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Generate GPCM Item Parameters

Source: R/irt_params_helpers.R
irt_params_gpcm.Rd

Creates a list of discrimination (a) and step (b) parameters suitable for passing to irt_design() with model = "GPCM".

Usage

irt_params_gpcm(
  n_items,
  n_categories,
  a_dist = "lnorm",
  a_mean = 0,
  a_sd = 0.25,
  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.

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 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. 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

Positive numeric vector of length n_items.

b

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

Details

The Generalized Partial Credit Model (Muraki, 1992) is partial-credit family — like the Partial Credit Model, step parameters within each item are NOT required to be ordered (the defining contrast with the Graded Response Model). Unlike PCM, GPCM allows per-item discrimination: a is a free positive vector rather than fixed at 1. See irt_params_pcm() for the Rasch-family alternative.

See also

irt_params_pcm() for the Rasch-family (a fixed at 1) alternative, irt_params_grm() for the ordered-threshold polytomous model, irt_design() to use the generated parameters.

Examples

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

# Tighter within-item step spread and a wider discrimination distribution
params <- irt_params_gpcm(
  n_items = 15, n_categories = 4,
  a_sd = 0.50, step_dispersion = 0.5, seed = 42
)