[R-sig-eco] Change in rotated NMDS scores as a response variable

[gabriel singer]

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.singer at univie.ac.at