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Bayesian Estimation of Circumplex Models Subject to Prior Theory Constraints and Scale-Usage Bias

Published online by Cambridge University Press:  01 January 2025

Peter Lenk ,
Michel Wedel  and
Ulf Böckenholt
Peter Lenk*
Affiliation:
University Of Michigan
Michel Wedel
Affiliation:
University Of Michigan
Ulf Böckenholt
Affiliation:
McGill University
*
Requests for reprints should be sent to Peter Lenk, The University of Michigan, 701 Tappan Street, Ann Arbor, MI 48109-1234, USA. E-mail: plenk@umich.edu
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Abstract

This paper presents a hierarchical Bayes circumplex model for ordinal ratings data. The circumplex model was proposed to represent the circular ordering of items in psychological testing by imposing inequalities on the correlations of the items. We provide a specification of the circumplex, propose identifying constraints and conjugate priors for the angular parameters, and accommodate theory-driven constraints in the form of inequalities. We investigate the performance of the proposed MCMC algorithm and apply the model to the analysis of value priorities data obtained from a representative sample of Dutch citizens.

Keywords

Bayesian inferencecircumplex correlationsinequality constraintslatent variablesordinal scales
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 1 , March 2006 , pp. 33 - 55
Copyright
Copyright © 2006 The Psychometric Society

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Footnotes

We wish to thank Michael Browne and two anonymous reviewers for their comments. The data for this study were collected as part of the project AIR2-CT94-1066, sponsored by the European Commission.

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