Optimal number of dimensions in multidimensional scaling I have run an experiment on consonance-dissonance evaluation of musical intervals on 40 individuals using all the possible intervals from 3 registers (plus their inversions), and I want to apply a multidimensional scale analysis.

My problem is that the stress plot indicates the following:


  


I guess it would not be desirable to limit my analysis to 2 or 3 dimensions since the stress is high at these points, but I am not sure if adding dimensions helps either. Is there an optimal number of dimensions that I should consider, or should I follow the stress curve wherever it may take me?
Thanks.
I guess it depends on your purpose. If you are doing the MDS for more heuristic purposes, then often two dimensions (or possibly three) will provide the greatest visual insight.

Also, my sense from looking at your dimension by stress plot is that the greatest gains are attained when going from one to two dimensions, that the gain from two to three dimensions is still substantial, but after that there are minimal gains.