[R] Stress with MDS

[Prof Brian Ripley]

I presume this is isoMDS which is part of package MASS, support software 
for a book.  The definitions of 'stress' are in that book, and the source 
code is part of the package.

It makes no sense to use a metric definition of stress with a non-metric 
method of fitting: the original and fitted distances are not even on the 
same scale.

As for 'nmds', you haven't told us where you found it: please remember to 
supply the 'at a minimum' infomation the posting guide asked for.  (There 
are at least two packages supplying a function of that name.)  It is 
standard academic practice (and basic courtesy) to acknowledge the 
authorship of software you use -- that includes isoMDS.

You need to do some background reading to answer your questions: the 
references in the help for isoMDS would be a good start.


On Wed, 20 Feb 2008, Montignies Francois wrote:

> Hi,
>
> I am looking for the best multidimensional configuration for my data (47*47
> distance matrix).
> I ve tried classical metric (cmdscale) and non metric MDS (isoMDS, nmds)
> but it is now difficult to choose the best solution because of the
> uncertainties in the definitions of the "stress" function.
>
> So, same problem, several questions :
>
> 1. Statistical consideration : With "cmdscale" we get eigen values. What is
> the best way to choose optimal dimensionality? With the eigen values and
> corresponding GOF like we do with PCA ? If I compute stress1, does it make
> any sense (I saw it in some publications)?
>
> 2. With isoMDS and nmds we get the final stress but i can't find the source
> code so i don't know what is in the box. Obviously, I got different values
> from isoMDS and  nmds . I started from the same initial configuration
> (cmdscale) and the same parameters (maxit,tol)to compare results.
> I tried to compute stress1 by myself and find values closed to nmds with
> ndms config, but far away from isoMDS with isoMDS config (plus a strange
> increasing value between k=4 and k=5). Could you help me please?  I lost
> myself...
>
> k	isoMDS$stress  stress1(isoMDS)  nmds$stress	stress1(nmds)
> 2	0,18830413	0.2912164	0.2758062	0.2658789
> 3	0,11521339	0.1866746	0.1754007	0.1727632
> 4	0,08733106	0.1638274	0.1281730	0.1271329
> 5	0,06942862	0.1991569	0.09756043	0.0970992
> 6	0,05751437	0.1563326	0.07846889	0.07822841
>
> Here is my stress1 function
>
> stress1<-function(datadist,fitteddist)
> {sqrt(sum((datadist-fitteddist)^2)/sum(datadist^2))}
>
> Best regards
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595