sdt_metad_dist: Distribution functions for meta-d' SDT

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

Distribution functions for meta-d' SDT

Description

Density and random generation for the meta-d' model (Maniscalco & Lau, 2012). Confidence thresholds are placed using the metacognitive sensitivity metad, then rescaled so the total "old"/"new" response rates match what type-1 d predicts. These are the simulation counterparts of the metad version of sdt_rating(). The old/new boundary is the middle threshold, so the number of rating categories must be even (an odd number of thresholds).

Usage

dsdt_metad(
  counts,
  stimulus,
  d,
  thresholds,
  metad,
  sdratio = 1,
  dist = c("normal", "gumbel_min", "gumbel_max", "logistic"),
  log = FALSE
)

rsdt_metad(
  n,
  n_trials,
  stimulus,
  d,
  thresholds,
  metad,
  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.
metad	Numeric vector. Metacognitive sensitivity (type-2 sensitivity), on the same scale as d (d', or d_a when sdratio is not 1), so the M-ratio metad / d is unaffected by sdratio. metad = d corresponds to ideal metacognition (recovers rating SDT).
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_metad returns the (log-)density (multinomial probability). rsdt_metad returns an integer matrix with one row per observation and one rating-count column per category (r1 ... rK).

References

Maniscalco, B., & Lau, H. (2012). A signal detection theoretic approach for estimating metacognitive sensitivity from confidence ratings. Consciousness and Cognition, 21(1), 422–430. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.concog.2011.09.021")}

Examples

# Density for a single observation (K=4) with imperfect metacognition
dsdt_metad(counts = c(5, 15, 25, 55), stimulus = 1,
           d = 1.5, thresholds = c(0.25, 0.75, 1.25), metad = 1.0)
# Generate meta-d' 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_metad(nrow(dat), 100, dat$stimulus, d = 1.5,
                             thresholds = c(0.25, 0.75, 1.25), metad = 1.0))
head(dat)

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