Feature Review
Diffusion Decision Model: Current Issues and History

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Trends

Diffusion models with drift and boundaries constant over time account for accuracy and correct and error response time distributions for many types of two-choice tasks in many populations of participants.

Collapsing decision bounds implement optimal decision making in certain cases, but fits to data show humans use constant boundaries.

Brief stimulus presentation produces time varying input, but data suggest that evidence is integrated to produce constant drift in the decision process. (Other tasks can produce nonstationary evidence.)

Evidence is assumed to vary from trial to trial, as in signal detection theory. This explains why incorrect decisions are often slower than correct decisions.

It is not clear if variability in a sequence of stimulus elements in expanded judgment tasks is equivalent to moment-by-moment internal noise in tasks with a single stationary stimulus.

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.

Section snippets

Modeling Simple Decision Making

Decision making is intimately involved in all of our everyday activities. Many decisions are made rapidly and at a low level cognitively, for example, deciding whether to drive left or right round a car in front. Others, such as deciding which candidate to vote for or which car to buy, are made at a higher level with prolonged deliberation. The diffusion models we discuss are of the former type. In the real world, they involve a rapid matching of a perceptual representation to stored knowledge

The Two-Choice Diffusion Model

Figure 2 shows simulated paths that represent the accumulation of evidence on individual trials (Figure 2A) and it shows the effects of changes in drift rate (Figure 2B) and boundary settings (Figure 2C) on RT distributions. Because there is a minimum on RTs but no maximum, the model automatically produces right-skewed distributions that have the same shape as those found in most simple two-choice tasks. That the model predicts RT distributions that are the same as those found experimentally is

Across-Trial Variability in Model Components

A problem with early random walk models, which were discrete time precursors of diffusion models, was that they predicted identical RT distributions for correct and incorrect responses (when the starting point is equidistant from the boundaries), which is never observed empirically. Several different approaches to this problem have been investigated, including: dynamically changing decision boundaries; nonlinear evidence accumulation processes; and non-normal random walk increments. The most

Response Signal and Go/No-Go Tasks: Implicit Boundaries

In the response signal task, a stimulus is presented and then after some amount of time, a signal is given. Participants are asked to choose between two alternatives just as in the usual two-choice procedure except that they are asked to respond as quickly as possible after the signal (in, say, 200–300 ms). The stimulus-to-signal time varies from trial to trial 47, 48, 49, 50, which means that processing can be assumed to be the same for all signal times up to each specific signal time [2]. A

Conflict Tasks

Another class of paradigms that appear to require dynamic changes in diffusion model parameters over time are conflict paradigms. In a reinforcement learning paradigm, subjects had to choose one of a pair of letters and feedback indicated which one was ‘correct’ on that trial. Feedback was probabilistic with one letter of the pair being reinforced more often than the other. Later in the session, conflict conditions were created by pairing the letters from different pairs that had low

Optimality

Considerations of optimality have played a significant role in the theoretical and experimental analysis of human and animal decision making. Theories of optimality prescribe how the available evidence should be used to produce a best decision, in some specified sense; experimental studies of optimality have investigated whether actual behavior approximates the theoretical ideal. In simple decision making, two different senses of optimality have been promoted (Box 6). One of these is based on

Collapsing Bounds

The link with optimality theory, on the one hand, and neural studies of decision making, on the other, has led to models in which decision bounds collapse over time. In the collapsing bound model, less evidence is required to trigger a decision as time passes, that is, the boundaries collapse from initially wide spacing toward the center (Figure 4B). Another assumption with much the same effect is that fixed boundaries are maintained, but an ‘urgency signal’ is added to the accumulated evidence

Expanded Judgment Tasks

Most recent applications of diffusion models have been to experimental tasks in which a single stimulus is presented and the noise in the evidence accumulation process arises from moment-by-moment variability in the cognitive representation of the stimulus. However, some of the earliest applications of random walk models 8, 22 were to expanded judgment tasks in which a noisy sequence of stimulus elements has to be integrated to make a decision. Studying such tasks was motivated by the Wald SPRT

Brief Stimulus Presentation

There is a growing interest in whether there is nonstationarity in processing that reflects changing stimulus information over time. This is often studied with stimuli flashed for very brief times (e.g., 50 ms) and is also partly motivated by the thought that stimulus quality can change during the time course of an expanded judgment task. In a highly relevant example from about 15 years ago, the question was whether drift rate tracks the stimulus or not. In other words, whether drift rate begins

Concluding Remarks

Current research in modeling decision processes has used diffusion models extensively. They are being applied in clinical and educational domains, economic decision making (Box 7), and the neuroscience of decision making. Here we have examined current issues that have a history in psychology and we have discussed the earlier research and how it complements new research. In some cases, the earlier research provides an answer to new research questions. Although we have separated the issues, many

Acknowledgments

We would like to thank Jerome Busemeyer, Josh Gold, and Tim Hanks for comments on the paper. Preparation of this article was supported by National Institute on Aging grant R01-AG041176, Department of Education/Institute of Educational Sciences grant R305A120189, and Australian Research Council grants DP140102970 and FT120100244.

Glossary

Accumulator
an assumed structure in an evidence accumulation model that has the purpose of gathering evidence in favor of one response.
Across-trial variability
the assumption that drift rates vary from decision to decision, motivated by the idea that, even if physical stimulus conditions are identical, the internal representation of the decision-relevant information is not.
Attractor model
a network (graph-based) model of interconnected nodes with a dynamic updating process. The updating process

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