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Bayesian Hierarchical Classes Analysis

Published online by Cambridge University Press:  01 January 2025

Iwin Leenen ,
Iven Van Mechelen ,
Andrew Gelman  and
Stijn De Knop
Iwin Leenen*
Affiliation:
Universidad Complutense de Madrid and University of Leuven
Iven Van Mechelen
Affiliation:
University of Leuven
Andrew Gelman
Affiliation:
Columbia University
Stijn De Knop
Affiliation:
University of Leuven
*
Requests for reprints should be sent to Iwin Leenen, IMIFAP, Málaga Norte 25, Col. Insurgentes Mixcoac, C.P. 03920, Mexico D.F., Mexico. E-mail: iwin@imifap.org.mx
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Abstract

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 diagnosis.

Keywords

Bayesianhierarchical classesMarkov chain Monte Carlo simulationMetropolis algorithmpsychiatric diagnosispsychology of choice
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 1 , March 2008 , pp. 39 - 64
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

Iwin Leenen is now at the Instituto Mexicano de Investigación de Familia y Población (IMIFAP), Mexico. The research reported in this paper was partially supported by the Spanish Ministerio de Educación y Ciencia (programa Ramón y Cajal) and by the Research Council of K.U.Leuven (PDM/99/037, GOA/2000/02, and GOA/2005/04).

The authors are grateful to Johannes Berkhof for fruitful discussions.

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