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Bayesian hierarchical classes analysis. (English) Zbl 1143.62094

Summary: 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. 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 diagnosis.

MSC:

62P15 Applications of statistics to psychology
62F15 Bayesian inference
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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