[R] Multidimensional scaling and distance matrices

[Federico Calboli]

Dear All,

I am in the somewhat unfortunate position of having to reproduce the
results previously obtained from (non-metric?) MDS on a "kinship" matrix
using Statistica. A kinship matrix measures affinity between groups, and
has its maximum values on the diagonal. 

Apparently, starting with a nxn kinship matrix, all it was needed to do
was to feed it to Statistica flagging that the matrix was NOT a distance
matrix but a kinship one. If Statistica transformed the kinship matrix
into a distance one (how?) is anybody's guess. 

A quick search immediately showed that a multidimensional scaling is
done on a distance matrix. See for instance:
MASS4, pg 304
"Elements of computational statistics", Jentle, pg 122
Edwards and Oman's article, page 2-7 R-News 3/3 

The fact that Statistica happily perform MDS on a "kinship" matrix is
puzzling. Indeed, I would expect errors, as in the following toy
example, without transforming the kinship matrix to distances:

> test
           V1          V2          V3          V4          V5
1 0.198716340 0.003612042 0.011926851 0.019737349 0.015021053
2 0.003612042 0.066742885 0.013809924 0.005121996 0.011175845
3 0.011926851 0.013809924 0.197337389 0.013893087 0.006405424
4 0.019737349 0.005121996 0.013893087 0.216047450 0.006218477
5 0.015021053 0.011175845 0.006405424 0.006218477 0.118812936

cmdscale(test)
   [,1] [,2]
V1  NaN  NaN
V2  NaN  NaN
V3  NaN  NaN
V4  NaN  NaN
V5  NaN  NaN
Warning messages:
1: some of the first 2 eigenvalues are < 0 in: cmdscale(test)
2: NaNs produced in: sqrt(ev)
> isoMDS(test)
Error in isoMDS(test) : NAs/Infs not allowed in d
> sammon(test)
Error in sammon(test) : initial configuration must be complete
In addition: Warning messages:
1: some of the first 2 eigenvalues are < 0 in: cmdscale(d, k)
2: NaNs produced in: sqrt(ev)


The colleagues who used the above routine are unable to tell me with
certainty whether Statistica used metric/non metric scaling, and if non
metric whether a Kruskall or a Sammon scaling. 

In any case, I would simply like to ask the memebers of the list if I am
correct in thinking that MDS can ONLY be performed on a distance matrix,
and I can therefore reasonably expect that some form of transformation
to a distance matrix has been performed by Statistica prior to the MDS.
It would at least be a first step to understand what exactly Statistica
did with the data.

Regards,

Federico Calboli
-- 



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Federico C. F. Calboli

Dipartimento di Biologia
Via Selmi 3
40126 Bologna
Italy

tel (+39) 051 209 4187
fax (+39) 051 251 208

f.calboli at ucl.ac.uk