Hierarchical classes models are models for N-way N-mode data that represent the association
among the N modes and simultaneously yield, for each mode, a hierarchical classification of its elements.
In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode
binary data. In line with the original model, the new probabilistic extension still represents both the association
among the two modes and the hierarchical classifications. A fully Bayesian method for fitting
the new model is presented and evaluated in a simulation study. Furthermore, we propose tools for model
selection and model checking based on Bayes factors and posterior predictive checks.We illustrate the advantages
of the new approach with applications in the domain of the psychology of choice and psychiatric