Quadratic (Conger / Fleiss) kappa under missing data (normal FIML)

Backend for `kappa(estimator = "nt_fiml")`. Estimates the quadratically weighted Conger and Fleiss agreement coefficients for continuous (or numerically scored) ratings with missing entries, via a saturated multivariate-normal covariance fitted by full-information maximum likelihood (the EM algorithm), valid under ignorable (MCAR or MAR) missingness. The coefficients are smooth functions of the fitted mean and covariance, and the standard error is a delta-method contraction of their gradient with the asymptotic covariance of the fitted moments. This is the quadratic-kappa counterpart of [alpha_continuous()] and shares its EM, casewise-score, and sandwich machinery.

This backend is normally reached through [kappa()], which checks that every rater is observed and every rater pair is jointly observed before dispatch. Direct callers should enforce the same fixed-rater condition; otherwise the saturated covariance functional is not identified from the observed missing-data pattern.

Usage

kappa_quadratic_fiml(x, em_options = list())

Arguments

x

A subjects-by-raters numeric matrix or data frame; `NA` marks missing entries. Rows that are entirely missing are dropped. The Conger and Fleiss quadratic kappas are scale-invariant, so no category-score vector is required.

em_options

Named list tuning the EM fit: `tol` (default `1e-8`) and `max_iter` (default `10000`). `fd_h` is accepted for backward compatibility and ignored because the observed information is analytic. Pass any subset.

Value

An object of class `misskappa_estimate` carrying the `Conger` and `Fleiss` coefficients and their 2x2 asymptotic covariance. Additional fields: `moments` (the fitted `mu`, `Sigma`, EM `iterations`, and `converged` flag) and `psi` (per-subject influence-function rows). Methods: `print`, `coef`, `vcov`, `confint`, `as.data.frame`, and `stats::influence`.