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Type:	Package
Title:	Compositional Data Analysis
Version:	2.4.2
Date:	2025-08-06
Depends:	R (≥ 3.5.0), ggplot2, pls, data.table
LinkingTo:	Rcpp, RcppEigen
Imports:	cvTools, fda, rrcov, cluster, dplyr, magrittr, GGally,ggfortify, kernlab, MASS, mclust, tidyr, robustbase, robustHD,sparsepca, splines, VIM, zCompositions, reshape2, Rcpp
Suggests:	e1071, fpc, knitr, testthat
VignetteBuilder:	knitr
Maintainer:	Matthias Templ <matthias.templ@gmail.com>
Description:	Methods for analysis of compositional data including robust methods (<doi:10.1007/978-3-319-96422-5>), imputation of missing values (<doi:10.1016/j.csda.2009.11.023>), methods to replace rounded zeros (<doi:10.1080/02664763.2017.1410524>, <doi:10.1016/j.chemolab.2016.04.011>, <doi:10.1016/j.csda.2012.02.012>), count zeros (<doi:10.1177/1471082X14535524>), methods to deal with essential zeros (<doi:10.1080/02664763.2016.1182135>), (robust) outlier detection for compositional data, (robust) principal component analysis for compositional data, (robust) factor analysis for compositional data, (robust) discriminant analysis for compositional data (Fisher rule), robust regression with compositional predictors, functional data analysis (<doi:10.1016/j.csda.2015.07.007>) and p-splines (<doi:10.1016/j.csda.2015.07.007>), contingency (<doi:10.1080/03610926.2013.824980>) and compositional tables (<doi:10.1111/sjos.12326>, <doi:10.1111/sjos.12223>, <doi:10.1080/02664763.2013.856871>) and (robust) Anderson-Darling normality tests for compositional data as well as popular log-ratio transformations (addLR, cenLR, isomLR, and their inverse transformations). In addition, visualisation and diagnostic tools are implemented as well as high and low-level plot functions for the ternary diagram.
License:	GPL-2 |GPL-3 [expanded from: GPL (≥ 2)]
LazyLoad:	yes
LazyData:	true
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	yes
Packaged:	2025-08-06 18:56:20 UTC; matthias
Author:	Matthias Templ [aut, cre], Karel Hron [aut], Peter Filzmoser [aut], Kamila Facevicova [ctb], Petra Kynclova [ctb], Jan Walach [ctb], Veronika Pintar [ctb], Jiajia Chen [ctb], Dominika Miksova [ctb], Bernhard Meindl [ctb], Alessandra Menafoglio [ctb], Alessia Di Blasi [ctb], Federico Pavone [ctb], Nikola Stefelova [ctb], Gianluca Zeni [ctb], Roman Wiederkehr [ctb]
Repository:	CRAN
Date/Publication:	2025-08-22 15:20:02 UTC

Robust Estimation for Compositional Data.

Description

The package contains methods for imputation of compositional data includingrobust methods, (robust) outlier detection for compositional data, (robust)principal component analysis for compositional data, (robust) factoranalysis for compositional data, (robust) discriminant analysis (Fisherrule) and (robust) Anderson-Darling normality tests for compositional dataas well as popular log-ratio transformations (alr, clr, ilr, and theirinverse transformations).

Author(s)

Matthias Templ, Peter Filzmoser, Karel Hron,

Maintainer: Matthias Templ <templ@tuwien.ac.at>

References

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

Filzmoser, P., and Hron, K. (2008) Outlier detection for compositional datausing robust methods.Math. Geosciences,40 233-248.

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal Component Analysis forCompositional Data with Outliers.Environmetrics,20 (6),621–632.

P. Filzmoser, K. Hron, C. Reimann, R. Garrett (2009): Robust Factor Analysisfor Compositional Data.Computers and Geosciences,35 (9),1854–1861.

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing valuesfor compositional data using classical and robust methodsComputational Statistics and Data Analysis,54 (12),3095–3107.

C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter (2008): StatisticalData Analysis Explained.Applied Environmental Statistics with R.John Wiley and Sons, Chichester, 2008.

Examples

## k nearest neighbor imputationdata(expenditures)expenditures[1,3]expenditures[1,3] <- NAimpKNNa(expenditures)$xImp[1,3]## iterative model based imputationdata(expenditures)x <- expendituresx[1,3]x[1,3] <- NAxi <- impCoda(x)$xImpxi[1,3]s1 <- sum(x[1,-3])impS <- sum(xi[1,-3])xi[,3] * s1/impSxi <- impKNNa(expenditures)xisummary(xi)## Not run: plot(xi, which=1)plot(xi, which=2)plot(xi, which=3)## pcadata(expenditures)p1 <- pcaCoDa(expenditures)p1plot(p1)## outlier detectiondata(expenditures)oD <- outCoDa(expenditures)oDplot(oD)## transformationsdata(arcticLake)x <- arcticLakex.alr <- addLR(x, 2)y <- addLRinv(x.alr)addLRinv(addLR(x, 3))data(expenditures)x <- expendituresy <- addLRinv(addLR(x, 5))head(x)head(y)addLRinv(x.alr, ivar=2, useClassInfo=FALSE)data(expenditures)eclr <- cenLR(expenditures)inveclr <- cenLRinv(eclr)head(expenditures)head(inveclr)head(cenLRinv(eclr$x.clr))require(MASS)Sigma <- matrix(c(5.05,4.95,4.95,5.05), ncol=2, byrow=TRUE)z <- pivotCoordInv(mvrnorm(100, mu=c(0,2), Sigma=Sigma))

GDP satisfaction

Description

Satisfaction of GDP in 31 countries. The GDP is measured per capita from the year 2012.

Usage

data(GDPsatis)

Format

A data frame with 31 observations and 8 variables

Details

country

community code

gdp

GDP per capita in 2012

very.bad

satisfaction very bad

bad

satisfaction bad

moderately.bad

satisfaction moderately bad

moderately.good

satisfaction moderately good

good

satisfaction good

very.good

satisfaction very good

Author(s)

Peter Filzmoser, Matthias Templ

Source

from Eurostat,https://ec.europa.eu/eurostat/

Examples

data(GDPsatis)str(GDPsatis)

Simplicial deviance

Description

Simplicial deviance

Usage

SDev(x)

Arguments

Value

The simplicial deviance

Author(s)

Matthias Templ

References

Juan Jose Egozcuea, Vera Pawlowsky-Glahn, Matthias Templ, Karel Hron (2015)Independence in Contingency Tables Using Simplicial Geometry.Communications in Statistics - Theory and Methods, Vol. 44 (18), 3978–3996.DOI:10.1080/03610926.2013.824980

Examples

data(precipitation) tab1prob <- prop.table(precipitation)SDev(tab1prob)

ZB-spline basis

Description

Spline basis system having zero-integral on I=[a,b] of the L^2_0 space (called ZB-splines) has beenproposed for an basis representation of fcenLR transformed probability density functions. The ZB-spline basis functions can be backtransformed to Bayes spaces using inverse of fcenLR transformation, resulting in compositional B-splines (CB-splines), and forming a basis system of the Bayes spaces.

Usage

ZBsplineBasis(t, knots, order, basis.plot = FALSE)

Arguments

Value

Author(s)

J. Machalovajitka.machalova@upol.cz, R. Talskatalskarenata@seznam.cz

References

Machalova, J., Talska, R., Hron, K. Gaba, A. Compositional splines for representation of density functions.Comput Stat (2020). https://doi.org/10.1007/s00180-020-01042-7

Examples

# Example: ZB-spline basis functions evaluated at a vector of argument values tt = seq(0,20,l=500)knots = c(0,2,5,9,14,20)order = 4ZBsplineBasis.out = ZBsplineBasis(t,knots,order, basis.plot=TRUE)# Back-transformation of ZB-spline basis functions from L^2_0 to Bayes space -> # CB-spline basis functionsCBsplineBasis=NULLfor (i in 1:ZBsplineBasis.out$nbasis){ CB_spline = fcenLRinv(t,diff(t)[1:2],ZBsplineBasis.out$ZBsplineBasis[,i]) CBsplineBasis = cbind(CBsplineBasis,CB_spline)}matplot(t,CBsplineBasis, type="l",lty=1, las=1,   col=rainbow(ZBsplineBasis.out$nbasis), xlab="t",   ylab="CB-spline basis",cex.lab=1.2,cex.axis=1.2)abline(v=knots, col="gray", lty=2)

Aitchison distance

Description

Computes the Aitchison distance between two observations, between two datasets or within observations of one data set.

Usage

aDist(x, y = NULL)iprod(x, y)

Arguments

Details

This distance measure accounts for the relative scale property ofcompositional data. It measures the distance between two compositions ifx andy are vectors. It evaluates the sum of the distances betweenx andy for each row ofx andy ifx andy are matrices or data frames. It computes a n times n distance matrix (with nthe number of observations/compositions) if onlyx is provided.

The underlying code is partly written in C and allows a fast computation also forlarge data sets whenevery is supplied.

Value

The Aitchison distance between two compositions or between two datasets, or a distance matrix in casey is not supplied.

Author(s)

Matthias Templ, Bernhard Meindl

References

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

Aitchison, J. and Barcelo-Vidal, C. and Martin-Fernandez, J.A. andPawlowsky-Glahn, V. (2000) Logratio analysis and compositional distance.Mathematical Geology,32, 271-275.

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing valuesfor compositional data using classical and robust methodsComputational Statistics and Data Analysis, vol 54 (12), pages3095-3107.

See Also

pivotCoord

Examples

data(expenditures)x <- xOrig <- expenditures## Aitchison distance between two 2 observations:aDist(x[1, ], x[2, ])aDist(as.numeric(x[1, ]), as.numeric(x[2, ]))## Aitchison distance of x:aDist(x)## Example of distances between matrices:## set some missing values:x[1,3] <- x[3,5] <- x[2,4] <- x[5,3] <- x[8,3] <- NA## impute the missing values:xImp <- impCoda(x, method="ltsReg")$xImp## calculate the relative Aitchsion distance between xOrig and xImp:aDist(xOrig, xImp)data("expenditures") aDist(expenditures)  x <- expenditures[, 1]y <- expenditures[, 2]aDist(x, y)aDist(expenditures, expenditures)

Additive logratio coordinates

Description

The additive logratio coordinates map D-part compositional data fromthe simplex into a (D-1)-dimensional real space.

Usage

addLR(x, ivar = ncol(x), base = exp(1))

Arguments

Details

The compositional parts are divided by the rationing part before thelogarithm is taken.

Value

A list of class “alr” which includes the following content:

The additional information suchascnames orivar is useful when an inverse mapping isapplied on the ‘same’ data set.

Author(s)

Matthias Templ

References

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

See Also

addLRinv,pivotCoord

Examples

data(arcticLake)x <- arcticLakex.alr <- addLR(x, 2)y <- addLRinv(x.alr)## This exactly fulfills:addLRinv(addLR(x, 3))data(expenditures)x <- expendituresy <- addLRinv(addLR(x, 5))head(x)head(y)## --> absolute values are preserved as well.## preserve only the ratios:addLRinv(x.alr, ivar=2, useClassInfo=FALSE)

Inverse additive logratio mapping

Description

Inverse additive logratio mapping, often called additive logistictransformation.

Usage

addLRinv(x, cnames = NULL, ivar = NULL, useClassInfo = TRUE)

Arguments

Details

The function allows also to preserve absolute values when class info isprovided. Otherwise only the relative information is preserved.

Value

the resulting compositional data matrix

Author(s)

Matthias Templ

References

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

See Also

pivotCoordInv,cenLRinv,cenLR,addLR

Examples

data(arcticLake)x <- arcticLakex.alr <- addLR(x, 2)y <- addLRinv(x.alr)## This exactly fulfills:addLRinv(addLR(x, 3))data(expenditures)x <- expendituresy <- addLRinv(addLR(x, 5, 2))head(x)head(y)## --> absolute values are preserved as well.## preserve only the ratios:addLRinv(x.alr, ivar=2, useClassInfo=FALSE)

Adjusting for original scale

Description

Results from the model based iterative methods provides the results inanother scale (but the ratios are still the same). This function rescale theoutput to the original scale.

Usage

adjust(x)

Arguments

Details

It is self-explaining if you try the examples.

Value

The object of class ‘imp’ but with the adjusted imputed data.

Author(s)

Matthias Templ

References

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation ofmissing values for compositional data using classical and robust methodsComputational Statistics and Data Analysis, In Press, CorrectedProof, ISSN: 0167-9473, DOI:10.1016/j.csda.2009.11.023

See Also

impCoda

Examples

data(expenditures)x <- expendituresx[1,3] <- x[2,4] <- x[3,3] <- x[3,4] <- NAxi <- impCoda(x)xxi$xImpadjust(xi)$xImp

Anderson-Darling Normality Tests

Description

This function provides three kinds of Anderson-Darling Normality Tests(Anderson and Darling, 1952).

Usage

adtest(x, R = 1000, locscatt = "standard")

Arguments

Details

Three version of the test are implemented (univariate, angle and radiustest) and it depends on the data which test is chosen.

If the data is univariate the univariate Anderson-Darling test for normalityis applied.

If the data is bivariate the angle Anderson-Darling test for normality isperformed out.

If the data is multivariate the radius Anderson-Darling test for normalityis used.

If ‘locscatt’ is equal to “robust” then within the procedure,robust estimates of mean and covariance are provided using ‘covMcd()’from package robustbase.

To provide estimates for the corresponding p-values, i.e. to compute theprobability of obtaining a result at least as extreme as the one that wasactually observed under the null hypothesis, we use Monte Carlo techniqueswhere we check how often the statistic of the underlying data is moreextreme than statistics obtained from simulated normal distributed data withthe same (column-wise-) mean(s) and (co)variance.

Value

Note

These functions are use byadtestWrapper.

Author(s)

Karel Hron, Matthias Templ

References

Anderson, T.W. and Darling, D.A. (1952) Asymptotic theory ofcertain goodness-of-fit criteria based on stochastic processes.Annalsof Mathematical Statistics,23 193-212.

See Also

adtestWrapper

Examples

adtest(rnorm(100))data(machineOperators)x <- machineOperatorsadtest(pivotCoord(x[,1:2]))adtest(pivotCoord(x[,1:3]))adtest(pivotCoord(x))adtest(pivotCoord(x[,1:2]), locscatt="robust")

Wrapper for Anderson-Darling tests

Description

A set of Anderson-Darling tests (Anderson and Darling, 1952) are applied asproposed by Aitchison (Aichison, 1986).

Usage

adtestWrapper(x, alpha = 0.05, R = 1000, robustEst = FALSE)## S3 method for class 'adtestWrapper'print(x, ...)## S3 method for class 'adtestWrapper'summary(object, ...)

Arguments

Details

First, the data is transformed using the ‘ilr’-transformation. Afterapplying this transformation

- all (D-1)-dimensional marginal, univariate distributions are tested usingthe univariate Anderson-Darling test for normality.

- all 0.5 (D-1)(D-2)-dimensional bivariate angle distributions are testedusing the Anderson-Darling angle test for normality.

- the (D-1)-dimensional radius distribution is tested using theAnderson-Darling radius test for normality.

A print and a summary method are implemented. The latter one provides a similar output is proposed by (Pawlowsky-Glahn, et al. (2008). In additionto that, p-values are provided.

Value

Author(s)

Matthias Templ and Karel Hron

References

Anderson, T.W. and Darling, D.A. (1952)Asymptotic theoryof certain goodness-of-fit criteria based on stochastic processes Annals ofMathematical Statistics,23 193-212.

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

See Also

adtest,pivotCoord

Examples

data(machineOperators)a <- adtestWrapper(machineOperators, R=50) # choose higher value of Rasummary(a)

child, middle and eldery population

Description

Percentages of childs, middle generation and eldery population in 195 countries.

Usage

data(ageCatWorld)

Format

A data frame with 195 rows and 4 variables

Details

<15

Percentage of people with age below 15

15-60

Percentage of people with age between 15 and 60

60+

Percentage of people with age above 60

country

country of origin

The rows sum up to 100.

Author(s)

extracted by Karel Hron and Eva Fiserova, implemented by Matthias Templ

References

Fiserova, E. and Hron, K. (2012). Statistical Inference in Orthogonal Regression for Three-Part Compositional Data Using a Linear Model with Type-II Constraints.Communications in Statistics - Theory and Methods, 41 (13-14), 2367-2385.

Examples

data(ageCatWorld)str(ageCatWorld)summary(ageCatWorld)rowSums(ageCatWorld[, 1:3])ternaryDiag(ageCatWorld[, 1:3])plot(pivotCoord(ageCatWorld[, 1:3]))

alcohol consumptions by country and type of alcohol

Description

country

Country

year

Year

beer

Consumption of pure alcohol on beer (in percentages)

wine

Consumption of pure alcohol on wine (in percentages)

spirits

Consumption of pure alcohol on spirits (in percentages)

other

Consumption of pure alcohol on other beverages (in percentages)

Usage

data(alcohol)

Format

A data frame with 193 rows and 6 variables

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

Source

Transfered from the World Health Organisation website.

Examples

data("alcohol")str(alcohol)summary(alcohol)

regional alcohol per capita (15+) consumption by WHO region

Description

country

Country

year

Year

recorded

Recorded alcohol consumption

unrecorded

Unrecorded alcohol consumption

Usage

data(alcoholreg)

Format

A data frame with 6 rows and 4 variables

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

Source

Transfered from the World Health Organisation website.

Examples

data("alcoholreg")alcoholreg

arctic lake sediment data

Description

Sand, silt, clay compositions of 39 sediment samples at different water depths in an Arctic lake.This data set can be found on page 359 of the Aitchison book (see reference).

Usage

data(arcticLake)

Format

A data frame with 39 rows and 3 variables

Details

sand

numeric vector of percentages of sand

silt

numeric vector of percentages of silt

clay

numeric vector of percentages of clay

The rows sum up to 100, except for rounding errors.

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

References

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

Examples

data(arcticLake)str(arcticLake)summary(arcticLake)rowSums(arcticLake)ternaryDiag(arcticLake)plot(pivotCoord(arcticLake))

Balance calculation

Description

Given a D-dimensional compositional data set and a sequential binary partition,the function bal calculates the balances in order to express the given datain the (D-1)-dimensional real space.

Usage

balances(x, y)

Arguments

Details

The sequential binary partition constructs an orthonormal basis in the (D-1)-dimensional hyperplanein real space, resulting in orthonormal coordinates with respect to the Aitchison geometry of compositional data.

Value

Author(s)

Veronika Pintar, Karel Hron, Matthias Templ

References

(Egozcue, J.J., Pawlowsky-Glahn, V. (2005) Groups of parts and their balances in compositional data analysis. Mathematical Geology, 37 (7), 795???828.)

Examples

data(expenditures, package = "robCompositions")y1 <- data.frame(c(1,1,1,-1,-1),c(1,-1,-1,0,0),                 c(0,+1,-1,0,0),c(0,0,0,+1,-1))y2 <- data.frame(c(1,-1,1,-1,-1),c(1,0,-1,0,0),                 c(1,-1,1,-1,1),c(0,-1,0,1,0))y3 <- data.frame(c(1,1,1,1,-1),c(-1,-1,-1,+1,0),                 c(-1,-1,+1,0,0),c(-1,1,0,0,0))y4 <- data.frame(c(1,1,1,-1,-1),c(0,0,0,-1,1),                 c(-1,-1,+1,0,0),c(-1,1,0,0,0))y5 <- data.frame(c(1,1,1,-1,-1),c(-1,-1,+1,0,0),                 c(0,0,0,-1,1),c(-1,1,0,0,0))b1 <- balances(expenditures, y1)b2 <- balances(expenditures, y5)b1$balancesb2$balancesdata(machineOperators)sbp <- data.frame(c(1,1,-1,-1),c(-1,+1,0,0),                 c(0,0,+1,-1))balances(machineOperators, sbp)

biomarker

Description

The function for identification of biomakers and outlier diagnostics as described in paper "Robust biomarker identification in a two-class problem based on pairwise log-ratios"

Usage

biomarker(  x,  cut = qnorm(0.975, 0, 1),  g1,  g2,  type = "tau",  diag = TRUE,  plot = FALSE,  diag.plot = FALSE)## S3 method for class 'biomarker'plot(x, cut = qnorm(0.975, 0, 1), type = "Vstar", ...)## S3 method for class 'biomarker'print(x, ...)## S3 method for class 'biomarker'summary(object, ...)

Arguments

Details

Robust biomarker identification and outlier diagnostics

The method computes variation matrices separately with observations from both groups and also together with all observations. Then,V statistics is then computed and normalized. The variables, for which accordingV* values are bigger that the cut-off value are considered as biomarkers.

Value

The function returns object of type "biomarker".Functionsprint,plot andsummary are available.

Author(s)

Jan Walach

See Also

plot.biomarker

Examples

# Data simulationset.seed(4523)n <- 40; p <- 50r <- runif(p, min = 1, max = 10)conc <- runif(p, min = 0, max = 1)*5+matrix(1,p,1)*5a <- conc*rS <- rnorm(n,0,0.3) %*% t(rep(1,p))B <- matrix(rnorm(n*p,0,0.8),n,p)R <- rep(1,n) %*% t(r)M <- matrix(rnorm(n*p,0,0.021),n,p)# Fifth observation is an outlierM[5,] <- M[5,]*3 + sample(c(0.5,-0.5),replace=TRUE,p)C <- rep(1,n) %*% t(conc)C[1:20,c(2,15,28,40)] <- C[1:20,c(2,15,28,40)]+matrix(1,20,4)*1.8X <- (1-S)*(C*R+B)*exp(M)# Biomarker identificationb <- biomarker(X, g1 = 1:20, g2 = 21:40, type = "tau")

Biplot method

Description

Provides robust compositional biplots.

Usage

## S3 method for class 'factanal'biplot(x, ...)

Arguments

Details

The robust compositional biplot according to Aitchison and Greenacre (2002),computed from resulting (robust) loadings and scores, is performed.

Value

The robust compositional biplot.

Author(s)

M. Templ, K. Hron

References

Aitchison, J. and Greenacre, M. (2002). Biplots of compositionaldata.Applied Statistics,51, 375-392. \

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal component analysis forcompositional data with outliers.Environmetrics,20 (6),621–632.

See Also

pfa

Examples

data(expenditures)res.rob <- pfa(expenditures, factors=2, scores = "regression")biplot(res.rob)

Biplot method

Description

Provides robust compositional biplots.

Usage

## S3 method for class 'pcaCoDa'biplot(x, y, ..., choices = 1:2)

Arguments

Details

The robust compositional biplot according to Aitchison and Greenacre (2002),computed from (robust) loadings and scores resulting frompcaCoDa, is performed.

Value

The robust compositional biplot.

Author(s)

M. Templ, K. Hron

References

Aitchison, J. and Greenacre, M. (2002). Biplots of compositionaldata.Applied Statistics,51, 375-392. \

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal component analysis forcompositional data with outliers.Environmetrics,20 (6),621–632.

See Also

pcaCoDa,plot.pcaCoDa

Examples

data(coffee)p1 <- pcaCoDa(coffee[,-1])p1plot(p1, which = 2, choices = 1:2)# exemplarly, showing the first and third PCa <- p1$princompOutputClrbiplot(a, choices = c(1,3))## with labels for the scores:data(arcticLake)rownames(arcticLake) <- paste(sample(letters[1:26], nrow(arcticLake), replace=TRUE),                               1:nrow(arcticLake), sep="")pc <- pcaCoDa(arcticLake, method="classical")plot(pc, xlabs=rownames(arcticLake), which = 2)plot(pc, xlabs=rownames(arcticLake), which = 3)

Bootstrap to find optimal number of components

Description

Combined bootstrap and cross validation procedure to find optimal number ofPLS components

Usage

bootnComp(X, y, R = 99, plotting = FALSE)

Arguments

Details

Heavily used internally in function impRZilr.

Value

Including other information in a list, the optimal number ofcomponents

Author(s)

Matthias Templ

See Also

impRZilr

Examples

## we refer to impRZilr()

Backwards pivot coordinates and their inverse

Description

Backwards pivot coordinate representation of a set of compositional ventors as a special case of isometric logratio coordinates and their inverse mapping.

Usage

bpc(X, base = exp(1))

Arguments

Details

bpc

Backwards pivot coordinates map D-part compositional data from the simplex into a (D-1)-dimensional real space isometrically. The first coordinate has form of pairwise logratio log(x2/x1) and serves as an alternative to additive logratio transformation with part x1 being the rationing element. The remaining coordinates are structured as detailed in Nesrstova et al. (2023). Consequently, when a specific pairwise logratio is of the main interest, the respective columns have to be placed at the first (the compositional part in denominator of the logratio, the rationing element) and the second position (the compositional part in numerator) in the data matrix X.

Value

Author(s)

Kamila Facevicova

References

Hron, K., Coenders, G., Filzmoser, P., Palarea-Albaladejo, J., Famera, M., Matys Grygar, M. (2022). Analysing pairwise logratios revisited. Mathematical Geosciences 53, 1643 - 1666.

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcTabbpcTabWrapperbpcPcabpcReg

Examples

data(expenditures)# default setting with ln()bpc(expenditures)# logarithm of base 2bpc(expenditures, base = 2)

Principal component analysis based on backwards pivot coordinates

Description

Performs classical or robust principal component analysis on system of backwards pivot coordinates and returns the result related to pairwise logratios as well as the clr representation.

Usage

bpcPca(X, robust = FALSE, norm.cat = NULL)

Arguments

Details

bpcPca

The compositional data set is repeatedly expressed in a set of backwards logratio coordinates, when each set highlights one pairwise logratio (or one pairwise logratio with the selected rationing category). For each set, robust or classical principal component analysis is performed and loadings respective to the first backwards pivot coordinate are stored. The procedure results in matrix of scores (invariant to the specific coordinate system), clr loading matrix and matrix with loadings respective to pairwise logratios.

Value

Author(s)

Kamila Facevicova

References

Hron, K., Coenders, G., Filzmoser, P., Palarea-Albaladejo, J., Famera, M., Matys Grygar, M. (2022). Analysing pairwise logratios revisited. Mathematical Geosciences 53, 1643 - 1666.

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcbpcPcaTabbpcReg

Examples

data(arcticLake)# classical estimation with all pairwise logratios:res.cla <- bpcPca(arcticLake)summary(res.cla)biplot(res.cla)head(res.cla$scores)res.cla$loadingsres.cla$loadings.clr# similar output as from pca CoDares.cla2 <- pcaCoDa(arcticLake, method="classical", solve = "eigen")biplot(res.cla2)head(res.cla2$scores)res.cla2$loadings# classical estimation focusing on pairwise logratios with clay:res.cla.clay <- bpcPca(arcticLake, norm.cat = "clay")biplot(res.cla.clay)# robust estimation with all pairwise logratios:res.rob <- bpcPca(arcticLake, robust = TRUE)biplot(res.rob)

Principal component analysis of compositional tables based on backwards pivot coordinates

Description

Performs classical or robust principal component analysis on a set of compositional tables, based on backwards pivot coordinates. Returns the result related to pairwise row and column balances and four-part log odds-ratios. The loadings in the clr space are available as well.

Usage

bpcPcaTab(  X,  obs.ID = NULL,  row.factor = NULL,  col.factor = NULL,  value = NULL,  robust = FALSE,  norm.cat.row = NULL,  norm.cat.col = NULL)

Arguments

Details

bpcPcaTab

The set of compositional tables is repeatedly expressed in a set of backwards logratio coordinates, when each set highlights different combination of pairs of row and column factor categories, as detailed in Nesrstova et al. (2023). For each set, robust or classical principal component analysis is performed and loadings respective to the first row, column and odds-ratio backwards pivot coordinates are stored. The procedure results in matrix of scores (invariant to the specific coordinate system), clr loading matrix and matrix with loadings related to the selected backwards coordinates.

Value

Author(s)

Kamila Facevicova

References

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcTabWrapperbpcPcabpcRegTab

Examples

data(manu_abs)manu_abs$output <- as.factor(manu_abs$output)manu_abs$isic <- as.factor(manu_abs$isic)# classical estimation with all pairwise balances and four-part ORs:res.cla <- bpcPcaTab(manu_abs, obs.ID = "country", row.factor = "output", col.factor = "isic", value = "value")summary(res.cla)biplot(res.cla)head(res.cla$scores)res.cla$loadingsres.cla$loadings.clr# classical estimation with LAB anf 155 as rationing categoriesres.cla.select <- bpcPcaTab(manu_abs, obs.ID = "country", row.factor = "output", col.factor = "isic", value = "value", norm.cat.row = "LAB", norm.cat.col = "155")summary(res.cla.select)biplot(res.cla.select)head(res.cla.select$scores)res.cla.select$loadingsres.cla.select$loadings.clr# robust estimation with all pairwise balances and four-part ORs:res.rob <- bpcPcaTab(manu_abs, obs.ID = "country", row.factor = "output", col.factor = "isic", value = "value", robust = TRUE)summary(res.rob)biplot(res.rob)head(res.rob$scores)res.rob$loadingsres.rob$loadings.clr

Classical and robust regression based on backwards pivot coordinates

Description

Performs classical or robust regression analysis of real response on compositional predictors, represented in backwards pivot coordinates. Also non-compositional covariates can be included (additively).

Usage

bpcReg(  X,  y,  external = NULL,  norm.cat = NULL,  robust = FALSE,  base = exp(1),  norm.const = F,  seed = 8)

Arguments

Details

bpcReg

The compositional part of the data set is repeatedly expressed in a set of backwards logratio coordinates, when each set highlights one pairwise logratio (or one pairwise logratio with the selected rationing category). For each set (supplemented by non-compositonal predictors), robust MM or classical least squares estimate of regression coefficients is performed and information respective to the first backwards pivot coordinate is stored. The summary therefore collects results from several regression models, each leading to the same overall model characteristics, like the F statistics or R^2.The coordinates are structured as detailed in Nesrstova et al. (2023).In order to maintain consistency of the iterative results collected in the output, a seed is set before robust estimation of each of the models considered. Its specific value can be set via parameter seed.

Value

A list containing:

Summary

the summary object which collects results from all coordinate systems. The names of the coefficients indicate the type of the respective coordinate (bpc.1 - the first backwards pivot coordinate) and the logratio quantified thereby. E.g. bpc.1_C2.to.C1 would therefore correspond to the logratio between compositional parts C1 and C2, schematically written log(C2/C1). See Nesrstova et al. (2023) for details.

Base

the base with respect to which logarithms are computed

Norm.const

the values of normalising constants (when results for orthonormal coordinates are reported).

Robust

TRUE if the MM estimator was applied.

lm

the lm object resulting from the first iteration.

Levels

the order of compositional parts cosidered in the first iteration.

Author(s)

Kamila Facevicova

References

Hron, K., Coenders, G., Filzmoser, P., Palarea-Albaladejo, J., Famera, M., Matys Grygar, M. (2022). Analysing pairwise logratios revisited. Mathematical Geosciences 53, 1643 - 1666.

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcbpcPcabpcRegTab

Examples

## How the total household expenditures in EU Member## States depend on relative contributions of ## single household expenditures:data(expendituresEU)y <- as.numeric(apply(expendituresEU,1,sum))# classical regression summarizing the effect of all pairwise logratios lm.cla <- bpcReg(expendituresEU, y)lm.cla# gives the same model characteristics as lmCoDaX:lm <- lmCoDaX(y, expendituresEU, method="classical")lm$ilr# robust regression, with Food as the rationing category and logarithm of base 2# response is part of the data matrix XexpendituresEU.y <- data.frame(expendituresEU, total = y)lm.rob <- bpcReg(expendituresEU.y, "total", norm.cat = "Food", robust = TRUE, base = 2)lm.rob## Illustrative example with exports and imports (categorized) as non-compositional covariatesdata(economy)X.ext <- economy[!economy$country2 %in% c("HR", "NO", "CH"), c("exports", "imports")]X.ext$imports.cat <- cut(X.ext$imports, quantile(X.ext$imports, c(0, 1/3, 2/3, 1)), labels = c("A", "B", "C"), include.lowest = TRUE)X.y.ext <- data.frame(expendituresEU.y, X.ext[, c("exports", "imports.cat")])lm.ext <- bpcReg(X.y.ext, y = "total", external = c("exports", "imports.cat"))lm.ext

Classical and robust regression based on backwards pivot coordinates

Description

Performs classical or robust regression analysis of real response on a compositional table, which is represented in backwards pivot coordinates. Also non-compositional covariates can be included (additively).

Usage

bpcRegTab(  X,  y,  obs.ID = NULL,  row.factor = NULL,  col.factor = NULL,  value = NULL,  external = NULL,  norm.cat.row = NULL,  norm.cat.col = NULL,  robust = FALSE,  base = exp(1),  norm.const = F,  seed = 8)

Arguments

Details

bpcRegTab

The set of compositional tables is repeatedly expressed in a set of backwards logratio coordinates, when each set highlights different combination of pairs of row and column factor categories, as detailed in Nesrstova et al. (2023).For each coordinates system (supplemented by non-compositonal predictors), robust MM or classical least squares estimate of regression coefficients is performed and information respective to the first row, column and table backwards pivot coordinate is stored. The summary therefore collects results from several regression models, each leading to the same overall model characteristics, like the F statistics or R^2. In order to maintain consistency of the iterative results collected in the output, a seed is set before robust estimation of each of the models considered. Its specific value can be set via parameter seed.

Value

A list containing:

Summary

the summary object which collects results from all coordinate systems. The names of the coefficients indicate the type of the respective coordinate (rbpb.1 - the first row backwards pivot balance, cbpb.1 - the first column backwards pivot balance and tbpc.1.1 - the first table backwards pivot coordinate) and the logratio or log odds-ratio quantified thereby. E.g. cbpb.1_C2.to.C1 would therefore correspond to the logratio between column categories C1 and C2, schematically written log(C2/C1), and tbpc.1.1_R2.to.R1.&.C2.to.C1 would correspond to the log odds-ratio computed from a 2x2 table, which is formed by row categories R1 and R2 and columns C1 and C2. See Nesrstova et al. (2023) for details.

Base

the base with respect to which logarithms are computed

Norm.const

the values of normalising constants (when results for orthonormal coordinates are reported).

Robust

TRUE if the MM estimator was applied.

lm

the lm object resulting from the first iteration.

Row.levels

the order of the row factor levels cosidered in the first iteration.

Col.levels

the order of the column factor levels cosidered in the first iteration.

Author(s)

Kamila Facevicova

References

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcTabWrapperbpcPcaTabbpcReg

Examples

# let's prepare some datadata(employment2)data(unemployed)table_data <- employment2[employment2$Contract == "FT", ]y <- unemployed[unemployed$age == "20_24" & unemployed$year == 2015,]countries <- intersect(levels(droplevels(y$country)), levels(table_data$Country))table_data <- table_data[table_data$Country %in% countries, ]y <- y[y$country %in% countries, c("country", "value")]colnames(y) <- c("Country", "unemployed")# response as part of Xtable_data.y <- merge(table_data, y, by = "Country")reg.cla <- bpcRegTab(table_data.y, y = "unemployed", obs.ID = "Country", row.factor = "Sex", col.factor = "Age", value = "Value")reg.cla# response as named arrayresp <- y$unemployednames(resp) <- y$Countryreg.cla2 <- bpcRegTab(table_data.y, y = resp, obs.ID = "Country", row.factor = "Sex", col.factor = "Age", value = "Value")reg.cla2# response as data.frame, robust estimator, 55plus as the rationing category, logarithm of base 2resp.df <- as.data.frame(y$unemployed)rownames(resp.df) <- y$Countryreg.rob <- bpcRegTab(table_data.y, y = resp.df, obs.ID = "Country", row.factor = "Sex", col.factor = "Age", value = "Value",norm.cat.col = "55plus", robust = TRUE, base = 2)reg.rob# Illustrative example with non-compositional predictors and response as part of Xx.ext <- unemployed[unemployed$age == "15_19" & unemployed$year == 2015,]x.ext <- x.ext[x.ext$country %in% countries, c("country", "value")]colnames(x.ext) <- c("Country", "15_19")table_data.y.ext <- merge(table_data.y, x.ext, by = "Country")reg.cla.ext <- bpcRegTab(table_data.y.ext, y = "unemployed", obs.ID = "Country", row.factor = "Sex", col.factor = "Age", value = "Value", external = "15_19")reg.cla.ext

Backwards pivot coordinates and their inverse

Description

Backwards pivot coordinate representation of a compositional table as a special case of isometric logratio coordinates and their inverse mapping.

Usage

bpcTab(x, row.factor = NULL, col.factor = NULL, value = NULL, base = exp(1))

Arguments

Details

bpcTab

Backwards pivot coordinates map IxJ-part compositional table from the simplex into a (IJ-1)-dimensional real space isometrically. Particularly the first coordinate from each group (rbpb.1, cbpb.1, tbpc.1) preserves the elemental information on the two-factorial structure. The first row and column backwards pivot balances rbpb.1 and cbpb.1 represent two-factorial counterparts to the pairwise logratios. More specifically, the first two levels of the considered factor are compared in the ratio, while the first level plays the role of the rationing category (denominator of the ratio) and the second level is treated as the normalized category (numerator of the ratio). All categories of the complementary factor are aggregated with the geometric mean.The first table backwards pivot coordinate, has form of a four-part log odds-ratio (again related to the first two levels of the row and column factors) and quantifies the relations between factors.All coordinates are structured as detailed in Nesrstova et al. (2023).

Value

Author(s)

Kamila Facevicova

References

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcbpcTabWrapperbpcPcaTabbpcRegTab

Examples

data(manu_abs)manu_USA <- manu_abs[which(manu_abs$country=='USA'),]manu_USA$output <- as.factor(manu_USA$output)manu_USA$isic <- as.factor(manu_USA$isic)# default setting with ln()bpcTab(manu_USA, row.factor = "output", col.factor = "isic", value = "value")# logarithm of base 2bpcTab(manu_USA, row.factor = "output", col.factor = "isic", value = "value",base = 2)# for base exp(1) is the result similar to tabCoord():r <- rbind(c(-1,1,0), c(-1,-1,1))c <- rbind(c(-1,1,0,0,0), c(-1,-1,1,0,0), c(-1,-1,-1,1,0), c(-1,-1,-1,-1,1))tabCoord(manu_USA, row.factor = "output", col.factor = "isic", value = "value",SBPr = r, SBPc = c)

Backwards pivot coordinates and their inverse

Description

For each compositional table in the sample a system of backwards pivot coordinates is computed as a special case of isometric logratio coordinates. For their inverse mapping, the contrast matrix is provided.

Usage

bpcTabWrapper(  X,  obs.ID = NULL,  row.factor = NULL,  col.factor = NULL,  value = NULL,  base = exp(1))

Arguments

Details

bpcTabWrapper

Backwards pivot coordinates map IxJ-part compositional table from the simplex into a (IJ-1)-dimensional real space isometrically. Particularly the first coordinate from each group (rbpb.1, cbpb.1, tbpc.1) preserves the elemental information on the two-factorial structure. The first row and column backwards pivot balances rbpb.1 and cbpb.1 represent two-factorial counterparts to the pairwise logratios. More specifically, the first two levels of the considered factor are compared in the ratio, while the first level plays the role of the rationing category (denominator of the ratio) and the second level is treated as the normalized category (numerator of the ratio). All categories of the complementary factor are aggregated with the geometric mean.The first table backwards pivot coordinate, has form of a four-part log odds-ratio (again related to the first two levels of the row and column factors) and quantifies the relations between factors.All coordinates are structured as detailed in Nesrstova et al. (2023).

Value

Author(s)

Kamila Facevicova

References

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcbpcPcaTabbpcRegTab

Examples

data(manu_abs)manu_abs$output <- as.factor(manu_abs$output)manu_abs$isic <- as.factor(manu_abs$isic)# default setting with ln()bpcTabWrapper(manu_abs, obs.ID = "country", row.factor = "output", col.factor = "isic", value = "value")# logarithm of base 2bpcTabWrapper(manu_abs, obs.ID = "country", row.factor = "output", col.factor = "isic", value = "value", base = 2)# for base exp(1) is the result similar to tabCoordWrapper():r <- rbind(c(-1,1,0), c(-1,-1,1))c <- rbind(c(-1,1,0,0,0), c(-1,-1,1,0,0), c(-1,-1,-1,1,0), c(-1,-1,-1,-1,1))tabCoordWrapper(manu_abs, obs.ID = "country", row.factor = "output", col.factor = "isic", value = "value", SBPr = r, SBPc = c)

hospital discharges on cancer and distribution of age

Description

Hospital discharges of in-patients on neoplasms (cancer) per 100.000 inhabitants (year 2007) and population age structure.

Format

A data set on 24 compositions on 6 variables.

Details

country

country

year

year

p1

percentage of population with age below 15

p2

percentage of population with age between 15 and 60

p3

percentage of population with age above 60

discharges

hospital discharges of in-patients on neoplasms (cancer) per 100.000 inhabitants

The response (discharges) is provided for the European Union countries (except Greece, Hungary and Malta) by Eurostat. As explanatory variables we use the age structure of the population in the same countries (year 2008). The age structure consists of three parts, age smaller than 15, age between 15 and 60 and age above 60 years, and they are expressed as percentages on the overall population in the countries. The data are provided by the United Nations Statistics Division.

Author(s)

conversion to R by Karel Hron and Matthias Templmatthias.templ@tuwien.ac.at

Source

https://www.ec.europa.eu/eurostat andhttps://unstats.un.org/home/

References

K. Hron, P. Filzmoser, K. Thompson (2012). Linear regression with compositional explanatory variables.Journal of Applied Statistics, Volume 39, Issue 5, 2012.

Examples

data(cancer)str(cancer)

malignant neoplasms cancer

Description

Two main types of malignant neoplasms cancer affecting colon and lung, respectively, in male and female populations. For this purpose population data (2012) from 35 OECD countries were collected.

Format

A data set on 35 compositional tables on 4 parts (row-wise sorted cells) and 5 variables.

Details

country

country

females-colon

number of colon cancer cases in female population

females-lung

number of lung cancer cases in female population

males-colon

number of colon cancer cases in male population

males-lung

number of lung cancer cases in male population

The data are obtained from the OECD website.

Author(s)

conversion to R by Karel Hron and intergration by Matthias Templmatthias.templ@tuwien.ac.at

Source

From OECD website

Examples

data(cancerMN)head(cancerMN)rowSums(cancerMN[, 2:5])

Compositional error deviation

Description

Normalized Aitchison distance between two data sets

Usage

ced(x, y, ni)

Arguments

Details

This function has been mainly written for procudures that evaluate imputation or replacement of rounded zeros. The ni parameter can thus, e.g. beused for expressing the number of rounded zeros.

Value

the compositinal error distance

Author(s)

Matthias Templ

References

Hron, K., Templ, M., Filzmoser, P. (2010) Imputation ofmissing values for compositional data using classical and robust methodsComputational Statistics and Data Analysis, 54 (12),3095-3107.

Templ, M., Hron, K., Filzmoser, P., Gardlo, A. (2016). Imputation of rounded zeros for high-dimensional compositional data.Chemometrics and Intelligent Laboratory Systems, 155, 183-190.

See Also

rdcm

Examples

data(expenditures)x <- expendituresx[1,3] <- NAxi <- impKNNa(x)$xImpced(expenditures, xi, ni = sum(is.na(x)))

Centred logratio coefficients

Description

The centred logratio (clr) coefficients map D-part compositional data from the simplexinto a D-dimensional real space.

Usage

cenLR(x, base = exp(1))

Arguments

Details

Each composition is divided by the geometric mean of its parts before thelogarithm is taken.

Value

the resulting clr coefficients, including

Note

The resulting data set is singular by definition.

Author(s)

Matthias Templ

References

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

See Also

cenLRinv,addLR,pivotCoord,addLRinv,pivotCoordInv

Examples

data(expenditures)eclr <- cenLR(expenditures)inveclr <- cenLRinv(eclr)head(expenditures)head(inveclr)head(pivotCoordInv(eclr$x.clr))

Inverse centred logratio mapping

Description

Applies the inverse centred logratio mapping.

Usage

cenLRinv(x, useClassInfo = TRUE)

Arguments

Value

the resulting compositional data set.

Author(s)

Matthias Templ

References

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

See Also

cenLR,addLR,pivotCoord,addLRinv,pivotCoordInv

Examples

data(expenditures)eclr <- cenLR(expenditures, 2)inveclr <- cenLRinv(eclr)head(expenditures)head(inveclr)head(cenLRinv(eclr$x.clr))

C-horizon of the Kola data with rounded zeros

Description

This data set is almost the same as the 'chorizon' data setin packagemvoutlier andchorizonDL, except that values below the detection limitare coded as zeros, and detection limits provided as attributes to the data set andless variables are included.

Format

A data frame with 606 observations on the following 62 variables.

*ID

a numeric vector

XCOO

a numeric vector

YCOO

a numeric vector

Ag

concentration in mg/kg

Al

concentration in mg/kg

Al_XRF

concentration in wt. percentage

As

concentration in mg/kg

Ba

concentration in mg/kg

Ba_INAA

concentration in mg/kg

Be

concentration in mg/kg

Bi

concentration in mg/kg

Ca

concentration in mg/kg

Ca_XRF

concentration in wt. percentage

Cd

concentration in mg/kg

Ce_INAA

concentration in mg/kg

Co

concentration in mg/kg

Co_INAA

concentration in mg/kg

Cr

concentration in mg/kg

Cr_INAA

concentration in mg/kg

Cu

concentration in mg/kg

Eu_INAA

concentration in mg/kg

Fe

concentration in mg/kg

Fe_XRF

concentration in wt. percentage

Hf_INAA

concentration in mg/kg

K

concentration in mg/kg

K_XRF

concentration in wt. percentage

La

concentration in mg/kg

La_INAA

concentration in mg/kg

Li

concentration in mg/kg

Lu_INAA

concentration in mg/kg

Mg

concentration in mg/kg

Mg_XRF

concentration in wt. percentage

Mn

concentration in mg/kg

Mn_XRF

concentration in wt. percentage

Na

concentration in mg/kg

Na_XRF

concentration in wt. percentage

Nd_INAA

concentration in mg/kg

Ni

concentration in mg/kg

P

concentration in mg/kg

P_XRF

concentration in wt. percentage

Pb

concentration in mg/kg

S

concentration in mg/kg

Sc

concentration in mg/kg

Sc_INAA

concentration in mg/kg

Si

concentration in mg/kg

Si_XRF

concentration in wt. percentage

Sm_INAA

concentration in mg/kg

Sr

concentration in mg/kg

Th_INAA

concentration in mg/kg

Ti

concentration in mg/kg

Ti_XRF

concentration in wt. percentage

V

concentration in mg/kg

Y

concentration in mg/kg

Yb_INAA

concentration in mg/kg

Zn

concentration in mg/kg

LOI

concentration in wt. percentage

pH

ph value

ELEV

elevation

*COUN

country

*ASP

a numeric vector

TOPC

a numeric vector

LITO

information on lithography

Note

For a more detailed description of this data set, see'chorizon' in packagemvoutlier.

Source

Kola Project (1993-1998)

References

Reimann, C., Filzmoser, P., Garrett, R.G. and Dutter, R. (2008)Statistical Data Analysis Explained: Applied Environmental Statisticswith R. Wiley.

See Also

'chorizon',chorizonDL

Examples

data(chorizonDL, package = "robCompositions")dim(chorizonDL)colnames(chorizonDL)zeroPatterns(chorizonDL)

Cluster analysis for compositional data

Description

Clustering in orthonormal coordinates or by using the Aitchison distance

Usage

clustCoDa(  x,  k = NULL,  method = "Mclust",  scale = "robust",  transformation = "pivotCoord",  distMethod = NULL,  iter.max = 100,  vals = TRUE,  alt = NULL,  bic = NULL,  verbose = TRUE)## S3 method for class 'clustCoDa'plot(  x,  y,  ...,  normalized = FALSE,  which.plot = "clusterMeans",  measure = "silwidths")

Arguments

Details

The compositional data set is either internally represented by orthonormal coordiantesbefore a cluster algorithm is applied, or - depending on the choice of parameters - the Aitchison distance is used.

Value

all relevant information such as cluster centers, cluster memberships, andcluster statistics.

Author(s)

Matthias Templ (accessing the basic features of hclust, Mclust, kmeans, etc. that are all written by others)

References

M. Templ, P. Filzmoser, C. Reimann.Cluster analysis applied to regional geochemical data: Problems and possibilities.Applied Geochemistry,23 (8), 2198–2213, 2008

Templ, M., Filzmoser, P., Reimann, C. (2008)Cluster analysis applied to regional geochemical data: Problems and possibilities, Applied Geochemistry, 23 (2008), pages 2198 - 2213.

Examples

data(expenditures)x <- expendituresrr <- clustCoDa(x, k=6, scale = "robust", transformation = "pivotCoord")rr2 <- clustCoDa(x, k=6, distMethod = "Aitchison", scale = "none",                  transformation = "identity")rr3 <- clustCoDa(x, k=6, distMethod = "Aitchison", method = "single",                 transformation = "identity", scale = "none")                 ## Not run: require(reshape2)plot(rr)plot(rr, normalized = TRUE)plot(rr, normalized = TRUE, which.plot = "partMeans")## End(Not run)

Q-mode cluster analysis for compositional parts

Description

Clustering using the variation matrix of compositional parts

Usage

clustCoDa_qmode(x, method = "ward.D2")

Arguments

Value

a hclust object

Author(s)

Matthias Templ (accessing the basic features of hclust that are all written by other authors)

References

Filzmoser, P., Hron, K. Templ, M. (2018)Applied Compositional Data Analysis, Springer, Cham.

Examples

data(expenditures) x <- expenditurescl <- clustCoDa_qmode(x)## Not run: require(reshape2)plot(cl)cl2 <- clustCoDa_qmode(x, method = "single")plot(cl2)## End(Not run)

coffee data set

Description

30 commercially available coffee samples of different origins.

Usage

data(coffee)

Format

A data frame with 30 observations and 7 variables.

Details

sort

sort of coffee

acit

acetic acid

metpyr

methylpyrazine

furfu

furfural

furfualc

furfuryl alcohol

dimeth

2,6 dimethylpyrazine

met5

5-methylfurfural

In the original data set, 15 volatile compounds (descriptors of coffee aroma) were selected for a statistical analysis. We selected six compounds (compositional parts) on three sorts of coffee.

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at, Karel Hron

References

M. Korhonov\'a, K. Hron, D. Klimc\'ikov\'a, L. Muller, P. Bedn\'ar, and P. Bart\'ak (2009). Coffee aroma - statistical analysis of compositional data.Talanta, 80(2): 710–715.

Examples

data(coffee)str(coffee)summary(coffee)

Compares Mahalanobis distances from two approaches

Description

Mahalanobis distances are calculated for each zero pattern.Two approaches are used. The first one estimates Mahalanobis distance for observations belonging to one each zero pattern each.The second method uses a more sophisticated approach described below.

Usage

compareMahal(x, imp = "KNNa")## S3 method for class 'mahal'plot(x, y, ...)

Arguments

Value

Author(s)

Matthias Templ, Karel Hron

References

Templ, M., Hron, K., Filzmoser, P. (2017) Exploratory tools for outlier detection in compositional data with structural zeros".Journal of Applied Statistics,44 (4), 734–752

See Also

impKNNa,pivotCoord

Examples

data(arcticLake)# generate some zerosarcticLake[1:10, 1] <- 0arcticLake[11:20, 2] <- 0m <- compareMahal(arcticLake)plot(m)

Compositional spline

Description

This code implements the compositional smoothing splines grounded on the theory of Bayes spaces.

Usage

compositionalSpline(  t,  clrf,  knots,  w,  order,  der,  alpha,  spline.plot = FALSE,  basis.plot = FALSE)

Arguments

Details

The compositional splines enable to construct a spline basis in the centred logratio (clr) space of density functions (ZB-spline basis) and consequently also in the original space of densities (CB-spline basis).The resulting compositional splines in the clr space as well as the ZB-spline basis satisfy the zero integral constraint. This enables to work with compositional splines consistently in the framework of the Bayes space methodology.

Augmented knot sequence is obtained from the original knots by adding #(order-1) multiple endpoints.

Value

Author(s)

J. Machalovajitka.machalova@upol.cz, R. Talskatalskarenata@seznam.cz

References

Machalova, J., Talska, R., Hron, K. Gaba, A. Compositional splines for representation of density functions.Comput Stat (2020). https://doi.org/10.1007/s00180-020-01042-7

Examples

# Example (Iris data):SepalLengthCm <- iris$Sepal.LengthSpecies <- iris$Speciesiris1 <- SepalLengthCm[iris$Species==levels(iris$Species)[1]]h1 <- hist(iris1, plot = FALSE)midx1 <- h1$midsmidy1 <- matrix(h1$density, nrow=1, ncol = length(h1$density), byrow=TRUE)clrf  <- cenLR(rbind(midy1,midy1))$x.clr[1,]knots <- seq(min(h1$breaks),max(h1$breaks),l=5)order <- 4der <- 2alpha <- 0.99sol1 <- compositionalSpline(t = midx1, clrf = clrf, knots = knots,   w = rep(1,length(midx1)), order = order, der = der,   alpha = alpha, spline.plot = TRUE)sol1$GCVZB_coef <- sol1$ZB_coeft <- seq(min(knots),max(knots),l=500)t_step <- diff(t[1:2])ZB_base <- ZBsplineBasis(t=t,knots,order)$ZBsplineBasissol1.t <- ZB_base%*%ZB_coefsol2.t <- fcenLRinv(t,t_step,sol1.t)h2 = hist(iris1,prob=TRUE,las=1)points(midx1,midy1,pch=16)lines(t,sol2.t,col="darkred",lwd=2)# Example (normal distrubution):# generate n values from normal distributionset.seed(1)n = 1000; mean = 0; sd = 1.5raw_data = rnorm(n,mean,sd)  # number of classes according to Sturges rulen.class = round(1+1.43*log(n),0)  # Interval midpointsparnition = seq(-5,5,length=(n.class+1))t.mid = c(); for (i in 1:n.class){t.mid[i]=(parnition[i+1]+parnition[i])/2}  counts = table(cut(raw_data,parnition))prob = counts/sum(counts)                # probabilitiesdens.raw = prob/diff(parnition)          # raw density dataclrf =  cenLR(rbind(dens.raw,dens.raw))$x.clr[1,]  # raw clr density data  # set the input parameters for smoothing knots = seq(min(parnition),max(parnition),l=5)w = rep(1,length(clrf))order = 4der = 2alpha = 0.5spline = compositionalSpline(t = t.mid, clrf = clrf, knots = knots,   w = w, order = order, der = der, alpha = alpha,   spline.plot=TRUE, basis.plot=FALSE)  # ZB-spline coefficientsZB_coef = spline$ZB_coef  # ZB-spline basis evaluated on the grid "t.fine"t.fine = seq(min(knots),max(knots),l=1000)ZB_base = ZBsplineBasis(t=t.fine,knots,order)$ZBsplineBasis  # Compositional spline in the clr space (evaluated on the grid t.fine)comp.spline.clr = ZB_base%*%ZB_coef  # Compositional spline in the Bayes space (evaluated on the grid t.fine)comp.spline = fcenLRinv(t.fine,diff(t.fine)[1:2],comp.spline.clr)  # Unit-integral representation of truncated true normal density function dens.true = dnorm(t.fine, mean, sd)/trapzc(diff(t.fine)[1:2],dnorm(t.fine, mean, sd))  # Plot of compositional spline together with raw density datamatplot(t.fine,comp.spline,type="l",    lty=1, las=1, col="darkblue", xlab="t",     ylab="density",lwd=2,cex.axis=1.2,cex.lab=1.2,ylim=c(0,0.28))matpoints(t.mid,dens.raw,pch = 8, col="darkblue", cex=1.3)  # Add true normal density functionmatlines(t.fine,dens.true,col="darkred",lwd=2)

Constant sum

Description

Closes compositions to sum up to a given constant (default 1), by dividingeach part of a composition by its row sum.

Usage

constSum(x, const = 1, na.rm = TRUE)

Arguments

Value

The data for which the row sums are equal toconst.

Author(s)

Matthias Templ

Examples

data(expenditures)constSum(expenditures)constSum(expenditures, 100)

Coordinate representation of compositional tables

Description

General approach to orthonormal coordinates for compositional tables

Usage

coord(x, SBPr, SBPc)## S3 method for class 'coord'print(x, ...)

Arguments

Details

A contingency or propability table can be considered as a two-factor composition, we refer to compositional tables. This function constructs orthonomal coordinates for compositional tables usingthe balances approach for given sequential binary partitions on rows and columns of the compositional table.

Value

Row and column balances and odds ratios as coordinate representations of the independence and interaction tables, respectively.

Author(s)

Kamila Facevicova, and minor adaption by Matthias Templ

References

Facevicova, K., Hron, K., Todorov, V., Templ, M. (2018)General approach to coordinate representation of compositional tables.Scandinavian Journal of Statistics, 45(4), 879-899.

Examples

x <- rbind(c(1,5,3,6,8,4),c(6,4,9,5,8,12),c(15,2,68,42,11,6),           c(20,15,4,6,23,8),c(11,20,35,26,44,8))xSBPc <- rbind(c(1,1,1,1,-1,-1),c(1,-1,-1,-1,0,0),c(0,1,1,-1,0,0),              c(0,1,-1,0,0,0),c(0,0,0,0,1,-1))SBPcSBPr <- rbind(c(1,1,1,-1,-1),c(1,1,-1,0,0),c(1,-1,0,0,0),c(0,0,0,1,-1))SBPrresult <- coord(x, SBPr,SBPc)resultdata(socExp)

Correlations for compositional data

Description

This function computes correlation coefficients between compositional parts basedon symmetric pivot coordinates.

Usage

corCoDa(x, ...)

Arguments

Value

A compositional correlation matrix.

Author(s)

Petra Kynclova

References

Kynclova, P., Hron, K., Filzmoser, P. (2017)Correlation between compositional parts based on symmetric balances.Mathematical Geosciences, 49(6), 777-796.

Examples

data(expenditures)corCoDa(expenditures)x <- arcticLake corCoDa(x)

Coordinate representation of a compositional cube and of a sample of compositional cubes

Description

cubeCoord computes a system of orthonormal coordinates of a compositional cube. Computation of either pivot coordinates or a coordinate system based on the given SBP is possible.

Wrapper (cubeCoordWrapper): For each compositional cube in the sample cubeCoordWrapper computes a system of orthonormal coordinates and provide a simple descriptive analysis. Computation of either pivot coordinates or a coordinate system based on the given SBP is possible.

Usage

cubeCoord(  x,  row.factor = NULL,  col.factor = NULL,  slice.factor = NULL,  value = NULL,  SBPr = NULL,  SBPc = NULL,  SBPs = NULL,  pivot = FALSE,  print.res = FALSE)cubeCoordWrapper(  X,  obs.ID = NULL,  row.factor = NULL,  col.factor = NULL,  slice.factor = NULL,  value = NULL,  SBPr = NULL,  SBPc = NULL,  SBPs = NULL,  pivot = FALSE,  test = FALSE,  n.boot = 1000)

Arguments

Details

cubeCoord

This transformation moves the IJK-part compositional cubes from the simplex into a (IJK-1)-dimensional real space isometrically with respect to its three-factorial nature.

Wrapper (cubeCoordWrapper): Each of n IJK-part compositional cubes from the sample is with respect to its three-factorial nature isometrically transformed from the simplex into a (IJK-1)-dimensional real space. Sample mean values and standard deviations are computed and using bootstrap an estimate of 95 % confidence interval is given.

Value

Author(s)

Kamila Facevicova

References

Facevicova, K., Filzmoser, P. and K. Hron (2019) Compositional Cubes: Three-factorial Compositional Data. Under review.

See Also

tabCoordtabCoordWrapper

Examples

###################### Coordinate representation of a CoDa Cube## Not run: ### example from Fa\v cevicov\'a (2019)data(employment2)CZE <- employment2[which(employment2$Country == 'CZE'), ]# pivot coordinatescubeCoord(CZE, "Sex", 'Contract', "Age", 'Value')# coordinates with given SBPr <- t(c(1,-1))c <- t(c(1,-1))s <- rbind(c(1,-1,-1), c(0,1,-1))cubeCoord(CZE, "Sex", 'Contract', "Age", 'Value', r,c,s)## End(Not run)###################### Analysis of a sample of CoDa Cubes## Not run: ### example from Fa\v cevicov\'a (2019)data(employment2)### Compositional tables approach,### analysis of the relative structure.### An example from Facevi\v cov\'a (2019)# pivot coordinatescubeCoordWrapper(employment2, 'Country', 'Sex', 'Contract', 'Age', 'Value',  test=TRUE)# coordinates with given SBP (defined in the paper)r <- t(c(1,-1))c <- t(c(1,-1))s <- rbind(c(1,-1,-1), c(0,1,-1))res <- cubeCoordWrapper(employment2, 'Country', 'Sex', 'Contract', "Age", 'Value', r,c,s, test=TRUE)### Classical approach,### generalized linear mixed effect model.library(lme4)employment2$y <- round(employment2$Value*1000)glmer(y~Sex*Age*Contract+(1|Country),data=employment2,family=poisson)### other relations within cube (in the log-ratio form)### e.g. ratio between women and man in the group FT, 15to24### and ratio between age groups 15to24 and 55plus# transformation matrixT <- rbind(c(1,rep(0,5), -1, rep(0,5)), c(rep(c(1/4,0,-1/4), 4)))T %*% t(res$Contrast.matrix) %*%res$Bootstrap[,1]## End(Not run)

Linear and quadratic discriminant analysis for compositional data.

Description

Linear and quadratic discriminant analysis for compositional data using either robust or classical estimation.

Usage

daCoDa(x, grp, coda = TRUE, method = "classical", rule = "linear", ...)

Arguments

Details

Compositional data are expressed in orthonormal (ilr) coordinates (ifcoda==TRUE). For linear discriminant analysis the functions LdaClassic (classical) and Linda (robust) from the package rrcov are used. Similarly, quadratic discriminant analysis uses the functions QdaClassic and QdaCov (robust) from the same package.

The classical linear and quadratic discriminant rules are invariant to ilr coordinates and clrcoefficients. The robust rules are invariant to ilr transformations ifaffine equivariant robust estimators of location and covariance are taken.

Value

An S4 object of class LdaClassic, Linda, QdaClassic or QdaCov. See package rrcov for details.

Author(s)

Jutta Gamper

References

Filzmoser, P., Hron, K., Templ, M. (2012) Discriminant analysis for compositional data and robust parameter estimation.Computational Statistics, 27(4), 585-604.

See Also

LdaClassic,Linda,QdaClassic,QdaCov

Examples

## toy data (non-compositional)require(MASS)x1 <- mvrnorm(20,c(0,0,0),diag(3))x2 <- mvrnorm(30,c(3,0,0),diag(3))x3 <- mvrnorm(40,c(0,3,0),diag(3))X <- rbind(x1,x2,x3)grp=c(rep(1,20),rep(2,30),rep(3,40))clas1 <- daCoDa(X, grp, coda=FALSE, method = "classical", rule="linear")summary(clas1)## predict runs only with newest verison of rrcov## Not run: predict(clas1)## End(Not run)# specify different prior probabilitiesclas2 <- daCoDa(X, grp, coda=FALSE, prior=c(1/3, 1/3, 1/3))summary(clas2)## compositional datadata(coffee)x <- coffee[coffee$sort!="robusta",2:7]group <- droplevels(coffee$sort[coffee$sort!="robusta"])cof.cla <- daCoDa(x, group, method="classical", rule="quadratic")cof.rob <- daCoDa(x, group, method="robust", rule="quadratic")## predict runs only with newest verison of rrcov## Not run: predict(cof.cla)@ctpredict(cof.rob)@ct## End(Not run)

Discriminant analysis by Fisher Rule.

Description

Discriminant analysis by Fishers rule using the logratio approach to compositional data.

Usage

daFisher(x, grp, coda = TRUE, method = "classical", plotScore = FALSE, ...)## S3 method for class 'daFisher'print(x, ...)## S3 method for class 'daFisher'predict(object, ..., newdata)## S3 method for class 'daFisher'summary(object, ...)

Arguments

Details

The Fisher rule leads only to linear boundaries. However, this method allowsfor dimension reduction and thus for a better visualization of theseparation boundaries. For the Fisher discriminant rule (Fisher, 1938; Rao,1948) the assumption of normal distribution of the groups is not explicitlyrequired, although the method looses its optimality in case of deviationsfrom normality.

The classical Fisher discriminant rule is invariant to ilr coordinates and clrcoefficients. The robust rule is invariant to ilr transformations ifaffine equivariant robust estimators of location and covariance are taken.

Robustification is done (method “robust”) by estimating thecolumnwise means and the covariance by the Minimum Covariance Estimator.

Value

an object of class “daFisher” including the followingelements

Author(s)

Peter Filzmoser, Matthias Templ.

References

Filzmoser, P. and Hron, K. and Templ, M. (2012) Discriminant analysis for compositional data and robust parameter estimation.Computational Statistics, 27(4), 585-604.

Fisher, R. A. (1938) The statistical utiliziation of multiple measurements.Annals of Eugenics, 8, 376-386.

Rao, C.R. (1948) The utilization of multiple measurements in problems ofbiological classification.Journal of the Royal Statistical Society,Series B, 10, 159-203.

See Also

Linda

Examples

## toy data (non-compositional)require(MASS)x1 <- mvrnorm(20,c(0,0,0),diag(3))x2 <- mvrnorm(30,c(3,0,0),diag(3))x3 <- mvrnorm(40,c(0,3,0),diag(3))X <- rbind(x1,x2,x3)grp=c(rep(1,20),rep(2,30),rep(3,40))#par(mfrow=c(1,2))d1 <- daFisher(X,grp=grp,method="classical",coda=FALSE)d2 <- daFisher(X,grp=grp,method="robust",coda=FALSE)d2summary(d2)predict(d2, newdata = X)## example with olive data:## Not run: data(olive, package = "RnavGraph")# exclude zeros (alternatively impute them if # the detection limit is known using impRZilr())ind <- which(olive == 0, arr.ind = TRUE)[,1]olives <- olive[-ind, ]x <- olives[, 4:10]grp <- olives$Region # 3 groupsres <- daFisher(x,grp)ressummary(res)res <- daFisher(x, grp, plotScore = TRUE)res <- daFisher(x, grp, method = "robust")ressummary(res)predict(res, newdata = x)res <- daFisher(x,grp, plotScore = TRUE, method = "robust")# 9 regionsgrp <- olives$Areares <- daFisher(x, grp, plotScore = TRUE)ressummary(res)predict(res, newdata = x)## End(Not run)

economic indicators

Description

Household and government consumptions, gross captial formation and import and exports of goods and services.

Usage

data(economy)

Format

A data frame with 30 observations and 7 variables

Details

country

country name

country2

country name, short version

HHconsumption

Household and NPISH final consumption expenditure

GOVconsumption

Final consumption expenditure of general government

capital

Gross capital formation

exports

Exports of goods and services

imports

Imports of goods and services

Author(s)

Peter Filzmoser, Matthias Templmatthias.templ@tuwien.ac.at

References

Eurostat,https://ec.europa.eu/eurostat/data

Examples

data(economy)str(economy)

education level of father (F) and mother (M)

Description

Education level of father (F) and mother (M) in percentages of low(l), medium (m), and high (h) of 31 countries in Europe.

Usage

data(educFM)

Format

A data frame with 31 observations and 8 variables

Details

country

community code

F.l

percentage of females with low edcuation level

F.m

percentage of females with medium edcuation level

F.h

percentage of females with high edcuation level

F.l

percentage of males with low edcuation level

F.m

percentage of males with medium edcuation level

F.h

percentage of males with high edcuation level

Author(s)

Peter Filzmoser, Matthias Templ

Source

from Eurostat,https://ec.europa.eu/eurostat/

Examples

data(educFM)str(educFM)

efsa nutrition consumption

Description

Comprehensive European Food Consumption Database

Format

A data frame with 87 observations on the following 22 variables.

Country

country name

Pop.Class

population class

grains

Grains and grain-based products

vegetables

Vegetables and vegetable products (including fungi)

roots

Starchy roots and tubers

nuts

Legumes, nuts and oilseeds

fruit

Fruit and fruit products

meat

Meat and meat products (including edible offal)

fish

Fish and other seafood (including amphibians, rept)

milk

Milk and dairy products

eggs

Eggs and egg products

sugar

Sugar and confectionary

fat

Animal and vegetable fats and oils

juices

Fruit and vegetable juice

nonalcoholic

Non-alcoholic beverages (excepting milk based beverages)

alcoholic

Alcoholic beverages

water

Drinking water (water without any additives)

herbs

Herbs, spices and condiments

small_children_food

Food for infants and small children

special

Products for special nutritional use

composite

Composite food (including frozen products)

snacks

Snacks, desserts, and other foods

Details

The Comprehensive Food Consumption Database is a source of information on food consumption across the European Union (EU). The food consumption are reported in grams per day (g/day).

Source

efsa

Examples

data(efsa)

election data

Description

Results of a election in Germany 2013 in differentfederal states

Usage

data(election)

Format

A data frame with 16 observations and 8 variables

Details

Votes for the political partiesin the elections (compositional variables), and their relation to the unemployment rateand the average monthly income (external non-compositional variables). Votes are for the Christian Democratic Union and Christian Social Union of Bavaria, alsocalled The Union (CDU/CSU), Social Democratic Party (SDP), The Left (DIE LINKE),Alliance '90/The Greens (GRUNE), Free Democratic Party (FDP) and the rest of theparties participated in the elections (other parties). The votes are examined in absolutevalues (number of valid votes). The unemployment in the federal states is reported inpercentages, and the average monthly income in Euros.

CDU_CSU

Christian Democratic Union and Christian Social Union of Bavaria, alsocalled The Union

SDP

Social Democratic Party

GRUENE

Alliance '90/The Greens

FDP

Free Democratic Party

DIE_LINKE

The Left

other_parties

Votes for the rest of theparties participated in the elections

unemployment

Unemployment in the federal states in percentages

income

Average monthly income in Euros

Author(s)

Petra Klynclova, Matthias Templ

Source

German Federal Statistical Office

References

Eurostat,https://ec.europa.eu/eurostat/data

Examples

data(election)str(election)

Austrian presidential election data

Description

Results the Austrian presidential election in October 2016.

Usage

data(electionATbp)

Format

A data frame with 2202 observations and 10 variables

Details

Votes for the candidates Hofer and Van der Bellen.

GKZ

Community code

Name

Name of the community

Eligible

eligible votes

Votes_total

total votes

Votes_invalid

invalid votes

Votes_valid

valid votes

Hofer_total

votes for Hofer

Hofer_perc

votes for Hofer in percentages

VanderBellen_total

votes for Van der Bellen

VanderBellen_perc

votes for Van der Bellen in percentages

Author(s)

Peter Filzmoser

Source

OpenData Austria,https://www.data.gv.at/

Examples

data(electionATbp)str(electionATbp)

employment in different countries by gender and status.

Description

employment in different countries by gender and status.

Usage

data(employment)

Format

A three-dimensional table

Examples

data(employment)str(employment)employment

Employment in different countries by Sex, Age, Contract, Value

Description

Estimated number of employees in 42 countries in 2015, distributed according to gender (Women/Men), age (15-24, 25-54, 55+) and type of contract (Full- and part-time).

Usage

data(employment2)

Format

A data.frame with 504 rows and 5 columns.

Details

For each country in the sample, an estimated number ofemployees in the year 2015 was available, divided according to gender and age ofemployees and the type of the contract. The data form a sample of 42 cubes with two rows (gender), two columns (type) of contract) and three slices (age), which allow for a deeper analysis of the overallemployment structure, not just from the perspective of each factor separately, butalso from the perspective of the relations/interactions between them. Thorough analysis of the sample is described in Facevicova (2019).

Country

Country

Sex

gender, males (M) and females (F)

Age

age class, young (category 15 - 24), middle-aged (25 - 54) and older(55+) employees

Contract

factor, defining the type of contract, full-time (FT) and part-time (PT) contracts

Value

Number of employees in the given category (in thousands)

Author(s)

Kamila Facevicova

Source

https://stats.oecd.org

References

Facevicova, K., Filzmoser, P. and K. Hron (2019) Compositional Cubes: Three-factorial Compositional Data. Under review.

Examples

data(employment2)head(employment2)

Employment in different countries by gender and status.

Description

gender

factor

status

factor, defining if part or full time work

country

country

value

employment

Usage

data(employment_df)

Format

A data.frame with 132 rows and 4 columns.

Examples

data(employment_df)head(employment_df)

synthetic household expenditures toy data set

Description

This data set from Aitchison (1986), p. 395, describes household expenditures (in former Hong Kong dollars) on five commundity groups.

Usage

data(expenditures)

Format

A data frame with 20 observations on the following 5 variables.

Details

housing

housing (including fuel and light)

foodstuffs

foodstuffs

alcohol

alcohol and tobacco

other

other goods (including clothing, footwear and durable goods)

services

services (including transport and vehicles)

This data set contains household expenditures on five commodity groups of 20 single men. The variables represent housing (including fuel and light), foodstuff, alcohol and tobacco, other goods (including clothing, footwear and durable goods) and services (including transport and vehicles). Thus they represent the ratios of the men's income spent on the mentioned expenditures.

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at, Karel Hron

References

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

Examples

data(expenditures)## imputing a missing value in the data set using k-nearest neighbor imputation:expenditures[1,3]expenditures[1,3] <- NAimpKNNa(expenditures)$xImp[1,3]

mean consumption expenditures data.

Description

Mean consumption expenditure of households at EU-level. The finalconsumption expenditure of households encompasses all domestic costs (byresidents and non-residents) for individual needs.

Format

A data frame with 27 observations on the following 12 variables.

Food

a numeric vector

Alcohol

a numeric vector

Clothing

a numeric vector

Housing

a numeric vector

Furnishings

a numeric vector

Health

a numeric vector

Transport

a numeric vector

Communications

a numeric vector

Recreation

a numeric vector

Education

a numeric vector

Restaurants

a numeric vector

Other

a numeric vector

Source

Eurostat

Examples

data(expendituresEU)

Title

Description

Title

Usage

fBPUpChi_PLS(Yp, r3, b, version = "cov")

Arguments

Value

A list with the following components:

bal

varbal

fcenLR transformation (functional)

Description

fcenLR[lambda] transformation: mapping from B^2(lambda) into L^2(lambda)

Usage

fcenLR(z, z_step, density)

Arguments

Value

Author(s)

R. Talskatalskarenata@seznam.cz, A. Menafoglio, K. Hronkarel.hron@upol.cz, J. J. Egozcue, J. Palarea-Albaladejo

References

Talska, R., Menafoglio, A., Hron, K., Egozcue, J. J., Palarea-Albaladejo, J. (2020). Weighting the domain of probability densities in functional data analysis.Stat(2020). https://doi.org/10.1002/sta4.283

Examples

# Example (normal density)t = seq(-4.7,4.7, length = 1000)t_step = diff(t[1:2])mean = 0; sd = 1.5f = dnorm(t, mean, sd)f1 = f/trapzc(t_step,f)f.fcenLR = fcenLR(t,t_step,f) f.fcenLRinv = fcenLRinv(t.fine,t_step,f.fcenLR)plot(t,f.fcenLR, type="l",las=1, ylab="fcenLR(density)",   cex.lab=1.2,cex.axis=1.2, col="darkblue",lwd=2)abline(h=0, col="red")plot(t,f.fcenLRinv, type="l",las=1,   ylab="density",cex.lab=1.2,cex.axis=1.2, col="darkblue",lwd=2,lty=1)lines(t,f1,lty=2,lwd=2,col="gold")

Inverse of fcenLR transformations (functional)

Description

Inverse of fcenLR transformations

Usage

fcenLRinv(z, z_step, fcenLR, k = 1)

Arguments

Details

By default, it returns a unit-integral representation of density.

Value

out ... grid evaluation of (i) lambda-density in B2(lambda), (ii) P-density in unweighted B2(lambda), (iii) P-density in B2(P)

Author(s)

R. Talskatalskarenata@seznam.cz, A. Menafoglio, K. Hronkarel.hron@upol.cz, J. J. Egozcue, J. Palarea-Albaladejo

Examples

# Example (normal density)t = seq(-4.7,4.7, length = 1000)t_step = diff(t[1:2])mean = 0; sd = 1.5f = dnorm(t, mean, sd)f1 = f/trapzc(t_step,f)f.fcenLR = fcenLR(t,t_step,f) f.fcenLRinv = fcenLRinv(t.fine,t_step,f.fcenLR)plot(t,f.fcenLR, type="l",las=1, ylab="fcenLR(density)",   cex.lab=1.2,cex.axis=1.2, col="darkblue",lwd=2)abline(h=0, col="red")plot(t,f.fcenLRinv, type="l",las=1,   ylab="density",cex.lab=1.2,cex.axis=1.2, col="darkblue",lwd=2,lty=1)lines(t,f1,lty=2,lwd=2,col="gold")

fcenLRp transformation (functional)

Description

fcenLR[P] transformation: mapping from B2(P) into L2(P)

Usage

fcenLRp(z, z_step, density, p)

Arguments

Value

Author(s)

R. Talskatalskarenata@seznam.cz, A. Menafoglio, K. Hronkarel.hron@upol.cz, J.J. Egozcue, J. Palarea-Albaladejo

References

Talska, R., Menafoglio, A., Hron, K., Egozcue, J. J., Palarea-Albaladejo, J. (2020). Weighting the domain of probability densities in functional data analysis.Stat(2020). https://doi.org/10.1002/sta4.283

fcenLRu transformation (functional)

Description

fcenLR[u] transformation: mapping from B2(P) into unweigted L2(lambda)

Usage

fcenLRu(z, z_step, density, p)

Arguments

Value

Author(s)

R. Talskatalskarenata@seznam.cz, A. Menafoglio, K. Hronkarel.hron@upol.cz, J. J. Egozcue, J. Palarea-Albaladejo

References

Talska, R., Menafoglio, A., Hron, K., Egozcue, J. J., Palarea-Albaladejo, J. (2020). Weighting the domain of probability densities in functional data analysis.Stat(2020). https://doi.org/10.1002/sta4.283

Examples

# Common example for all transformations - fcenLR, fcenLRp, fcenLRu # Example (log normal distribution under the reference P) t = seq(1,10, length = 1000)t_step = diff(t[1:2])# Log normal density w.r.t. Lebesgue reference measure in B2(lambda)f = dlnorm(t, meanlog = 1.5, sdlog = 0.5)# Log normal density w.r.t. Lebesgue reference measure in L2(lambda)f.fcenLR = fcenLR(t,t_step,f) # New reference given by exponential densityp = dexp(t,0.25)/trapzc(t_step,dexp(t,0.25))# Plot of log normal density w.r.t. Lebesgue reference measure # in B2(lambda) together with the new reference density pmatplot(t,f,type="l",las=1, ylab="density",cex.lab=1.2,cex.axis=1.2,   col="black",lwd=2,ylim=c(0,0.3),xlab="t")matlines(t,p,col="blue")text(2,0.25,"p",col="blue")text(4,0.22,"f",col="black")# Log-normal density w.r.t. exponential distribution in B2(P) # (unit-integral representation)fp = (f/p)/trapzc(t_step,f/p)# Log-normal density w.r.t. exponential distribution in L2(P)fp.fcenLRp = fcenLRp(t,t_step,fp,p)# Log-normal density w.r.t. exponential distribution in L2(lambda)fp.fcenLRu = fcenLRu(t,t_step,fp,p)# Log-normal density w.r.t. exponential distribution in B2(lambda)fp.u = fcenLRinv(t,t_step,fp.fcenLRu)# Plotlayout(rbind(c(1,2,3,4),c(7,8,5,6)))par(cex=1.1)plot(t, f.fcenLR, type='l', ylab=expression(fcenLR[lambda](f)),   xlab='t',las=1,ylim=c(-3,3),  main=expression(bold(atop(paste('(a) Representation of f in ', L^2, (lambda)),'[not weighted]'))))abline(h=0,col="red")plot(t, f, type='l', ylab=expression(f[lambda]),   xlab='t',las=1,ylim=c(0,0.4),  main=expression(bold(atop(paste('(b) Density f in ', B^2, (lambda)),'[not weighted]'))))plot(t, fp, type='l', ylab=expression(f[P]), xlab='t',  las=1,ylim=c(0,0.4),  main=expression(bold(atop(paste('(c) Density f in ', B^2, (P)),'[weighted with P]'))))plot(t, fp.fcenLRp, type='l', ylab=expression(fcenLR[P](f[P])),   xlab='t',las=1,ylim=c(-3,3),   main=expression(bold(atop(paste('(d) Representation of f in ', L^2, (P)),'[weighted with P]'))))abline(h=0,col="red")plot(t, fp.u, type='l', ylab=expression(paste(omega^(-1),(f[P]))),   xlab='t',las=1,ylim=c(0,0.4),   main=expression(bold(atop(paste('(e) Representation of f in ', B^2, (lambda)),'[unweighted]'))))plot(t, fp.fcenLRu, type='l', ylab=expression(paste(fcenLR[u](f[P]))),   xlab='t',las=1,ylim=c(-3,3),  main=expression(bold(atop(paste('(f) Representation of f in ', L^2, (lambda)),'[unweighted]'))))abline(h=0,col="red")

country food balances

Description

Food balance in each country (2018)

Format

A data frame with 115 observations on the following 116 variables.

country

Country name

Cereals - Excluding Beer

Food balance on cereals

Wheat and products

Wheat-based products

Rice and products

Rice and rice-based products

Barley and products

Barley and barley-based products

Maize and products

Maize and maize-based products

Rye and products

Rye and rye-based products

Oats

Oats

Millet and products

Millet and millet-based products

Cereals, Other

Other cereals

Starchy Roots

Starchy roots group

Cassava and products

Cassava and derivatives

Potatoes and products

Potatoes and related products

Sweet potatoes

Sweet potatoes

Roots, Other

Other root crops

Sugar Crops

Sugar crops group

Sugar cane

Sugar cane

Sugar & Sweeteners

Sugar and sweeteners group

Sugar (Raw Equivalent)

Raw equivalent sugar content

Sweeteners, Other

Other sweeteners

Honey

Honey

Pulses

Pulses group

Beans

Beans

Peas

Peas

Pulses, Other and products

Other pulses and products

Treenuts

Tree nuts group

Nuts and products

Nuts and their products

Oilcrops

Oilcrops group

Soyabeans

Soybeans

Groundnuts

Groundnuts

Rape and Mustardseed

Rape and mustard seed

Coconuts - Incl Copra

Coconuts including copra

Sesame seed

Sesame seeds

Olives (including preserved)

Olives including preserved

Vegetable Oils

Vegetable oils group

Soyabean Oil

Soybean oil

Groundnut Oil

Groundnut oil

Sunflowerseed Oil

Sunflower seed oil

Rape and Mustard Oil

Rape and mustard oil

Cottonseed Oil

Cottonseed oil

Palmkernel Oil

Palm kernel oil

Palm Oil

Palm oil

Coconut Oil

Coconut oil

Sesameseed Oil

Sesame seed oil

Olive Oil

Olive oil

Ricebran Oil

Rice bran oil

Maize Germ Oil

Maize germ oil

Oilcrops Oil, Other

Other oilcrops oils

Vegetables

Vegetables group

Tomatoes and products

Tomatoes and products

Onions

Onions

Vegetables, Other

Other vegetables

Fruits - Excluding Wine

Fruits group, excluding wine

Oranges, Mandarines

Oranges and mandarins

Lemons, Limes and products

Lemons, limes and products

Grapefruit and products

Grapefruits and products

Citrus, Other

Other citrus fruits

Bananas

Bananas

Plantains

Plantains

Apples and products

Apples and products

Pineapples and products

Pineapples and products

Dates

Dates

Grapes and products (excl wine)

Grapes and non-wine products

Fruits, Other

Other fruits

Stimulants

Stimulants group

Coffee and products

Coffee and products

Cocoa Beans and products

Cocoa beans and products

Tea (including mate)

Tea including mate

Spices

Spices group

Pepper

Pepper

Pimento

Pimento

Cloves

Cloves

Spices, Other

Other spices

Alcoholic Beverages

Alcoholic beverages group

Wine

Wine

Beer

Beer

Beverages, Fermented

Fermented beverages

Beverages, Alcoholic

Alcoholic beverages (other)

Meat

Meat group

Bovine Meat

Beef and veal

Mutton & Goat Meat

Mutton and goat meat

Pigmeat

Pork

Poultry Meat

Poultry

Meat, Other

Other meats

Offals

Offals group

Offals, Edible

Edible offals

Animal fats

Animal fats

Butter, Ghee

Butter and ghee

Cream

Cream

Fats, Animals, Raw

Raw animal fats

Eggs

Eggs

Milk - Excluding Butter

Milk excluding butter

Fish, Seafood

Fish and seafood group

Freshwater Fish

Freshwater fish

Miscellaneous

Miscellaneous group

Infant food

Infant food

Fish, Body Oil

Fish body oil

Fish, Liver Oil

Fish liver oil

Demersal Fish

Demersal fish

Pelagic Fish

Pelagic fish

Marine Fish, Other

Other marine fish

Crustaceans

Crustaceans

Cephalopods

Cephalopods

Molluscs, Other

Other molluscs

Aquatic Products, Other

Other aquatic products

Aquatic Animals, Others

Other aquatic animals

Aquatic Plants

Aquatic plants

Sorghum and products

Sorghum and its products

Oilcrops, Other

Other oilcrops

Sugar beet

Sugar beet

Yams

Yams

Sunflower seed

Sunflower seed

Sugar non-centrifugal

Non-centrifugal sugar

Meat, Aquatic Mammals

Meat from aquatic mammals

Palm kernels

Palm kernels

value.Alcohol, Non-Food

Non-food alcohol (value)

Source

https://www.fao.org/home/en/

Examples

data(foodbalance)

GEMAS geochemical data set

Description

Geochemical data set on agricultural and grazing land soil

Usage

data(gemas)

Format

A data frame with 2108 observations and 30 variables

Details

COUNTRY

country name

longitude

longitude in WGS84

latitude

latitude in WGS84

Xcoord

UTM zone east

Ycoord

UTM zone north

MeanTemp

Annual mean temperature

AnnPrec

Annual mean precipitation

soilclass

soil class

sand

sand

silt

silt

clay

clay

Al

Concentration of aluminum (in mg/kg)

Ba

Concentration of barium (in mg/kg)

Ca

Concentration of calzium (in mg/kg)

\

Cr

Concentration of chromium (in mg/kg)

Fe

Concentration of iron (in mg/kg)

K

Concentration of pottasium (in mg/kg)

Mg

Concentration of magnesium (in mg/kg)

Mn

Concentration of manganese (in mg/kg)

Na

Concentration of sodium (in mg/kg)

Nb

Concentration of niobium (in mg/kg)

Ni

Concentration of nickel (in mg/kg)

P

Concentration of phosphorus (in mg/kg)

Si

Concentration of silicium (in mg/kg)

Sr

Concentration of strontium (in mg/kg)

Ti

Concentration of titanium (in mg/kg)

V

Concentration of vanadium (in mg/kg)

\

Y

Concentration of yttrium (in mg/kg)

Zn

Concentration of zinc (in mg/kg)

Zr

Concentration of zirconium (in mg/kg)

LOI

Loss on ignition (in wt-percent)

The sampling, at a density of 1 site/2500 sq. km, was completed at the beginning of 2009 by collecting 2211 samples of agricultural soil (Ap-horizon, 0-20 cm, regularly ploughed fields), and 2118 samples from land under permanent grass cover (grazing land soil, 0-10 cm), according to an agreed field protocol.All GEMAS project samples were shipped to Slovakia for sample preparation, where they were air dried, sieved to <2 mm using a nylon screen, homogenised and split to subsamples for analysis. They were analysed for a large number of chemical elements. In this sample, the main elements by X-ray fluorescence are included as well as the composition on sand, silt, clay.

Author(s)

GEMAS is a cooperation project between the EuroGeoSurveys Geochemistry Expert Group and Eurometaux. Integration in R, Peter Filzmoser and Matthias Templ.

References

Reimann, C., Birke, M., Demetriades, A., Filzmoser, P. and O'Connor, P. (Editors), 2014. Chemistry of Europe's agricultural soils - Part A: Methodology and interpretation of the GEMAS data set. Geologisches Jahrbuch (Reihe B 102), Schweizerbarth, Hannover, 528 pp. + DVD Reimann, C., Birke, M., Demetriades, A., Filzmoser, P. & O'Connor, P. (Editors), 2014. Chemistry of Europe's agricultural soils - Part B: General background information and further analysis of the GEMAS data set. Geologisches Jahrbuch (Reihe B 103), Schweizerbarth, Hannover, 352 pp.

Examples

data(gemas)str(gemas)## sample sites## Not run: require(ggmap)map <- get_map("europe", source = "stamen", maptype = "watercolor", zoom=4)ggmap(map) + geom_point(aes(x=longitude, y=latitude), data=gemas)map <- get_map("europe", zoom=4)ggmap(map) + geom_point(aes(x=longitude, y=latitude), data=gemas, size=0.8)## End(Not run)

gjovik

Description

Gjovik geochemical data set

Format

A data frame with 615 observations and 63 variables.

ID

a numeric vector

MAT

type of material

mE32wgs

longitude

mN32wgs

latitude

XCOO

X coordinates

YCOO

Y coordinates

ALT

altitute

kmNS

some distance north-south

kmSN

some distance south-north

LITHO

lithologies

Ag

a numeric vector

Al

a numeric vector

As

a numeric vector

Au

a numeric vector

B

a numeric vector

Ba

a numeric vector

Be

a numeric vector

Bi

a numeric vector

Ca

a numeric vector

Cd

a numeric vector

Ce

a numeric vector

Co

a numeric vector

Cr

a numeric vector

Cs

a numeric vector

Cu

a numeric vector

Fe

a numeric vector

Ga

a numeric vector

Ge

a numeric vector

Hf

a numeric vector

Hg

a numeric vector

In

a numeric vector

K

a numeric vector

La

a numeric vector

Li

a numeric vector

Mg

a numeric vector

Mn

a numeric vector

Mo

a numeric vector

Na

a numeric vector

Nb

a numeric vector

Ni

a numeric vector

P

a numeric vector

Pb

a numeric vector

Pd

a numeric vector

Pt

a numeric vector

Rb

a numeric vector

Re

a numeric vector

S

a numeric vector

Sb

a numeric vector

Sc

a numeric vector

Se

a numeric vector

Sn

a numeric vector

Sr

a numeric vector

Ta

a numeric vector

Te

a numeric vector

Th

a numeric vector

Ti

a numeric vector

Tl

a numeric vector

U

a numeric vector

V

a numeric vector

W

a numeric vector

Y

a numeric vector

Zn

a numeric vector

Zr

a numeric vector

Details

Geochemical data set. 41 sample sites have been investigated. At each site, 15 different sample materials have been collected and analyzed for the concentration of more than 40 chemical elements. Soil: CHO - C horizon, OHO - O horizon. Mushroom: LAC - milkcap. Plant: BIL - birch leaves, BLE - blueberry leaves, BLU - blueberry twigs, BTW - birch twigs, CLE - cowberry leaves, COW - cowberry twigs, EQU - horsetail, FER - fern, HYL - terrestrial moss, PIB - pine bark, SNE - spruce needles, SPR - spruce twigs.

Author(s)

Peter Filzmoser, Dominika Miksova

References

C. Reimann, P. Englmaier, B. Flem, O.A. Eggen, T.E. Finne, M. Andersson & P. Filzmoser (2018). The response of 12 different plant materials and one mushroom to Mo and Pb mineralization along a 100-km transect in southern central Norway. Geochemistry: Exploration, Environment, Analysis, 18(3), 204-215.

Examples

data(gjovik)str(gjovik)

gmean

Description

This function calculates the geometric mean.

Usage

gm(x)

Arguments

Details

gm calculates the geometric mean for all positive entries of a vector. Please note that there is a faster version available implemented with Rcppbut it currently do not pass CRAN checks cause of use of Rcpp11 features. This C++ versionaccounts for over- and underflows. It is placed in inst/doc

Author(s)

Matthias Templ

Examples

gm(c(3,5,3,6,7))

Geometric mean

Description

Computes the geometric mean(s) of a numeric vector, matrix or data.frame

Usage

gmean_sum(x, margin = NULL)gmean(x, margin = NULL)

Arguments

Details

gmean_sum calculates the totals based on geometric means whilegmeancalculates geometric means on rows (margin = 1), on columns (margin = 2), or on all values (margin = 3)

Value

geometric means (ifgmean is used) or totals (ifgmean_sum is used)

Author(s)

Matthias Templ

Examples

data("precipitation")gmean_sum(precipitation)gmean_sum(precipitation, margin = 2)gmean_sum(precipitation, margin = 1)gmean_sum(precipitation, margin = 3)addmargins(precipitation)addmargins(precipitation, FUN = gmean_sum)addmargins(precipitation, FUN = mean)addmargins(precipitation, FUN = gmean)data("arcticLake", package = "robCompositions")gmean(arcticLake$sand)gmean(as.numeric(arcticLake[1, ]))gmean(arcticLake)gmean(arcticLake, margin = 1)gmean(arcticLake, margin = 2)gmean(arcticLake, margin = 3)

government spending

Description

Government expenditures based on COFOG categories

Format

A (tidy) data frame with 5140 observations on the following 4 variables.

country

Country of origin

category

The COFOG expenditures are divided into in the following ten categories: general public services; defence; public order and safety; economic affairs; environmental protection; housing and community amenities; health; recreation, culture and religion; education; and social protection.

year

Year

value

COFOG spendings/expenditures

Details

The general government sector consists of central, state and local governments, and the social security funds controlled by these units. The data are based on the system of national accounts, a set of internationally agreed concepts, definitions, classifications and rules for national accounting. The classification of functions of government (COFOG) is used as classification system. The central government spending by category is measured as a percentage of total expenditures.

Author(s)

translated fromhttps://data.oecd.org/ and restructured by Matthias Templ

Source

OECD:https://data.oecd.org/

Examples

data(govexp)str(govexp)

haplogroups data

Description

Distribution of European Y-chromosome DNA (Y-DNA) haplogroups by region inpercentage.

Format

A data frame with 38 observations on the following 12 variables:

I1

pre-Germanic (Nordic)

I2b

pre-Celto-Germanic

I2a1

Sardinian, Basque

I2a2

Dinaric, Danubian

N1c1

Uralo-Finnic, Baltic, Siberian

R1a

Balto-Slavic, Mycenaean Greek, Macedonia

R1b

Italic, Celtic, Germanic; Hittite, Armenian

G2a

Caucasian, Greco-Anatolian

E1b1b

North and Eastern Africa, Near Eastern, Balkanic

J2

Mesopotamian, Minoan Greek, Phoenician

J1

Semitic (Arabic, Jewish)

T

Near-Eastern, Egyptian, Ethiopian, Arabic

Details

Human Y-chromosome DNA can be divided into genealogical groups sharing acommon ancestor, called haplogroups.

Source

Eupedia:https://www.eupedia.com/europe/european_y-dna_haplogroups.shtml

Examples

data(haplogroups)

honey compositions

Description

The contents of honey, syrup, and adulteration mineral elements.

Format

A data frame with 429 observations on the following 17 variables.

class

adulterated honey, Honey or Syrup

group

group information

group3

detailed group information

group1

less detailed group information

region

region

Al

chemical element

B

chemical element

Ba

chemical element

Ca

chemical element

Fe

chemical element

K

chemical element

Mg

chemical element

Mn

chemical element

Na

chemical element

P

chemical element

Sr

chemical element

Zn

chemical element

Details

Discrimination of honey and adulteration by elemental chemometrics profiling.

Note

In the original paper, sparse PLS-DA were applied optimize the classify model and test effectiveness. Classify accuracy were exceed 87.7 percent.

Source

Mendeley Data, contributed by Liping Luo and translated to R by Matthias Templ

References

Tao Liu, Kang Ming, Wei Wang, Ning Qiao, Shengrong Qiu, Shengxiang Yi, Xueyong Huang, Liping Luo,Discrimination of honey and syrup-based adulteration by mineral element chemometrics profiling,'Food Chemistry, Volume 343, 2021,doi:10.1016/j.foodchem.2020.128455.

Examples

data(honey)

ilr coordinates in 2x2 compositional tables

Description

ilr coordinates of original, independent and interaction compositional table using SBP1 and SBP2

Usage

ilr.2x2(x, margin = 1, type = "independence", version = "book")

Arguments

Value

The ilr coordinates

Author(s)

Kamila Facevicova, Matthias Templ

References

Facevicova, K., Hron, K., Todorov, V., Guo, D., Templ, M. (2014).Logratio approach to statistical analysis of 2x2 compositional tables.Journal of Applied Statistics, 41 (5), 944–958.

Examples

data(employment) ilr.2x2(employment[,,"AUT"])ilr.2x2(employment[,,"AUT"], version = "paper")ilr.2x2(employment, margin = 3, version = "paper")ilr.2x2(employment[,,"AUT"], type = "interaction")

Replacement of rounded zeros and missing values.

Description

Parametric replacement of rounded zeros and missing values for compositionaldata using classical and robust methods based on ilr coordinates withspecial choice of balances. Values under detection limit should be savedwith the negative value of the detection limit (per variable). Missingvalues should be coded as NA.

Usage

impAll(x)

Arguments

Details

This is a wrapper function that callsimpRZilr() for the replacementof zeros andimpCoda for the imputation of missing valuessequentially. The detection limit is automatically derived form negativenumbers in the data set.

Value

The imputed data set.

Note

This function is mainly used by the compositionsGUI.

References

Hron, K., Templ, M., Filzmoser, P. (2010) Imputation ofmissing values for compositional data using classical and robust methods,Computational Statistics and Data Analysis, 54 (12),3095-3107.

Martin-Fernandez, J.A., Hron, K., Templ, M., Filzmoser, P.,Palarea-Albaladejo, J. (2012) Model-based replacement of rounded zeros incompositional data: Classical and robust approaches,ComputationalStatistics, 56 (2012), 2688 - 2704.

See Also

impCoda,impRZilr

Examples

## see the compositionsGUI

Imputation of missing values in compositional data

Description

This function offers different methods for the imputation of missing valuesin compositional data. Missing values are initialized with proper values.Then iterative algorithms try to find better estimations for the formermissing values.

Usage

impCoda(  x,  maxit = 10,  eps = 0.5,  method = "ltsReg",  closed = FALSE,  init = "KNN",  k = 5,  dl = rep(0.05, ncol(x)),  noise = 0.1,  bruteforce = FALSE)

Arguments

Details

eps: The algorithm is finished as soon as the imputed values stabilize, i.e.until the sum of Aitchison distances from the present and previous iterationchanges only marginally (eps).\

method: Several different methods can be chosen, such as ‘ltsReg’:least trimmed squares regression is used within the iterative procedure.‘lm’: least squares regression is used within the iterativeprocedure. ‘classical’: principal component analysis is used withinthe iterative procedure. ‘ltsReg2’: least trimmed squares regressionis used within the iterative procedure. The imputated values are perturbedin the direction of the predictor by values drawn form a normal distributionwith mean and standard deviation related to the corresponding residuals andmultiplied bynoise.

Value

Author(s)

Matthias Templ, Karel Hron

References

Hron, K., Templ, M., Filzmoser, P. (2010) Imputation ofmissing values for compositional data using classical and robust methodsComputational Statistics and Data Analysis, 54 (12),3095-3107.

See Also

impKNNa,pivotCoord

Examples

data(expenditures)x <- expendituresx[1,3]x[1,3] <- NAxi <- impCoda(x)$xImpxi[1,3]s1 <- sum(x[1,-3])impS <- sum(xi[1,-3])xi[,3] * s1/impS# other methodsimpCoda(x, method = "lm")impCoda(x, method = "ltsReg")

Imputation of missing values in compositional data using knn methods

Description

This function offers several k-nearest neighbor methods for the imputationof missing values in compositional data.

Usage

impKNNa(  x,  method = "knn",  k = 3,  metric = "Aitchison",  agg = "median",  primitive = FALSE,  normknn = TRUE,  das = FALSE,  adj = "median")

Arguments

Details

The Aitchisonmetric should be chosen when dealing with compositionaldata, the Euclideanmetric otherwise.

Ifprimitive== FALSE, a sequential search for thek-nearest neighbors is applied for every missing value where allinformation corresponding to the non-missing cells plus the information inthe variable to be imputed plus some additional information is available. Ifprimitive== TRUE, a search of thek-nearest neighborsamong observations is applied where in addition to the variable to beimputed any further cells are non-missing.

Ifnormknn is TRUE (prefered option) the imputed cells from a nearestneighbor method are adjusted with special adjustment factors (more detailscan be found online (see the references)).

Value

Author(s)

Matthias Templ

References

Aitchison, J., Barcelo-Vidal, C., Martin-Fernandez, J.A.,Pawlowsky-Glahn, V. (2000) Logratio analysis and compositional distance,Mathematical Geology, 32(3), 271-275.

Hron, K., Templ, M., Filzmoser, P. (2010) Imputation of missing valuesfor compositional data using classical and robust methodsComputational Statistics and Data Analysis, 54 (12),3095-3107.

See Also

impCoda

Examples

data(expenditures)x <- expendituresx[1,3]x[1,3] <- NAxi <- impKNNa(x)$xImpxi[1,3]

alr EM-based imputation of rounded zeros

Description

A modified EM alr-algorithm for replacing rounded zeros in compositionaldata sets.

Usage

impRZalr(  x,  pos = ncol(x),  dl = rep(0.05, ncol(x) - 1),  eps = 1e-04,  maxit = 50,  bruteforce = FALSE,  method = "lm",  step = FALSE,  nComp = "boot",  R = 10,  verbose = FALSE)

Arguments

Details

Statistical analysis of compositional data including zeros runs intoproblems, because log-ratios cannot be applied. Usually, rounded zeros areconsiderer as missing not at random missing values. The algorithm firstapplies an additive log-ratio transformation to the compositions. Then therounded zeros are imputed using a modified EM algorithm.

Value

Author(s)

Matthias Templ and Karel Hron

References

Palarea-Albaladejo, J., Martin-Fernandez, J.A. Gomez-Garcia, J. (2007) A parametric approach for dealing with compositional rounded zeros.Mathematical Geology, 39(7), 625-645.

See Also

impRZilr

Examples

data(arcticLake)x <- arcticLake## generate rounded zeros artificially:x[x[,1] < 5, 1] <- 0x[x[,2] < 47, 2] <- 0xia <- impRZalr(x, pos=3, dl=c(5,47), eps=0.05)xia$xImp

EM-based replacement of rounded zeros in compositional data

Description

Parametric replacement of rounded zeros for compositional data usingclassical and robust methods based on ilr coordinates with a specialchoice of balances.

Usage

impRZilr(  x,  maxit = 10,  eps = 0.1,  method = "pls",  dl = rep(0.05, ncol(x)),  variation = FALSE,  nComp = "boot",  bruteforce = FALSE,  noisemethod = "residuals",  noise = FALSE,  R = 10,  correction = "normal",  verbose = FALSE)

Arguments

Details

Statistical analysis of compositional data including zeros runs intoproblems, because log-ratios cannot be applied. Usually, rounded zeros areconsidered as missing not at random missing values.

The algorithm iteratively imputes parts with rounded zeros whereas in eachstep (1) compositional data are expressed in pivot coordinates (2) tobit regression isapplied (3) the rounded zeros are replaced by the expected values (4) thecorresponding inverse ilr mapping is applied. After all parts areimputed, the algorithm starts again until the imputations do not change.

Value

Author(s)

Matthias Templ and Peter Filzmoser

References

Martin-Fernandez, J.A., Hron, K., Templ, M., Filzmoser, P., Palarea-Albaladejo, J. (2012)Model-based replacement of rounded zeros in compositional data: Classical and robust approaches.Computational Statistics and Data Analysis, 56 (9), 2688-2704.

Templ, M., Hron, K., Filzmoser, P., Gardlo, A. (2016) Imputation of rounded zerosfor high-dimensional compositional data.Chemometrics and IntelligentLaboratory Systems, 155, 183-190.

See Also

impRZalr

Examples

data(arcticLake)x <- arcticLake## generate rounded zeros artificially:#x[x[,1] < 5, 1] <- 0x[x[,2] < 44, 2] <- 0xia <- impRZilr(x, dl=c(5,44,0), eps=0.01, method="lm")xia$x

EM-based replacement of rounded zeros in compositional data

Description

Parametric replacement of rounded zeros for compositional data usingclassical and robust methods based on ilr coordinates with a specialchoice of balances.

Usage

imputeBDLs(  x,  maxit = 10,  eps = 0.1,  method = "subPLS",  dl = rep(0.05, ncol(x)),  variation = TRUE,  nPred = NULL,  nComp = "boot",  bruteforce = FALSE,  noisemethod = "residuals",  noise = FALSE,  R = 10,  correction = "normal",  verbose = FALSE,  test = FALSE)adjustImputed(xImp, xOrig, wind)checkData(x, dl)## S3 method for class 'replaced'print(x, ...)

Arguments

Details

Statistical analysis of compositional data including zeros runs intoproblems, because log-ratios cannot be applied. Usually, rounded zeros areconsiderer as missing not at random missing values.

The algorithm iteratively imputes parts with rounded zeros whereas in eachstep (1) compositional data are expressed in pivot coordinates (2) tobit regression isapplied (3) the rounded zeros are replaced by the expected values (4) thecorresponding inverse ilr mapping is applied. After all parts areimputed, the algorithm starts again until the imputations do not change.

Value

Author(s)

Matthias Templ, method subPLS from Jiajia Chen

References

Templ, M., Hron, K., Filzmoser, P., Gardlo, A. (2016). Imputation of rounded zeros for high-dimensional compositional data.Chemometrics and Intelligent Laboratory Systems, 155, 183-190.

Chen, J., Zhang, X., Hron, K., Templ, M., Li, S. (2018). Regression imputation with Q-mode clustering for rounded zero replacement in high-dimensional compositional data.Journal of Applied Statistics, 45 (11), 2067-2080.

See Also

imputeBDLs

Examples

p <- 10n <- 50k <- 2T <- matrix(rnorm(n*k), ncol=k)B <- matrix(runif(p*k,-1,1),ncol=k)X <- T %*% t(B)E <-  matrix(rnorm(n*p, 0,0.1), ncol=p)XE <- X + Edata <- data.frame(pivotCoordInv(XE))col <- ncol(data)row <- nrow(data)DL <- matrix(rep(0),ncol=col,nrow=1)for(j in seq(1,col,2)){DL[j] <- quantile(data[,j],probs=0.06,na.rm=FALSE)}for(j in 1:col){          data[data[,j]<DL[j],j] <- 0}## Not run: # under dontrun because of long exectution timeimp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="subPLS")impimp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="pls", variation = FALSE)impimp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="lm")impimp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="lmrob")impdata(mcad)## generate rounded zeros artificially:x <- mcadx <- x[1:25, 2:ncol(x)]dl <- apply(x, 2, quantile, 0.1)for(i in seq(1, ncol(x), 2)){  x[x[,i] < dl[i], i] <- 0} ni <- sum(x==0, na.rm=TRUE) ni/(ncol(x)*nrow(x)) * 100dl[seq(2, ncol(x), 2)] <- 0replaced_lm <- imputeBDLs(x, dl=dl, eps=1, method="lm",    verbose=FALSE, R=50, variation=TRUE)$xreplaced_lmrob <- imputeBDLs(x, dl=dl, eps=1, method="lmrob",    verbose=FALSE, R=50, variation=TRUE)$xreplaced_plsfull <- imputeBDLs(x, dl=dl, eps=1,   method="pls", verbose=FALSE, R=50,   variation=FALSE)$x ## End(Not run)

Imputation of values above an upper detection limit in compositional data

Description

Parametric replacement of values above upper detection limit for compositional data usingclassical and robust methods (possibly also the pls method) based on ilr-transformations with specialchoice of balances.

Usage

imputeUDLs(  x,  maxit = 10,  eps = 0.1,  method = "lm",  dl = NULL,  variation = TRUE,  nPred = NULL,  nComp = "boot",  bruteforce = FALSE,  noisemethod = "residuals",  noise = FALSE,  R = 10,  correction = "normal",  verbose = FALSE)

Arguments

Details

imputeUDLs

An imputation method for right-censored compositional data. Statistical analysis is not possible with values reported in data, for example as ">10000". These values are replaced using tobit regression.

The algorithm iteratively imputes parts with values above upper detection limitwhereas in each step (1) compositional data are expressed in pivot coordinates (2) tobit regression isapplied (3) the values above upper detection limit are replaced by the expected values (4) thecorresponding inverse ilr mapping is applied. After all parts areimputed, the algorithm starts again until the imputations only change marginally.

Value

Author(s)

Peter Filzmoser, Dominika Miksova based on function imputeBDLs code from Matthias Templ

References

Martin-Fernandez, J.A., Hron K., Templ, M., Filzmoser, P. and Palarea-Albaladejo, J. (2012).Model-based replacement of rounded zeros in compositional data: Classical and robust approaches.Computational Statistics and Data Analysis, 56, 2688-2704.

Templ, M. and Hron, K. and Filzmoser and Gardlo, A. (2016). Imputation of rounded zeros for high-dimensional compositional data.Chemometrics and Intelligent Laboratory Systems, 155, 183-190.

See Also

imputeBDLs

Examples

data(gemas)  # read datadat <- gemas[gemas$COUNTRY=="HEL",c(12:29)]UDL <- apply(dat,2,max)names(UDL) <- names(dat)UDL["Mn"] <- quantile(dat[,"Mn"], probs = 0.8)  # UDL present only in one variablewhichudl <- dat[,"Mn"] > UDL["Mn"] # classical methodimp.lm <- datimp.lm[whichudl,"Mn"] <- Infres.lm <- imputeUDLs(imp.lm, dl=UDL, method="lm", variation=TRUE)imp.lm <- res.lm$x

Independence 2x2 compositional table

Description

Estimates the expected frequencies from an 2x2 table under the null hypotheses of independence.

Usage

ind2x2(x, margin = 3, pTabMethod = c("dirichlet", "half", "classical"))

Arguments

Value

The independence table(s) with either relative or absolute frequencies.

Author(s)

Kamila Facevicova, Matthias Templ

References

Facevicova, K., Hron, K., Todorov, V., Guo, D., Templ, M. (2014).Logratio approach to statistical analysis of 2x2 compositional tables.Journal of Applied Statistics, 41 (5), 944–958.

Examples

data(employment) ind2x2(employment)

Independence table

Description

Estimates the expected frequencies from an m-way table under the null hypotheses of independence.

Usage

indTab(  x,  margin = c("gmean_sum", "sum"),  frequency = c("relative", "absolute"),  pTabMethod = c("dirichlet", "half", "classical"))

Arguments

Details

Because of the compositional nature of probability tables, the independence tables should be estimated using geometric marginals.

Value

The independence table(s) with either relative or absolute frequencies.

Author(s)

Matthias Templ

References

Egozcue, J.J., Pawlowsky-Glahn, V., Templ, M., Hron, K. (2015)Independence in contingency tables using simplicial geometry.Communications in Statistics - Theory and Methods, 44 (18), 3978–3996.

Examples

data(precipitation) tab1 <- indTab(precipitation)tab1sum(tab1)## Not run: data("PreSex", package = "vcd")indTab(PreSex)## End(Not run)

value added, output and input for different ISIC codes and countries.

Description

value added, output and input for different ISIC codes and countries.

Usage

data(instw)

Format

A data.frame with 1555 rows and 7 columns:

ct

ct

isic

ISIC classification, Rev 3.2

VA

value added

OUT

output

INP

input

IS03

country code

mht

mht

A data.frame with 1555 rows and 7 columns.

Examples

data(instw)head(instw)

Interaction 2x2 table

Description

Estimates the interactions from an 2x2 table under the null hypotheses of independence.

Usage

int2x2(x, margin = 3, pTabMethod = c("dirichlet", "half", "classical"))

Arguments

Value

The independence table(s) with either relative or absolute frequencies.

Author(s)

Kamila Facevicova, Matthias Templ

References

Facevicova, K., Hron, K., Todorov, V., Guo, D., Templ, M. (2014).Logratio approach to statistical analysis of 2x2 compositional tables.Journal of Applied Statistics, 41 (5), 944–958.

Examples

data(employment) int2x2(employment)

Interaction array

Description

Estimates the interaction compositional table with normalization for further analysis according to Egozcue et al. (2015)

Usage

intArray(x)

Arguments

Details

Estimates the interaction table using its ilr coordinates.

Value

The interaction array

Author(s)

Matthias Templ

References

Egozcue, J.J., Pawlowsky-Glahn, V., Templ, M., Hron, K. (2015)Independence in contingency tables using simplicial geometry.Communications in Statistics - Theory and Methods, 44 (18), 3978–3996.

See Also

intTab

Examples

data(precipitation) tab1prob <- prop.table(precipitation)tab1 <- indTab(precipitation)tabINT <- intTab(tab1prob, tab1)intArray(tabINT)

Interaction table

Description

Estimates the interaction table based on clr and inverse clr coefficients.

Usage

intTab(x, y, frequencies = c("relative", "absolute"))

Arguments

Details

Because of the compositional nature of probability tables, the independence tables should be estimated using geometric marginals.

Value

intTab

The interaction table(s) with either relative or absolute frequencies.

signs

The sign illustrates if there is an excess of probability (plus), or a deficit (minus) regarding to the estimated probability table and the independece table in the clr space.

Author(s)

Matthias Templ

References

Egozcue, J.J., Pawlowsky-Glahn, V., Templ, M., Hron, K. (2015)Independence in contingency tables using simplicial geometry.Communications in Statistics - Theory and Methods, 44 (18), 3978–3996.

Examples

data(precipitation)tab1prob <- prop.table(precipitation)tab1 <- indTab(precipitation)intTab(tab1prob, tab1)

equivalence class

Description

Checks if two vectors or two data frames are from the same equivalence class

Usage

is.equivalent(x, y, tollerance = .Machine$double.eps^0.5)

Arguments

Value

logical TRUE if the two vectors are from the same equivalence class.

Author(s)

Matthias Templ

References

Filzmoser, P., Hron, K., Templ, M. (2018)Applied Compositional Data Analysis.Springer, Cham.

See Also

all.equal

Examples

is.equivalent(1:10, 1:10*2)is.equivalent(1:10, 1:10+1)data(expenditures)x <- expendituresis.equivalent(x, constSum(x))y <- xy[1,1] <- x[1,1]+1is.equivalent(y, constSum(x))

ISIC codes by name

Description

code

ISIC code, Rev 3.2

description

Description of ISIC codes

Usage

data(isic32)

Format

A data.frame with 24 rows and 2 columns.

Examples

data(instw)instw

labour force by status in employment

Description

Labour force by status in employment for 124 countries, latest update: December 2009

Format

A data set on 124 compositions on 9 variables.

Details

country

country

year

year

employeesW

percentage female employees

employeesM

percentage male employees

employersW

percentage female employers

employersM

percentage male employers

ownW

percentage female own-account workers and contributing family workers

ownM

percentage male own-account workers and contributing family workers

source

HS: household or labour force survey. OE: official estimates. PC: population census

Author(s)

conversion to R by Karel Hron and Matthias Templmatthias.templ@tuwien.ac.at

Source

from UNSTATS website

References

K. Hron, P. Filzmoser, K. Thompson (2012). Linear regression with compositional explanatory variables.Journal of Applied Statistics, Volume 39, Issue 5, 2012.

Examples

data(laborForce)str(laborForce)

European land cover

Description

Land cover data from Eurostat (2015) extended with (log) population and (log) pollution

Format

A data set on 28 compositions on 7 variables.

Details

Woodland

Coverage in km2

Cropland

Coverage in km2

Grassland

Coverage in km2

Water

Coverage in km2

Artificial

Coverage in km2

Pollution

log(Pollution) values per country

PopDensity

log(PopDensity) values per country

Author(s)

conversion to R by Karel Hron

Source

Lucas land cover

Examples

data(landcover)str(landcover)

life expectancy and GDP (2008) for EU-countries

Description

Social-economic data for compositional regression.

Format

A data set on 27 compositions on 9 variables.

Details

country

country

agriculture

GDP on agriculture, hunting, forestry, fishing (ISIC A-B, x1)

manufacture

GDP on mining, manufacturing, utilities (ISIC C-E, x2)

construction

GDP on construction (ISIC F, x3)

wholesales

GDP on wholesale, retail trade, restaurants and hotels (ISIC G-H, x4)

transport

GDP on transport, storage and communication (ISIC I, x5)

other

GDP on other activities (ISIC J-P, x6)

lifeExpMen

life expectancy for men and women

lifeExpWomen

life expectancy for men and women

Author(s)

conversion to R by Karel Hron and Matthias Templmatthias.templ@tuwien.ac.at

Source

https://www.ec.europa.eu/eurostat andhttps://unstats.un.org/home/

References

K. Hron, P. Filzmoser, K. Thompson (2012). Linear regression with compositional explanatory variables.Journal of Applied Statistics, Volume 39, Issue 5, 2012.

Examples

data(lifeExpGdp)str(lifeExpGdp)

Classical and robust regression of non-compositional (real) response oncompositional and non-compositional predictors

Description

Delivers appropriate inference for regression of y on a compositional matrixX or and compositional and non-compositional combined predictors.

Usage

lmCoDaX(  y,  X,  external = NULL,  method = "robust",  pivot_norm = "orthonormal",  max_refinement_steps = 200)

Arguments

Details

Compositional explanatory variables should not be directly used in a linearregression model because any inference statistic can become misleading.While various approaches for this problem were proposed, here an approachbased on the pivot coordinates is used. Further these compositional explanatory variables can be supplemented with external non-compositional dataand factor variables.

Value

An object of class ‘lts’ or ‘lm’ and two summaryobjects.

Author(s)

Peter Filzmoser, Roman Wiedemeier, Matthias Templ

References

Filzmoser, P., Hron, K., Thompsonc, K. (2012) Linear regressionwith compositional explanatory variables.Journal of AppliedStatistics, 39, 1115-1128.

See Also

lm

Examples

## How the total household expenditures in EU Member## States depend on relative contributions of ## single household expenditures:data(expendituresEU)y <- as.numeric(apply(expendituresEU,1,sum))lmCoDaX(y, expendituresEU, method="classical")## How the relative content of sand of the agricultural## and grazing land soils in Germany depend on## relative contributions of the main chemical trace elements,## their different soil types and the Annual mean temperature:data("gemas")gemas$COUNTRY <- as.factor(gemas$COUNTRY)gemas_GER <- dplyr::filter(gemas, gemas$COUNTRY == 'POL')ssc <- cenLR(gemas_GER[, c("sand", "silt", "clay")])$x.clry <- ssc$sandX <- dplyr::select(gemas_GER, c(MeanTemp, soilclass, Al:Zr))X$soilclass <- factor(X$soilclass)lmCoDaX(y, X, external = c('MeanTemp', 'soilclass'),method='classical', pivot_norm = 'orthonormal')lmCoDaX(y, X, external = c('MeanTemp', 'soilclass'),method='robust', pivot_norm = 'orthonormal')

machine operators

Description

Compositions of eight-hour shifts of 27 machine operators

Usage

data(machineOperators)

Format

A data frame with 27 observations on the following 4 variables.

Details

hqproduction

high-quality production

lqproduction

low-quality production

setting

machine settings

repair

machine repair

The data set from Aitchison (1986), p. 382, contains compositions of eight-hour shifts of 27 machine operators. The parts represent proportions of shifts in each activity: high-quality production, low-quality production, machine setting and machine repair.

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

References

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

Examples

data(machineOperators)str(machineOperators)summary(machineOperators)rowSums(machineOperators)

Distribution of manufacturing output

Description

The data consists of values of the manufacturing output in 42 countries in 2009. The output, given in national currencies, is structured according to the 3-digit ISIC category and its components. Thorough analysis of the sample is described in Facevicova (2018).

Usage

data(manu_abs)

Format

A data frame with 630 observations of 4 variables.

Details

country

Country

isic

3-digit ISIC category. The categories are 151 processed meat, fish, fruit, vegetables, fats; 152 Dairy products; 153 Grain mill products, starches, animal feeds; 154 Other food products and 155 Beverages.

output

The output components are Labour, Surplus and Input.

value

Value of manufacturing output in the national currency

Author(s)

Kamila Facevicova

Source

Elaboration based on the INDSTAT 4 database (UNIDO 2012a), see also UNIDO, 2012b.UNIDO (2012a), INDSTAT 4 Industrial Statistics Database at 3- and 4-digit level of ISIC Revision 3 and 4. Vienna. Available from https://stat.unido.org. UNIDO (2012b) International Yearbook of Industrial Statistics, Edward Elgar Publishing Ltd, UK.

References

Facevicova, K., Hron, K., Todorov, V. and M. Templ (2018) General approach to coordinate representation of compositional tables. Scandinavian Journal of Statistics, 45(4).

Examples

data(manu_abs)### Compositional tables approach### analysis of the relative structureresult <- tabCoordWrapper(manu_abs, obs.ID='country',row.factor = 'output', col.factor = 'isic', value='value', test = TRUE)result$Bootstrap### Classical approach### generalized linear mixed effect model## Not run: library(lme4)m <- glmer(value~output*as.factor(isic)+(1|country),data=manu_abs,family=poisson)summary(m)## End(Not run)

metabolomics mcad data set

Description

The aim of the experiment was to ascertain novel biomarkers of MCAD (Medium chain acyl-CoA dehydrogenase) deficiency. The data consists of 25 patients and 25 controls and the analysis was done by LC-MS.Rows represent patients and controls and columns represent chemical entities with their quantity.

Usage

data(mcad)

Format

A data frame with 50 observations and 279 variables

Details

group

patient group

...

the remaining variables columns are represented by m/z which are chemical characterizations of individual chemical components on exact mass measurements..

References

Najdekr L., Gardlo A., Madrova L., Friedeckyy D., Janeckova H., Correa E.S., Goodacre R., Adam T., Oxidized phosphatidylcholines suggest oxidative stress in patients with medium-chain acyl-CoA dehydrogenase deficiency,Talanta 139, 2015, 62-66.

Examples

data(mcad)str(mcad)

missing or zero pattern structure.

Description

Analysis of the missing or the zero patterns structure of a data set.

Usage

missPatterns(x)zeroPatterns(x)

Arguments

Details

Here, one pattern defines those observations that have the same structureregarding their missingness or zeros. For all patterns a summary iscalculated.

Value

Author(s)

Matthias Templ. The code is based on a previous version from AndreasAlfons and Matthias Templ from package VIM

See Also

aggr

Examples

data(expenditures)## set NA's artificial:expenditures[expenditures < 300] <- NA## detect the NA structure:missPatterns(expenditures)

mortality and life expectancy in the EU

Description

country

country name

country2

country name, short version

sex

gender

lifeExpectancy

life expectancy

infectious

certain infectious and parasitic diseases (A00-B99)

neoplasms

malignant neoplasms (C00-C97)

endocrine

endocrine nutritional and metabolic diseases (E00-E90)

mental

mental and behavioural disorders (F00-F99)

nervous

diseases of the nervous system and the sense organs (G00-H95)

circulatory

diseases of the circulatory system (I00-I99)

respiratory

diseases of the respiratory system (J00-J99)

digestive

diseases of the digestive system (K00-K93)

Usage

data(mortality)

Format

A data frame with 60 observations and 12 variables

Author(s)

Peter Filzmoser, Matthias Templmatthias.templ@tuwien.ac.at

References

Eurostat,https://ec.europa.eu/eurostat/data

Examples

data(mortality)str(mortality)## totals (mortality)aggregate(mortality[,5:ncol(mortality)],           list(mortality$country2), sum)

mortality table

Description

Mortality data by gender, unknown year

Usage

data(mortality_tab)

Format

A table

Details

female

mortality rates for females by age groups

male

mortality rates for males by age groups

Author(s)

Matthias Templ

Examples

data(mortality_tab)mortality_tab

Normalize a vector to length 1

Description

Scales a vector to a unit vector.

Usage

norm1(x)

Arguments

Author(s)

Matthias Templ

Examples

data(expenditures)i <- 1D <- 6vec <- c(rep(-1/i, i), 1, rep(0, (D-i-1)))norm1(vec)

nutrient contents

Description

Nutrients on more than 40 components and 965 generic food products

Usage

data(nutrients)

Format

A data frame with 965 observations on the following 50 variables.

Details

ID

ID, for internal use

ID_V4

ID V4, for internal use

ID_SwissFIR

ID, for internal use

name_D

Name in German

name_F

Name in French

name_I

Name in Italian

name_E

Name in Spanish

category_D

Category name in German

category_F

Category name in French

category_I

Category name in Italy

category_E

Category name in Spanish

gravity

specific gravity

‘⁠energy_kJ ⁠’

energy in kJ per 100g edible portion

energy_kcal

energy in kcal per 100g edible portion

protein

protein in gram per 100g edible portion

alcohol

alcohol in gram per 100g edible portion

water

water in gram per 100g edible portion

carbohydrates

crbohydrates in gram per 100g edible portion

starch

starch in gram per 100g edible portion

sugars

sugars in gram per 100g edible portion

‘⁠dietar_ fibres ⁠’

dietar fibres in gram per 100g edible portion

fat

fat in gram per 100g edible portion

cholesterol

cholesterolin milligram per 100g edible portion

fattyacids_monounsaturated

fatty acids monounsatrurated in gram per 100g edible portion

fattyacids_saturated

fatty acids saturated in gram per 100g edible portion

fatty_acids_polyunsaturated

fatty acids polyunsaturated in gram per 100g edible portion

vitaminA

vitamin A in retinol equivalent per 100g edible portion

‘⁠all-trans_retinol_equivalents ⁠’

all trans-retinol equivalents in gram per 100g edible portion

‘⁠beta-carotene-activity ⁠’

beta-carotene activity in beta-carotene equivalent per 100g edible portion

‘⁠beta-carotene ⁠’

beta-carotene in micogram per 100g edible portion

vitaminB1

vitamin B1 in milligram per 100g edible portion

vitaminB2

vitamin B2 in milligram per 100g edible portion

vitaminB6

vitamin B6 in milligram per 100g edible portion

vitaminB12

vitamin B12 in micogram per 100g edible portion

niacin

niacin in milligram per 100g edible portion

folate

folate in micogram per 100g edible portion

pantothenic_acid

pantothenic acid in milligram per 100g edible portion

vitaminC

vitamin C in milligram per 100g edible portion

vitaminD

vitamin D in micogram per 100g edible portion

vitaminE

vitamin E in alpha-tocopherol equivalent per 100g edible portion

Na

Sodium in milligram per 100g edible portion

K

Potassium in milligram per 100g edible portion

Cl

Chloride

Ca

Calcium

Mg

Magnesium

P

Phosphorus

Fe

Iron

I

Iodide in milligram per 100g edible portion

Zn

Zink

unit

a factor with levelsper 100g edible portionper 100ml food volume

Author(s)

Translated from the Swiss nutrion data base by Matthias Templmatthias.templ@tuwien.ac.at

Source

From the Swiss nutrition data base 2015 (second edition)

Examples

data(nutrients)str(nutrients)head(nutrients[, 41:49])

nutrient contents (branded)

Description

Nutrients on more than 10 components and 9618 branded food products

Usage

data(nutrients_branded)

Format

A data frame with 9618 observations on the following 18 variables.

Details

name_D

name (in German)

category_D

factor specifying the category names

category_F

factor specifying the category names

category_I

factor specifying the category names

category_E

factor specifying the category names

gravity

specific gravity

energy_kJ

energy in kJ

‘⁠energy_kcal ⁠’

energy in kcal

protein

protein in gram

alcohol

alcohol in gram

water

water in gram

carbohydrates_available

available carbohydrates in gram

sugars

sugars in gram

dietary_fibres

dietary fibres in gram

fat_total

total fat in gram

fatty_acids_saturated

saturated acids fat in gram

Na

Sodium in gram

unit

a factor with levelsper 100g edible portionper 100ml food volume

Author(s)

Translated from the Swiss nutrion data base by Matthias Templmatthias.templ@tuwien.ac.at

Source

From the Swiss nutrition data base 2015 (second edition)

Examples

data(nutrients_branded)str(nutrients_branded)

Orthonormal basis

Description

Orthonormal basis from cenLR transformed data to pivotCoord transformated data.

Usage

orthbasis(D)

Arguments

Details

For the chosen balances for “pivotCoord”, this is the orthonormal basisthat transfers the data from centered logratio to isometric logratio.

Value

the orthonormal basis.

Author(s)

Karel Hron, Matthias Templ. Some code lines of this function are a copy from function gsi.buildilr from

See Also

pivotCoord,cenLR

Examples

data(expenditures)V <- orthbasis(ncol(expenditures))xcen <- cenLR(expenditures)$x.clrxi <- as.matrix(xcen) %*% V$Vxixi2 <- pivotCoord(expenditures)xi2

Outlier detection for compositional data

Description

Outlier detection for compositional data using standard and robuststatistical methods.

Usage

outCoDa(x, quantile = 0.975, method = "robust", alpha = 0.5, coda = TRUE)## S3 method for class 'outCoDa'print(x, ...)## S3 method for class 'outCoDa'plot(x, y, ..., which = 1)

Arguments

Details

The outlier detection procedure is based on (robust) Mahalanobis distancesin isometric logratio coordinates. Observations withsquared Mahalanobis distance greater equal a certain quantile of thechi-squared distribution are marked as outliers.

If method “robust” is chosen, the outlier detection is based on thehomogeneous majority of the compositional data set. If method“standard” is used, standard measures of location and scatter areapplied during the outlier detection procedure. Method “robust”can be used if the number of variables is greater than the numberof observations. Here the OGK estimator is chosen.

plot method: the Mahalanobis distance are plotted against the index.The dashed line indicates the (1 - alpha) quantile of the chi-squareddistribution. Observations with Mahalanobis distance greater than thisquantile could be considered as compositional outliers.

Value

Note

It is highly recommended to use the robust version of the procedure.

Author(s)

Matthias Templ, Karel Hron

References

Egozcue J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G.,Barcelo-Vidal, C. (2003) Isometric logratio transformations for compositionaldata analysis.Mathematical Geology, 35 (3) 279-300.

Filzmoser, P., and Hron, K. (2008) Outlier detection for compositional datausing robust methods.Math. Geosciences, 40, 233-248.

Rousseeuw, P.J., Van Driessen, K. (1999) A fast algorithm for the minimumcovariance determinant estimator.Technometrics, 41, 212-223.

See Also

pivotCoord

Examples

data(expenditures)oD <- outCoDa(expenditures)oD## providing a function:oD <- outCoDa(expenditures, coda = log)## for high-dimensional data:oD <- outCoDa(expenditures, method = "robustHD")

Propability table

Description

Calculates the propability table using different methods

Usage

pTab(x, method = "dirichlet", alpha = 1/length(as.numeric(x)))

Arguments

Value

The probablity table

Author(s)

Matthias Templ

References

Egozcue, J.J., Pawlowsky-Glahn, V., Templ, M., Hron, K. (2015)Independence in contingency tables using simplicial geometry.Communications in Statistics - Theory and Methods, 44 (18), 3978–3996.

Examples

data(precipitation) pTab(precipitation)pTab(precipitation, method = "dirichlet")

special payments

Description

Payments splitted by different NACE categories and kind of employment in Austria 2004

Usage

data(payments)

Format

A data frame with 535 rows and 11 variables

Details

nace

NACE classification, 2 digits

oenace_2008

Corresponding Austrian NACE classification (in German)

year

year

month

month

localunit

local unit ID

spay

special payments (total)

spay_wc

special payments for white colar workers

spay_bc

special payments for blue colar workers

spay_traintrade

special payments for trainees in trade businness

spay_home

special payments for home workers

spay_traincomm

special payments for trainees in commercial businness

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

Source

statCube data base at the website of Statistics Austria. The product and all material contained therein are protected by copyright with all rights reserved by the Bundesanstalt Statistik Oesterreich (STATISTICS AUSTRIA). It is permitted to reproduce, distribute, make publicly available and process the content for non-commercial purposes. Prior to any use for commercial purposes a written consent of STATISTICS AUSTRIA must be obtained. Any use of the contained material must be correctly reproduced and clearly cite the source STATISTICS AUSTRIA. If tables published by STATISTICS AUSTRIA are partially used, displayed or otherwise changed, a note must be added at an adequate position to show data was extracted or adapted.

Examples

data(payments)str(payments)summary(payments)

Robust principal component analysis for compositional data

Description

This function applies robust principal component analysis for compositionaldata.

Usage

pcaCoDa(  x,  method = "robust",  mult_comp = NULL,  external = NULL,  solve = "eigen")## S3 method for class 'pcaCoDa'print(x, ...)## S3 method for class 'pcaCoDa'summary(object, ...)

Arguments

Details

The compositional data set is expressed in isometric logratio coordinates.Afterwards, robust principal component analysis is performed. Resultingloadings and scores are back-transformed to the clr space where thecompositional biplot can be shown.

mult_comp is used when there are more than one group of compositionalparts in the data. To give an illustrative example, lets assume that onevariable group measures angles of the inner ear-bones of animals which sumup to 100 and another one having percentages of a whole on the thickness ofthe inner ear-bones included. Then two groups of variables exists which areboth compositional parts. The isometric logratio coordinates are then internally appliedto each group independently whenever themult_comp is set correctly.

Value

Author(s)

Karel Hron, Peter Filzmoser, Matthias Templ and a contribution for dimnames in external variables by Amelia Landre.

References

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal componentanalysis for compositional data with outliers.Environmetrics,20, 621-632.

Kynclova, P., Filzmoser, P., Hron, K. (2016) Compositional biplots including external non-compositional variables.Statistics: A Journal of Theoretical and Applied Statistics,50, 1132-1148.

See Also

print.pcaCoDa,summary.pcaCoDa,biplot.pcaCoDa,plot.pcaCoDa

Examples

data(arcticLake)## robust estimation (default):res.rob <- pcaCoDa(arcticLake)res.robsummary(res.rob)plot(res.rob)## classical estimation:res.cla <- pcaCoDa(arcticLake, method="classical", solve = "eigen")biplot(res.cla)## just for illustration how to set the mult_comp argument:data(expenditures)p1 <- pcaCoDa(expenditures, mult_comp=list(c(1,2,3),c(4,5)))p1## example with external variables:data(election)# transform external variableselection$unemployment <- log((election$unemployment/100)/(1-election$unemployment/100))election$income <- scale(election$income)res <- pcaCoDa(election[,1:6], method="classical", external=election[,7:8])resbiplot(res, scale=0)

Perturbation and powering

Description

Perturbation and powering for two compositions.

Usage

perturbation(x, y)powering(x, a)

Arguments

Value

Result of perturbation or powering

Author(s)

Matthias Templ

References

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

Examples

data(expenditures)x <- expenditures[1 ,]y <- expenditures[2, ]perturbation(x, y)powering(x, 2)

Factor analysis for compositional data

Description

Computes the principal factor analysis of the input data which aretransformed and centered first.

Usage

pfa(  x,  factors,  robust = TRUE,  data = NULL,  covmat = NULL,  n.obs = NA,  subset,  na.action,  start = NULL,  scores = c("none", "regression", "Bartlett"),  rotation = "varimax",  maxiter = 5,  control = NULL,  ...)

Arguments

Details

The main difference to usual implementations is that uniquenesses are norlonger of diagonal form. This kind of factor analysis is designed forcentered log-ratio transformed compositional data. However, if thecovariance is not specified, the covariance is estimated from isometriclog-ratio transformed data internally, but the data used for factor analysisare backtransformed to the clr space (see Filzmoser et al., 2009).

Value

Author(s)

Peter Filzmoser, Karel Hron, Matthias Templ

References

C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter (2008):Statistical Data Analysis Explained.Applied Environmental Statisticswith R. John Wiley and Sons, Chichester, 2008.

P. Filzmoser, K. Hron, C. Reimann, R. Garrett (2009): Robust Factor Analysisfor Compositional Data.Computers and Geosciences,35 (9),1854–1861.

Examples

data(expenditures)x <- expendituresres.rob <- pfa(x, factors=1)res.cla <- pfa(x, factors=1, robust=FALSE)## the following produce always the same result:res1 <- pfa(x, factors=1, covmat="covMcd")res2 <- pfa(x, factors=1, covmat=robustbase::covMcd(pivotCoord(x))$cov)res3 <- pfa(x, factors=1, covmat=robustbase::covMcd(pivotCoord(x)))

PhD students in the EU

Description

PhD students in Europe based on the standard classification system splittedby different kind of studies (given as percentages).

Format

A data set on 32 compositions and 11 variables.

Details

Due to unknown reasons the rowSums of the percentages is not always 100.

country

country of origin (German)

countryEN

country of origin (English)

country2

country of origin, 2-digits

total

total phd students (in 1.000)

male

male phd students (in 1.000)

female

total phd students (in 1.000)

technical

phd students in natural and technical sciences

socio-economic-low

phd students in social sciences, economic sciences and law sciences

human

phd students in human sciences including teaching

health

phd students in health and life sciences

agriculture

phd students in agriculture

Source

Eurostat

References

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing values for compositional data using classical and robust methods.Computational Statistics and Data Analysis, vol 54 (12), pages 3095-3107.

Examples

data(phd)str(phd)

PhD students in the EU (totals)

Description

PhD students in Europe by different kind of studies.

Format

A data set on 29 compositions and 5 variables.

Details

technical

phd students in natural and technical sciences

socio-economic-low

phd students in social sciences, economic sciences and law sciences

human

phd students in human sciences including teaching

health

phd students in health and life sciences

agriculture

phd students in agriculture

Source

Eurostat

References

Hron, K. and Templ, M. and Filzmoser, P. (2010) Imputation of missing values for compositional data using classical and robust methods.Computational Statistics and Data Analysis, vol 54 (12), pages 3095-3107.

Examples

data("phd_totals")str(phd_totals)

Pivot coordinates and their inverse

Description

Pivot coordinates as a special case of isometric logratio coordinates and their inverse mapping.

Usage

pivotCoord(  x,  pivotvar = 1,  fast = FALSE,  method = "pivot",  base = exp(1),  norm = "orthonormal")isomLR(x, fast = FALSE, base = exp(1), norm = "sqrt((D-i)/(D-i+1))")isomLRinv(x)pivotCoordInv(x, norm = "orthonormal")isomLRp(x, fast = FALSE, base = exp(1), norm = "sqrt((D-i)/(D-i+1))")isomLRinvp(x)

Arguments

Details

Pivot coordinates map D-part compositional data from the simplexinto a (D-1)-dimensional real space isometrically. From our choice of pivotcoordinates, all the relative information about one of parts (or about two parts) is aggregated in the first coordinate(or in the first two coordinates in case of symmetric pivot coordinates, respectively).

Value

The data represented in pivot coordinates

Author(s)

Matthias Templ, Karel Hron, Peter Filzmoser

References

Egozcue J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G.,Barcel'o-Vidal, C. (2003) Isometric logratio transformations for compositionaldata analysis.Mathematical Geology,35(3) 279-300.

Filzmoser, P., Hron, K., Templ, M. (2018)Applied Compositional Data Analysis.Springer, Cham.

Examples

require(MASS)Sigma <- matrix(c(5.05,4.95,4.95,5.05), ncol=2, byrow=TRUE)z <- pivotCoordInv(mvrnorm(100, mu=c(0,2), Sigma=Sigma))data(expenditures)## first variable as pivot variablepivotCoord(expenditures)## third variable as pivot variablepivotCoord(expenditures, 3) x <- exp(mvrnorm(2000, mu=rep(1,10), diag(10)))system.time(pivotCoord(x))system.time(pivotCoord(x, fast=TRUE))## without normalizing constantpivotCoord(expenditures, norm = "orthogonal") # or:pivotCoord(expenditures, norm = "1")## other normalizationpivotCoord(expenditures, norm = "-sqrt((D-i)/(D-i+1))")# symmetric balances (results in 2-dim symmetric pivot coordinates)pivotCoord(expenditures, method = "symm")

Plot method for objects of class imp

Description

This function provides several diagnostic plots for the imputed data set inorder to see how the imputated values are distributed in comparison with theoriginal data values.

Usage

## S3 method for class 'imp'plot(  x,  ...,  which = 1,  ord = 1:ncol(x),  colcomb = "missnonmiss",  plotvars = NULL,  col = c("skyblue", "red"),  alpha = NULL,  lty = par("lty"),  xaxt = "s",  xaxlabels = NULL,  las = 3,  interactive = TRUE,  pch = c(1, 3),  ask = prod(par("mfcol")) < length(which) && dev.interactive(),  center = FALSE,  scale = FALSE,  id = FALSE,  seg.l = 0.02,  seg1 = TRUE)

Arguments

Details

The first plot (which== 1) is a multiple scatterplot where for theimputed values another plot symbol and color is used in order to highlightthem. Currently, the ggpairs functions from the GGally package is used.

Plot 2 is a parallel coordinate plot in which imputed values in certainvariables are highlighted. In parallel coordinate plots, the variables arerepresented by parallel axes. Each observation of the scaled data is shownas a line. If interactive is TRUE, the variables to be used forhighlighting can be selected interactively. Observations which includesimputed values in any of the selected variables will be highlighted. Avariable can be added to the selection by clicking on a coordinate axis. Ifa variable is already selected, clicking on its coordinate axis will removeit from the selection. Clicking anywhere outside the plot region quits theinteractive session.

Plot 3 shows a ternary diagram in which imputed values are highlighted, i.e.those spikes of the chosen plotting symbol are colored in red for which ofthe values are missing in the unimputed data set.

Value

None (invisible NULL).

Author(s)

Matthias Templ

References

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

Wegman, E. J. (1990)Hyperdimensional data analysis using parallelcoordinates Journal of the American Statistical Association 85, 664–675.

See Also

impCoda,impKNNa

Examples

data(expenditures)expenditures[1,3]expenditures[1,3] <- NAxi <- impKNNa(expenditures)xisummary(xi)## Not run: plot(xi, which=1)plot(xi, which=2)plot(xi, which=3)plot(xi, which=3, seg1=FALSE)

Plot method

Description

Provides a screeplot and biplot for (robust) compositional principal components analysis.

Usage

## S3 method for class 'pcaCoDa'plot(x, y, ..., which = 1, choices = 1:2)

Arguments

Value

The robust compositional screeplot.

Author(s)

M. Templ, K. Hron

References

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal Component Analysis forCompositional Data with Outliers.Environmetrics,20 (6),621–632.

See Also

pcaCoDa,biplot.pcaCoDa

Examples

data(coffee)## Not run: p1 <- pcaCoDa(coffee[,-1])plot(p1)plot(p1, type="lines")plot(p1, which = 2)plot(p1, which = 3)## End(Not run)

plot smoothSpl

Description

plot densities of objects of class smoothSpl

Usage

## S3 method for class 'smoothSpl'plot(x, y, ..., by = 1, n = 10, index = NULL)

Arguments

Author(s)

Alessia Di Blasi, Federico Pavone, Gianluca Zeni

Function calculating a set of (D-1) principal balances based on PLS.

Description

Function calculating a set of (D-1) principal balances based on PLS.

Usage

pls_pb(Xcoda, ycoda, version = "cov")

Arguments

Details

The function creates a set of (D-1) principal balances based on PLS. The procedure builds on the method building principal balances based on PCA, introduced in Martin-Fernandez et al. (2018)For detailed information regarding PLS principal balances, see Nesrstová et al. (2023).

Value

A list with the following components:

bal

A matrix of (D-1) principal balances.

cov

Covariance of each balance with the response variable.

Author(s)

Viktorie Nesrstová

References

J. A. Martín-Fernández, V. Pawlowsky-Glahn, J. J. Egozcue, and R. Tolosona-Delgado. Advances in principal balances for compositional data. Mathematical Geosciences, 50(3):273–298, 2018. Available at:https://link.springer.com/article/10.1007/s11004-017-9712-zDOI:doi:10.1007/s11004-017-9712-z

Nesrstová, V, Wilms, I, Palarea-Albaladejo, J, et al. Principal balances of compositional data for regression and classification using partial least squares. Journal of Chemometrics. 2023; 37(12):e3518.. Available at:https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/full/10.1002/cem.3518DOI:doi:10.1002/cem.3518

Examples

## Not run:   if (requireNamespace("MASS", quietly = TRUE)) {# 1. Generate sample data ------------------------------------------------------n <- 100              # observationsD <- 15               # parts/variablesSig <- diag(D-1)      # positive-definite symmetric matrix -> covariance matrixmu <- c(rep(0, D-1))  # means of variablesset.seed(123)# ilr coordinatesZ <- MASS::mvrnorm(n,mu,Sigma = Sig)# Z -> CoDa XV <- compositions::ilrBase(D = D)  # ilrBase() in library(compositions)X <- as.matrix(as.data.frame(acomp(exp(Z%*%t(V)))))# Response y:beta <- runif(D-1,0.1,1)eps <- rnorm(n)y <- Z%*%beta+eps# 2. Calculate PLS PBsPLS_balances <- fBalChip_PLS(X,y,version = "cov")     # version = "cov" -> max. covariancebalances <- PLS_balances$bal  }## End(Not run)

24-hour precipitation

Description

table containing counts for 24-hour precipitation for season at the rain-gouge.

Usage

data(precipitation)

Format

A table with 4 rows and 6 columns

Details

spring

numeric vector on counts for different level of precipitation

summer

numeric vector on counts for different level of precipitation

autumn

numeric vector on counts for different level of precipitation

winter

numeric vector on counts for different level of precipitation

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

References

Romero R, Guijarro J A, Ramis C, Alonso S (1998). A 30-years (196493) daily rainfalldata base for the Spanish Mediterranean regions: first exploratory study.International Journal of Climatology 18, 541560.

Examples

data(precipitation)precipitationstr(precipitation)

Print method for objects of class imp

Description

The function returns a few information about how many missing values areimputed and possible other information about the amount of iterations, forexample.

Usage

## S3 method for class 'imp'print(x, ...)

Arguments

Value

None (invisible NULL).

Author(s)

Matthias Templ

See Also

impCoda,impKNNa

Examples

data(expenditures)expenditures[1,3]expenditures[1,3] <- NA## Not run: xi <- impCoda(expenditures)xisummary(xi)plot(xi, which=1:2)## End(Not run)

production splitted by nationality on enterprise level

Description

nace

NACE classification, 2 digits

oenace_2008

Corresponding Austrian NACE classification (in German)

year

year

month

month

enterprise

enterprise ID

total

total ...

home

home ...

EU

EU ...

non-EU

non-EU ...

Usage

data(production)

Format

A data frame with 535 rows and 9 variables

Author(s)

Matthias Templmatthias.templ@tuwien.ac.at

Source

statCube data base at the website of Statistics Austria. The product and all material contained therein are protected by copyright with all rights reserved by the Bundesanstalt Statistik Oesterreich (STATISTICS AUSTRIA). It is permitted to reproduce, distribute, make publicly available and process the content for non-commercial purposes. Prior to any use for commercial purposes a written consent of STATISTICS AUSTRIA must be obtained. Any use of the contained material must be correctly reproduced and clearly cite the source STATISTICS AUSTRIA. If tables published by STATISTICS AUSTRIA are partially used, displayed or otherwise changed, a note must be added at an adequate position to show data was extracted or adapted.

Examples

data(production)str(production)summary(production)

Relative simplicial deviance

Description

Relative simplicial deviance

Usage

rSDev(x, y)

Arguments

Value

The relative simplicial deviance

Author(s)

Matthias Templ

References

Egozcue, J.J., Pawlowsky-Glahn, V., Templ, M., Hron, K. (2015)Independence in contingency tables using simplicial geometry.Communications in Statistics - Theory and Methods, 44 (18), 3978–3996.

Examples

data(precipitation) tabprob <- prop.table(precipitation)tabind <- indTab(precipitation)tabint <- intTab(tabprob, tabind)rSDev(tabprob, tabint$intTab)

Relative simplicial deviance tests

Description

Monte Carlo based contingency table tests considering the compositional approach to contingency tables.

Usage

rSDev.test(x, R = 999, method = "multinom")

Arguments