Abstract
The different purposes of MDS are explained: MDS as a psychological model of similarity judgments; MDS for visualizing proximity data; and MDS for testing structural hypotheses.
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Notes
- 1.
Most early MDS programs were set, by default, to deliver a 2-dimensional solution for data that were assumed to have an ordinal scale level.
- 2.
This is easy to see from an example: If point \(i\) has the coordinates \((0,0)\) and \(j\) the coordinates \((3,2)\), we get the intra-dimensional distances \(|0-3|=3\) and \(|0-2|=2\), respectively. The overall distance \(d_{ij}\), with \(p=1\), is thus equal to \(2+3=5.00\). For \(p=2\), the overall distance is 3.61. For \(p=10\), it is equal to 3.01.
- 3.
For the consequences of choosing other coordinate systems and for the many peculiar laws of such “taxicab geometries”, see http://taxicabgeometry.net.
References
Borg, I. (2008). Employee surveys in management: Theories, tools, andpractical applications. Cambridge, MA: Hogrefe.
Borg, I. Leutner, D. (1983). Dimensional models for the perception of rectangles. Perception and Psychophysics, 34, 257–269.
Garner, W. R. (Ed.). (1974). The processing of information and structure. Potomac, MD: Erlbaum.
Guttman, L.& Levy, S. (1991). Two structural laws for intelligence tests. Intelligence, 15, 79–103.
Kruskal, J. B.,& Wish, M. (1978). Multidimensional scaling. Beverly Hills, CA: Sage.
Liu, C., Borg, I.,& Spector, P.E. (2004). Measurement equivalence of a German job satisfaction survey used in a multinational organization: Implications of Schwartz’s culture model. Journal of Applied Psychology, 89, 1070–1082.
Torgerson, W. S. (1958) .Theory and methods of scaling. New York: Wiley.
Wish, M. (1971). Individual differences in perceptions and preferences among nations. In C. W. King& D. Tigert (Eds.), Attitude research reaches new heights (pp. 312–328). Chicago: American Marketing Association.
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Borg, I., Groenen, P.J.F., Mair, P. (2013). The Purpose of MDS. In: Applied Multidimensional Scaling. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31848-1_2
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