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Pipeline stage: link a calibration to an item bank

Source: R/pipeline-bank.R
link_to_bank.Rd

Puts a calibrated pipeline on the scale of an existing item bank through the anchor items the two have in common, then checks the anchors. Methods:

Usage

link_to_bank(
  p,
  bank,
  method = c("stocking-lord", "haebara", "mean-sigma", "mean-mean", "fixed"),
  anchors = NULL,
  ...
)

Arguments

p

a calibrated pipeline from calibrate().

bank

an item bank from mv_bank() or bank_items().

method

linking method; see above.

anchors

anchor items to use. Defaults to every active bank item that is also in the pipeline with the same item type.

...

further arguments passed to mirt::mirt() for "fixed".

Value

The pipeline with p$link (a list with method, A, B and anchors, a tibble of the anchors' bank and linked locations and their displacement) and the linking flags added. With "fixed", p$model is replaced by the fixed-anchor model.

Details

  • "stocking-lord" (default) and "haebara": characteristic-curve methods. They find the slope A and intercept B of the change of scale (theta on the bank scale = A x theta + B) that make the anchors' test characteristic curve (Stocking-Lord) or item curves (Haebara) match the bank's, weighted by a standard normal ability distribution.

  • "mean-sigma" and "mean-mean": moment methods based on the anchors' locations (and discriminations).

  • "fixed": fixed-anchor calibration. The model is refitted with the anchor parameters fixed at their bank values and the ability mean and variance free, so every new item lands on the bank scale directly.

For the Rasch model the slope is fixed at 1. The checks (thresholds from mv_rules()):

  • too_few_anchors (review): fewer than min_anchors anchor items, or fewer than min_anchor_share of the test.

  • anchor_drift (review): an anchor whose location on the bank scale differs from its bank value by more than anchor_displacement. Drifting anchors can be left out with the anchors argument.

  • linking_constants (review): a slope A outside link_slope_min to link_slope_max, which suggests a very different ability spread or unstable anchors.

  • not_converged (block): the fixed-anchor calibration did not converge.

The constants and the anchor table are kept in p$link and shown in the report.

Examples

# \donttest{
set.seed(1)
a <- matrix(rlnorm(40, 0.2, 0.2)); d <- matrix(rnorm(40))
form_x <- simdata(a[1:25, , drop = FALSE], d[1:25, , drop = FALSE], 1500,
                  itemtype = "2PL")
form_y <- simdata(a[16:40, , drop = FALSE], d[16:40, , drop = FALSE], 1500,
                  itemtype = "2PL", Theta = matrix(rnorm(1500, 0.5, 1.2)))
colnames(form_x) <- sprintf("I%02d", 1:25)
colnames(form_y) <- sprintf("I%02d", 16:40)
px <- calibrate(add_responses(mv_pipeline("Form X"), form_x), model = "2PL")
bank <- bank_items(px)$bank
py <- calibrate(add_responses(mv_pipeline("Form Y"), form_y), model = "2PL")
py <- link_to_bank(py, bank)
py$link$A; py$link$B
#> [1] 1.209101
#> [1] 0.4655744
py <- bank_items(py, bank)
# }