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Fit a unidimensional 2PL IRT model

Source: R/parameters.R
fit_2pl.Rd

Estimates per-item discriminations a_j and intercepts d_j by maximizing the IRT marginal likelihood under a standard-normal ability prior using L-BFGS-B. The response probability is plogis(d + a * theta), where a is the discrimination and d is the intercept. Difficulty is returned as b = -d / a.

Usage

fit_2pl(
  resp,
  n_quad = 31,
  initial_pars = NULL,
  quadrature = NULL,
  slope_lower = 1e-04,
  slope_upper = NULL,
  control = list(maxit = 500)
)

Arguments

resp

A numeric item response matrix with rows for subjects and columns for items. Values must be binary 0/1; NA is allowed.

n_quad

Number of standard-normal quadrature nodes.

initial_pars

Optional starting item parameters (matrix or data frame with a/a1 and d columns). If omitted, a_j = 1 and d_j = qlogis(p_j) where p_j is the observed proportion correct for item j.

quadrature

Optional quadrature grid with theta and weight columns.

slope_lower, slope_upper

Bounds on the discriminations. NULL leaves the corresponding side unbounded.

control

Control list passed to stats::optim().

Value

A list with pars, a data frame containing item, a, d, and b; par, the raw parameter vector; optimizer details (value, convergence, message); and model, which is NULL and retained for backward compatibility.

Details

This is the 2PL counterpart of fit_1pl() and uses the same marginal likelihood, quadrature, and gradient machinery as fit_mixed_subjects_mml() at lambda = 0, so a human-only baseline fit and the mixed-subjects estimator are optimized on a common objective.

See also

fit_1pl() for the shared-discrimination version.

Examples

set.seed(1)
pars <- data.frame(a = c(1, 1.2, 0.9, 1.1, 0.8), d = c(0, 0.5, -0.5, 0.2, -0.3))
resp <- simulate_2pl(rnorm(500), pars)
fit <- fit_2pl(resp)
fit$pars
#>   item         a           d           b
#> 1    1 1.4084028 -0.04161168  0.02954530
#> 2    2 0.7733562  0.59261605 -0.76629121
#> 3    3 0.6796751 -0.40146365  0.59066992
#> 4    4 1.2116623  0.10508500 -0.08672796
#> 5    5 0.6915083 -0.32087732  0.46402525