Simulate an item bank with features and known difficulties

Difficulty is `b = X w + family effect + noise`. Legacy (`train`) items have calibrated difficulties from large samples (true value plus `legacy_se` error). New generated items (`new`) come from the same families plus one family never seen in training. Optionally, one seen family is "rogue": its new items are `rogue_shift` harder than its history implies, as when a generation template changes.

Usage

cs_simulate(
  n_train = 400,
  n_new = 150,
  n_families = 10,
  n_features = 32,
  signal_sd = 0.8,
  family_sd = 0.4,
  resid_sd = 0.5,
  legacy_se = 0.1,
  rogue_shift = 1.2,
  seed = NULL
)

Arguments

n_train, n_new

Numbers of legacy and new items.

n_families

Number of template families seen in training; one more family appears only among new items.

n_features

Feature (embedding) dimension.

signal_sd, family_sd, resid_sd

SDs of the feature signal, family effects and item-specific residual.

legacy_se

Calibration error of legacy difficulties.

rogue_shift

Shift for the rogue family's new items (0 for none).

seed

Optional seed.

Value

A `cs_sim`: `$items` (`item`, `family`, `set`, `b_true`, `b_legacy`, `rogue`) and `$features` (matrix, rownames = item ids).

Examples

sim <- cs_simulate(n_train = 200, n_new = 60, seed = 1)
table(sim$items$set, sim$items$rogue)
#>        
#>         FALSE TRUE
#>   new      51    9
#>   train   200    0
dim(sim$features)
#> [1] 260  32