cswald_dist: Distribution functions for the censored shifted Wald model...

In bmm: Easy and Accessible Bayesian Measurement Models Using 'brms'

Distribution functions for the censored shifted Wald model (cswald)

Description

These functions provide the density, distribution, quantile, and random generation functions for the censored shifted Wald model: cswald. The random generation (rcswald) and distribution functions (pcswald, qcswald) use rtdists::rdiffusion(), rtdists::pdiffusion(), and rtdists::qdiffusion() internally for the "crisk" version, which is theoretically consistent since the censored shifted Wald model is an approximation to the Wiener diffusion model for tasks with high accuracy (few errors).

Usage

dcswald(
  rt,
  response,
  drift,
  bound,
  ndt,
  zr = 0.5,
  s = 1,
  version = c("simple", "crisk"),
  log = TRUE
)

rcswald(n, drift, bound, ndt, zr = 0.5, s = 1)

pcswald(
  q,
  response,
  drift,
  bound,
  ndt,
  zr = 0.5,
  s = 1,
  version = "simple",
  lower.tail = TRUE,
  log.p = FALSE
)

qcswald(
  p,
  response,
  drift,
  bound,
  ndt,
  zr = 0.5,
  s = 1,
  version = "simple",
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

rt	A vector of response times in seconds for which the likelihood should be evaluated
response	A vector of responses coded numerically: 0 = lower response, 1 = upper response
drift	The drift rate
bound	The boundary separation
ndt	The non-decision time
zr	The relative starting point (proportion of boundary separation). Default is 0.5 (unbiased). Values must be between 0 and 1.
s	The diffusion constant - the standard deviation of the noise in the evidence accumulation process. Default is s = 1
version	A character string specifying the version of the cswald for which the likelihood should be returned. Available versions are "simple" and "crisk", the default is "simple."
log	A single logical value indicating if log-likelihoods should be returned, the default is TRUE
n	The number of random samples that should be generated
q	A vector of quantiles (response times) at which to evaluate the CDF
lower.tail	Logical; if TRUE (default), probabilities are P(RT <= q), otherwise P(RT > q)
log.p	Logical; if TRUE, probabilities are returned on the log scale. Default is FALSE
p	A vector of probabilities for which to compute quantiles

Details

Cumulative Distribution Function (pcswald)

For the "simple" version, the CDF is only defined for response = 1 (correct responses), as errors are treated as censored observations. The CDF returns the probability that a correct response occurs by time q. For response = 0, NA is returned with a warning.

For the "crisk" version (competing risks), the CDF computes the defective cumulative distribution P(RT <= q, response = r), which is the probability of responding with the specified response by time q. This uses

rtdists::pdiffusion() internally for accurate computation.

Quantile Function (qcswald)

The quantile function returns the response time q such that P(RT <= q) = p. Similar to the CDF, for the "simple" version this is only defined for response = 1. For the "crisk" version, this uses rtdists::qdiffusion() internally.

Value

• dcswald() returns a numeric vector of (log-)likelihoods.

• rcswald() returns a data.frame with columns rt (response times) and response (1 = upper, 0 = lower).

• pcswald() returns a numeric vector of (log-)probabilities.

• qcswald() returns a numeric vector of quantiles (response times).

See Also

rtdists::rdiffusion(), rtdists::pdiffusion(), rtdists::qdiffusion() for the underlying functions

Examples

dat <- rcswald(n = 1000, drift = 2, bound = 1, ndt = 0.3)
head(dat)
hist(dat$rt)

bmm documentation built on March 30, 2026, 5:08 p.m.