# Variance explained by ordination axes

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• #414
rainman
Member

Hi all,

Is there a way to find out how much variance is explained by each of the axes in an ordination plot?

Cheers,
Tom.

#479
lee
Keymaster

Hi

No, it isn’t easy to determine the variance explained by MDS (which SSH is) style ordination programs. MDS-style programs don’t use variance in their operation. In some cases, the MDS axes are rotated to ‘simple structure’ which usually means that they are rotated to maximise the variance on the ordination axes (eg VARIMAX rotation is common).

I don’t use Principle Components in PATN (as it has too many traps for the unwary), but you can easily export the SSH vectors from PATN and import them into any standard stats program and determine the relative variances, but the result will not have axes that in any way correspond to the SSH axes. SSH simply aims to get the maximum information in the selected number of axes.

Hope that helps.

Lee

#503
rainman
Member

Hi Lee,

Apparently in the DOS version one was able to get this stat when running the varimax rotation procedure.

Obviously it would be great to obtain this stat in the windows version too. I mean, if you’re looking at axis y, which shows the most meaningful result for your experiment (given your a priori groups etc…), you could be missing what is ‘actually’ happening in your dataset. That is, axis x could be accounting for more of the variability – in a way which you may not have previously considered.

Does PATN automatically employ varimax rotation and present that result? And, if so, does VR move the data points relative to the axes themselves, or merely spin the ordination (as one can do in the current windows version 3.11)?

Tom.

#504
lee
Keymaster

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

#505
rainman
Member

Yes, thanks. That’s what I thought, but it was making my head hurt ðŸ™‚

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