|
Forrest Young had a paper on this, that I usually cite in this regard, in
which he used simulation studies to show good metric recovery with nonmetric
MDS:
Young, F.W. (1970). Nonmetric
multidimensional scaling: recovery of metric information. Psychometrika, 46, 357-388.
-Jim Corter
-----Original Message-----
From: J. Douglas
Carroll [mailto:[EMAIL PROTECTED]
Sent: Thu 11/20/2003
12:22 PM
To: [EMAIL PROTECTED]
Cc:
Subject: Re: Nonmetric MDS yields metric
information?
Roger Shepard has written a paper on this-- I recall one in an
early issue
of Journal of Mathematical Psychology. Also, Jean Paul
Benzecri, the French
statistician associated primarily with correspondence
analysis sent Roger some
theorems he proved establishing that, under very
general conditions, ordinal
proximity data leads asymptotically to a metric
solution as n (number of
stimuli or other objects) grows large-- but I'm
not at all sure that this
material was ever published (although Roger may
refer to this in the paper
of his I recall in JMP). This was all done
circa 1963-65, but I don't have
precise reference for Shepard's JMP
paper. Maybe someone else on this
mailing list does. You might
try searching on Roger Shepard and Journal of
Math Psych-- I don't think he
had too many papers on the subject of nonmetric
MDS in that journal, so you
should be able to find it fairly easily. I seem
to recall it's title
was something like "Metric structure from nonmetric data."
Doug
Carroll.
At 04:40 PM 11/20/2003 +0100, Simon Gollick
wrote:
>Dear Listmembers,
>
>in my final paper IÂm dealing
with both metric MDS
>(TorgersonsÂs Triadic combinations from his book
1958)
>and nonmetric MDS (KruskalÂs algorithm) as "milestones
>of
MDS". The most important advantage of nonmetric MDS
>are the low
requirements to data, i.e. the algorithm
>requires only ordinal data to
reconstruct a
>configuration of objects. Nevertheless the
procedure
>yields metric information within the configuration.
My
>problem is how to give a reasonable justification for
>that
fact. I suppose it`s because of the constraints
>simultaneously
concerning all objects.
>What is the minimum number of objects to have
no
>noticeable difference between an ordinal and an
metric
>configuration?
>Could anyone perhaps give me an statement
on this
>subject or at least a reference for a
quotation?
>
>Many thanks an best regards,
>
>Simon
Gollick
>
>
>__________________________________________________________________
>
>Gesendet
von Yahoo! Mail - http://mail.yahoo.de
>Logos und
KlingeltÃne fÃrs Handy bei http://sms.yahoo.de
######################################################################
# 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:
[EMAIL PROTECTED]
#
######################################################################
|
