Gradient of ML ability scores with respect to item parameters — ability

Computes the implicit derivative of bounded maximum-likelihood ability scores with respect to 2PL item parameters. The column order is all discriminations followed by all intercepts.

Usage

ability_gradient(resp, item_pars, theta = NULL, bounds = c(-6, 6), eps = 1e-10)

Arguments

resp: Response matrix with rows for subjects and columns for items.
item_pars: Item parameters in slope-intercept form, or a "mixedsubjects_fit" object.
theta: Optional precomputed ability estimates. If omitted, score_theta() is used.
bounds: Bounds passed to score_theta() when theta is omitted.
eps: Tolerance used to mark near-zero test information as undefined.

Value

A matrix with one row per response pattern and one column per item parameter.

Examples

pars <- data.frame(a = c(1, 1.2), d = c(0, -0.5))
resp <- matrix(c(1, 0, 0, 1), nrow = 2, byrow = TRUE)
ability_gradient(resp, pars)
#>         a_Item1    a_Item2    d_Item1    d_Item2
#> [1,]  0.7734458 -0.7106064 -0.4193319 -0.4838901
#> [2,] -1.1679932  0.6298063 -0.3996755 -0.5002704