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November 2006

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Subject:
From:
"J. Douglas Carroll" <[log in to unmask]>
Reply To:
Classification, clustering, and phylogeny estimation
Date:
Mon, 27 Nov 2006 17:13:17 -0500
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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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   #Psychology, Rutgers University, Graduate School of Management,      #
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