Re: statistical method

[J. Douglas Carroll]

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
e-mail: [EMAIL PROTECTED]
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
> [mailto:[EMAIL PROTECTED] On Behalf Of shannon
> Sent: Wednesday, March 09, 2005 9:19 AM
> To: CLASS-L@LISTS.SUNYSB.EDU
> 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
> e-mail: [EMAIL PROTECTED]
> web page: http://ilya.wustl.edu/~shannon
>

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