Quadratic vector agreement from covariance moments — kappa_vector

Internal backend for vector-valued quadratic agreement. For a subjects-by-raters-by-features array, estimates Conger and Fleiss kappas generated by the squared vector loss `(x - y)' W (x - y)`, where `W` is a full symmetric positive-semidefinite feature-weight matrix. The `"pairwise"` method uses pairwise-available covariance moments and is MCAR-oriented; the `"nt_fiml"` method fits the saturated normal mean/covariance by EM and is the vector analogue of [kappa_quadratic_fiml()].

Both methods need each rater-feature cell to be observed at least once. The `"pairwise"` method additionally requires every rater-feature pair to overlap at least once, because each covariance entry is estimated from directly co-observed rows. Direct `"nt_fiml"` callers should enforce the same complete pairwise co-observation condition when the saturated covariance functional is the target.

Usage

kappa_vector_quadratic(
  x,
  method = c("pairwise", "nt_fiml"),
  W = NULL,
  em_options = list()
)

Arguments

x: Numeric array with dimensions subjects, raters, features.
method: `"pairwise"` or `"nt_fiml"`.
W: Optional features-by-features symmetric positive-semidefinite weight matrix. Defaults to the identity matrix.
em_options: Used only by `"nt_fiml"`; named list with `tol` and `max_iter`. `fd_h` is accepted for backward compatibility and ignored because the observed information is analytic.

Value

A `misskappa_estimate` object with `Conger` and `Fleiss` coefficients, covariance matrix, per-subject influence functions, and fitted mean/covariance moments.