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 Michael On 10 December 2010 06:38, Michael Friendly <frien...@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 > 4700 Keele Street Web: http://www.datavis.ca > Toronto, ONT M3J 1P3 CANADA > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
