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 Subject: Re: statistical method From: "J. Douglas Carroll" <[log in to unmask]> Reply To: Classification, clustering, and phylogeny estimation Date: Wed, 9 Mar 2005 12:38:02 -0500 Content-Type: text/plain Parts/Attachments: text/plain (121 lines)
```Maybe this is the usage of this term in some statistical fields, but the
mathematical psychologist Clyde Coombs's (as far as I know original) use of
the word "unfolding" implied finding a real valued continuum (a single
dimension defined on at least an interval, not merely an ordinal, scale)
such that all the input orders can be generated via a model in which each
order is inversely related to the order of distances from an "ideal point"
on that continuum.  Unfolding was later generalized by some students of
Coombs's to the multidimensional case, in which the single dimension was
generalized to a multidimensional space, and the input orders were assumed
to be inversely monotonically related to (Euclidean) distances from a set
of ideal points in this multidimensional space.  This generalization is
referred to as "MULTIDIMENSIONAL unfolding".

While it's certainly true that, in Coombs's original unidimensional version
of unfolding analysis, an order can be associated with the unidimensional
continuum resulting from unfolding analysis, its purpose was NOT to
determine an ordering, but to determine an underlying
continuum.  Furthermore, the order defined by the resulting continuum will
generally NOT be in any realistic sense a "consensus order"; in extreme
cases its average rank order correlation (calculated by any reasonable rank
order correlation coefficient) with the input orders could be zero, in fact.

Doug Carroll

At 10:27 AM 3/9/2005 -0600, shannon wrote:
>Yes -- unfolding is the word. Thanks
>
>
>Bill
>---
>
>                    Joint Meeting of the Interface and
>                 Classification Society of North America
>
>                 http://ilya.wustl.edu/if_csna_2005_meeting/
>                 Abstracts and Registration Deadline is 4/9/05
>
>
>William D. Shannon, Ph.D.
>
>Associate Professor of Biostatistics in Medicine
>Division of General Medical Sciences and Biostatistics
>
>Washington University School of Medicine
>Campus Box 8005, 660 S. Euclid
>St. Louis, MO   63110
>
>Phone: 314-454-8356
>Fax: 314-454-5113
>web page: http://ilya.wustl.edu/~shannon
>
>
>On Wed, 9 Mar 2005, Paul R Swank wrote:
>
> > Do you mean unfolding?
> >
> > Paul R. Swank, Ph.D.
> > Professor, Developmental Pediatrics
> > Medical School
> > UT Health Science Center at Houston
> >
> >
> > -----Original Message-----
> > From: Classification, clustering, and phylogeny estimation
> > Sent: Wednesday, March 09, 2005 9:19 AM
> > Subject: statistical method
> >
> >
> > What is the name of the statistical method which generates an order from a
> > set of orders:
> >
> >       Vote preferences:       A > B > C > D
> >                               B > A > C > D
> >                               A > B > C > D
> >                               A > C > D > B
> >                               etc
> >
> > It is something like peeling?
> >
> >
> > Bill
> > ---
> >
> >                  Joint Meeting of the Interface and
> >               Classification Society of North America
> >
> >               http://ilya.wustl.edu/if_csna_2005_meeting/
> >               Abstracts and Registration Deadline is 4/9/05
> >
> >
> > William D. Shannon, Ph.D.
> >
> > Associate Professor of Biostatistics in Medicine
> > Division of General Medical Sciences and Biostatistics
> >
> > Washington University School of Medicine
> > Campus Box 8005, 660 S. Euclid
> > St. Louis, MO   63110
> >
> > Phone: 314-454-8356
> > Fax: 314-454-5113
> > web page: http://ilya.wustl.edu/~shannon
> >

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