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Multidimensional Scaling

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Modern Psychometrics with R

Part of the book series: Use R! ((USE R))

Abstract

Multidimensional scaling (MDS) a multivariate method, applicable to a variety of data scenarios. It aims to represent input proximities among objects, such as variables or persons, by means of fitted distances in a low-dimensional space. The chapter starts with general elaborations on proximities, followed by exploratory MDS using the SMACOF framework. Within this context, goodness-of-fit assessment in MDS is discussed in detail. Another section covers confirmatory MDS where it is distinguished between internal and external constraints on the configuration. What follows is a section on unfolding, a technique for dual scaling based on preference data. In the last part of this chapter, basic MDS is extended to multiple input dissimilarity matrices (individual differences scaling). In addition, Procrustes is introduced for matching multiple MDS configurations.

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Notes

  1. 1.

    The upper stress value is not trivial to determine (see De Leeuw and Stoop, 1984), but it cannot become larger than 1.

  2. 2.

    From now on, whenever we say “stress,” we are referring to “stress-1.”

  3. 3.

    Note that in the example above we had such an information about symptom regions by means of the DSM-IV clusters, but this was not anyhow incorporated into the model fit.

  4. 4.

    Fitting an exploratory MDS first and then using the resulting configurations as starting values are in general a good strategy, unless we have a starting solution that is based on a theory.

  5. 5.

    In the fMRI area, MDS applications fall under the umbrella term representational similarity analysis (see Sect. 14.5).

  6. 6.

    Details on how the dissimilarity matrices were assessed can be found in Vaziri-Pashkam and Xu (2017).

  7. 7.

    How these matrices are derived from the brain scans is described in detail in Sects. 14.2.4 and 14.5.

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Authors and Affiliations

  1. Department of Psychology, Harvard University, Cambridge, MA, USA

    Patrick Mair

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Mair, P. (2018). Multidimensional Scaling. In: Modern Psychometrics with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-93177-7_9

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