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?
