I agree with Doug's observations but the problem is that I don't know how to
tell whether the nonmetric-MDS will give a much better solution unless I try
it and see what the stress value is. Linear-MDS takes less computing and
avoids some of the degeneracy problems that Doug alludes to. I think they
are usually worth a try as 2D nonmetric-MDS can sometimes give a better fit
than a 3D metric-MDS. PCA, PCoord (classical scaling) can be much worse for
relationships among close points.
Jim Rohlf
> -----Original Message-----
> From: Classification, clustering, and phylogeny estimation
> [mailto:[log in to unmask]]On Behalf Of J. Douglas Carroll
> Sent: Tuesday, November 12, 2002 9:40 PM
> To: [log in to unmask]
> Subject: Re: MDS with a 400X400 Matrix
>
>
> To whomever it may concern (especially Jim Rohlf and David Dubin),
>
> I sent an e-mail response to this same broadcast e-mail sent out via the
> CLASS-L system, but addressed it directly to Jim Rohlf, since, for some
> reason I misinterpreted this as being an inquiry initiated by him, not
> one from someone else (Dirk Meurer, I now see) simply passed on by Jim
> as administrator of CLASS-L. I had thought at the time that perhaps
> David and Mark Rorvig, prior to Rorvig's tragic and untimely death last
> year, had put together such a program. While I gather from this message
> from David that, instead, Michael Trosset (who was also involved
> in the same
> DIMACS Workshop on MDS Algorithms I mentioned in that earlier
> e-mail addressed
> to Jim) has done so. I would therefore endorse David's
> recommendation that
> this software developed by Trosset be used for this purpose. I personally
> think that, in practice, it seldom makes a great difference
> whether one uses
> an MDS procedure that is purely "metric" (as long as you're
> reasonably careful
> to make sure the data are transformed, if necessary, to a form as
> consistent
> as possible with the assumptions that the procedure is based on-- in
> particular,
> most likely that they be DISsimilarities-- which may simply
> entail reversing
> the scale, if data are similarities, by, say, subtracting all
> values from the
> largest similarity value in the matrix, and possibly, if the
> particular method
> assumes RATIO SCALE instead of merely INTERVAL SCALE dissimilarities, that
> these
> dissimilarity values are transformed so that it is reasonable to
> assume that a
> dissimlarity of zero (0) corresponds to a DISTANCE of zero (0) in the
> recovered
> multidimensional representation-- or "nonmetric" (in which the
> similarities or
> dissimilarities are assumed only to be monotonic with the proximities--
> monotone
> non-increasing or monotone non-decreasing respectively for the two types--
> sim.'s
> or dissim.'s-- of proximity data). The metric MDS procedures are
> sufficiently
> robust under even fairly severe nonlinearities in the monotonic "distance
> function"
> transforming proximities into distances in the underlying representation
> that the
> solutions are usually almost totally indistinguishable (as long
> as the same
> dimensionality is assumed in two analyses, of course), although,
> as is well
> known,
> an orthogonal rotation of a two-way MDS solution (based, as almost all MDS
> algorithms are, on assumption of Euclidean metric in the
> underlying space), no
> matter HOW obtained, is necessary to bring even what are really identical
> solutions
> into exact congruence (since Euclidean spaces are defined only up to
> similarity
> transforms-- including an orthogonal rotation, as well as translation of
> the origin
> and, in some cases a possible uniform dilation resulting in multiplication
> of all
> distances by a positive constant-- but the latter two types of
> transformations are
> typically resolved by normalization conventions, so generally do
> not need to be
> considered). In fact, not only are metric solutions (in the same
> dimensionality)
> usually as good as nonmetric ones, there is considerable empirical and
> theoretical
> evidence that, for certain types of data, they are in fact
> BETTER-- being less
> susceptible to various degeneracies and quasi-degeneracies that can affect
> many
> nonmetric MDS analyses, if the data exhibit certain characteristics that
> are not at
> all unusual in the case of realistic proximity data from various domains.
>
> Best,
>
> Doug Carroll.
>
> At 03:52 PM 11/12/2002 -0600, David Dubin wrote:
> >Michael Trosset wrote a program for classical metric MDS that Mark Rorvig
> >and I used with success on matrices much larger than 400 by 400. But it
> >doesn't do nonmetric MDS. The program is written in Fortran and
> requires the
> >ARPACK libraries. I was able to compile with g77 on Linux and
> Solaris with
> >little trouble.
> >
> >Dave Dubin
> >
> >Dirk Meurer <[log in to unmask]> writes:
> >
> > > Dear Listmembers,
> > > I would like to do a MDS with a 400X400 square, symetric matrix of
> > > (dis)similaritys. Most MDS-Software is limited to a much
> smaller amount
> > > of variables though. I have been told, that SAS might be able
> to process
> > > the analyis I need, but this is quite inconvenient for me in terms of
> > > access to the software, hardware-requirements etc. Could anybody tell
> > > me, if there is a stand-alone program that can do MDS (preferably
> > > nonmetric) with a matrix of that size?
> > >
> > > Thanks a lot for your help,
> > > dirk
> > >
> > > P.S: My Matrix is not suitable for factor analysis and clustering does
> > > not produce the results I need.
> > >
>
>
>
> ######################################################################
> # J. Douglas Carroll, Board of Governors Professor of Management and #
> #Psychology, Rutgers University, Graduate School of Management, #
> #Marketing Dept., MEC125, 111 Washington Street, Newark, New Jersey #
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