Abstract
The basic ideas of MDS are introduced doing MDS by hand. Then, MDS is done using statistical software. The goodness of the MDS configuration is evaluated by correlating its distances with the data. Unfolding is introduced with a small example.
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- 1.
The first principal axis is a straight line which runs through the point cloud so that it is closest to the points. That is, the sum of the (squared) distances of the points from this line is minimal. The second principal axis is perpendicular to the first and explains the maximum of the remaining variance.
- 2.
The code can be greatly simplified by using plot(result) and plot(result, plot.type = "Shepard") for plots with default properties. The plots can be modified by various arguments (as in the first plot command). The user can also generate his/her own plots using other R-functions or packages as shown here for the Shepard diagram.
- 3.
A Shepard diagram is a scatter plot of the data versus the MDS/unfolding distances, together with the regression line used in the particular scaling model.
- 4.
“Weakly” means that the trend line exhibits some horizontal sections. In practice, this is irrelevant, because if you tilt the steps just a little, the regression trend keeps dropping as you move to the right on the X-axis.
References
De Leeuw, J., & Mair, P. (2009). Multidimensional scaling using majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1–30. http://www.jstatsoft.org/v31/i03/.
R Development Core Team. (2017). R: A language and environment for statistical computing [Manual]. Vienna, Austria. https://www.R-project.org/.
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Borg, I., Groenen, P.J.F., Mair, P. (2018). First Steps. In: Applied Multidimensional Scaling and Unfolding. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-73471-2_1
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DOI: https://doi.org/10.1007/978-3-319-73471-2_1
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