[R-sig-eco] eig values in MDS

[Jari Oksanen]

On 27/07/10 19:53 PM, "barbara costa" <rbarbarahc at gmail.com> wrote:

 
>  Hello,
>> Do you know how well a MDS can summarize the data set by evaluating the eig
>> values?
>> eig values between what? what is the max value that translates a really
>> good MDS?
>> thanks

Barbara,

Eigenvector methods have eigenvalues. Others don't. Metric MDS is an
eigenvector method and it has eigenvalues. However, you may have a problem
with negative eigenvalues, and then you must understand what you're doing if
you want to get the proportions explained. I do not want to go into details
here, because it is a lengthy issue, but read

Gower, JC (1985) Properties of Euclidean and non-Euclidean distance
matrices. Linear Alg Appl 67: 81--97

Please note that you can get goodness of fit measure for metric scaling
(metric MDS) in base R with function cmdscale() if you set eig=TRUE, but the
implementation has one plain bug (it does not remove the zero eigenvalue but
largest negative eigenvalue) and it is against the Gower reference above.
Package vegan implements function wcmdscale() for weighted metric MDS which
corrects the bug of zero eigenvalue and accords Gower, but understanding
Gower may stretch your mind. Here examples on both:

library(vegan)
data(dune)
cmdscale(vegdist(dune), eig = TRUE)$GOF
summary(eigenvalues(wcmdscale(vegdist(dune), eig=TRUE)))

If you meant the eigenvalue of nonmetric MDS, there is no such a thing,
because NMDS is not an eigenvector method and therefore has no eigenvalues.

Cheers, Jari Oksanen