Simulate many-facet Rasch data — simulate

Generates fully crossed ratings from a many-facet Rasch model (Linacre 1989), with optional erratic raters, item-by-rater interaction, or halo. A positive rater proportion selects at least one rater when the requested departures can coexist.

Usage

simulate_mfrm(
  n_persons = 80,
  n_items = 5,
  n_raters = 6,
  n_categories = 4,
  theta_sd = 1.2,
  item_sd = 1,
  rater_severity_sd = 0.6,
  erratic_raters = 0,
  interaction = NULL,
  halo = 0,
  seed = NULL
)

Arguments

n_persons, n_items, n_raters: Facet sizes (fully crossed).
n_categories: Rating categories.
theta_sd: Realised sample standard deviation of person ability.
item_sd: Realised sample standard deviation of the deterministic item difficulties; zero gives equal item difficulties.
rater_severity_sd: Realised sample standard deviation of rater severities (the core facet; recovered in facet_effects).
erratic_raters: Proportion of raters who rate at random (feeds the rater fit residual). Erratic and halo raters are disjoint, and together must leave at least one ordinary rater.
interaction: NULL, or list(rater=, item=, bias=): one rater is unusually harsh (positive) or lenient (negative) on one item. Feeds the item-by-rater interaction (fit with interaction = ).
halo: Proportion of raters showing a halo effect: they rate by the person's overall level and barely differentiate items (feeds the rater fit residual and the item-by-rater interaction). Its requested count must fit among the non-erratic raters and leave an ordinary rater. A positive halo proportion requires item_sd > 0.
seed: Optional non-negative whole-number RNG seed. See rasch_rng for generator support.

Value

A long data frame of class "rasch_sim" (person, item, rater, score) ready for rasch_mfrm, with the truth attached.

Examples

d <- simulate_mfrm(60, 5, 6, rater_severity_sd = 0.8, seed = 1)
mf <- rasch_mfrm(d, person = "person", item = "item", score = "score",
                 facets = "rater")
cor(mf$facet_effects$rater$severity, attr(d, "truth")$severity)  # recovered
#> [1] 0.9911336