Simulate extended frame-of-reference data with differing units

Generates data whose latent unit differs across item-set by person-group frames (Humphry 2005): a person in group g responding to an item in set s does so at the frame unit rho = alpha_set * phi_group scaling the whole exponent. The planted set- and group-unit ratios are recovered by rasch_efrm.

Usage

simulate_efrm(
  n_per_group = 300,
  items_per_set = 8,
  n_sets = 2,
  n_groups = 2,
  set_unit_ratio = 1.3,
  group_unit_ratio = 1,
  theta_sd = 1.3,
  seed = NULL
)

Arguments

n_per_group

Persons in each group.

items_per_set

Items in each set.

n_sets, n_groups

Numbers of item sets and person groups.

set_unit_ratio, group_unit_ratio

Geometric span of the set and group units across their levels (1 = equal units, i.e. an ordinary Rasch fit).

theta_sd

Spread of person ability.

seed

Optional RNG seed.

Value

A wide data frame of class "rasch_sim" (id, item columns, group) with attr(x, "truth")$item_sets the set map to pass to rasch_efrm.

Examples

d <- simulate_efrm(300, 8, set_unit_ratio = 1.3, seed = 1)
tr <- attr(d, "truth")
ef <- rasch_efrm(d, item_sets = tr$item_sets, groups = "group")
ef$alpha_table   # recovers the ~1.3 set-unit ratio
#>    set     alpha se_log_alpha
#> 1 set1 0.8913905   0.04276361
#> 2 set2 1.1218428   0.04276361