Concurrent calibration with anchor items

Formula: jointly fit b_F, b_R on the combined sample with anchors

Usage

Cnsint(y, item = NULL, group = NULL, anchor = NULL, iters = 200)

Arguments

y: An n x k matrix of 0/1 responses, both groups stacked.
item: Ignored; the columns are the items.
group: Group label per examinee, or NULL.
anchor: Zero-based indices of the anchor items, or NULL.
iters: Joint MAP cycles.

Value

List with estimate, b, b_focal, b_reference, drift, theta_mean_focal, theta_mean_reference, n, k, n_anchor, method.

Details

Both groups are calibrated in ONE run, so the common anchor items put every parameter on a single scale with no separate linking transformation. Any drift between the two groups' anchor difficulties is therefore an estimate of anchor instability rather than of scale.

References

Wingersky & Lord (1984), Applied Psychological Measurement 8(3):347-364; Kolen & Brennan (2014), Test Equating, Scaling, and Linking, 3rd ed., Springer, ch. 6.

Examples

set.seed(20)
n <- 200; k <- 6
theta <- c(rnorm(100, 0), rnorm(100, 0.5))
b <- seq(-1, 1, length.out = k)
y <- matrix(rbinom(n * k, 1, plogis(outer(theta, b, "-"))), n, k)
r <- Cnsint(y, group = rep(c("F", "R"), each = 100), anchor = 0:2)
r$theta_mean_focal - r$theta_mean_reference
#> [1] -0.4311336