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 <kateboer...@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 > kateboer...@gmail.com > http://www.oregonstate.edu/~boersmak/ > > _______________________________________________ > R-sig-ecology mailing list > R-sig-ecology@r-project.org > https://stat.ethz.ch/mailman/listinfo/r-sig-ecology _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
