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THE MULTIDIMENSIONAL ANALYSIS OF ‘ELASTIC’ DISTANCES
Author(s) -
McGee Victor E.
Publication year - 1966
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.2044-8317.1966.tb00367.x
Subject(s) - thurstone scale , monotonic function , multidimensional scaling , judgement , scaling , mathematics , line (geometry) , function (biology) , computer science , mathematical optimization , mathematical analysis , statistics , geometry , evolutionary biology , political science , law , biology
A new orientation to the problem of multidimensional scaling is presented using the notion of ‘elastic’ distances. Making use of a rational theory of judgement variability (in line with Thurstone's remarks about discriminal processes); a monotonic distance function (in line with Shepard's suggestions); an algorithm for determining the monotonic transformations at each iteration (as provided by Kruskal); and a criterion which yields information about the tolerance for variability of judgement that any solution demands, a hybrid analytical approach is proposed as a practical multidimensional scaling procedure. The approach is illustrated using experimental data.