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Generate PCM Item Parameters

Source: R/irt_params_helpers.R
irt_params_pcm.Rd

Creates a list of discrimination (a, fixed at 1) and step (b) parameters suitable for passing to irt_design() with model = "PCM".

Usage

irt_params_pcm(
  n_items,
  n_categories,
  b_dist = "normal",
  b_mean = 0,
  b_sd = 1,
  b_range = c(-2, 2),
  step_dispersion = 1,
  seed = NULL
)

Arguments

n_items

Positive integer. Number of items.

n_categories

Positive integer >= 2. Number of response categories per item. Produces n_categories - 1 step columns in b.

b_dist

Character string for the item-center distribution: either "normal" (default) or "even".

b_mean

Numeric. Mean of item centers when b_dist = "normal". Default: 0.

b_sd

Numeric. SD of item centers when b_dist = "normal". Default: 1.

b_range

Length-2 numeric vector giving the minimum and maximum item-center values. Only used when b_dist = "even". Default: c(-2, 2).

step_dispersion

Non-negative numeric. SD of the within-item step offsets drawn from rnorm(0, step_dispersion) and added to each item's center. Default: 1.0, consistent with mirt::simdata's polytomous conventions and the PCM examples in Embretson & Reise (2000). 0 is allowed (all steps within an item equal the item center — degenerate but useful for design exploration).

seed

Optional integer seed for reproducibility.

Value

A named list with elements:

a

Numeric vector of length n_items, all 1 (Rasch family).

b

Numeric matrix with n_items rows and n_categories - 1 columns. Steps are NOT sorted within row.

Details

The Partial Credit Model (Masters, 1982) is a Rasch-family polytomous model: every item shares the same discrimination (fixed at 1), and the step parameters within each item are NOT required to be ordered. This is the defining contrast with the Graded Response Model — see irt_params_grm() for the ordered-threshold alternative.

See also

irt_params_grm() for the ordered-threshold polytomous model, irt_design() to use the generated parameters.

Examples

# PCM parameters: 15 items, 4 response categories
params <- irt_params_pcm(n_items = 15, n_categories = 4, seed = 42)

# Tighter within-item step spread (steps closer to the item center)
params <- irt_params_pcm(
  n_items = 15, n_categories = 4, step_dispersion = 0.5, seed = 42
)