At 07:58 PM 11/12/2002 -0500, F. James Rohlf wrote:
>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  #
> >    #07102-3027.  Tel.: (973) 353-5814, Fax: (973) 353-5376.             #
> >    # Home: 14 Forest Drive, Warren, New Jersey 07059-5802.              #
> >    # Home Phone: (908) 753-6441 or 753-1620, Home Fax: (908) 757-1086.  #
> >    # E-mail: [log in to unmask]                                   #
> >    ######################################################################
> >



   ######################################################################
   # 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  #
   #07102-3027.  Tel.: (973) 353-5814, Fax: (973) 353-5376.             #
   # Home: 14 Forest Drive, Warren, New Jersey 07059-5802.              #
   # Home Phone: (908) 753-6441 or 753-1620, Home Fax: (908) 757-1086.  #
   # E-mail: [log in to unmask]                                   #
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