compositions (version 2.0-0)

compositions-package: compositions

Description

"compositions" is a package for the analysis of compositional and multivariate positive data (generally called "amounts"), based on several alternative approaches.

Details

The DESCRIPTION file: compositions compositions To get detailed "getting started" introduction use help.start() or help.start(browser="myfavouritebrowser") Go to "Packages" then "compositions" and then "overview" and then launch the file "UsingCompositions.pdf" from there. Please also check the web-site: http://www.stat.boogaart.de/compositions for improved material and our new book expected to appear spring 2009.

The package is devoted to the analysis of multiple amounts. Amounts have typically non-negative values, and often sum up to 100% or one. These constraints lead to spurious effects on the covariance structure, as pointed out by Chayes (1960). The problem is treated rigorously in the monography by Aitchison (1986), who characterizes compositions as vectors having a relative scale, and identifies its sample space with the D-part simplex. However still (i.e. 2005) most statistical packages do not provided any support for this scale.

The grounding idea of the package exploits the class concept: the analyst gives the data a compositional or amount class, and then all further analysis are (should be) automatically done in a consistent way, e.g. x <- acomp(X); plot(x) should plot the data as a composition (in a ternary diagram) directly without any further interaction of the user.

The package provides four different approaches to analyse amounts. These approaches are associated to four R-classes, representing four different geometries of the sampling space of amounts. These geometries depend on two questions: whether the total sum of the amounts is a relevant information, and which is the meaningful measure of difference of the data.

rplus : (Real Plus) The total amount matters, and amounts should be compared on an absolute basis. i.e. the difference between 1g and 2g is the same as the difference between 1kg and 1001g, one gram.

aplus : (Aitchison Plus) The total amount matters, but amounts should be compared relatively, i.e. the difference between 1mg and 2mg is the same as that of 1g and 2g: the double.

acomp : (Aitchison composition) the total amount is constant (or an artifact of the sampling/measurement procedure), and the meaningful difference is a relative one. This class follows the original proposals of Aitchison.

rcomp : (Real composition) the sum is a constant, and the difference in amount from 0% to 1% and from 10% to 11% is regarded as equal. This class represents the raw/naive treatment of compositions as elements of the real simplex based on an absolute geometry. This treatment is implicitly used in most amalgamation problems. However the whole approach suffers from the drawbacks and problems discussed in Chayes (1960) and Aitchison (1986).

The aim of the package is to provide all the functionality to do a consistent analysis in all of these approaches and to make the results obtained with different geometries as easy to compare as possible.

References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn (2002) A consise guide to the algebraic geometric structure of the simplex, the sample space for compositional data analysis, Terra Nostra, Schriften der Alfred Wegener-Stiftung, 03/2003

Billheimer, D., P. Guttorp, W.F. and Fagan (2001) Statistical interpretation of species composition, Journal of the American Statistical Association, 96 (456), 1205-1214

Chayes, F. (1960). On correlation between variables of constant sum. Journal of Geophysical Research 65~(12), 4185--4193.

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\'a ndez, J.A. (Eds.) Proceedings of the 1st International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-111-X, http://ima.udg.es/Activitats/CoDaWork03

Mateu-Figueras, G. and Barcel\'o-Vidal, C. (Eds.) Proceedings of the 2nd International Workshop on Compositional Data Analysis, Universitat de Girona, ISBN 84-8458-222-1, http://ima.udg.es/Activitats/CoDaWork05

van den Boogaart, K.G. and R. Tolosana-Delgado (2008) "compositions": a unified R package to analyze Compositional Data, Computers & Geosciences, 34 (4), pages 320-338, doi:10.1016/j.cageo.2006.11.017.

See Also

compositions-package, missingsInCompositions, robustnessInCompositions, outliersInCompositions,

Examples

# NOT RUN {
library(compositions)      # load library
data(SimulatedAmounts)     # load data sa.lognormals
x <- acomp(sa.lognormals)  # Declare the dataset to be compositional
                           # and use relative geometry
plot(x)                    # plot.acomp : ternary diagram
ellipses(mean(x),var(x),r=2,col="red")  # Simplex 2sigma predictive region
pr <- princomp(x)
straight(mean(x),pr$Loadings) 

x <- rcomp(sa.lognormals)  # Declare the dataset to be compositional
                           # and use absolute geometry
plot(x)                    # plot.acomp : ternary diagram
ellipses(mean(x),var(x),r=2,col="red")  # Real 2sigma predictive region
pr <- princomp(x)          
straight(mean(x),pr$Loadings) 
# }