Abstract
The data for MDS, proximities, are discussed. Proximities can be collected directly as judgments of similarity; proximities can be derived from data vectors; proximities may result from converting other indexes; and co-occurrence data are yet another popular form of proximities.
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Notes
- 1.
For other forms of standardization, the results are essentially the same. For example, when turning the variables first into z-scores (with mean zero and \(sd=1\)), Eq. (4.1) changes to \(const= \sqrt{2N}\). Note, however, that when you compute a product-moment correlation, you implicitly standardize your variables. If that makes sense, you should also standardize them before computing distances, but then using correlations or distances does not make a difference in ordinal MDS.
- 2.
An R-function, dist.binary(), for computing ten different S-coefficients—including \(S_2\), \(S_3\), and \(S_4\) – among the columns of a binary data matrix can be found at https://rdrr.io/rforge/ade4/src/R/dist.binary.R.
- 3.
If you have many cases of no co-occurrence, then your dissimilarity matrix becomes very sparse. Then, of course, MDS may become rather arbitrary, producing fancy configurations based on almost no data.
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Borg, I., Groenen, P.J.F., Mair, P. (2018). Proximities. In: Applied Multidimensional Scaling and Unfolding. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-73471-2_4
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