| compositions-package {compositions} | R Documentation |
Compositional Data Analysis
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:
| Package: | compositions |
| Version: | 2.0-8 |
| Date: | 2024-01-25 |
| Title: | Compositional Data Analysis |
| Author: | K. Gerald van den Boogaart <boogaart@hzdr.de>, Raimon Tolosana-Delgado, Matevz Bren |
| Maintainer: | K. Gerald van den Boogaart <support@boogaart.de> |
| Depends: | R (>= 3.6) |
| Imports: | methods, utils, grDevices, stats, tensorA, robustbase, bayesm, graphics, MASS |
| Suggests: | rgl (>= 1.0.1), combinat, energy, knitr, rmarkdown |
| Description: | Provides functions for the consistent analysis of compositional data (e.g. portions of substances) and positive numbers (e.g. concentrations) in the way proposed by J. Aitchison and V. Pawlowsky-Glahn. |
| License: | GPL (>= 2) |
| URL: | http://www.stat.boogaart.de/compositions/ |
| VignetteBuilder: | knitr |
| RoxygenNote: | 7.1.1 |
Index of help topics:
structure
Aar Composition of glaciar sediments from the Aar
massif (Switzerland)
acomp Aitchison compositions
acompmargin Marginal compositions in Aitchison Compositions
Activity10 Activity patterns of a statistician for 20 days
Activity31 Activity patterns of a statistician for 20 days
alr Additive log ratio transform
AnimalVegetation Animal and vegetation measurement
+.aplus vectorial arithmetic for data sets with aplus
class
aplus Amounts analysed in log-scale
apt Additive planar transform
ArcticLake Artic lake sediment samples of different water
depth
arrows3D arrows in 3D, based on package rgl
as.data.frame.acomp Convert "compositions" classes to data frames
axis3D Drawing a 3D coordiante system to a plot, based
on package rgl
balance Compute balances for a compositional dataset.
barplot.acomp Bar charts of amounts
Bayesite Permeabilities of bayesite
binary Treating binary and g-adic numbers
biplot3D Three-dimensional biplots, based on package rgl
Blood23 Blood samples
Boxite Compositions and depth of 25 specimens of
boxite
boxplot.acomp Displaying compositions and amounts with
box-plots
cdt Centered default transform
ClamEast Color-size compositions of 20 clam colonies
from East Bay
ClamWest Color-size compositions of 20 clam colonies
from West Bay
clo Closure of a composition
clr Centered log ratio transform
clr2ilr Convert between clr and ilr, and between cpt
and ipt.
ClusterFinder1 Heuristics to find subpopulations of outliers
CoDaDendrogram Dendrogram representation of acomp or rcomp
objects
coloredBiplot A biplot providing somewhat easier access to
details of the plot.
colorsForOutliers1 Create a color/char palette or for groups of
outliers
CompLinModCoReg Compositional Linear Model of Coregionalisation
compOKriging Compositional Ordinary Kriging
compositions-package library(compositions)
ConfRadius Helper to compute confidence ellipsoids
cor.acomp Correlations of amounts and compositions
Coxite Compositions, depths and porosities of 25
specimens of coxite
cpt Centered planar transform
DiagnosticProb Diagnostic probabilities
dist Distances in variouse approaches
ellipses Draw ellipses
endmemberCoordinates Recast amounts as mixtures of end-members
Firework Firework mixtures
geometricmean The geometric mean
getDetectionlimit Gets the detection limit stored in the data set
Glacial Compositions and total pebble counts of 92
glacial tills
groupparts Group amounts of parts
Hongite Compositions of 25 specimens of hongite
HouseholdExp Household Expenditures
Hydrochem Hydrochemical composition data set of Llobregat
river basin water (NE Spain)
idt Isometric default transform
iit Isometric identity transform
ilr Isometric log ratio transform
ilrBase The canonical basis in the clr plane used for
ilr and ipt transforms.
ilt Isometric log transform
ipt Isometric planar transform
is.acomp Check for compositional data type
IsMahalanobisOutlier Checking for outliers
isoPortionLines Isoportion- and Isoproportion-lines
juraset The jura dataset
kingTetrahedron Ploting composition into rotable tetrahedron
Kongite Compositions of 25 specimens of kongite
lines.rmult Draws connected lines from point to point.
logratioVariogram Empirical variograms for compositions
MahalanobisDist Compute Mahalanobis distances based von robust
Estimations
mean.acomp Mean amounts and mean compositions
meanRow The arithmetic mean of rows or columns
Metabolites Steroid metabolite patterns in adults and
children
missingProjector Returns a projector the the observed space in
case of missings.
missingsInCompositions
The policy of treatment of missing values in
the "compositions" package
missingSummary Classify and summarize missing values in a
dataset
mix.2aplus Transformations from 'mixtures' to
'compositions' classes
mix.Read Reads a data file in a mixR format
mvar Metric summary statistics of real, amount or
compositional data
names.acomp The names of the parts
normalize Normalize vectors to norm 1
norm.default Vector space norm
oneOrDataset Treating single compositions as one-row
datasets
OutlierClassifier1 Detect and classify compositional outliers.
outlierplot Plot various graphics to analyse outliers.
outliersInCompositions
Analysing outliers in compositions.
pairwisePlot Creates a paneled plot like pairs for two
different datasets.
parametricPosdefMat Unique parametrisations for matrices.
perturbe Perturbation of compositions
plot3D plot in 3D based on rgl
plot3D.acomp 3D-plot of compositional data
plot3D.aplus 3D-plot of positive data
plot3D.rmult plot in 3D based on rgl
plot3D.rplus plot in 3D based on rgl
plot.acomp Ternary diagrams
plot.aplus Displaying amounts in scatterplots
plot.logratioVariogram
Empirical variograms for compositions
plot.missingSummary Plot a Missing Summary
pMaxMahalanobis Compute distributions of empirical Mahalanobis
distances based on simulations
PogoJump Honk Kong Pogo-Jumps Championship
power.acomp Power transform in the simplex
powerofpsdmatrix power transform of a matrix
princomp.acomp Principal component analysis for Aitchison
compositions
princomp.aplus Principal component analysis for amounts in log
geometry
princomp.rcomp Principal component analysis for real
compositions
princomp.rmult Principal component analysis for real data
princomp.rplus Principal component analysis for real amounts
print.acomp Printing compositional data.
qHotellingsTsq Hotellings T square distribution
qqnorm.acomp Normal quantile plots for compositions and
amounts
R2 R square
rAitchison Aitchison Distribution
+.rcomp Arithmetic operations for compositions in a
real geometry
rcomp Compositions as elements of the simplex
embedded in the D-dimensional real space
rcompmargin Marginal compositions in real geometry
rDirichlet Dirichlet distribution
read.geoeas Reads a data file in a geoeas format
relativeLoadings Loadings of relations of two amounts
replot Modify parameters of compositional plots.
rlnorm.rplus The multivariate lognormal distribution
+.rmult vectorial arithmetic for datasets in a
classical vector scale
rmult Simple treatment of real vectors
rnorm.acomp Normal distributions on special spaces
robustnessInCompositions
Handling robustness issues and outliers in
compositions.
+.rplus vectorial arithmetic for data sets with rplus
class
rplus Amounts i.e. positive numbers analysed as
objects of the real vector space
runif.acomp The uniform distribution on the simplex
scalar Parallel scalar products
scale Normalizing datasets by centering and scaling
Sediments Proportions of sand, silt and clay in sediments
specimens
segments.rmult Draws straight lines from point to point.
SerumProtein Serum Protein compositions of blood samples
ShiftOperators Shifts of machine operators
simpleMissingSubplot Ternary diagrams
SimulatedAmounts Simulated amount datasets
simulateMissings Artifical simulation of various kinds of
missings
Skulls Measurement of skulls
SkyeAFM AFM compositions of 23 aphyric Skye lavas
split.acomp Splitting datasets in groups given by factors
straight Draws straight lines.
summary.acomp Summarizing a compositional dataset in terms of
ratios
summary.aplus Summaries of amounts
summary.rcomp Summary of compositions in real geometry
sumMissingProjector Compute the global projector to the observed
subspace.
Supervisor Proportions of supervisor's statements assigned
to different categories
ternaryAxis Axis for ternary diagrams
totals Total sum of amounts
tryDebugger Empirical variograms for compositions
ult Uncentered log transform
var.acomp Variances and covariances of amounts and
compositions
variation Variation matrices of amounts and compositions
var.lm Residual variance of a model
vcovAcomp Variance covariance matrix of parameters in
compositional regression
vgmFit Compositional variogram model fitting
vgram2lrvgram vgram2lrvgram
vgram.sph Variogram functions
WhiteCells White-cell composition of 30 blood samples by
two different methods
Yatquat Yatquat fruit evaluation
zeroreplace Zero-replacement routine
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.
Note
The package compositions has grown a lot in the last year: missings, robust estimations, outlier detection and classification, codadendrogram. This makes everything much more complex especially from the side of programm testing. Thus we would like to urge our users to report all errors and problems of the lastest version (please check first) to support@boogaart.de.
Author(s)
K. Gerald van den Boogaart <boogaart@hzdr.de>, Raimon Tolosana-Delgado, Matevz Bren
Maintainer: K. Gerald van den Boogaart <support@boogaart.de>
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, https://ima.udg.edu/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, https://ima.udg.edu/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
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)