Hi all,

I have a principal coordinate analysis of a distance matrix (pairwise simpson dissimilarity matrix) with a lot of negative Eigenvalues (some of them quite high).

I want to calculate the explained variance of the first axis, which is as i understand usually calculated as its relative eigenvalue.

In R, the function cmdscale() yields two "Goodness of Fit"-values, if you type the option, eig=TRUE. However, both values are quite different (0.13 and 0.21 in my case), because each has a different strategy of dealing with negative eigenvalues when calculating the sum of all eigenvalues.

1) sum(absolute(eigenvalues))

2) sum(eigenvalues>0) (essentially rejecting all sub-zero eigenvalues) Additionally, there are correction methods, most notably from Lingoes (1971) and Cailliez (1983) both of which are featured in the R function pcoa().

While "lingoes" failed, "cailliez" produced a pcoa without negative eigenvalues.

However, the relative Eigenvalue of the first axis now is 0.004. So I can choose between 0.4%, 13% or 21% explained variance...

So that is my problem. My Question would be: what would be the preferred way to calculate explained variance of the first pcoa axis? Or is there a preferable solution alltogether to my method of breaking down the dimensions of my distance matrix?

Thanks in advance

Roman