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] # > ###################################################################### >