Abstract
Ways to assess the goodness of an MDS solution are discussed. The Stress measure and some of its variants are introduced. Criteria for evaluating Stress are presented.
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Notes
- 1.
More precisely, it is “weakly monotonically descending”, where “weak” means that it admits horizontal steps. A “strictly” monotonically descending function, in contrast, always runs downwards from left to right. Strictness is theoretically more desirable but mathematically more complicated and practically irrelevant because the angle of descent can be arbitrarily small.
- 2.
The square root has no deeper meaning here; its purpose is to make the resulting values less condensed by introducing more scatter.
References
Spence, I., & Graef, J. (1974). The determination of the underlying dimensionality of an empirically obtained matrix of proximities. Multivariate Behavioral Research, 9, 331–341.
Spence, I., & Ogilvie, J. C. (1973). A table of expected stress values for random rankings in nonmetric multidimensional scaling. Multivariate Behavioral Research, 8, 511–517.
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Borg, I., Groenen, P.J., Mair, P. (2013). The Goodness of an MDS Solution. In: Applied Multidimensional Scaling. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31848-1_3
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DOI: https://doi.org/10.1007/978-3-642-31848-1_3
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