Does item-level DIF add up to different pass rates?

Differential test functioning for the translated form. With difficulties on the reference scale (`b_ref`) and DIF effects `delta`, the translated form has difficulties `b_ref + delta`. For the translated-language population (ability N(-c, sigma_focal^2) on the reference scale) the function computes the pass rate at raw cut `cut` on the translated form versus on a DIF-free form, using exact score distributions. It also computes the expected raw-score shift for an examinee exactly at the cut. Intervals propagate both the linking uncertainty (the focal group's mean ability is `-c`) and the posterior uncertainty of each item's DIF.

Usage

td_impact(dif, cut, n_draws = 200, level = 0.9, seed = NULL)

Arguments

dif: An `td_dif`.
cut: Raw-score passing standard.
n_draws: Posterior draws.
level: Interval level.
seed: Optional seed.

Value

A data frame with estimate and interval for `pass_rate_fair`, `pass_rate_translated`, `pass_rate_change` and `score_shift_at_cut`.

Examples

sim <- td_simulate(n_ref = 400, n_focal = 120, n_items = 20, seed = 5)
dif <- td_dif(td_calibrate(sim$responses, sim$group))
td_impact(dif, cut = 12, n_draws = 50, seed = 1)
#>               quantity     estimate       lower      upper
#> 1       pass_rate_fair 0.2267433549  0.11089795 0.35274110
#> 2 pass_rate_translated 0.2274804477  0.17208872 0.27368403
#> 3     pass_rate_change 0.0007370928 -0.07930847 0.07321356
#> 4   score_shift_at_cut 0.0129088588 -1.01415063 1.40106100