Limits...
Time-varying boundaries for diffusion models of decision making and response time.

Zhang S, Lee MD, Vandekerckhove J, Maris G, Wagenmakers EJ - Front Psychol (2014)

Bottom Line: Diffusion models are widely-used and successful accounts of the time course of two-choice decision making.We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries.We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference.

View Article: PubMed Central - PubMed

Affiliation: Department of Cognitive Sciences, University of California Irvine, Irvine, CA, USA.

ABSTRACT
Diffusion models are widely-used and successful accounts of the time course of two-choice decision making. Most diffusion models assume constant boundaries, which are the threshold levels of evidence that must be sampled from a stimulus to reach a decision. We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries. We then develop a computational method for finding time-varying boundaries from empirical data, and apply our new method to two problems. The first problem involves finding the time-varying boundaries that make diffusion models equivalent to the alternative sequential sampling class of accumulator models. The second problem involves finding the time-varying boundaries, at the individual level, that best fit empirical data for perceptual stimuli that provide equal evidence for both decision alternatives. We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference.

No MeSH data available.


Related in: MedlinePlus

Illustration of numerical problems with the basic algorithm The left-hand panel shows the boundary returned by the algorithm without correction. The right-hand panel shows with asterisks the response time distributions generated by the boundaries in the left-hand panel. The target densities generated by the accumulator model are shown in solid lines.
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FA1: Illustration of numerical problems with the basic algorithm The left-hand panel shows the boundary returned by the algorithm without correction. The right-hand panel shows with asterisks the response time distributions generated by the boundaries in the left-hand panel. The target densities generated by the accumulator model are shown in solid lines.

Mentions: Figure A1 shows the numerical problem in the main algorithm that requires the addition of the piece-wise linear correction. It shows the results of applying the unmodified Algorithm 1 to the response time distribution generated by an accumulator model with with Gaussian evidence distribution parameters μ = 0.01 and σ = 0.1 considered in the top-left of Figure 3. The left hand panel of Figure A1 shows the boundaries found, which differ from those in Figure 3 after the 26th sample, as indicated by the broken lines. The right hand panel of Figure A1 shows the target response time distributions generated by the accumulator model as solid lines, and the distributions generated from the boundary found by the unmodified algorithm as a line with asterisk markers. Using a small tolerance for the difference between these expected and generated distributions, it is possible to identify the critical point, highlighted by the magnification in the right hand panel, beyond which the piece-wise linear correction is applied.


Time-varying boundaries for diffusion models of decision making and response time.

Zhang S, Lee MD, Vandekerckhove J, Maris G, Wagenmakers EJ - Front Psychol (2014)

Illustration of numerical problems with the basic algorithm The left-hand panel shows the boundary returned by the algorithm without correction. The right-hand panel shows with asterisks the response time distributions generated by the boundaries in the left-hand panel. The target densities generated by the accumulator model are shown in solid lines.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4260487&req=5

FA1: Illustration of numerical problems with the basic algorithm The left-hand panel shows the boundary returned by the algorithm without correction. The right-hand panel shows with asterisks the response time distributions generated by the boundaries in the left-hand panel. The target densities generated by the accumulator model are shown in solid lines.
Mentions: Figure A1 shows the numerical problem in the main algorithm that requires the addition of the piece-wise linear correction. It shows the results of applying the unmodified Algorithm 1 to the response time distribution generated by an accumulator model with with Gaussian evidence distribution parameters μ = 0.01 and σ = 0.1 considered in the top-left of Figure 3. The left hand panel of Figure A1 shows the boundaries found, which differ from those in Figure 3 after the 26th sample, as indicated by the broken lines. The right hand panel of Figure A1 shows the target response time distributions generated by the accumulator model as solid lines, and the distributions generated from the boundary found by the unmodified algorithm as a line with asterisk markers. Using a small tolerance for the difference between these expected and generated distributions, it is possible to identify the critical point, highlighted by the magnification in the right hand panel, beyond which the piece-wise linear correction is applied.

Bottom Line: Diffusion models are widely-used and successful accounts of the time course of two-choice decision making.We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries.We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference.

View Article: PubMed Central - PubMed

Affiliation: Department of Cognitive Sciences, University of California Irvine, Irvine, CA, USA.

ABSTRACT
Diffusion models are widely-used and successful accounts of the time course of two-choice decision making. Most diffusion models assume constant boundaries, which are the threshold levels of evidence that must be sampled from a stimulus to reach a decision. We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries. We then develop a computational method for finding time-varying boundaries from empirical data, and apply our new method to two problems. The first problem involves finding the time-varying boundaries that make diffusion models equivalent to the alternative sequential sampling class of accumulator models. The second problem involves finding the time-varying boundaries, at the individual level, that best fit empirical data for perceptual stimuli that provide equal evidence for both decision alternatives. We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference.

No MeSH data available.


Related in: MedlinePlus