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Distribution functions for m-AFC SDT

Source: R/distributions.R
sdt_mafc_dist.Rd

Density and random generation for m-alternative forced choice signal detection theory (DeCarlo, 2012). Models accuracy in tasks where one of m alternatives contains the signal. Only the d parameter is estimated (no criterion). All arguments are recycled to the length of the longest one, so passing vectors of d, m, or n_trials generates (or evaluates) one observation per element.

Usage

dsdt_mafc(
  n_correct,
  n_trials,
  m,
  d,
  dist = c("normal", "gumbel_min", "gumbel_max", "logistic"),
  log = FALSE
)

rsdt_mafc(
  n,
  n_trials,
  m,
  d,
  dist = c("normal", "gumbel_min", "gumbel_max", "logistic")
)

Arguments

n_correct

Integer vector. Number of correct responses.

n_trials

Integer vector. Total number of trials per observation.

m

Integer vector. Number of alternatives per observation. Must be at least 2.

d

Numeric vector. Sensitivity \(d'\): the distance between the signal and distractor distributions in SD units. m-AFC assumes a common scale for the two distributions, so this is also the balanced index \(d_a\) that sdt_yn() reports.

dist

Character. The distribution assumed for the latent evidence, given here by its cumulative distribution function:

  • "normal" (default): Gaussian, \(\Phi(x)\)

  • "gumbel_min": smallest extreme value, \(1 - \exp(-\exp(x))\) (the complementary log-log distribution)

  • "gumbel_max": largest extreme value, \(\exp(-\exp(-x))\) (the log-log distribution, as in evd::pgumbel)

  • "logistic": \(1 / (1 + \exp(-x))\)

log

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

n

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

Value

dsdt_mafc returns the (log-)density (binomial probability). rsdt_mafc returns an integer vector with the number of correct responses per observation.

References

DeCarlo, L. T. (2012). On a signal detection approach to m-alternative forced choice with bias, with maximum likelihood and Bayesian approaches to estimation. Journal of Mathematical Psychology, 56(3), 196–207. doi:10.1016/j.jmp.2012.02.004

Examples

# 4-AFC density
dsdt_mafc(n_correct = 80, n_trials = 100, m = 4, d = 1.5)
#> [1] 0.008272764
# Generate 4-AFC data for 20 subjects with varying sensitivity
dat <- data.frame(id = 1:20, n_trials = 200L)
dat$n_correct <- rsdt_mafc(nrow(dat), dat$n_trials, m = 4,
                           d = rnorm(20, 1.5, 0.4))
head(dat)
#>   id n_trials n_correct
#> 1  1      200       128
#> 2  2      200       166
#> 3  3      200       135
#> 4  4      200       158
#> 5  5      200       130
#> 6  6      200       106