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QUANTITATIVE INTERPRETATION OF STRESS IN KRUSKAL'S MULTIDIMENSIONAL SCALING TECHNIQUE
Author(s) -
Wagenaar W. A.,
Padmos P.
Publication year - 1971
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.2044-8317.1971.tb00452.x
Subject(s) - multidimensional scaling , mathematics , interpretation (philosophy) , curse of dimensionality , kruskal's algorithm , representation (politics) , scaling , dimension (graph theory) , set (abstract data type) , stress (linguistics) , statistics , data set , dimensionality reduction , basis (linear algebra) , algorithm , combinatorics , computer science , artificial intelligence , geometry , linguistics , philosophy , politics , minimum spanning tree , political science , law , programming language
Some aspects of the quantitative interpretation of stress are discussed on the basis of random sets of synthetic dissimilarity matrices. In Section 1 the relation between measurement error and stress is studied. Synthetic dissimilarities are obtained starting from a random configuration of n points ( n = 8, 10, and 12) in t dimensions (1 ≤ t ≤ 3), and adding a fractional error to the interpoint distances. These dissimilarity sets are then analysed in m dimensions (1 ≤ m ≤ 5). The results give an idea of how the stress is influenced by measurement error and the chosen dimensionality of the analysis. In practice, the results can be used for estimating both the true dimensionality and the measurement error of a set of data. In Section 2 the probability distribution of the stress‐percentages in m dimensions (1 ≤ m ≤ 5) is estimated in cases of randomly chosen dissimilarities among n points (7 ≤ n ≤ 12). The results can be an aid in determining the significance of a multidimensional representation of experimental data.