cswald: Censored-Shifted Wald Model

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

Censored-Shifted Wald Model

Description

Censored-Shifted Wald Model

Usage

cswald(rt, response, links = NULL, version = c("simple", "crisk"), ...)

Arguments

rt	The name of the variable in the dataset containing the response times. Response times should be coded in seconds (not milliseconds).
response	The name of the variable in the dataset containing the response/decision. Responses should be coded as 0 (lower boundary) or 1 (upper boundary). Alternatively, character values "lower" and "upper" or logical values (FALSE/TRUE) are accepted and will be converted automatically.
links	A named list of link functions for the model parameters. Available parameters depend on the version: "simple" has drift, bound, ndt, and s; "crisk" additionally has zr. Default links are "log" for most parameters and "logit" for zr.
version	A character string specifying which version of the cswald model to use. Options are: "simple" (default): The standard censored shifted Wald model, which treats error responses as censored correct responses. Best suited for tasks with few errors (<20%). Note: The bound parameter in the simple version represents the distance from the starting point to the correct boundary, which is half the total boundary separation in the diffusion model (assuming an unbiased starting point). To convert to the full boundary separation (as in DDM or crisk), multiply by 2. "crisk": The competing risks version, which models both response types as arising from racing accumulators toward opposite boundaries. Better suited for tasks with substantial error rates. The bound parameter represents the total boundary separation, consistent with the diffusion model parameterization. For more details, see Miller et al. (2017).
...	Additional arguments passed internally (for testing purposes).

Details

• Domain: Decision Making / Response times

• Task: Choice Reaction Time tasks (with few errors)

• Name: Censored-Shifted Wald Model

• Citation:

  • Miller, R., Scherbaum, S., Heck, D. W., Goschke, T., & Enge, S. (2017). On the Relation Between the (Censored) Shifted Wald and the Wiener Distribution as Measurement Models for Choice Response Times. Applied Psychological Measurement, 42(2), 116-135. https://doi.org/10.1177/0146621617710465

• Version: simple

• Requirements:

  • Reaction times should be passed in seconds

• The response variable should be passed numerically: 0 = lower response, 1 = upper response

• Parameters:

  • drift: drift rate

  • bound: boundary (distance from starting point to correct boundary)

  • ndt: non-decision time

  • s: diffusion constant

• Fixed parameters:

  • mu = 0

  • s = 0

• Default parameter links:

  • drift = log; bound = log; ndt = log; s = log

• Default priors:

  • drift:

    • main: normal(0,1)

    • effects: normal(0,0.3)

  • bound:

    • main: normal(0,0.3)

    • effects: normal(0,0.3)

  • ndt:

    • main: normal(-2,0.3)

    • effects: normal(0,0.3)

  • s:

    • main: normal(0,0.3)

    • effects: normal(0,0.2)

Value

An object of class bmmodel

See Also

dcswald() and rcswald() for the density and random generation functions.

Examples

# generate simulated data from the diffusion model
dat <- rcswald(n = 500, drift = 2, bound = 1.5, ndt = 0.3, zr = 0.5, s = 1)

# specify the model
model <- cswald(rt = "rt", response = "response", version = "simple")

# specify the formula
formula <- bmf(
  drift ~ 1,
  bound ~ 1,
  ndt ~ 1
)

# fit the model
fit <- bmm(
  formula = formula,
  data = dat,
  model = model,
  cores = 4,
  backend = "cmdstanr"
)

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