ddWDM {WienR}

Wrapper function for the partial derivative of the first-passage time probability density function of the diffusion model

Description

Calculates the partial derivative of the first-passage time probability density function of the diffusion model with respect to one of t, a, v, w, t0, sv, sw, or st0, or calculate the gradient.

Usage

ddWDM(
  wrt,
  t,
  response,
  a,
  v,
  w,
  t0 = 0,
  sv = 0,
  sw = 0,
  st0 = 0,
  precision = NULL,
  K = NULL,
  n.threads = FALSE,
  n.evals = 6000
)

Arguments

wrt

partial derivative w.r.t. one of the following:

• "t" the first-passage time,

• "a" the upper barrier,

• "v" the drift rate,

• "w" the relative starting point,

• "t0" the non-decision time,

• "sv" the inter-trial variability of drift rate,

• "sw" the inter-trial variability of relative starting point,

• "st0" the inter-trial variability of non-decision time, or

• "grad" all the above but t.

t

First-passage time. Numeric vector.

response

Response boundary. Character vector with "upper" and "lower" as possible values. Alternatively a numeric vector with 1=lower and 2=upper.

a

Upper barrier. Numeric vector.

v

Drift rate. Numeric vector.

w

Relative starting point. Numeric vector.

t0

Non-decision time. Numeric vector

sv

Inter-trial variability of drift rate. Numeric vector. Standard deviation of a normal distribution N(v, sv).

sw

Inter-trial variability of relative starting point. Numeric vector. Range of uniform distribution U(w-0.5*sw, w+0.5*sw).

st0

Inter-trial variability of non-decision time. Numeric vector. Range of uniform distribution U(t0, t0+st0).

precision

Optional numeric value. Precision of the partial derivative. Numeric value. Default is NULL, which takes default value 1e-12.

K

Optional. Number of iterations to calculate the infinite sums. Numeric value (integer). Default is NULL.

• precision = NULL and K = NULL: Default precision = 1e-12 used to calculate internal K.

• precision != NULL and K = NULL: precision is used to calculate internal K,

• precision = NULL and K != NULL: K is used as internal K,

• precision != NULL and K != NULL: if internal K calculated through precision is smaller than K, K is used.

We recommend using either default (precision = K = NULL) or only precision.

n.threads

Optional numerical or logical value. Number of threads to use. If not provided (or 1 or FALSE) parallelization is not used. If set to TRUE then all available threads are used.

n.evals

Optional. Number of maximal function evaluations in the numeric integral if sv, sw, and/or st0 are not zero. Default is 6000 and 0 implies no limit and the numeric integration goes on until the specified precision is guaranteed.

Value

A list of the class Diffusion_deriv containing

• deriv: the derivatives of the PDF with respect to the chosen wrt,

• call: the function call,

• err: the absolute error. Only provided if sv, sw, or st0 is non-zero. If numerical integration is used, the precision cannot always be guaranteed.

Author(s)

Raphael Hartmann

References

Hartmann, R., & Klauer, K. C. (2021). Partial derivatives for the first-passage time distribution in Wiener diffusion models. Journal of Mathematical Psychology, 103, 102550. doi:10.1016/j.jmp.2021.102550

Examples

ddWDM(wrt = "a", t = 1.2, response = "upper", a = 1.1, v = 13, w = .6, precision = NULL, K = NULL)