Gradient of ML ability scores w.r.t. 1PL item parameters — ability_gradient

Computes the implicit derivative of bounded maximum-likelihood ability scores with respect to the 1PL parameters (a_shared, d_1, ..., d_J).

Usage

ability_gradient_1pl(
  resp,
  item_pars,
  theta = NULL,
  bounds = c(-6, 6),
  eps = 1e-10
)

Arguments

resp: Response matrix.
item_pars: Item parameters with all a equal (1PL), or a "mixedsubjects_1pl_fit" object.
theta: Optional precomputed ability estimates.
bounds: Bounds passed to score_theta().
eps: Tolerance for near-zero test information.

Value

A matrix with one row per response pattern and J + 1 columns (a_shared, then one column per item's d_j).

Details

The gradient for the shared discrimination is the sum of the per-item discrimination gradients: da_shared = sum_j da_j (chain rule via the constraint a_j = a_shared).