Fixed-effects modeling of Cohen's weighted kappa for bivariate multinomial data

Cohen's kappa and weighted kappa statistics are the conventional methods that are used widely in measuring agreement for categorical responses. In this paper, we propose a general framework for the fixed-effects modeling of Cohen's weighted kappa for bivariate multinomial data which reduces to Cohen's weighted kappa under certain conditions and hence can be considered as a generalization of the conventional Cohen's weighted kappa. Properties of the proposed method are investigated followed by an evaluation of the asymptotic performance through bootstrap simulation studies and two illustrative examples. Our derivation shows that the Fleiss-Cohen weights, one of the popular weight schemes for Cohen's weighted kappa, might have some unappealing analytical properties, although these do not appear to cause an issue in application.