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

[Don McKenzie]

Kate — others can give you more in-depth information, but I believe (i.e., my students and I and colleagues believe it) NMDS does indeed use pairwise distance measures, in place of  eigenvector calculations, in computing ordination scores.  Some of these distance-based measures, like the Sorensen’s distance, are not true “metrics”, in that they do not obey the triangle inequality; hence “non-metric” scaling, but still fully quantitative with the scores being continuous variables.  As such they can be used as response variables in OLS and other regression-type models.

Others may correct me if I misspoke.  

As you probably know, there has been considerable heat generated in the ecological community over the relative value of distance-based vs. eigenvector methods for ordination.  My sense from the debate is that when your community data are presence-absence the distance-based measures are more robust, but you will hear arguments against that too.

> On Jul 16, 2015, at 12:19 PM, 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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