Stocking-Lord IRT linking

As Haebara, but differencing the SUMMED test characteristic curves before squaring.

Usage

morie_equating_stocking_lord(
  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

as morie_equating_haebara.

Details

That single change is the whole distinction and it has a consequence: Stocking-Lord permits item-level misfits to cancel, since only the test total has to match. It is the right criterion when the test score is what will be reported and the wrong one when individual item parameters will be used downstream.

References

Stocking, M. L. and Lord, F. M. (1983). Developing a common metric in item response theory. Applied Psychological Measurement, 7(2), 201-210.

Examples

a <- c(1.0, 1.2, 0.8); b <- c(-0.5, 0.2, 1.1)
r <- morie_equating_stocking_lord(a, b, a / 1.3, (b - 0.4) / 1.3)
round(c(r$A, r$B), 3)
#> [1] 0.861 0.341