Behaviormetrika
Online ISSN : 1349-6964
Print ISSN : 0385-7417
ISSN-L : 0385-7417
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A BAYESIAN APPROACH TO ASYMMETRIC MULTIDIMENSIONAL SCALING
Kensuke Okada
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2012 Volume 39 Issue 1 Pages 49-62

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Abstract

We propose a Bayesian approach to asymmetric multidimensional scaling (MDS), which incorporates an asymmetric data structure. The asymmetry is represented by the hill-climbing model, which introduces a slope vector that measures the extent of the difficulty in going from one point to another instead of vice versa, in the MDS space. By using Bayesian estimation with Markov chain Monte Carlo algorithm, both point and interval estimation of the parameters become possible,in addition to the many advantages of Bayesian estimation. The asymmetry is evaluated on the basis of the posterior credibility region of the slope vector. A numerical simulation demonstrates that the proposed method is effective for recovering the true parameter values. The proposed method is demonstrated by the analysis of brand-switching data.

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© 2012 The Behaviormetric Society
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