Open AccessA probabilistic multidimensional scaling with unique axes 1
Author(s) -
TSUCHIYA TAKAHIRO
Publication year - 1996
Publication title -
japanese psychological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.392
H-Index - 30
eISSN - 1468-5884
pISSN - 0021-5368
DOI - 10.1111/j.1468-5884.1996.tb00025.x
Subject(s) - scaling , multidimensional scaling , probabilistic logic , maxima , maxima and minima , mathematics , polar coordinate system , polar , maximum likelihood , statistics , transformation (genetics) , statistical model , algorithm , statistical physics , mathematical analysis , geometry , physics , art , biochemistry , chemistry , astronomy , performance art , gene , art history
A probabilistic multidimensional scaling model is proposed. The model assumes that the coordinates of each stimulus are normally distributed with variance Σ i = diag(σ 2 1 , … σ 2 Ri ). The advantage of this model is that axes are determined uniquely. The distribution of the distance between two stimuli is obtained by polar coordinates transformation. The method of maximum likelihood estimation for means and variances using the EM algorithm is discussed. Further, simulated annealing is suggested as a means of obtaining initial values in order to avoid local maxima. A simulation study shows that the estimates are accurate, and a numerical example concerning the location of Japanese cities shows that natural axes can be obtained without introducing individual parameters.