A mixture model-based rater bias index

Mixture models are outstanding procedures to evaluate rater agreement that assume that the objects to be classified by two observers are extracted from a population that is a mixture of two finite subpopulations, the first one representing systematic agreement and the second one random agreement and disagreement. A generalization of the basic mixture model to include four subpopulations representing two latent variables with two classes allows us to preserve its nature (the fit of the model and the systematic subpopulation are the same) and to distinguish a subpopulation for random agreement and two subpopulations for disagreement (one for the upper triangle and the other for the lower triangle of contingency table). In this context, it is possible to define a new rater bias measure based on a mixture model, which is similar to the descriptive index proposed by Ludbrook.