Fit a mixed-subjects 1PL calibration (frozen expected-count)

Analogous to fit_mixed_subjects() but estimates a shared discrimination parameter a across all items (1PL model). Posterior quadrature weights are frozen at the initial parameter estimates.

Usage

fit_mixed_subjects_1pl(
  observed,
  predicted,
  generated,
  lambda = 1,
  n_quad = 31,
  initial_pars = NULL,
  quadrature = NULL,
  common_predicted_weights = TRUE,
  slope_lower = 1e-04,
  slope_upper = NULL,
  control = list(maxit = 500),
  ...
)

Arguments

observed

Human response matrix, with rows for subjects and columns for items. Values must be binary when initial_pars is omitted.

predicted

Binary LLM responses (0/1) for the same rows and items as observed. Probabilities are not accepted: fractional values are not a valid likelihood input for the marginal IRT objective and break the PPI correction, so sample binary responses from any probabilities first (e.g. rbinom).

generated

Binary generated or unlabeled LLM responses (0/1) for the same item columns. Probabilities are not accepted (see predicted).

lambda

Power-tuning parameter in [0, 1].

n_quad

Number of standard-normal quadrature nodes.

initial_pars

Optional starting item parameters. If omitted, a 2PL model is fit to observed.

quadrature

Optional quadrature grid with theta and weight columns.

common_predicted_weights

Logical; if TRUE, reuse the observed human posterior weights for predicted.

slope_lower

Lower bound for discrimination parameters during optimization. Use NULL for no lower bound.

slope_upper

Upper bound for discrimination parameters during optimization. Use NULL (the default) for no upper bound. Setting a finite bound (e.g. 4) can stabilize the frozen expected-count fit when the LLM parameters differ substantially from the human parameters.

control

Control list passed to stats::optim().

...

Additional arguments passed to fit_1pl() when initial_pars is omitted.

Value

An object of class c("mixedsubjects_1pl_fit", "mixedsubjects_fit").

See also

fit_mixed_subjects_mml_1pl() for the marginal-likelihood version; fit_mixed_subjects() for the 2PL version.

Examples

set.seed(1)
pars <- data.frame(a = 1, d = c(-0.5, 0, 0.5))
observed  <- simulate_2pl(rnorm(40), pars)
generated <- simulate_2pl(rnorm(100), pars)
fit <- fit_mixed_subjects_1pl(
  observed, observed, generated,
  lambda = 0.5, initial_pars = pars, n_quad = 7,
  control = list(maxit = 50)
)
fit$item_pars
#>   item        a           d           b
#> 1    1 1.049967 -0.38433720  0.36604710
#> 2    2 1.049967 -0.04797307  0.04569009
#> 3    3 1.049967  0.37394087 -0.35614552