I am wanting to know if I can use the ratio of Constrained/Total Inertia in my CCA to describe 'The variability explained by my constraining variables'. I am asking because I've seen different interpretations and thought I would get another opinion.
I believe this question was asked more or less here -but without a reply
I also found this code-interpretation question on SO
G. Simpson suggested in the link above that Inertia could be used in this way (Constrained/Total = amount of variance explained by CCA). I've seen other tutorials suggesting the same thing.
But, in this helpful Vegan tutorial, J. Oksanen suggests that "Total inertia does not have a clear meaning in CCA and the meaning of this proportion is just as obscure...total inertia may be random noise. It may be better to concentrate on results instead of these proportions"
So to recap my question: " Is it valid to report the proportion of inertia the constrained variables account for as 'variance explained'? Or is there a better way to report how a CCA performed?
Example of output:
Inertia Proportion Rank Total 4.5922 1.0000 Constrained 0.5126 0.1116 3 Unconstrained 4.0796 0.8884 17 Inertia is mean squared contingency coefficient Eigenvalues for constrained axes: CCA1 CCA2 CCA3 0.29170 0.17300 0.04792