sdt_cdp_dist: Distribution functions for Continuous Dual-Process SDT (CDP)

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

Distribution functions for Continuous Dual-Process SDT (CDP)

Description

Density and random generation for the continuous dual-process signal detection theory model (Wixted & Mickes, 2010). Two correlated continuous dimensions, Familiarity (F) and Recollection (R), generate the aggregate strength S = F + R that drives old/new confidence; Remember/Know judgments split "old" responses on R, and an optional Know/Guess split uses F. The response is a vector of counts across the response categories (multinomial likelihood), in the same format sdt_cdp() is fit to. See sdt_cdp() for the model and sdt_rating() when no R/K split is available.

Usage

dsdt_cdp(
  counts,
  stimulus,
  dfam,
  drec,
  thresholds,
  rcrit,
  kcrit = NULL,
  sigmar = 0,
  rho = 0,
  n_new = NULL,
  dist = "normal",
  log = FALSE
)

rsdt_cdp(
  n,
  n_trials,
  stimulus,
  dfam,
  drec,
  thresholds,
  rcrit,
  kcrit = NULL,
  sigmar = 0,
  rho = 0,
  n_new = NULL,
  dist = "normal"
)

Arguments

counts	Integer matrix with one row per observation and one column per response category in the canonical order new, ⁠[guess]⁠, know, remember (each block ordered by confidence; see sdt_cdp()), or a vector for a single observation. n_new + 2 * n_old columns (R/K) or n_new + 3 * n_old (R/K/G).
stimulus	Integer vector (0/1). Stimulus type: 0 = new/lure, 1 = old/target.
dfam, drec	Numeric vectors. Familiarity and recollection sensitivities: the target means on the F and R axes, each in units of the corresponding lure SD (both lure SDs are 1). They are component means of a bivariate latent space, not the balanced d_a that the other SDT models report as d – the old/new decision here is read off the aggregate strength S = F + R, so the model's discriminability is a derived quantity rather than either of these.
thresholds	Numeric vector of n_new + n_old - 1 ordered confidence thresholds on the aggregate F+R axis, or a matrix with one row per observation.
rcrit	Numeric vector. Remember criterion on the recollection axis.
kcrit	Know criterion on the familiarity axis. NULL (default) for the R/K model; finite values enable the R/K/G model.
sigmar	Numeric vector. Log SD of the recollection target distribution (0 = SD 1).
rho	Numeric vector. F-R correlation on the unconstrained scale; tanh(rho) is the correlation. 0 (default) = independent processes (classic CDP).
n_new	Integer number of "new" confidence levels. Defaults to half the number of confidence levels, rounded down (so 3 of 7); the number of "old" levels follows as length(thresholds) + 1 - n_new.
dist	Noise distribution. Only "normal" is currently supported.
log	Logical; if TRUE return the log-density (default FALSE).
n	Integer. Number of observations to generate. n_trials, stimulus, thresholds, and the model parameters are recycled to this length.
n_trials	Integer vector. Number of trials per observation.

Value

dsdt_cdp returns the (log-)density (multinomial probability). rsdt_cdp returns an integer matrix with one row per observation and the canonical response count columns (new1, ..., ⁠remember<K>⁠) that sdt_cdp() expects – cbind() it to a design data frame for a ready-to-fit data set.

References

Wixted, J. T., & Mickes, L. (2010). A continuous dual-process model of remember/know judgments. Psychological Review, 117(4), 1025–1054. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1037/a0020874")}

Examples

# CDP density (R/K, 1 new + 3 old levels: 3 thresholds, 7 count columns)
dsdt_cdp(
  counts = c(40, 5, 12, 30, 10, 18, 60), stimulus = 1,
  dfam = 0.8, drec = 1.0,
  thresholds = c(-0.5, 0.3, 1.0),
  rcrit = 0.7, n_new = 1
)
# Generate CDP count data (R/K, 3 new + 3 old levels) for 10 subjects
dat <- expand.grid(id = 1:10, stimulus = c(0L, 1L))
dat <- cbind(dat, rsdt_cdp(nrow(dat), 100, dat$stimulus,
                           dfam = 0.8, drec = 1.0,
                           thresholds = c(-1.1, -0.5, 0, 0.6, 1.3),
                           rcrit = 0.5, n_new = 3))
head(dat)

bmm documentation built on Oct. 16, 2026, 9:08 a.m.