[R-sig-eco] distances in NMDS ordination space

[Gavin Simpson]

Hi Kate,

The Euclidean distances between points in the NMDS ordination are an
approximation to the rank ordering of the original distances. Hence I would
consider whether the (approximate) rank ordering of the original distances
is the correct metric for the thing you want to include in your model. You
would also need to consider the stress of the solution, the error in the
mapping.

I'm not convinced that NMDS distances are better than embedding the
original distances in a Euclidean space using PCoA. Each has difficulties
(ranks vs imaginary eigenvalues).

HTH

Gavin

On 16 July 2015 at 13:19, Kate Boersma <kateboersma at gmail.com> wrote:

> Hi all.
>
> I have a methodological question regarding non-metric multidimensional
> scaling. This is not specific to R. Feel free to refer me to another
> venue/resource if there is one more appropriate to my question.
>
> Correct me if I'm wrong: NMDS axes are non-metric, which is why NMDS
> frequently makes sense for community data, but it also means that distances
> in NMDS ordination space cannot be interpreted simplistically as they can
> in eigenvalue-based methods like PCA. This is why it is inadvisable
> (meaningless) to use NMDS axes as response variables in a linear modeling
> framework (e.g., with environmental variables as predictors).
>
> My question is this: Does that mean that it is also inadvisable to use
> distances among points in ordination space as response variables?
>
> My (potentially flawed) understanding: While the coordinates may not make
> sense in isolation, they should be meaningful relative to each other. In a
> 2D ordination, if communities A & B are closer together in ordination space
> than communities C & D, that means they have more similar species
> compositions. Therefore, I should be able to predict the distance between
> points in a linear modeling framework.
>
> Alternately, I could use the actual distances among communities from my
> dissimilarity matrix with a method like db-RDA. But I used NMDS over RDA or
> CCA for a reason. It seems more straightforward to use the distances from
> my NMDS ordination instead of generating new coordinates from a PCoA to fit
> an RDA framework (as in db-RDA)... but this logic only works if NMDS
> distances are informative.
>
> Are these comparable analyses? If not, why not?
>
> I'd love your opinions.
>
> Thank you,
> Kate
>
> --
> Kate Boersma, PhD
> Department of Biology
> University of San Diego
> 5998 Alcala Park
> San Diego CA 92110
> kateboersma at gmail.com
> http://www.oregonstate.edu/~boersmak/
>
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-- 
Gavin Simpson, PhD

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