Abstract
Various mistakes that users tend to make when using MDS are discussed, from using MDS for the wrong type of data, using MDS programs with suboptimal specifications, to misinterpreting MDS solutions.
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Notes
- 1.
Note that we set the argument eps to an extra-small value here to make the program iterate on and on until it reaches such an exotically small raw Stress value if it can be reached in itmax=3333 iterations. Without this argument, mds() will use the default value eps=1e-06 which causes it to stop earlier.
- 2.
Note that if you plot the correlations of Table 7.1 rather than the dissimilarities on the Y-axis of the Shepard diagram of the interval MDS—using plot(aus1, plot.type="Shepard", shepard.x=kipt)—the regression line is slightly curved. This is so because transforming the correlations into dissimilarities via \(\delta _{ij} = \sqrt{ 1-r_{ij} }\)—which is what \({\small \texttt {diss <- sim2diss(kipt, method="corr") }}\) is doing—is a slightly nonlinear function. This is irrelevant for ordinal MDS, but it shows up in interval MDS.
- 3.
Procrustean fittings can also be used for configurations that differ in the number of points and in their dimensionalities. For example, the configuration in Fig. 2.13 was fitted to the configuration in Fig. 2.12 to make comparisons easier. The target X was derived from Fig. 2.12 by roughly reading off the X- and Y-coordinates of the centroids of the various value groups. In case of different dimensionalities, one can simply add column vectors with only zeroes to X or to Y.
References
Alderfer, C. P. (1972a). Existence, relatedness, and growth. New York: Free Press.
Alderfer, C. P. (1972b). Existence, relatedness, and growth. New York: Free Press.
Borg, I., & Braun, M. (1996). Work values in East and West Germany: Different weights but identical structures. Journal of Organizational Behavior, 17, 541–555.
Borg, I., & Mair, P. (2017). The choice of initial configurations in multidimensional scaling: local minima, fit, and interpretability. Austrian Journal of Statistics, 46, 19–32.
Borg, I., & Shye, S. (1995). Facet theory: Form and content. Newbury Park, CA: Sage.
Buja, A., Logan, B. F., Reeds, J. R., & Shepp, L. A. (1994). Inequalities and positive-definite functions arising from a problem in multidimensional scaling. The Annals of Statistics, 22, 406–438.
Guthrie, J. T. (1973). Models of reading and reading disability. Journal of Educational Psychology, 65 9–18.
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. (2018). Typical Mistakes in MDS. In: Applied Multidimensional Scaling and Unfolding. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-73471-2_7
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DOI: https://doi.org/10.1007/978-3-319-73471-2_7
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