The package distinguishes missing completely at random (MCAR) estimators from missing at random (MAR) likelihood estimators. In raw rater matrices, NA means the rating was not observed. In the C++ API, categorical missingness is encoded by misskappa::na_code.
The available-case estimator uses the observed rater pairs directly:
\[ \widehat D_o = \frac{\sum_i \sum_{r<s} R_{ir}R_{is} \ell_{X_{ir},X_{is}}} {\sum_i \sum_{r<s} R_{ir}R_{is}}, \]
where \(R_{ir}=1\) when the rating is observed. This targets the pairwise-observed estimand unless missingness is MCAR.
The IPW estimator reweights observed pairs by estimated observation probabilities. In schematic form,
\[ \widehat D_o^{\mathrm{IPW}} = \frac{1}{n}\sum_i \sum_{r<s} \frac{R_{ir}R_{is}}{\widehat\pi_r\widehat\pi_s} \ell_{X_{ir},X_{is}}, \]
with corresponding weighted marginal estimates for chance disagreement. This is the MCAR correction used for the raw categorical estimator.
The FIML estimator fits a categorical full-data distribution under MAR by EM. For observed pattern \(o_i\), the likelihood contribution is
\[ L_i(\theta) = \sum_{x_{\mathrm{mis}}} p_\theta(x_{\mathrm{obs},i}, x_{\mathrm{mis}}), \]
and agreement coefficients are computed from the fitted full-data distribution. The implementation returns Wald covariance estimates through Louis’ observed information when available.
Gwet’s estimator is retained for comparison with the agreement-coefficient literature. It uses its own chance-disagreement convention and should be interpreted as a comparator rather than the default missing-data target.