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. A positive careless-response or missingness proportion selects at least one person or response cell.

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,
  n_categories = 2,
  theta_sd = 1.3,
  seed = NULL,
  item_drift = NULL,
  careless = 0,
  missing = 0
)

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: Ratio of the last generated set or group unit to the first. Intermediate units are geometrically spaced; 1 gives equal units and hence an ordinary Rasch fit.
n_categories: Response categories per item: 2 (the default) gives dichotomous items; larger values give partial credit items whose evenly spaced thresholds are centred on the item locations, with the frame unit scaling the whole exponent as in the dichotomous case.
theta_sd: Realised sample standard deviation of person ability. This must be positive when more than one item set is generated because relative set units are identified from person variation shared across sets.
seed: Optional non-negative whole-number RNG seed. See rasch_rng for generator support.
item_drift: Optional list(items=, group=, shift=). The named item or items move by shift logits in one generated person group, violating item invariance across frames. At least one item in every affected set must remain invariant: shifting a set's items together is a frame-origin difference, not item drift within that set. A non-zero drift requires at least two person groups.
careless: Proportion of persons whose complete response vectors are replaced by random category choices. At least one person in every group must retain model-based responses.
missing: Proportion of response cells set missing completely at random after the responses are generated. It must leave at least one observed response.

Value

A wide data frame of class "rasch_sim", containing an ID, item columns, and group. Its truth attribute contains the item-set map required by rasch_efrm.

Examples

d <- simulate_efrm(200, 6, set_unit_ratio = 1.3, seed = 1)
tr <- attr(d, "truth")
ef <- rasch_efrm(d, item_sets = tr$item_sets, groups = "group",
                 id = "id", boot_reps = 0)    # point estimates only
ef$alpha_table   # planted ratio 1.3, recovered within small-sample noise
#>   set alpha se_log_alpha
#>  set1 0.850             
#>  set2 1.176