For INDSCAL, the only transformations allowed are
permutations, possible reflections of axes, and
uniform dilations (multiplication of all
coordinates by the same positive constant).
For MDPREF any nonsingular linear transformation
is allowed to be applied to one set (say, the
stimuli), while the "inverse adjoint" of that
transformation should be applied to the other set
(in this case, the subject vectors). The inverse
adjoint is simply the inverse of the transpose of
the matrix involved. If the transformation
matrix is orthogonal, the inverse adjoint of the
matrix is the matrix itself-- so if an orthogonal
transformation is applied to the stimuli (say)
the same orthogonal transformation is applied to
the vectors-- simply rigidly rotating the entire
configuration without changing relationships
among the geometric entities involved.
Best,
Doug Carroll
At 09:29 AM 11/27/2006, Arnaud Trollé wrote:
Hi everyone,
I'm a PhD student working in the field of sound
quality. I'm using MDS tools for my data
analysis and I'd like to use procrustean
analysis to compare some results coming from 2
different data sets. On this subject, could
anyone tell me which specific procrustes
transformations may be authorized (i.e. make
sense) when comparing two perceptual spaces
(with the same dimensionality) given by the MDS
model INDSCAL, and also when comparing two
outcomes (configurations of stimulus points) given by MDPREF ?
Thank you very much in advance,
Arnaud.
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