[R] Number of dimension in Multidimensional Scaling

Michael Friendly friendly at yorku.ca
Thu Dec 9 20:38:43 CET 2010

On 12/9/2010 7:26 AM, Petar Milin wrote:
> Hello!
> Very often one can hear that MDS usually ends with two-dimensional
> solution. Of course, there are methods, like Scree-test (proposed by
> Kruskal and Wish, 1981), to determine optimal number of dimensions.
> However, I am trying to find references to this two-dimensional
> gold-standard. Can anyone point me to authors which explicitly states
> that two-dimensions are typical and easiest to represent graphically? In
> Baayen's book (2008) one can find this statement. Are there more?

In nonmetric MDS, goodness of fit is assessed by a Stress statistic 
(actually, there are several), measuring normalized
SS (observed distances - fitted distances)
There is no significance test of adequacy of 2, 3, 4, ... dimensions,
so it is common practice to plot Stress vs # dimensions and look for
an elbow, as in the Scree plot for exploratory factor analysis.

I can't think of anyone who says 2 dimensions are typical, but
they are certainly easier to plot and interpret graphically,
or at least were before dynamic interactive graphics allowed one
to easily plot in 3D and rotate by direct manipulation (rgl, rggobi+ggobi)

My favorite recent book:

  Borg, I. and Groenen, P.: "Modern Multidimensional Scaling: theory and 
applications" (2nd ed.), Springer-Verlag New York, 2005

Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA

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