  We formulate three generalized Bayesian models for analyzing interrater and
intrarater reliability in the presence of multilevel data. Stan implementations
of these models provide new estimates of interrater and intrarater reliability.
We also derive formulas for calculating marginal correlations under each of the
three models. Comparisons of the kappa estimates and marginal correlations
across the different models are presented from two real-world datasets.
Simulations demonstrate properties of the different measures of agreement under
different model assumptions.
