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)
```

*compositions*version 2.0-8 Index]