R help - May 2013 - rda variance partioning in vegan problems

This is not a request for coding help so there is no reproducible code,
rather I am trying to figure out if anyone had had a similar experience.

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,
geography, surficial geology, etc).  To partition out their unique and
binary interactive variance, I run the ~30 conditioned RDAs necessary to
determine the "pure effects" of each group and the "pure binary
interactions" of those groups with each other. 

My method for partitioning the variance of binary interactions is as
follows:
Inertia of the interaction of water chemistry and geography = inertia of the
combined effect (conditioned on the remaining groups) -  Inertia of just
Waterchemistry - inertia of just geography.

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 have checked for coding errors.

Thanks,
Thomas

On May 1, 2013, at 8:37 PM, Thomas Parr wrote:
> This is not a request for coding help so there is no reproducible code,
So this is a general statistical problem? 

Perhaps you should try: CrossValidated.com
> 
> rather I am trying to figure out if anyone had had a similar experience.
> 
> My question is related to partitioning the variance in rda (vegan) results
> for multiple groups of variables.
Sounds like a question for authors of the package.
>  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,
> geography, surficial geology, etc).  To partition out their unique and
> binary interactive variance, I run the ~30 conditioned RDAs necessary to
> determine the "pure effects" of each group and the "pure
binary
> interactions" of those groups with each other. 
> 
> My method for partitioning the variance of binary interactions is as
> follows:
> Inertia of the interaction of water chemistry and geography = inertia of
the
> combined effect (conditioned on the remaining groups) -  Inertia of just
> Waterchemistry - inertia of just geography.
> 
> 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?
And how exactly would one tell if there is no data? (or even results?)
> (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). 
> 
Again... with no data. How would one explain this?
> I have checked for coding errors.
-- 

David Winsemius
Alameda, CA, USA

Thomas,


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 ?kland (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