Finds the (A, B) transform minimising the quadrature-weighted squared
difference between the reference and transformed item characteristic
curves, ITEM BY ITEM.
Usage
morie_equating_haebara(
a_ref,
b_ref,
a_focal,
b_focal,
n_quad = 41,
theta_range = 4
)
Arguments
- a_ref, b_ref
reference-form discriminations and difficulties.
- a_focal, b_focal
focal-form parameters for the same anchors.
- n_quad
quadrature points.
- theta_range
half-width of the quadrature grid.
Value
list with A, B, criterion,
a_transformed, b_transformed.
Details
Using the whole response curve rather than two moments is the point:
mean/mean and mean/sigma linking match summary statistics of the item
parameters and can agree perfectly while the curves themselves do
not. Haebara's criterion cannot be satisfied by two items whose
misfits cancel, because it squares before summing.
References
Haebara, T. (1980). Equating logistic ability scales by a
weighted least squares method. Japanese Psychological
Research, 22(3), 144-149.
Examples
a <- c(1.0, 1.2, 0.8); b <- c(-0.5, 0.2, 1.1)
r <- morie_equating_haebara(a, b, a / 1.3, (b - 0.4) / 1.3)
round(c(r$A, r$B), 3)
#> [1] 0.910 0.335
