In this paper, the notion of Markov move from algebraic statistics is used to analyze the weighted kappa indices in rater agreement problems. In particular, the problem of the maximum kappa and its dependence on the choice of the weighting schemes are discussed. The Markov moves are also used in a simulated annealing algorithm to actually find the configuration of maximum agreement.
Keywords: Markov bases; algebraic statistics; ordinal data; pairwise agreement; rater agreement; simulated annealing.
© 2022. The Author(s).