, their ease of characterization with coarse-grained order parameters and their concentration on the essential physics of the problem to connect with experimental observables for a target protein. The maturation of experimental protein folding has driven the need for more quantitative protein simulations to better understand the balance between sequence details and fold topology. In the past year, we have seen the emergence of more complex minimalist models, ranging from all-atom Gō potentials to coarse-grained bead models in which Gō interactions are replaced or supplemented by more physically motivated potentials. The reduced computational cost at the coarse-grained level of abstraction will potentially enable both folding studies on a genomic scale and systematic application in protein design.