I have a question on NMDS. I runned an NMDS on my data and it extracts 4 axes. I now have to plot my results, but I don't know if I should plot all axes combination or just the first 2. Is it correct to say the the first two axes best explain my data, so that I can just plot the first two? Or all the extracted axes have the same importance?
Thank you very much for your answer. The thing is that I increased the number of component until I got an acceptable stress value and with 3 component is above 0.2, with 4 component is about 0.16. That's why I have to consider 4 component. So, if I understood weel, do you suggest to plot just the first 2 component?
That is not what I am suggesting. As I said above, there is no order to components, and the first two may or may not be most informative.
What I suggest is to run nMDS only with two components, even if that doesn't produce the lowest stress value, and make a plot of those two components. Then do nMDS with 3 components, and plot them in 3D. If either or both plots are already informative and data points are separated well, you can stop there and use those plots, even with the knowledge that going for 4 components would have given you a lower stress score.
It is quite common that we plot only the first 2 or 3 PCA components, because that is how much we can plot at one time. Even when the first 2-3 components explain only 30-40% of total variance - that would be the nMDS equivalent of not having the lowest stress value - that is often enough to clearly see groups of data points.
The only difference is that with PCA we know that components are ordered by descending ability to explain variance, so the first 2-3 components will always explain more variance than any other random 2-3 components. That's why with PCA we can calculate 20 components but only plot the first 2-3, while with nMDS we can't calculate 20 components and rely on order of components to decide which 2-3 of them to plot.
Ok, thanks a lot!