Hi Jari,
Thanks for your response -- I will definitely be forwarding this on to my
colleagues!
Cheers,
Erin
On Apr 24, 2013, at 2:47 AM, Jari Oksanen wrote:
> Howdy folks,
>
> This is the second time this week we have this issue. There are two (or
> three) separate points:
>
> (1) You should not correlate environmental variables with axes in any
> ordination method. This applies to PCoA, PCA, CA or anything else just as
> well as to NMDS. You can see this by fitting the vectors: they are rarely
> parallel to the axes. Even in CCA/RDA, the vectors for constraints are rarely
> parallel to the axes.
>
> (2) The ordination space in NMDS is metric. The non-metric part is the
> monotonic (non-metric) regression from metric ordination space to observed
> dissimilarities. The observed dissimilarities between sampling units
> ("plots", "sites") need not be metric, but they can be semimetric or
> non-metric, but the ordination space derived from them is metric.
>
> (3) As a separate issue, it is often better to use fitted surfaces than
> fitted vectors. Fitted vectors are appropriate when the fitted surface is a
> plane (first degree linear trend surface). This is rarely the case, and this
> applies to all ordination methods: the fitted surfaces in CA, PCoA or PCA are
> usually just as non-planar as in NMDS.
>
> For point 2: Look at the stressplot(<NMDS-result>). Here horizontal axis
> gives Euclidean distances in NMDS space -- these are metric. The vertical
> axis gives the observed dissimilarities -- these can be anything. The fit
> lines gives the monotonic regression -- this is non-metric.
>
> With vegan::metaMDS() the ordination space is not only metric, but it is
> strictly Euclidean. We do and we can rotate the ordination space.
>
> As a historic note, the vector fitting code for vegan was based on a Bell
> Labs document that describes vector fitting for their NMDS (KYST software).
> The Bell folks invented NMDS, and they regarded vector fitting suitable for
> NMDS from the very beginning. That is, form 1960s.
>
> Cheers, Jari Oksanen
> ________________________________________
> From: r-sig-ecology-boun...@r-project.org
> [r-sig-ecology-boun...@r-project.org] on behalf of Erin Nuccio
> [enuc...@gmail.com]
> Sent: 24 April 2013 12:30
> To: r-sig-ecology@r-project.org
> Subject: [R-sig-eco] envfit and NMDS
>
> Hello list,
>
> I commonly see envfit used for NMDS, and am curious if envfit is considered a
> non-metric vector fitting tool. This question came up during a conversation
> with a colleague who only uses envfit with PCoA, because they are concerned
> that to do this would be problematic for the same reason you are not supposed
> to correlate environmental variables with NMDS axes (you can't correlate
> something that's non-metric with a metric variable). To me, it seems like by
> projecting the metric variable into non-metric space, you're essentially
> making it non-metric, and the correlation would be fine.
>
> If anyone could weigh in and clear up the confusion, that would be great.
> Thanks,
> Erin
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