I used NMDS axes of an ecological community as proxys for the community similarity in the different samples. I would like to "quantify" the importance of the different NMDS axis according to the stressreduction. Now my question is: If I calculate an NMDS with one dimension would the NMDS axis of that be the same as the first axis of a NMDS calculated with two dimensions? Of course, I tried that myself using the metaMDS function in vegan and the axis are not exactly same but correlate with a coefficient >0.9. How can that be explained?

  • $\begingroup$ NMDS is an iterative fitting procedure ( stats.stackexchange.com/a/14017) which results (coordinates) depend on the number of dimensions requested - unlike that in PCA. So, the first axis might be different in 2dim and 1dim analysis. If happens it is strongly correlated that is due to the peculiarities of the data analyzed. $\endgroup$ – ttnphns Mar 23 '18 at 16:11

Assuming the dimensions are relatively independent (e.g., orthogonal), then the results should be comparable.  If not, then the first dimension of an analysis with 2 or more dimensions may not be the same as the single-dimension analysis.  Though I do not know of a statistical test for this comparison (i.e., one that would give a P-value to assess the difference), a visual inspection of the one dimension from the two solutions would be a reasonable assessment of the argument that a one dimensional solution may suffice.

Hope this helps.

  • $\begingroup$ Assuming the dimensions are relatively independent That is unclear. What dimensions? Could you elaborate and support your statement, please? $\endgroup$ – ttnphns Mar 23 '18 at 16:15
  • $\begingroup$ @ttnphns This is meant to reference the same issue as you mention in your other comment above. The estimated dimensions/axes/components etc. may (or may not) be orthogonal (independent). If they are faced to be when there is strong correlations in the data, the solutions could end up being different. $\endgroup$ – Gregg H Mar 23 '18 at 18:00
  • $\begingroup$ Sorry, no, I commented about a very different issue. $\endgroup$ – ttnphns Mar 23 '18 at 18:39

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