Distribution functions for meta-d' SDT — sdt_metad

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. 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)
#> [1] 6.662953e-05
# 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)
#>   id stimulus r1 r2 r3 r4
#> 1  1        0 57 27  7  9
#> 2  2        0 62 21  5 12
#> 3  3        0 52 19 16 13
#> 4  4        0 52 29 10  9
#> 5  5        0 55 28  8  9
#> 6  6        0 52 25  9 14