[R-sig-eco] Compositional Data Analysis: Simplex Scaling Function Selection (Rich Shepard)

[Serge-Étienne Parent]

Hello Rich,

If your data are compositions, you will probably use acomp (for 
Aitchison composition) to close the simplex between 0 and 1. There are 
three major data transformation techniques for compositional data: 
additive log-ratio, centered log-ratio and isometric log-ratio. The 
"best" transformation is still a matter of debate. ALRs are not suited 
for euclidean-distance-based analyses. They do not preserve the 
distance between sites, while CLRs and ILRs do. With CLRs, you can 
quickly get singularities, since the CLRs of each site add up to zero. 
CLRs are mostly used for their ease of interpretation in biplots. ILRs 
do not suffer from singularities. But they rely on an orthogonal basis 
(the sequential binary partition), that has to be designed by the 
analyst. The good news is that no matter how the SBP is designed (as 
long as it is valid), linear statistics conducted on ILRs will return 
the same results, as the distances between points are preserved. 
However, if you use non-linear techniques, like variograms or 
machine-learning, your results will depend on the designed SBP. In some 
cases, ILR variables will be difficult to interpret. In other cases, 
they will improve interpretability. ILRs were highly recommended by 
Filzmoser and Hron (2011)* for conducting robust statistics. I 
systematically use ILRs for my works in agroecology.

In these two papers, I used ILRs in plant nutrition.
http://journal.frontiersin.org/Journal/10.3389/fpls.2013.00039/abstract
http://journal.frontiersin.org/Journal/10.3389/fpls.2013.00449/abstract

Regards,

S.-É. Parent
Université Laval
Canada

* Filzmoser, P., and Hron, K. (2011). “Robust statistical 
analysis,” in Compositional Data Analysis: Theory and Applications, 
eds V. Pawlowsky-Glahn and A. Buccianti (New York: John Wiley and 
Sons), 57–72.



Le ven 26 sep 2014 à 15:07, Rich Shepard <rshepard at appl-ecosys.com> a 
écrit :
> On Fri, 26 Sep 2014, Kari Lintulaakso wrote:
> 
>> you might be interested of http://www.compositionaldata.com/.
> 
> Karl,
> 
>   Yes, I am familiar with that Web site. I was disappointed that the 
> forum
> lacked any activity. No response to my posts.
> 
>> They have a forum for CoDa related questions. There seems to be a new
>> R-package for CoDa: zCompositions.
> 
>   zCompositions is installed here. It focuses on principled methods 
> to deal
> with zeros and left-censoring in compositional data sets.
> 
>   Also installed are robCompositions for various imputation methods 
> for
> missing data and the new (version 1.4.0) compositions.
> 
>   The tools are present and the documents read. Now I need to learn 
> how to
> select the appropriate options for the data sets to be analyzed and 
> the
> questions to be answered.
> 
> Many thanks,
> 
> Rich
> 
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