New Research In
Physical Sciences
Social Sciences
Featured Portals
Articles by Topic
Biological Sciences
Featured Portals
Articles by Topic
- Agricultural Sciences
- Anthropology
- Applied Biological Sciences
- Biochemistry
- Biophysics and Computational Biology
- Cell Biology
- Developmental Biology
- Ecology
- Environmental Sciences
- Evolution
- Genetics
- Immunology and Inflammation
- Medical Sciences
- Microbiology
- Neuroscience
- Pharmacology
- Physiology
- Plant Biology
- Population Biology
- Psychological and Cognitive Sciences
- Sustainability Science
- Systems Biology
Testing the drift-diffusion model
Contributed by Drew Fudenberg, October 31, 2020 (sent for review June 4, 2020; reviewed by Bo Honore, Antonio Rangel, and Michael Woodford)

Significance
The drift-diffusion model (DDM) has been widely used in psychology and neuroeconomics to explain observed patterns of choices and response times. This paper provides an identification and characterization theorems for this model: We show that the parameters are uniquely pinned down and determine which datasets are consistent with some form of DDM. We then develop a statistical test of the model based on finite datasets using spline estimation. These results establish the empirical content of the model and provide a way for researchers to see when it is applicable.
Abstract
The drift-diffusion model (DDM) is a model of sequential sampling with diffusion signals, where the decision maker accumulates evidence until the process hits either an upper or lower stopping boundary and then stops and chooses the alternative that corresponds to that boundary. In perceptual tasks, the drift of the process is related to which choice is objectively correct, whereas in consumption tasks, the drift is related to the relative appeal of the alternatives. The simplest version of the DDM assumes that the stopping boundaries are constant over time. More recently, a number of papers have used nonconstant boundaries to better fit the data. This paper provides a statistical test for DDMs with general, nonconstant boundaries. As a by-product, we show that the drift and the boundary are uniquely identified. We use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic based on finite samples.
Footnotes
↵1D.F., W.N., P.S., and T.S. contributed equally to this work.
- ↵2To whom correspondence may be addressed. Email: drewf{at}mit.edu.
Author contributions: D.F., W.N., P.S., and T.S. designed research, performed research, analyzed data, and wrote the paper.
Reviewers: B.H., Princeton University; A.R., California Institute of Technology; and M.W., Columbia University.
The authors declare no competing interest.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2011446117/-/DCSupplemental.
Data Availability.
The code for our simulations is available at Open Science Framework, https://osf.io/9n6j7/?view_only=0c9f90f8d23547c19dfb15cdd99417c0.
Published under the PNAS license.
References
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- ↵
- I. Krajbich,
- A. Rangel
- ↵
- ↵
- ↵
- ↵
- ↵
- A. Wald
- ↵
- ↵
- ↵
- ↵
- ↵
- J. Drugowitsch,
- R. Moreno-Bote,
- A. K. Churchland,
- M. N. Shadlen,
- A. Pouget
- ↵
- D. Fudenberg,
- P. Strack,
- T. Strzalecki
- ↵
- S. Tajima,
- J. Drugowitsch,
- N. Patel,
- A. Pouget
- ↵
- G. E. Hawkins,
- B. U. Forstmann,
- E. J. Wagenmakers,
- R. Ratcliff,
- S. D. Brown
- ↵
- K. Chiong,
- M. Shum,
- R. Webb,
- R. Chen
- ↵
- ↵
- ↵
- ↵
- ↵
- D. J. Koehler,
- N. Harvey
- J. R. Busemeyer,
- J. G. Johnson
- ↵
- C. Alós-Ferrer,
- E. Fehr,
- N. Netzer
- ↵
- F. Echenique,
- K. Saito
- ↵
- B. Hebert,
- M. Woodford
- ↵
- M. Woodford
- ↵
- Y. K. Che,
- K. Mierendorff
- ↵
- A. Liang,
- X. Mu,
- V. Syrgkanis
- ↵
- A. Liang,
- X. Mu
- ↵
- W. Zhong
- ↵
- C. Alós-Ferrer,
- E. Fehr,
- N. Netzer
- ↵
- J. Aczél
- ↵
- P. Natenzon
- ↵
- D. McFadden
- ↵
- A. Pakes,
- D. Pollard
- ↵
- W. K. Newey
- ↵
- R. De Jong,
- H. J. Bierens
- ↵
- Y. Hong,
- H. White
- ↵
- V. Chernozhukov,
- W. K. Newey,
- A. Santos
- ↵
- ↵
- A. Buonocore,
- V. Giorno,
- A. Nobile,
- L. Ricciardi
Log in using your username and password
Log in through your institution
Purchase access
Subscribers, for more details, please visit our Subscriptions FAQ.
Please click here to log into the PNAS submission website.
Citation Manager Formats
Sign up for Article Alerts
Article Classifications
- Social Sciences
- Economic Sciences
- Biological Sciences
- Psychological and Cognitive Sciences