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Bayesian Model Comparison for the Order Restricted RC Association Model

Published online by Cambridge University Press:  01 January 2025

G. Iliopoulos,
M. Kateri and
I. Ntzoufras
G. Iliopoulos
Affiliation:
University of Piraeus
M. Kateri*
Affiliation:
University of Piraeus
I. Ntzoufras
Affiliation:
Athens University of Economics and Business
*
Requests for reprints should be sent to M. Kateri, Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece. E-mail: mkateri@unipi.gr
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Abstract

Association models constitute an attractive alternative to the usual log-linear models for modeling the dependence between classification variables. They impose special structure on the underlying association by assigning scores on the levels of each classification variable, which can be fixed or parametric. Under the general row-column (RC) association model, both row and column scores are unknown parameters without any restriction concerning their ordinality. However, when the classification variables are ordinal, order restrictions on the scores arise naturally. Under such restrictions, we adopt an alternative parameterization and draw inferences about the equality of adjacent scores using the Bayesian approach. To achieve that, we have constructed a reversible jump Markov chain Monte Carlo algorithm for moving across models of different dimension and estimate accurately the posterior model probabilities which can be used either for model comparison or for model averaging. The proposed methodology is evaluated through a simulation study and illustrated using actual datasets.

Keywords

contingency tablesordinal variablesreversible jump MCMC algorithmequality of oddsBayesian model averaging

Information

Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 4 , December 2009, pp. 561 - 587
Copyright
Copyright © 2009 The Psychometric Society

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