Fit a many-facet Rasch rating scale model

Usage

df_fit(data, engine = NULL, max_iter = 1000, tol = NULL)

Arguments

data: A `df_data` object.
engine: `"tam"` (marginal ML via `TAM::tam.mml.mfr`, the default when TAM is installed) or `"jmle"` (built-in joint maximum likelihood, the FACETS approach).
max_iter, tol: Convergence controls; `tol = NULL` uses each engine's default (1e-4 for TAM, 1e-6 for JMLE).

Value

A `df_fit` object: `$data`, `$par` (named `theta`, `delta`, `lambda`, `tau`; for TAM also `theta_prior`, the fitted population mean and SD), `$engine`, `$converged`, `$iterations`, and for TAM the fitted `$model`.

Details

Both engines report parameters in the same parameterization: item difficulties and rater severities centered at 0, thresholds centered at 0, and person measures on the resulting logit scale. For TAM, `par$theta` holds EAPs.

JMLE person measures are clamped to [-7, 7], so extreme scores get a finite but arbitrary measure. JMLE's known small-sample spread inflation is not corrected.

Examples

sim <- df_simulate(n_persons = 200, n_items = 3, n_raters = 6, seed = 1)
fit <- df_fit(sim$data, engine = "jmle")
cor(fit$par$lambda, sim$par$lambda[names(fit$par$lambda)])
#> [1] 0.9958962
# \donttest{
if (requireNamespace("TAM", quietly = TRUE)) {
  fit_tam <- df_fit(sim$data, engine = "tam")
  fit_tam$par$tau
}
#> [1] -1.6106372 -0.5208191  0.5767848  1.5546715
# }