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Distribution functions for Confidence Rating SDT

Source: R/distributions.R
sdt_rating_dist.Rd

Density and random generation for confidence rating signal detection theory models. The response is a vector of counts across K ordered rating categories (multinomial likelihood).

Usage

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

rsdt_rating(
  n,
  n_trials,
  stimulus,
  d,
  thresholds,
  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.

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_rating returns the (log-)density (multinomial probability). rsdt_rating returns an integer matrix with one row per observation and one rating-count column per category (r1 ... rK).

References

Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics. Wiley.

Selker, R., van den Bergh, D., Criss, A. H., & Wagenmakers, E.-J. (2019). Parsimonious estimation of signal detection models from confidence ratings. Behavior Research Methods, 51(5), 1953–1967. doi:10.3758/s13428-019-01231-3

Examples

# Density for a single observation (K=4)
dsdt_rating(counts = c(5, 15, 25, 55), stimulus = 1,
            d = 1.5, thresholds = c(0.25, 0.75, 1.25))
#> [1] 4.384333e-05
# Generate 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_rating(nrow(dat), 100, dat$stimulus,
                              d = 1.5, thresholds = c(0.25, 0.75, 1.25)))
head(dat)
#>   id stimulus r1 r2 r3 r4
#> 1  1        0 57 15 15 13
#> 2  2        0 67 18  7  8
#> 3  3        0 67 17  8  8
#> 4  4        0 69 13  9  9
#> 5  5        0 59 20 11 10
#> 6  6        0 58 14 20  8