Distribution functions for Continuous Dual-Process SDT (CDP)

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. 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
)
#> [1] 1.870555e-27
# 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)
#>   id stimulus new1 new2 new3 know4 know5 know6 remember4 remember5 remember6
#> 1  1        0   25    8   18     4     9     6         5        13        12
#> 2  2        0   26   16   11    15     6     1         8         7        10
#> 3  3        0   23   15   18     8     3     4         3         8        18
#> 4  4        0   28   13   13    12     9     2         4         8        11
#> 5  5        0   23   16   13    13     8     2         4         4        17
#> 6  6        0   18   17   12     9     5     8         7        10        14