Abstract
Different forms of confirmatory MDS are introduced, from weak forms with external starting configurations, to enforcing theoretical constraints onto the MDS point coordinates or onto certain regions of the MDS space.
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Notes
- 1.
The unavoidable shearing can become extreme with other data. It can make the solutions essentially worthless. Presently, you can only cross your fingers and hope that shearings do not become so strong.
- 2.
- 3.
To see this graphically, first rotate any of the configurations in Fig. 5.4 by 30\(^\circ \), say, and then stretch or compress it along the \(X\)- and the \(Y\)-axis.
- 4.
Cmda is, unfortunately, an old MS-DOS program that is not easy to use. A more user-friendly version that allows one to impose external constraints onto the MDS distances does not exist.
- 5.
Note that Cmda does not only allow the user to impose equality constraints, as in this example. Order constraints are also possible, for example requesting d(1,5) > d(5,9) > d(9,13). Moreover, Cmda can handle equality constraints both under the primary and also under the secondary approach to ties.
- 6.
Proxscal, in contrast, begins from the start with a configuration that perfectly satisfies the external restrictions, and then successively optimizes its fit to the proximities.
- 7.
The present version of Proxscal (in SPSS 20) does not properly handle ordinal re-scalings of external scales if the primary approach toties is chosen. The solution in Fig. 6.5 was generated by an experimental MDS program written by Patrick Groenen in Matlab.
References
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Borg, I., Groenen, P.J., Mair, P. (2013). Confirmatory MDS. In: Applied Multidimensional Scaling. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31848-1_6
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DOI: https://doi.org/10.1007/978-3-642-31848-1_6
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