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Functional relations in multidimensional scaling
Author(s) -
Lee SikYum,
Bentler P. M.
Publication year - 1980
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1980.tb00604.x
Subject(s) - scaling , multidimensional scaling , mathematics , euclidean geometry , linear model , linear scale , mathematical optimization , computer science , algorithm , statistics , geometry , geodesy , geography
Theory testing with multidimensional scaling models requires the ability to specify models with functional relations among parameters, to estimate the parameters of such models, and to compare the resulting models to models without functional constraints. The non‐linear optimization theory relevant to general multidimensional scaling models with functional relations is developed via first‐order necessary conditions. A Gauss‐Newton based algorithm is developed to implement the theory. The specific case of constraints to yield a circular configuration in the linear Euclidian distance model is studied in detail, and it is applied to some classical colour data.