SequentialSamplingModels.jl

A collection of sequential sampling models based on the Distributions.jl API.

Currently Supported models

• LBA: Linear Ballistic Accumulator
• LNR: Lognormal Race Model
• Wald: a shifted Wald represented a single boundary diffusion process
• WaldMixture: a shifted Wald represented a single boundary diffusion process with across-trial variability in the drift rate

Racing Diffusion Constructor

• ν: a vector of drift rates
• k: k = b - A where b is the decision threshold, and A is the maximum starting point
• A: the maximum starting point diffusion process, sampled from Uniform distribution
• θ: a encoding-motor time offset

Usage

using SequentialSamplingModels
dist = DiffusionRace(;ν=[1,2], k=.3, A=.7, θ=.2)
data = rand(dist, 10)
like = pdf.(dist, data)
loglike = logpdf.(dist, data)

References

Tillman, G., Van Zandt, T., & Logan, G. D. (2020). Sequential sampling models without random between-trial variability: The racing diffusion model of speeded decision making. Psychonomic Bulletin & Review, 27, 911-936.

Linear Ballistic Accumulator Constructor

• ν: a vector of drift rates
• A: max start point
• k: A + k = b, where b is the decision threshold
• σ: drift rate standard deviation (default=1)
• τ: a encoding-response offset

Usage

using SequentialSamplingModels
dist = LBA(ν=[3.0,2.0], A = .8, k = .2, τ = .3) 
choice,rt = rand(dist, 10)
like = pdf.(dist, choice, rt)
loglike = logpdf.(dist, choice, rt)

References

Lognormal Race Model Constructor

• μ: a vector of means in log-space
• σ: a standard deviation parameter in log-space
• ϕ: a encoding-response offset

Usage

using SequentialSamplingModels
dist = LNR(μ=[-2,-3], σ=1.0, ϕ=.3)
data = rand(dist, 10)
like = pdf.(dist, data)
loglike = logpdf.(dist, data)

References

Rouder, J. N., Province, J. M., Morey, R. D., Gomez, P., & Heathcote, A. (2015). The lognormal race: A cognitive-process model of choice and latency with desirable psychometric properties. Psychometrika, 80(2), 491-513.

Wald Constructor

• υ: drift rate
• α: decision threshold
• θ: a encoding-response offset

Usage

using SequentialSamplingModels
dist = Wald(υ=3.0, α=.5, θ=.130)
rt = rand(dist, 10)
like = pdf.(dist, rt)
loglike = logpdf.(dist, rt)

WaldA Constructor

• ν: drift rate
• k: k = b - A where b is the decision threshold, and A is the maximum starting point
• A: the maximum starting point diffusion process, sampled from Uniform distribution
• θ: a encoding-motor time offset

Usage

using SequentialSamplingModels
dist = WaldA(ν=.5, σ=1.0, ϕ=.3)
data = rand(dist, 10)
like = pdf.(dist, data)
loglike = logpdf.(dist, data)

References

Tillman, G., Van Zandt, T., & Logan, G. D. (2020). Sequential sampling models without random between-trial variability: The racing diffusion model of speeded decision making. Psychonomic Bulletin & Review, 27, 911-936.

WaldMixture Constructor

• υ: drift rate
• σ: standard deviation of drift rate
• α: decision threshold
• θ: a encoding-response offset

Usage

using SequentialSamplingModels
dist = WaldMixture(υ=3.0, σ=.2, α=.5, θ=.130)
rt = rand(dist, 10)
like = pdf.(dist, rt)
loglike = logpdf.(dist, rt)

References

Steingroever, H., Wabersich, D., & Wagenmakers, E. J. (2020). Modeling across-trial variability in the Wald drift rate parameter. Behavior Research Methods, 1-17.