Kappa-like indices of observer agreement viewed from a latent class perspective

It is common practice to assess consistency of diagnostic ratings in terms of 'agreement beyond chance'. To explore the interpretation of such a term we consider relevant statistical techniques such as Cohen's kappa and log-linear models for agreement on nominal ratings. We relate these approaches to a special latent class concept that decomposes observed ratings into a class of systematically consistent and a class of fortuitous ratings. This decomposition provides a common framework in which the specific premises of Cohen's kappa and of log-linear models can be identified and put into perspective. As a result it is shown that Cohen's kappa may be an inadequate and biased index of chance-corrected agreement in studies of intra-observer as well as inter-observer consistency. We suggest a more critical use and interpretation of measures gauging observer reliability by the amount of agreement beyond chance.