[R] rda variance partioning in vegan problems

Jari Oksanen jari.oksanen at oulu.fi
Thu May 2 08:10:34 CEST 2013


Thomas Parr <thomas.parr <at> maine.edu> writes:

> My question is related to partitioning the variance in rda (vegan) results
> for multiple groups of variables.  I have a  high dimensional dataset with
> 79 explanatory variables and 9 response variables. Within those 79
> explanatory variables there are ~8 groups (e.g. water chemistry, land cover,
> When I do this for each combination two problems arise:
> 1. I get small negative numbers when 0 should be the lowest possible number.
> Does this occur because of internal rounding in the RDA code, or is there
> something else going on? (If Total inertia is 9 and explainable inertia is
> 5.4, a "small negative number" for an interaction inertia might be -0.003
> after the above partitioning procedure.)
> 2. The sum of partitioned inertia is greater than the constrained inertia on
> the full model (in this case Total Inertia is 9, explainable inertia is
> 5.41, and the sum of partitioned inertia is 5.57). 

(I had to prune your original message because I'm using Gmane interface,
and it does not allow full quoting of original messages in short 
answers. Gmane neither allows me write this message on the top -- and
my regular Exchange client only allows top-posting)

These two issues are related. (1) You can get "negative components" of
variation, and (2) because you have "negative components", the apparent
(but false) sum of partitioned inertia can be higher than total inertia.

I calls this false sum, because it was calculated ignoring some of the
negative components. If you estimate all components, including all 
negative components, the sums will match.

There are various reasons why you can get negative components, and they 
really are due to the methodology and its assumptions. Legendre & Legendre 
(2012) "Numerical Ecology" book discusses some reason. The issue was also
discussed by Rune Økland (2003) J. Veg. Sci. 9, 693-700. I don't quite
agree with these analyses, but the margin of this page is too narrow
to contain the full analysis.

Cheers, Jari Oksanen

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