I'd appreciate pointers, eg references, even KEYWORDs for the following.
Replies to me please, and if anything useful emerges I'll mail to anyone
interested the results.
I'm working with a colleague in botany who is interested in the way forests
have changed over the past millenia. His data are pollen counts in cores
(from the forest floor) at various depths. These tell him which species
were generating pollen and therefore the composition of the forest in the
immediate environs at that time. These data come to him/me in the shape of
proportions of the pollen for each of up to 60 taxa. (Technically this is
compositional data, but I don't think that is the key issue)
He has perhaps 20-40 time points and a number of sites. Many of the taxa
are completely absent, so the effective dimensionality is perhaps 20. Refer
to this vector as Y(t) and index the 20 taxa by j and site i.
Some taxa 'die out' and are replaced by others. This can happen a number of
times. So some of the series Yj(t) become smaller, some become larger, some
increase and then decrease etc. One can think of this as the forest -
Y(t) - moving through a 20 dimensional space.
Some low-dimensional ways of looking at this space will be better than
others at emphasising movement. Thus, one could plot the first 2 PCs and
then join the dots in time order. It's a pretty tangled ball of wool! But
since it doesn't claim any optimality properties in respect of multivariate
trends that's not surprising. Other 'ordination methods' (such as Corresp
Anal) equally have no properties in terms of time.
One approach I am exploring is to determine (via Can Corr Anal) those line
combs (and hence a low dim view) that maximally correlate with functions of
time. This works to an extent. But it can't be novel! However I'm not
having much success with literature searches.
Hence the request, to references please, especially on the CCA aproach, or
to keywords, and by email to me directly ( in view of the latest reminder
from our leader Matt Whiley)
With thanks
JH
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John Haslett E-mail [log in to unmask]
Professor Phone +353 1 6081114 (direct)
Department of Statistics +353 1 6081767 (sec)
Trinity College Fax +353 1 6615046
Dublin 2,Ireland
WWW: http://www2.tcd.ie/Statistics/staff/jhaslett.html
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