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Research Article

Testing the drift-diffusion model

View ORCID ProfileDrew Fudenberg, Whitney Newey, View ORCID ProfilePhilipp Strack, and View ORCID ProfileTomasz Strzalecki
PNAS December 29, 2020 117 (52) 33141-33148; first published December 11, 2020; https://doi.org/10.1073/pnas.2011446117
Drew Fudenberg
aDepartment of Economics, Massachusetts Institute of Technology, Cambridge, MA 02139;
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  • For correspondence: drewf@mit.edu
Whitney Newey
aDepartment of Economics, Massachusetts Institute of Technology, Cambridge, MA 02139;
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Philipp Strack
bDepartment of Economics, Yale University, New Haven, CT 06520;
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Tomasz Strzalecki
cDepartment of Economics, Harvard University, Cambridge, MA 02138
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  1. Contributed by Drew Fudenberg, October 31, 2020 (sent for review June 4, 2020; reviewed by Bo Honore, Antonio Rangel, and Michael Woodford)

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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.

  • response times
  • drift-diffusion model
  • statistical test

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.

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Testing the drift-diffusion model
Drew Fudenberg, Whitney Newey, Philipp Strack, Tomasz Strzalecki
Proceedings of the National Academy of Sciences Dec 2020, 117 (52) 33141-33148; DOI: 10.1073/pnas.2011446117

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Testing the drift-diffusion model
Drew Fudenberg, Whitney Newey, Philipp Strack, Tomasz Strzalecki
Proceedings of the National Academy of Sciences Dec 2020, 117 (52) 33141-33148; DOI: 10.1073/pnas.2011446117
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    • Abstract
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