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 article, we relate the models to both earlier and more recent research in psychology.

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.

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.basal ganglia ͉ fMRI ͉ linear ballistic accumulator model ͉ speed-accuracy tradeoff W hether buying new shoes, participating in traffic, playing chess, or shooting basketball, one invariably faces the dilemma of when to stop deliberating and make a decision. In many situations, it is maladaptive to ponder over alternative courses of action for a very long time. In basketball, for instance, one has to shoot the ball before a defender can block the shot. However, decisions taken without sufficient thought may lead to poor results; a shot that is taken too hastily may not go in.The foregoing example shows that decision-making involves a delicate balance between the competing demands of response speed and choice accuracy, a balance that is usually referred to as the speed-accuracy tradeoff (1). In the cognitive sciences, this tradeoff is thought to be modulated by a response threshold that determines the amount of diagnostic information that is required to make a decision and initiate an action (2, 3). Because the accumulation of diagnostic information takes time, high response thresholds lead to accurate, yet slow, decisions, and low response thresholds lead to fast yet error-prone decisions.The behavioral consequences of the speed-accuracy tradeoff are both profound and predictable, and the tradeoff therefore constitutes one of the most important benchmark findings for formal models of decision-making (4, 5). In light of its ubiquity and impact, it is surprising that relatively little is known about the neural underpinnings of the speed-accuracy tradeoff (but see refs. 6 and 7...

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 fonn ofthe 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.Curve fitting without benefit of a model is notoriously a black art.

Decision-makers effortlessly balance the need for urgency against the need for caution. Theoretical and neurophysiological accounts have explained this tradeoff solely in terms of the quantity of evidence required to trigger a decision (the "threshold"). This explanation has also been used as a benchmark test for evaluating new models of decision making, but the explanation itself has not been carefully tested against data. We rigorously test the assumption that emphasizing decision speed versus decision accuracy selectively influences only decision thresholds. In data from a new brightness discrimination experiment we found that emphasizing decision speed over decision accuracy not only decreases the amount of evidence required for a decision but also decreases the quality of information being accumulated during the decision process. This result was consistent for 2 leading decision-making models and in a model-free test. We also found the same model-based results in archival data from a lexical decision task (reported by Wagenmakers, Ratcliff, Gomez, & McKoon, 2008) and new data from a recognition memory task. We discuss discuss implications for theoretical development and applications.