acomp(X,parts=1:NCOL(oneOrDataset(X)),total=1,warn.na=FALSE,detectionlimit=NULL,BDL=NULL,MAR=NULL,MNAR=NULL,SZ=NULL)"acomp" representing one closed composition
or a matrix of class "acomp" representing
multiple closed compositions each in one row."acomp" follow his
approach.
Compositions have some important properties: Amounts are always
positive. The amount of every part is limited to the whole. The
absolute amount of the whole is noninformative since it is typically due
to artifacts on the measurement procedure. Thus only relative changes
are relevant. If the relative amount of one part
increases, the amounts of other parts must decrease, introducing
spurious anticorrelation (Chayes 1960), when analysed directly. Often
parts (e.g H2O, Si) are missing in the dataset leaving the total
amount unreported and longing for analysis procedures avoiding
spurious effects when applied to such subcompositions. Furthermore,
the result of an analysis should be indepent of the units (ppm, g/l, vol.%, mass.%, molar
fraction) of the dataset.
From these properties Aitchison showed that the
analysis should be based on ratios or log-ratios only. He introduced
several transformations (e.g. clr,alr),
operations (e.g. perturbe, power.acomp),
and a distance (dist) which are compatible
with these
properties. Later it was found that the set of compostions equipped with
perturbation as addition and power-transform as scalar multiplication
and the dist as distance form a D-1 dimensional
euclidean vector space (Billheimer, Fagan and Guttorp, 2001), which
can be mapped isometrically to a usual real vector space by ilr
(Pawlowsky-Glahn and Egozcue, 2001).
The general approach in analysing acomp objects is thus to perform
classical multivariate analysis on clr/alr/ilr-transformed coordinates
and to backtransform or display the results in such a way that they
can be interpreted in terms of the original compositional parts.
A side effect of the procedure is to force the compositions to sum up to a
total, which is done by the closure operation clo . Pawlowsky-Glahn, V. and J.J. Egozcue (2001) Geometric approach to
statistical analysis on the simplex. SERRA 15(5), 384-398
Pawlowsky-Glahn, V. (2003) Statistical modelling on coordinates. In:
Thi'o-Henestrosa, S. and Mart'in-Fern'andez, J.A. (Eds.)
Proceedings of the 1st International Workshop on Compositional Data Analysis,
Universitat de Girona, ISBN 84-8458-111-X,
clr,rcomp, aplus,
princomp.acomp,
plot.acomp, boxplot.acomp,
barplot.acomp, mean.acomp,
var.acomp, variation.acomp,
cov.acomp, msddata(SimulatedAmounts)
plot(acomp(sa.lognormals))Run the code above in your browser using DataLab