Compute posterior quadrature weights for a 2PL model — posterior_weights

Computes each subject's posterior distribution over a fixed quadrature grid under a 2PL model, using stable log-likelihood calculations. Fractional responses in [0, 1] are allowed at this low level, which is useful when LLM output is stored as probabilities rather than sampled binary responses.

Usage

posterior_weights_2pl(
  resp,
  item_pars,
  quadrature = NULL,
  n_quad = 31,
  iterlim = 1e+05
)

Arguments

resp: A response matrix with rows for subjects and columns for items. Values may be binary, fractional in [0, 1], or NA.
item_pars: Item parameters in slope-intercept form. Supply a data frame or matrix with columns a/a1 and d, or a fitted mirt model.
quadrature: Optional quadrature data frame with theta and weight columns. If omitted, a standard-normal grid is created.
n_quad: Number of quadrature nodes used when quadrature is omitted.
iterlim: Maximum number of Newton-Raphson iterations passed to rmutil::gauss.hermite() when quadrature is omitted.

Value

A matrix with one row per subject and one column per quadrature node. Rows sum to one. Attributes theta and weight contain the grid.

Details

Note: the high-level mixed-subjects fitting functions (fit_mixed_subjects_mml() and relatives) require binary predicted and generated; fractional input is supported only in these low-level quadrature utilities. If you have LLM-derived probabilities, sample binary responses from them (e.g. with stats::rbinom()) before calibrating.

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)
W <- posterior_weights_2pl(resp, pars, n_quad = 5)
rowSums(W)
#> [1] 1 1