hmmm... I think Gavin´s approach definitely has more power, though I
don´t quite see why the original idea should not work. Orthogonality is
not an implicit feature of an NMDS but it´s also not "prevented"...
First, I think quite often NMDS still reproduces/extracts orthogonal
features of a dataset.
Second, even if NMDS does not care for orthogonality, a "specific"
feature of the dataset (say, the "moisture information" in herb data)
can behave more or less linearly or at least monotonic in *any*
direction on a 2D-plane, in which case the extraction of a rotated axis
makes complete sense. However, even in this case an ordisurf fit will
greatly help to understand if that´s a legitimate and reasonable
approach as I understand.
gabriel
On 3/10/11 1:04 PM, Gavin Simpson wrote:
On Fri, 2011-02-18 at 10:41 -0800, Erik Frenzel wrote:
Hello all,
I'm interested in adapting a technique from a recent paper
Harrison, S., E. I. Damschen and J. B. Grace 2010. Ecological
contingency in the effects of climate change on forest herbs.
Proceedings of the National Academy of Sciences (USA), 107:
19362-19367.
In which a plot's change in NMDS scores over time was used as a
response variable:
"To measure the overall resemblance of any given herb community to
communities found in warm (steep, southerly) versus cool (moderate,
northerly) topographic microclimates, we used an ordination approach
(also see 28). We ordinated the
herb data using NMS ordination in PC-ORD version 4.14 (39), excluding
species found in<5% of samples. We rotated axis 1 of the ordination
to maximize its correlation with Whittaker’s topographic moisture
gradient, so that a low axis 1 score indicated a community in a mesic
environment such as a moderate north-facing slope, and a high axis 1
score indicated a community in a warm environment such as a steep
south-facing slope. Under a warming climate, we expect the community
at any given site to show a higher axis 1 score in 2007–2009 than in
1949–1951, indicating that herb composition has shifted over time in
the same direction that composition changes over space from mesic
(cooler and moister) to xeric (warmer and drier) topographic
microclimates. For each site we calculated the difference between its
1949–1951 and 2007–2009 axis 1 ordination scores. In this case, a high
value means a community that has shifted to become more dominated by
xeric-adapted species."
Jari Oksanen has a post on the the r-forge page
(https://r-forge.r-project.org/forum/message.php?msg_id=1311&group_id=68)
warning against using rotated NMDS scores in a Structural Equation
Model. Are there problems with using a "change in scores" as a
response variable in this kind of hypothesis testing?
I'm genuinely underwhelmed by this approach. i) there isn't such a thing
as nMDS axes so does it make sense to take some 1-d coordinate system
out of a 2-d coordinate system and relate it to an external variable? It
would be like trying to identify patterns in all the cities of the world
on the basis of what line of longitude they happened to lie on. Where
this sort of thing does make sense is in methods that do identify
orthogonal components from a data matrix such that axis 1 explains a
component of the variation in the data, and axis 2 another, different
(orthogonal) component of the variation.
If this were me, I would have taken the 2-d nMDS configuration and
fitted a response surface for Whittaker's topographic moisture into the
ordination (using ordisurf) and then take the fitted values of the
response surface for each site as the species-related topographic
moisture "information", which could be plotted as a function of time.
HTH
G
This was done in PC Ord. Has anyone used "metaMDSrotate" in vegan to
do this kind of analysis in R? Does anyone have any examples or code
they'd be willing to share or point me to?
Thanks,
Erik
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Dr. Gabriel Singer
Department of Limnology - University of Vienna
and Wassercluster Lunz Biologische Station GmbH
+43-(0)664-1266747
gabriel.sin...@univie.ac.at
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