Distribution functions for dual-process SDT (DPSDT)

Density and random generation for the dual-process signal detection model (Yonelinas, 1994), with recall-to-reject of new items (Rn; as in Yonelinas, 2024). Extends rating SDT with recollection probabilities Ro (old items recollected as old) and Rn (new items recall-rejected) that add mass to the most-confident rating category. These are the simulation counterparts of the dpsdt version of sdt_rating(); here Ro/Rn are supplied directly as probabilities in [0, 1].

Usage

dsdt_dpsdt(
  counts,
  stimulus,
  d,
  thresholds,
  Ro,
  Rn = 0,
  sdratio = 1,
  dist = c("normal", "gumbel_min", "gumbel_max", "logistic"),
  log = FALSE
)

rsdt_dpsdt(
  n,
  n_trials,
  stimulus,
  d,
  thresholds,
  Ro,
  Rn = 0,
  sdratio = 1,
  dist = c("normal", "gumbel_min", "gumbel_max", "logistic")
)

Arguments

counts: Integer matrix with one row per observation and one column per rating category, ordered from "definitely noise" (1) to "definitely signal" (K), or a vector for a single observation.
stimulus: Integer vector (0/1). Stimulus type: 0 = noise, 1 = signal.
d: Numeric vector. Sensitivity: \(d'\) when sdratio is 1, and otherwise the balanced index \(d_a\) (see sdt_yn()). The separation between the distributions in noise units is d * sqrt((1 + sdratio^2) / 2).
thresholds: Numeric vector of length K-1 with the ordered decision thresholds, or an n-by-(K-1) matrix with one row per observation. The thresholds are positions on the noise-standardized axis, measured from the mean of the noise distribution (the signal mean sits at d * sqrt((1 + sdratio^2) / 2)), and are not rescaled by sdratio.
Ro: Numeric vector in [0, 1]. Recollection probability for old (signal) items.
Rn: Numeric vector in [0, 1]. Recall-to-reject probability for new (noise) items. Defaults to 0, the classic one-sided model, as the dpsdt version fixes it off unless Rn is in the formula.
sdratio: Numeric vector. Ratio of signal to noise standard deviations (default 1, i.e., equal variance). Must be positive. Note that this is the natural scale: the sdratio parameter of sdt_rating() is sampled on the log scale, so it corresponds to log(sdratio) here.
dist: Character. Noise distribution: "normal" (default), "logistic", "gumbel_min", or "gumbel_max".
log: Logical. If TRUE, returns 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_dpsdt returns the (log-)density (multinomial probability). rsdt_dpsdt returns an integer matrix with one row per observation and one rating-count column per category (r1 ... rK).

References

Yonelinas, A. P. (1994). Receiver-operating characteristics in recognition memory: Evidence for a dual-process model. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20(6), 1341–1354. doi:10.1037/0278-7393.20.6.1341

Yonelinas, A. P. (2024). The role of recollection and familiarity in visual working memory: A mixture of threshold and signal detection processes. Psychological Review, 131(2), 321–348. doi:10.1037/rev0000432

Examples

# Density for a single observation (K=4) with recollection of old items;
# Rn defaults to 0 (no recall-to-reject), the one-sided model
dsdt_dpsdt(counts = c(2, 8, 20, 70), stimulus = 1,
           d = 1.5, thresholds = c(0.25, 0.75, 1.25), Ro = 0.3)
#> [1] 3.023007e-05
# Generate DPSDT rating data (K=4) for 10 subjects and both stimulus types
dat <- expand.grid(id = 1:10, stimulus = c(0L, 1L))
dat <- cbind(dat, rsdt_dpsdt(nrow(dat), 100, dat$stimulus, d = 1.5,
                             thresholds = c(0.25, 0.75, 1.25),
                             Ro = 0.3, Rn = 0.1))
head(dat)
#>   id stimulus r1 r2 r3 r4
#> 1  1        0 60 18 13  9
#> 2  2        0 64 17  4 15
#> 3  3        0 58 13 13 16
#> 4  4        0 69 14  6 11
#> 5  5        0 67 15  3 15
#> 6  6        0 55 20 11 14