Propagated ability risk from item-parameter uncertainty — ability

Computes g_i' Sigma g_i for each response pattern, where g_i is the gradient of the ability estimate with respect to item parameters. If theta_true is supplied, the returned total risk also includes squared ability estimation error.

Usage

ability_risk(
  resp,
  fit_or_pars,
  vcov = NULL,
  theta_true = NULL,
  bounds = c(-6, 6)
)

Arguments

resp: Target response matrix.
fit_or_pars: A "mixedsubjects_fit" object or item-parameter data frame.
vcov: Optional covariance matrix. Required when fit_or_pars is item parameters rather than a fitted mixed-subjects object.
theta_true: Optional true theta values for simulation studies.
bounds: Bounds passed to score_theta().

Value

A list with summary and per-pattern details.

Examples

set.seed(1)
pars <- data.frame(a = c(1, 1.2), d = c(0, -0.5))
resp <- simulate_2pl(rnorm(30), pars)
Sigma <- diag(0.01, 4)
ability_risk(resp, pars, vcov = Sigma)$summary
#>   mean_param_var mean_squared_error mean_total_risk
#> 1     0.09088749                 NA      0.09088749