Quadratic kappa under missing data (normal FIML)

Backend for `kappa(estimator = "nt_fiml")`. Estimates the quadratically weighted Conger, Fleiss, and Brennan-Prediger agreement coefficients for continuous (or numerically scored) ratings with missing entries, via a multivariate-normal covariance fitted by full-information maximum likelihood (the EM algorithm), valid under ignorable (MCAR or MAR) missingness. The default covariance model is saturated. `em_options = list(covariance = "variance_components")` fits the compound-symmetry (fixed-rater) covariance model \(\Sigma = \psi J + e I\). It treats raters as fixed, distinct from ten Hove's random-rater MLE-RE / ICC. 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, for the default saturated covariance model, every rater pair is jointly observed before dispatch. Direct callers should enforce the same fixed-rater condition. For `covariance = "variance_components"` this is a connected rater co-observation graph.

Usage

kappa_quadratic_fiml(x, values = NULL, 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.

values

Optional finite numeric score vector defining the uniform Brennan-Prediger chance baseline. If `NULL`, the continuous uniform baseline on the observed score range is used.

em_options

Named list tuning the EM fit: `tol` (default `1e-8`), `max_iter` (default `10000`), `covariance`, and `mean`. `covariance = "saturated"` fits the unrestricted normal FIML model. `"variance_components"` fits the compound-symmetry covariance model \(\Sigma = \psi J + e I\) with \(\psi \ge 0\). `mean = "free"` estimates one mean per rater/item (default). `mean = "equal"` estimates a common mean and is supported with `covariance = "variance_components"`, giving the exchangeable normal model used by counts-format normal FIML. `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`, `Fleiss`, and `Brennan-Prediger` coefficients and their 3x3 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`.