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Bayesian Mixture Model of Extended Redundancy Analysis

Published online by Cambridge University Press:  01 January 2025

Minjung Kyung ,
Ju-Hyun Park  and
Ji Yeh Choi Open the ORCID record for Ji Yeh Choi [Opens in a new window]
Minjung Kyung
Affiliation:
Duksung Women’s University
Ju-Hyun Park
Affiliation:
Dongguk University
Ji Yeh Choi*
Affiliation:
York University
*
Correspondence should be made to Ji Yeh Choi, Department of Psychology, York University, 4700 Keele St., Toronto, ON, Canada. Email: jychoi@yorku.ca
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Abstract

Extended redundancy analysis (ERA), a generalized version of redundancy analysis (RA), has been proposed as a useful method for examining interrelationships among multiple sets of variables in multivariate linear regression models. As a limitation of the extant RA or ERA analyses, however, parameters are estimated by aggregating data across all observations even in a case where the study population could consist of several heterogeneous subpopulations. In this paper, we propose a Bayesian mixture extension of ERA to obtain both probabilistic classification of observations into a number of subpopulations and estimation of ERA models within each subpopulation. It specifically estimates the posterior probabilities of observations belonging to different subpopulations, subpopulation-specific residual covariance structures, component weights and regression coefficients in a unified manner. We conduct a simulation study to demonstrate the performance of the proposed method in terms of recovering parameters correctly. We also apply the approach to real data to demonstrate its empirical usefulness.

Keywords

Bayesianextended redundancy analysisfinite mixture modelclustering
Type
Theory & Methods
Information
Psychometrika , Volume 87 , Issue 3 , September 2022 , pp. 946 - 966
Copyright
Copyright © 2021 The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-021-09809-7.

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