Re: Variance and ordnation axes
Multidimensional scaling (MDS) works totally differently to Principal Component Analysis. Variance doesn’t come into MDS and for very good reason. Variance asumes normality and one is wise not to assme that with most ecological data.
MDS (SSH in PATN) starts by distributing your objects randomly in your selected number of dimensions, usually 3. It then iterates between the association matrix and the Euclidean Distances in the 3d-space to maximise the relationship. Basically MDS moves the objects each iteration to improve the relationship between the two matrices. No variances involved, at all. Zip.
The result of SSH is hopefully, the best configuration posible. The axes are 100% arbitrary because they relate to the random coordinates allocated at step 1. PATN’s strength is that you can view the configuration dynamically in 3 (or whatever) dimensions. There is absolutely no implied relationship between the axes you may care to optionally view and any trends or gradients you may interpret. The axes are there for perspective.
Varimax in the current version of PATN would be a waste of time. First, we aren’t using variance, and second, you can do far better visually than any mathematical attempt to maximise (or minimise) variance anyway. Another way of saying it is – variance is appliable to PCA but PATN v3 doesn’t use PCA for very good reasons.
Any better?
Lee