Density, Distribution, and Sampling Functions for Evidence Accumulation Models
Continuous Dual-Stage Two-Phase Model of Selective Attention
Custom Time-Dependent Drift Diffusion Model
Custom Time- and Weight-Dependent Drift Diffusion Model
Custom Time- and Evidence-Dependent Drift Diffusion Model
Generate Grid for PDF of the Continuous Dual-Stage Two-Phase Model of ...
Generate Grid for PDF of Custom Time-Dependent Drift Diffusion Model
Generate Grid for PDF of Custom Time- and Weight-Dependent Drift Diffu...
Generate Grid for PDF of Custom Time- and Evidence-Dependent Drift Dif...
Generate Grid for PDF of Diffusion Model of Conflict Tasks
Generate Grid for PDF of the Exponential Threshold Model
Generate Grid for PDF of the Leaky Integration Model
Generate Grid for PDF of the Leaky Integration Model With Flip
Generate Grid for PDF of the Linear Threshold Model
Diffusion Model for Conflict Tasks
Generate Grid for PDF of Piecewise Attention Model
Generate Grid for PDF of the Revised Diffusion Model of Conflict Tasks
Generate Grid for PDF of the Rational Threshold Model
Generate Grid for PDF of the Simple Drift Diffusion Model
Generate Grid for PDF of the Sequential Dual Process Model
Generate Grid for PDF of the Shrinking Spotlight Model
Generate Grid for PDF of the Urgency Gating Model
Generate Grid for PDF of the Urgency Gating Model With Flip
Generate Grid for PDF of the Weibull Dual-Stage Two-Phase Model of Sel...
Generate Grid for PDF of the Weibull Threshold Model
Exponential Threshold Model
Leaky Integration Model
Leaky Integration Model With Flip
Linear Threshold Model
Piecewise Attention Model
Revised Diffusion Model of Conflict Tasks
Rational Threshold Model
Simple Drift Diffusion Model
Sequential Dual Process Model
Shrinking Spotlight Model
Urgency Gating Model
Urgency Gating Model With Flip
Weibull Dual-Stage Two-Phase Model of Selective Attention
Weibull Threshold Model
Calculate the probability density functions (PDFs) for two threshold evidence accumulation models (EAMs). These are defined using the following Stochastic Differential Equation (SDE), dx(t) = v(x(t),t)*dt+D(x(t),t)*dW, where x(t) is the accumulated evidence at time t, v(x(t),t) is the drift rate, D(x(t),t) is the noise scale, and W is the standard Wiener process. The boundary conditions of this process are the upper and lower decision thresholds, represented by b_u(t) and b_l(t), respectively. Upper threshold b_u(t) > 0, while lower threshold b_l(t) < 0. The initial condition of this process x(0) = z where b_l(t) < z < b_u(t). We represent this as the relative start point w = z/(b_u(0)-b_l(0)), defined as a ratio of the initial threshold location. This package generates the PDF using the same approach as the 'python' package it is based upon, 'PyBEAM' by Murrow and Holmes (2023) <doi:10.3758/s13428-023-02162-w>. First, it converts the SDE model into the forwards Fokker-Planck equation dp(x,t)/dt = d(v(x,t)*p(x,t))/dt-0.5*d^2(D(x,t)^2*p(x,t))/dx^2, then solves this equation using the Crank-Nicolson method to determine p(x,t). Finally, it calculates the flux at the decision thresholds, f_i(t) = 0.5*d(D(x,t)^2*p(x,t))/dx evaluated at x = b_i(t), where i is the relevant decision threshold, either upper (i = u) or lower (i = l). The flux at each thresholds f_i(t) is the PDF for each threshold, specifically its PDF. We discuss further details of this approach in this package and 'PyBEAM' publications. Additionally, one can calculate the cumulative distribution functions of and sampling from the EAMs.