R: Compositional Data Analysis

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: | 1.40-3
Date: | 2019-11-25
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 (>= 2.2.0), tensorA, robustbase, bayesm
Suggests: | rgl,combinat, energy
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

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

Further information is available in the following vignettes:

`UsingCompositions` | Using Animal (source, pdf)

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, 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

    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)

[Package compositions version 1.40-3 Index]