James Lyons-Weiler weiler at ERS.UNR.EDU
Mon Aug 19 14:56:59 CDT 1996

On Mon, 19 Aug 1996, Tim Dickinson wrote:

> On Tue, 6 Aug 1996, Utteridge Timothy Michael Arthur wrote:
(some useful stuff on dca deleted>

> james lyons-weiler also responded to this posting, as follows (in
> part):
> >...So far as what the [ordination] results mean, Tausch et al. (1995)
> >J. Veg. Sci 6:897-902 have shown that any software package that conducts
> >ordination analyses like PCA, DCA, and classification (cluster) analyses
> >such as UPGMA or TWINSPAN have a MAJOR problem: their results depend on
> >data entry order (which species comes first in the matrix, or which
> >character is character #1).  That means that the software may settle on
> >a different answer depending on a completelty arbitrary characteristic of
> >the data.  The problem is due to the fact that multidimensional analyses
> >are computationally complex, so the programmers have to use various
> >estimation steps for eigenvalues.  If they didn't, the programs would take
> >much longer to give an answer.
> well, i haven't seen the rausch et al. paper yet (i just sent off
> for a reprint, and haven't yet looked in the library for j. veg.
> sci.), but i did write an s-plus function to jumble the rows and
> columns of a symmetric resemblance matrix and find its
> eigenstructure each time. as far as i can tell it does what i said
> it does, and there is no difference in either the eigenvalues or the
> eigenvectors regardless of the sequence of rows and columns. s-plus
> is certainly a well-crafted piece of software, so maybe the problem
> identified by rausch et al. only crops up in less carefully
> programmed eigenanalysis routines. i can't see how the sequence of
> rows or columns in a data matrix could affect calculation of the
> resemblances themselves.

Data entry order does not influence the calculation of pairwise distances
or similarity.  The problem comes with the estimation i.e., approximation
of eigenvalues.

> if this really is a problem perhaps
> someone can enlighten me.
Some matrices are worse than others on the entry order side of things.
The problem is not knwoing whether or not the problem exist for a
particular matrix.



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