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Distribution functions for Ranking SDT

Source: R/distributions.R
sdt_ranking_dist.Rd

Density and random generation for ranking signal detection theory (Meyer-Grant et al., 2026). Models rank ordering of m items by perceived strength. Only d is estimated (no criterion or stimulus column). Supports Gumbel-min (closed form) and Gaussian UV-SDT (numerical integration).

Usage

dsdt_ranking(
  counts,
  m,
  d,
  sdratio = 1,
  dist = c("gumbel_min", "normal"),
  log = FALSE
)

rsdt_ranking(n, n_trials, m, d, sdratio = 1, dist = c("gumbel_min", "normal"))

Arguments

counts

Integer matrix with one row per observation and one rank-count column per rank position (1 = most likely target), or a vector for a single observation. Columns beyond a row's set size m must be 0.

m

Integer vector. Number of ranked items per observation. Must be at least 2 and no larger than the number of count columns.

d

Numeric vector. Sensitivity: the distance between the target and lure distributions. It is \(d'\) when sdratio is 1 and, for dist = "gumbel_min", the \(g'\) of Meyer-Grant et al. (2026). With another sdratio it is the balanced index \(d_a\) that sdt_yn() reports (in root-mean-square SD units).

sdratio

Numeric vector. Ratio of signal to noise standard deviations (default 1, i.e., equal variance). Must be positive. Only used when dist = "normal".

dist

Character. The distribution assumed for the latent evidence: "gumbel_min" (default), the smallest extreme value distribution with cumulative distribution function \(1 - \exp(-\exp(x))\), evaluated in closed form; or "normal", Gaussian UV-SDT by numerical integration.

log

Logical. If TRUE, returns log-density (default FALSE).

n

Integer. Number of observations to generate. n_trials, m, d, and sdratio are recycled to this length.

n_trials

Integer vector. Number of ranking trials per observation.

Value

dsdt_ranking returns the (log-)density (multinomial probability). rsdt_ranking returns an integer matrix with one row per observation and one rank-count column per rank position (rank1 ... rank max(m)); rows with a smaller set size have structural zeros in the surplus columns, matching the wide format sdt_ranking() expects.

Parameter scales

These functions take sdratio as the ratio itself, while sdt_ranking() estimates its logarithm (0 = equal variance): a fitted sdratio of 0.375 is a ratio of exp(0.375) = 1.455, and passing 0.375 here instead asks for a signal distribution 2.7 times narrower than the noise. That is a legal value and raises no error, so exponentiate first. d carries across unchanged.

References

Meyer-Grant, C. G., Kellen, D., Harding, S. M., & Singmann, H. (2026). Extreme-value signal detection theory for recognition memory: The parametric road not taken. Psychological Review. Advance online publication. doi:10.1037/rev0000615

Examples

# Gumbel-min ranking density
dsdt_ranking(counts = c(40, 30, 20, 10), m = 4, d = 1.0)
#> [1] 4.92936e-06
# Generate ranking data (m=4, Gumbel-min) for 10 subjects
dat <- data.frame(id = 1:10, set_size = 4L)
dat <- cbind(dat, rsdt_ranking(10, 100, m = 4, d = 1.0))
head(dat)
#>   id set_size rank1 rank2 rank3 rank4
#> 1  1        4    56    25     8    11
#> 2  2        4    54    20    13    13
#> 3  3        4    58    17    16     9
#> 4  4        4    59    20     8    13
#> 5  5        4    48    27    20     5
#> 6  6        4    55    23    11    11