Mixed-subjects objective function — mixed_subjects

Evaluates the rectified mixed-subjects loss for 2PL item parameters. The parameter vector must contain all discriminations first, followed by all intercepts. The response probability is plogis(d + a * theta).

Usage

mixed_subjects_loss(pars, q_observed, q_predicted, q_llm, lambda = 0)

Arguments

pars: Numeric vector of item parameters: all discriminations a followed by all intercepts d.
q_observed: Quadrature summary for observed human responses, usually returned by mixed_subjects_quadrature().
q_predicted: Quadrature summary for LLM responses/predictions on the same labeled human subjects.
q_llm: Quadrature summary for generated or unlabeled LLM responses.
lambda: Power-tuning parameter in [0, 1].

Value

A scalar loss.

Details

The objective is L_observed(pars) + lambda * (L_generated(pars) - L_predicted(pars)). Setting lambda = 0 gives the human-only expected-count objective.

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)
q <- mixed_subjects_quadrature(resp, item_pars = pars, N_quad = 5)
mixed_subjects_loss(c(pars$a, pars$d), q, q, q, lambda = 0.5)
#> [1] 1.57952