[R] Stress with MDS

[Montignies Francois]

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