I am using Non-metric MultiDimensional Scaling (NMDS) on a Bray-Curtis dissimilarity matrix. Then, I am trying to link the resulting NMDS axes (let's say "components") to environmental variables, as done by the envfit function from R package vegan (but without using this package) and described here. My objective is to plot the variable vectors in the NMDS space (as illustrated here).

However, it is not clear in both the literature and in the package documentation whether each environmental variable and/or explanatory NMDS components should be scaled (i.e. by subtracting its mean and/or dividing by its standard deviation) before processing the analysis. This directly affects the regression coefficients and therefore the vector coordinates (i.e. the arrow length in the plot).

I tried many times scaling or not the variables (and NMDS components) before processing the regressions, but the vector lengths always exceeds the NMDS axis scales. What am I doing wrong? Is there some sort of "vector rescaling" needed before plotting, as describe in this tutorial saying that vectors should be scaled by square root of r2?


1 Answer 1


Check out the 2005 vegan tutorial: https://tinyurl.com/yxbt9ry3 I only skimmed it looking for something different, but it seems scaling is implemented in the function.

  • $\begingroup$ I checked this tutorial. As described in the one I cited, the vegan packages only specifies that the Dims (vectors) should be scaled by the square root of r2. But what does "scaled" mean? $\endgroup$
    – G.L
    Aug 10, 2020 at 7:21
  • $\begingroup$ I'm not use if I get your question correctly. Are you asking why you should scale data, e.g. what the purpose of scaling is? $\endgroup$
    – mucl
    Aug 11, 2020 at 9:19
  • $\begingroup$ My question is: what "scaling" means here. There are many ways to "scale" in statistics. Does it mean multiplying, dividing, ... the Dims (vectors) by the square root of r2? $\endgroup$
    – G.L
    Aug 18, 2020 at 8:09

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