[R] Number of dimension in Multidimensional Scaling

Michael Bedward michael.bedward at gmail.com
Fri Dec 10 01:04:08 CET 2010

Just to add to Michael F's comments: I've looked for that elbow many a
time but never found it :)  Admittedly, I typically deal with fairly
noisy, ecological data, but I think it's a mistake to try to identify
the "optimal" number of dimensions. Better instead to concentrate on a
"useful" number, ie. usefully descriptive; able to be related to other
variables etc.

Just my 2c


On 10 December 2010 06:38, Michael Friendly <friendly at yorku.ca> wrote:
> 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
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