Solved – NMDS: why is the r-squared for a factor variable so low

multidimensional scalingrr-squared

I am doing an NMDS ordination. The data come from a number of sites scattered around two lakes. In the plots, I coloured the samples from the two lakes blue and green. There seems to be some pretty decent separation between the lakes in the NMDS ordination plot. However, when I use lakes as a factor variable with envfit, I only get an R squared value of 0.19 (although the pvalue was less than 0.001). The R squared value is way lower than I thought. Am I missing something or am I reading too much into this? enter image description here

Best Answer

Let me take a crack. I believe factorfit finds average ordination scores for each level of your factor (and places an arrowhead), and performs a regression (with goodness of fit)... Although it appears that you have separation due to your factor in nMDS space, the R^2 is likely low simply due to high variance in ordination score around an expected regression score. This could simply be due to other variables that you include in your nMDS ordination, and if you only included [species] important to the distinction between habitat, your R^2 would of course go up. Remember that the axes in nMDS are not linear combinations of descriptors... Thus points are arranged by similarity in k-dimensions, and not according to scores of any specific variable.

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