Generate 3PL Item Parameters

Creates a list of discrimination (a), difficulty (b), and guessing (c) parameters suitable for passing to irt_design() with model = "3PL".

Usage

irt_params_3pl(
  n_items,
  a_dist = "lnorm",
  a_mean = 0,
  a_sd = 0.25,
  b_dist = "normal",
  b_mean = 0,
  b_sd = 1,
  b_range = c(-2, 2),
  c_shape1 = 5,
  c_shape2 = 17,
  seed = NULL
)

Arguments

n_items

Positive integer. Number of items.

a_dist

Character string for the discrimination distribution. Currently only "lnorm" (log-normal) is supported. Default: "lnorm".

a_mean

Numeric. meanlog for the log-normal distribution. Default: 0.

a_sd

Numeric. sdlog for the log-normal distribution. Default: 0.25.

b_dist

Character string for the difficulty distribution. One of "normal" or "even". Default: "normal".

b_mean

Numeric. Mean of the normal distribution for b. Only used when b_dist = "normal". Default: 0.

b_sd

Numeric. SD of the normal distribution for b. Only used when b_dist = "normal". Default: 1.

b_range

Numeric vector of length 2. Range for evenly-spaced b values. Only used when b_dist = "even". Default: c(-2, 2).

c_shape1

Positive numeric. First shape parameter of the Beta distribution used to generate c. Default: 5.

c_shape2

Positive numeric. Second shape parameter. Default: 17. The default Beta(5, 17) has E[c] ~= 0.227, SD ~= 0.087, consistent with typical four-option multiple-choice items.

seed

Optional integer seed for reproducibility. If NULL (default), the current RNG state is used.

Value

A named list with elements a, b, c, each a numeric vector of length n_items.

See also

irt_params_2pl(), irt_params_grm(), irt_design().

Examples

# Default 3PL parameters for 30 items
params <- irt_params_3pl(n_items = 30, seed = 42)

# Custom guessing distribution (e.g., 5-option items, lower chance level)
params <- irt_params_3pl(
  n_items = 30, c_shape1 = 4, c_shape2 = 16, seed = 42
)