Distribution functions for the censored shifted Wald model (cswald)

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

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).

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.

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)
#>          rt response
#> 1 0.3586012        1
#> 2 0.3997922        1
#> 3 0.7422927        1
#> 4 0.8045497        1
#> 5 0.5244073        1
#> 6 0.5207823        1
hist(dat$rt)