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

[Rich Shepard]

On Fri, 26 Sep 2014, Serge-Étienne Parent wrote:

> If your data are compositions, you will probably use acomp (for Aitchison 
> composition) to close the simplex between 0 and 1.

Serge-Étienne,

   The composistions are proportions based on the total of the individual
groups counts so the simplex is alrady closed ... if my understanding is
correct.


> There are three major data transformation techniques for compositional
> data:

   I've read the pros and cons of each in several references and decided that
the ilr is most appropriate because it avoids the short-comings of alr and
clr that you point out.

> 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.

   'Sequential binary partition' is a term I've not seen. I will read about
it.

   After summarizing the data (mean, standard deviation) and constructing a
ternary plot matrix (because there are five groups in each data set), I need
to explore the relationships among the different streams and explanatory
variables such as basin characteristics, hydrology, and water chemistry. Not
yet decided what models to use and will probably look at several before
determining which is most useful.

   The major challenge will be making all this clearly understood by
non-technical decision-makers such as regulators and their legislative
bosses. And this is going to be an interesting exercise. :-)

Thanks very much,

Rich