Type:	Package
Title:	Compositional Data Analysis
Version:	2.4.1
Date:	2023-08-21
Depends:	R (≥ 3.5.0), ggplot2, pls, data.table
LinkingTo:	Rcpp, RcppEigen
Imports:	cvTools, e1071, fda, rrcov, cluster, dplyr, magrittr, fpc, GGally, ggfortify, kernlab, MASS, mclust, tidyr, robustbase, robustHD, splines, VIM, zCompositions, reshape2, Rcpp
Suggests:	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:	7.2.3
NeedsCompilation:	yes
Packaged:	2023-08-25 15:02:41 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:	2023-08-25 15:30:06 UTC

Robust Estimation for Compositional Data.

Description

The package contains methods for imputation of compositional data including robust methods, (robust) outlier detection for compositional data, (robust) principal component analysis for compositional data, (robust) factor analysis for compositional data, (robust) discriminant analysis (Fisher rule) and (robust) Anderson-Darling normality tests for compositional data as well as popular log-ratio transformations (alr, clr, ilr, and their inverse transformations).

Author(s)

Matthias Templ, Peter Filzmoser, Karel Hron,

Maintainer: Matthias Templ <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.

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

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

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

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, 54 (12), 3095–3107.

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

Examples

## k nearest neighbor imputation
data(expenditures)
expenditures[1,3]
expenditures[1,3] <- NA
impKNNa(expenditures)$xImp[1,3]

## iterative model based imputation
data(expenditures)
x <- expenditures
x[1,3]
x[1,3] <- NA
xi <- impCoda(x)$xImp
xi[1,3]
s1 <- sum(x[1,-3])
impS <- sum(xi[1,-3])
xi[,3] * s1/impS

xi <- impKNNa(expenditures)
xi
summary(xi)
## Not run: plot(xi, which=1)
plot(xi, which=2)
plot(xi, which=3)

## pca
data(expenditures)
p1 <- pcaCoDa(expenditures)
p1
plot(p1)

## outlier detection
data(expenditures)
oD <- outCoDa(expenditures)
oD
plot(oD)

## transformations
data(arcticLake)
x <- arcticLake
x.alr <- addLR(x, 2)
y <- addLRinv(x.alr)
addLRinv(addLR(x, 3))
data(expenditures)
x <- expenditures
y <- 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 been proposed for an basis representation of fcenLR transformed probability density functions. The ZB-spline basis functions can be back transformed 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. Machalova jitka.machalova@upol.cz, R. Talska talskarenata@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 t
t = seq(0,20,l=500)
knots = c(0,2,5,9,14,20)
order = 4

ZBsplineBasis.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 functions
CBsplineBasis=NULL
for (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 data sets 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 of compositional data. It measures the distance between two compositions if x and y are vectors. It evaluates the sum of the distances between x and y for each row of x and y if x and y are matrices or data frames. It computes a n times n distance matrix (with n the number of observations/compositions) if only x is provided.

The underlying code is partly written in C and allows a fast computation also for large data sets whenever y is supplied.

Value

The Aitchison distance between two compositions or between two data sets, or a distance matrix in case codey is not supplied.

Author(s)

Matthias Templ, Bernhard Meindl

References

Aitchison, J. (1986) The Statistical Analysis of Compositional 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. and Pawlowsky-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 values for compositional data using classical and robust methods Computational Statistics and Data Analysis, vol 54 (12), pages 3095-3107.

See Also

pivotCoord

Examples

data(expenditures)
x <- xOrig <- expenditures
## Aitchison distance between two 2 observations:
aDist(x[1, ], 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 from the 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 the logarithm is taken.

Value

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

The additional information such as cnames or ivar is useful when an inverse mapping is applied on the ‘same’ data set.

Author(s)

Matthias Templ

References

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

See Also

addLRinv, pivotCoord

Examples

data(arcticLake)
x <- arcticLake
x.alr <- addLR(x, 2)
y <- addLRinv(x.alr)
## This exactly fulfills:
addLRinv(addLR(x, 3))
data(expenditures)
x <- expenditures
y <- 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 logistic transformation.

Usage

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

Arguments

Details

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

Value

the resulting compositional data matrix

Author(s)

Matthias Templ

References

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

See Also

pivotCoordInv, cenLRinv, cenLR, addLR

Examples

data(arcticLake)
x <- arcticLake
x.alr <- addLR(x, 2)
y <- addLRinv(x.alr)
## This exactly fulfills:
addLRinv(addLR(x, 3))
data(expenditures)
x <- expenditures
y <- 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 in another scale (but the ratios are still the same). This function rescale the output 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 of missing values for compositional data using classical and robust methods Computational Statistics and Data Analysis, In Press, Corrected Proof, ISSN: 0167-9473, DOI:10.1016/j.csda.2009.11.023

See Also

impCoda

Examples

data(expenditures)
x <- expenditures
x[1,3] <- x[2,4] <- x[3,3] <- x[3,4] <- NA
xi <- impCoda(x)
x
xi$xImp
adjust(xi)$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 radius test) and it depends on the data which test is chosen.

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

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

If the data is multivariate the radius Anderson-Darling test for normality is 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 the probability of obtaining a result at least as extreme as the one that was actually observed under the null hypothesis, we use Monte Carlo techniques where we check how often the statistic of the underlying data is more extreme than statistics obtained from simulated normal distributed data with the same (column-wise-) mean(s) and (co)variance.

Value

Note

These functions are use by adtestWrapper.

Author(s)

Karel Hron, Matthias Templ

References

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

See Also

adtestWrapper

Examples

adtest(rnorm(100))
data(machineOperators)
x <- machineOperators
adtest(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 as proposed 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. After applying this transformation

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

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

- the (D-1)-dimensional radius distribution is tested using the Anderson-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 addition to that, p-values are provided.

Value

Author(s)

Matthias Templ and Karel Hron

References

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

Aitchison, J. (1986) The Statistical Analysis of Compositional Data Monographs 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 R
a
summary(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 Templ matthias.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 Templ matthias.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 Templ matthias.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 data in 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 hyperplane in 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$balances
b2$balances

data(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 according V* values are bigger that the cut-off value are considered as biomarkers.

Value

The function returns object of type "biomarker". Functions print, plot and summary are available.

Author(s)

Jan Walach

See Also

plot.biomarker

Examples

# Data simulation
set.seed(4523)
n <- 40; p <- 50
r <- runif(p, min = 1, max = 10)
conc <- runif(p, min = 0, max = 1)*5+matrix(1,p,1)*5
a <- conc*r
S <- 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 outlier
M[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)*1.8
X <- (1-S)*(C*R+B)*exp(M)
# Biomarker identification
b <- 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 compositional data. Applied Statistics, 51, 375-392. \

Filzmoser, P., Hron, K., Reimann, C. (2009) Principal component analysis for compositional 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 from pcaCoDa, is performed.

Value

The robust compositional biplot.

Author(s)

M. Templ, K. Hron

References

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

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

See Also

pcaCoDa, plot.pcaCoDa

Examples

data(coffee)
p1 <- pcaCoDa(coffee[,-1])
p1
plot(p1, which = 2, choices = 1:2)

# exemplarly, showing the first and third PC
a <- p1$princompOutputClr
biplot(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 of PLS 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 of components

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

bpcTab bpcTabWrapper bpcPca bpcReg

Examples

data(expenditures)

# default setting with ln()
bpc(expenditures)

# logarithm of base 2
bpc(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

bpc bpcPcaTab bpcReg

Examples

data(arcticLake)

# classical estimation with all pairwise logratios:
res.cla <- bpcPca(arcticLake)
summary(res.cla)
biplot(res.cla)
head(res.cla$scores)
res.cla$loadings
res.cla$loadings.clr

# similar output as from pca CoDa
res.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

bpcTabWrapper bpcPca bpcRegTab

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$scores)
res.cla$loadings
res.cla$loadings.clr

# classical estimation with LAB anf 155 as rationing categories
res.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$scores)
res.cla.select$loadings
res.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$scores)
res.rob$loadings
res.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

bpc bpcPca bpcRegTab

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 X
expendituresEU.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 covariates
data(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

bpcTabWrapper bpcPcaTab bpcReg

Examples

# let's prepare some data
data(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 X
table_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 array
resp <- y$unemployed
names(resp) <- y$Country
reg.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 2
resp.df <- as.data.frame(y$unemployed)
rownames(resp.df) <- y$Country
reg.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 X
x.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

bpc bpcTabWrapper bpcPcaTab bpcRegTab

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 2
bpcTab(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

bpc bpcPcaTab bpcRegTab

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 2
bpcTabWrapper(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 Templ matthias.templ@tuwien.ac.at

Source

https://www.ec.europa.eu/eurostat and https://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 Templ matthias.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. be used 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 of missing values for compositional data using classical and robust methods Computational 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 <- expenditures
x[1,3] <- NA
xi <- impKNNa(x)$xImp
ced(expenditures, xi, ni = sum(is.na(x)))

Centred logratio coefficients

Description

The centred logratio (clr) coefficients map D-part compositional data from the simplex into 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 the logarithm 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 of Compositional 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 of Compositional 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 set in package mvoutlier and chorizonDL, except that values below the detection limit are coded as zeros, and detection limits provided as attributes to the data set and less 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 package mvoutlier.

Source

Kola Project (1993-1998)

References

Reimann, C., Filzmoser, P., Garrett, R.G. and Dutter, R. (2008) Statistical Data Analysis Explained: Applied Environmental Statistics with 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 coordiantes before 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, and cluster 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 <- expenditures
rr <- 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 <- expenditures
cl <- 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 Templ matthias.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 zeros
arcticLake[1:10, 1] <- 0
arcticLake[11:20, 2] <- 0
m <- 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. Machalova jitka.machalova@upol.cz, R. Talska talskarenata@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$Sepal.Length
Species <- iris$Species
iris1 <- SepalLengthCm[iris$Species==levels(iris$Species)[1]]
h1 <- hist(iris1, plot = FALSE)
midx1 <- h1$mids
midy1 <- matrix(h1$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 <- 4
der <- 2
alpha <- 0.99

sol1 <- compositionalSpline(t = midx1, clrf = clrf, knots = knots, 
  w = rep(1,length(midx1)), order = order, der = der, 
  alpha = alpha, spline.plot = TRUE)
sol1$GCV
ZB_coef <- sol1$ZB_coef
t <- seq(min(knots),max(knots),l=500)
t_step <- diff(t[1:2])
ZB_base <- ZBsplineBasis(t=t,knots,order)$ZBsplineBasis
sol1.t <- ZB_base%*%ZB_coef
sol2.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 distribution
set.seed(1)
n = 1000; mean = 0; sd = 1.5
raw_data = rnorm(n,mean,sd)
  
# number of classes according to Sturges rule
n.class = round(1+1.43*log(n),0)
  
# Interval midpoints
parnition = 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)                # probabilities
dens.raw = prob/diff(parnition)          # raw density data
clrf =  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 = 4
der = 2
alpha = 0.5
spline = compositionalSpline(t = t.mid, clrf = clrf, knots = knots, 
  w = w, order = order, der = der, alpha = alpha, 
  spline.plot=TRUE, basis.plot=FALSE)
  
# ZB-spline coefficients
ZB_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 data
matplot(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 function
matlines(t.fine,dens.true,col="darkred",lwd=2)

Constant sum

Description

Closes compositions to sum up to a given constant (default 1), by dividing each 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 to const.

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 using the 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))
x
SBPc <- 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))
SBPc
SBPr <- 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))
SBPr
result <- coord(x, SBPr,SBPc)
result
data(socExp)

Correlations for compositional data

Description

This function computes correlation coefficients between compositional parts based on 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

tabCoord tabCoordWrapper

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 coordinates
cubeCoord(CZE, "Sex", 'Contract', "Age", 'Value')

# coordinates with given SBP

r <- 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 coordinates
cubeCoordWrapper(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 matrix
T <- 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 (if coda==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 clr coefficients. The robust rules are invariant to ilr transformations if affine 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 probabilities
clas2 <- daCoDa(X, grp, coda=FALSE, prior=c(1/3, 1/3, 1/3))
summary(clas2)

## compositional data
data(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)@ct
predict(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 allows for dimension reduction and thus for a better visualization of the separation boundaries. For the Fisher discriminant rule (Fisher, 1938; Rao, 1948) the assumption of normal distribution of the groups is not explicitly required, although the method looses its optimality in case of deviations from normality.

The classical Fisher discriminant rule is invariant to ilr coordinates and clr coefficients. The robust rule is invariant to ilr transformations if affine equivariant robust estimators of location and covariance are taken.

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

Value

an object of class “daFisher” including the following elements

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 of biological 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)
d2
summary(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 groups
res <- daFisher(x,grp)
res
summary(res)
res <- daFisher(x, grp, plotScore = TRUE)
res <- daFisher(x, grp, method = "robust")
res
summary(res)
predict(res, newdata = x)
res <- daFisher(x,grp, plotScore = TRUE, method = "robust")

# 9 regions
grp <- olives$Area
res <- daFisher(x, grp, plotScore = TRUE)
res
summary(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 Templ matthias.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 different federal states

Usage

data(election)

Format

A data frame with 16 observations and 8 variables

Details

Votes for the political parties in the elections (compositional variables), and their relation to the unemployment rate and the average monthly income (external non-compositional variables). Votes are for the Christian Democratic Union and Christian Social Union of Bavaria, also called 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 the parties participated in the elections (other parties). The votes are examined in absolute values (number of valid votes). The unemployment in the federal states is reported in percentages, and the average monthly income in Euros.

• CDU_CSU Christian Democratic Union and Christian Social Union of Bavaria, also called 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 the parties 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 of employees in the year 2015 was available, divided according to gender and age of employees 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 overall employment structure, not just from the perspective of each factor separately, but also from the perspective of the relations/interactions between them. Thorough analysis of the sample is described in Facevicova (2019).

• CountryCountry

• Sexgender, males (M) and females (F)

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

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

• ValueNumber 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

• genderfactor

• statusfactor, defining if part or full time work

• countrycountry

• valueemployment

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 Templ matthias.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] <- NA
impKNNa(expenditures)$xImp[1,3]

mean consumption expenditures data.

Description

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

Format

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

• Fooda numeric vector

• Alcohola numeric vector

• Clothinga numeric vector

• Housinga numeric vector

• Furnishingsa numeric vector

• Healtha numeric vector

• Transporta numeric vector

• Communicationsa numeric vector

• Recreationa numeric vector

• Educationa numeric vector

• Restaurantsa numeric vector

• Othera numeric vector

Source

Eurostat

Examples

data(expendituresEU)

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 = 1.5
f = 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 = 1.5
f = 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 density
p = 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 p
matplot(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)

# Plot
layout(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.

• countrycountry

• Cereals - Excluding BeerFood balance on cereals

• ...... #'

• Alcohol - Non-FoodFood balance on alcohol

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

• MeanTempAnnual 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 Rcpp but it currently do not pass CRAN checks cause of use of Rcpp11 features. This C++ version accounts 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 while gmean calculates geometric means on rows (margin = 1), on columns (margin = 2), or on all values (margin = 3)

Value

geometric means (if gmean is used) or totals (if gmean_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 from https://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 in percentage.

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; Hitite, Armenian

• G2a Caucasian, Greco-Anatolien

• E1b1b North and Eastern Afrika, 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 in genealogical groups sharing a common 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

• Mnchemical 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 compositional data using classical and robust methods based on ilr coordinates with special choice of balances. Values under detection limit should be saved with the negative value of the detection limit (per variable). Missing values should be coded as NA.

Usage

impAll(x)

Arguments

Details

This is a wrapper function that calls impRZilr() for the replacement of zeros and impCoda for the imputation of missing values sequentially. The detection limit is automatically derived form negative numbers 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 of missing 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 in compositional data: Classical and robust approaches, Computational Statistics, 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 values in compositional data. Missing values are initialized with proper values. Then iterative algorithms try to find better estimations for the former missing 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 iteration changes 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 iterative procedure. ‘classical’: principal component analysis is used within the iterative procedure. ‘ltsReg2’: least trimmed squares regression is used within the iterative procedure. The imputated values are perturbed in the direction of the predictor by values drawn form a normal distribution with mean and standard deviation related to the corresponding residuals and multiplied by noise.

Value

Author(s)

Matthias Templ, Karel Hron

References

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

See Also

impKNNa, pivotCoord

Examples

data(expenditures)
x <- expenditures
x[1,3]
x[1,3] <- NA
xi <- impCoda(x)$xImp
xi[1,3]
s1 <- sum(x[1,-3])
impS <- sum(xi[1,-3])
xi[,3] * s1/impS

# other methods
impCoda(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 imputation of 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 Aitchison metric should be chosen when dealing with compositional data, the Euclidean metric otherwise.

If primitive == FALSE, a sequential search for the k-nearest neighbors is applied for every missing value where all information corresponding to the non-missing cells plus the information in the variable to be imputed plus some additional information is available. If primitive == TRUE, a search of the k-nearest neighbors among observations is applied where in addition to the variable to be imputed any further cells are non-missing.

If normknn is TRUE (prefered option) the imputed cells from a nearest neighbor method are adjusted with special adjustment factors (more details can 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 values for compositional data using classical and robust methods Computational Statistics and Data Analysis, 54 (12), 3095-3107.

See Also

impCoda

Examples

data(expenditures)
x <- expenditures
x[1,3]
x[1,3] <- NA
xi <- impKNNa(x)$xImp
xi[1,3]

alr EM-based imputation of rounded zeros

Description

A modified EM alr-algorithm for replacing rounded zeros in compositional data 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 into problems, because log-ratios cannot be applied. Usually, rounded zeros are considerer as missing not at random missing values. The algorithm first applies an additive log-ratio transformation to the compositions. Then the rounded 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] <- 0
x[x[,2] < 47, 2] <- 0
xia <- 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 using classical and robust methods based on ilr coordinates with a special choice 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 into problems, because log-ratios cannot be applied. Usually, rounded zeros are considered as missing not at random missing values.

The algorithm iteratively imputes parts with rounded zeros whereas in each step (1) compositional data are expressed in pivot coordinates (2) tobit regression is applied (3) the rounded zeros are replaced by the expected values (4) the corresponding inverse ilr mapping is applied. After all parts are imputed, 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 zeros for high-dimensional compositional data. Chemometrics and Intelligent Laboratory Systems, 155, 183-190.

See Also

impRZalr

Examples

data(arcticLake)
x <- arcticLake
## generate rounded zeros artificially:
#x[x[,1] < 5, 1] <- 0
x[x[,2] < 44, 2] <- 0
xia <- 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 using classical and robust methods based on ilr coordinates with a special choice 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 into problems, because log-ratios cannot be applied. Usually, rounded zeros are considerer as missing not at random missing values.

The algorithm iteratively imputes parts with rounded zeros whereas in each step (1) compositional data are expressed in pivot coordinates (2) tobit regression is applied (3) the rounded zeros are replaced by the expected values (4) the corresponding inverse ilr mapping is applied. After all parts are imputed, 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 <- 10
n <- 50
k <- 2
T <- 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 + E
data <- 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 time
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="subPLS")
imp
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="pls", variation = FALSE)
imp
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="lm")
imp
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="lmrob")
imp

data(mcad)
## generate rounded zeros artificially:
x <- mcad
x <- 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)) * 100
dl[seq(2, ncol(x), 2)] <- 0
replaced_lm <- imputeBDLs(x, dl=dl, eps=1, method="lm",  
  verbose=FALSE, R=50, variation=TRUE)$x
replaced_lmrob <- imputeBDLs(x, dl=dl, eps=1, method="lmrob",  
  verbose=FALSE, R=50, variation=TRUE)$x
replaced_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 using classical and robust methods (possibly also the pls method) based on ilr-transformations with special choice 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 limit whereas in each step (1) compositional data are expressed in pivot coordinates (2) tobit regression is applied (3) the values above upper detection limit are replaced by the expected values (4) the corresponding inverse ilr mapping is applied. After all parts are imputed, 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 data
dat <- gemas[gemas$COUNTRY=="HEL",c(12:29)]
UDL <- apply(dat,2,max)
names(UDL) <- names(dat)
UDL["Mn"] <- quantile(dat[,"Mn"], probs = 0.8)  # UDL present only in one variable
whichudl <- dat[,"Mn"] > UDL["Mn"] 
# classical method
imp.lm <- dat
imp.lm[whichudl,"Mn"] <- Inf
res.lm <- imputeUDLs(imp.lm, dl=UDL, method="lm", variation=TRUE)
imp.lm <- res.lm$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)
tab1
sum(tab1)

## Not run: 
data("PreSex", package = "vcd")
indTab(PreSex)

## End(Not run)

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

Description

• ctct

• isicISIC classification, Rev 3.2

• VAvalue added

• OUToutput

• INPinput

• IS03country code

• mhtmht

Usage

data(instw)

Format

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

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

• signsThe 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 <- expenditures
is.equivalent(x, constSum(x))
y <- x
y[1,1] <- x[1,1]+1
is.equivalent(y, constSum(x))

ISIC codes by name

Description

• codeISIC code, Rev 3.2

• descriptionDescription 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 Templ matthias.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 Templ matthias.templ@tuwien.ac.at

Source

https://www.ec.europa.eu/eurostat and https://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 on compositional and non-compositional predictors

Description

Delivers appropriate inference for regression of y on a compositional matrix X 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 linear regression model because any inference statistic can become misleading. While various approaches for this problem were proposed, here an approach based on the pivot coordinates is used. Further these compositional explanatory variables can be supplemented with external non-compositional data and factor variables.

Value

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

Author(s)

Peter Filzmoser, Roman Wiedemeier, Matthias Templ

References

Filzmoser, P., Hron, K., Thompsonc, K. (2012) Linear regression with compositional explanatory variables. Journal of Applied Statistics, 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.clr
y <- ssc$sand
X <- dplyr::select(gemas_GER, c(MeanTemp, soilclass, Al:Zr))
X$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 Templ matthias.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.

• valueValue 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 structure

result <- 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 structure regarding their missingness or zeros. For all patterns a summary is calculated.

Value

Author(s)

Matthias Templ. The code is based on a previous version from Andreas Alfons 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 Templ matthias.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

• femalemortality rates for females by age groups

• malemortality 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 <- 1
D <- 6
vec <- 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

• carbohydratescrbohydrates 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 levels per 100g edible portion per 100ml food volume

Author(s)

Translated from the Swiss nutrion data base by Matthias Templ matthias.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 levels per 100g edible portion per 100ml food volume

Author(s)

Translated from the Swiss nutrion data base by Matthias Templ matthias.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 basis that 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)$x.clr
xi <- as.matrix(xcen) %*% V$V
xi
xi2 <- pivotCoord(expenditures)
xi2

Outlier detection for compositional data

Description

Outlier detection for compositional data using standard and robust statistical 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 distances in isometric logratio coordinates. Observations with squared Mahalanobis distance greater equal a certain quantile of the chi-squared distribution are marked as outliers.

If method “robust” is chosen, the outlier detection is based on the homogeneous majority of the compositional data set. If method “standard” is used, standard measures of location and scatter are applied during the outlier detection procedure. Method “robust” can be used if the number of variables is greater than the number of 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-squared distribution. Observations with Mahalanobis distance greater than this quantile 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 compositional data analysis. Mathematical Geology, 35 (3) 279-300.

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

Rousseeuw, P.J., Van Driessen, K. (1999) A fast algorithm for the minimum covariance 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 Templ matthias.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 compositional data.

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. Resulting loadings and scores are back-transformed to the clr space where the compositional biplot can be shown.

mult_comp is used when there are more than one group of compositional parts in the data. To give an illustrative example, lets assume that one variable group measures angles of the inner ear-bones of animals which sum up to 100 and another one having percentages of a whole on the thickness of the inner ear-bones included. Then two groups of variables exists which are both compositional parts. The isometric logratio coordinates are then internally applied to each group independently whenever the mult_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 component analysis 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.rob
summary(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 variables
election$unemployment <- log((election$unemployment/100)/(1-election$unemployment/100))
election$income <- scale(election$income)

res <- pcaCoDa(election[,1:6], method="classical", external=election[,7:8])
res
biplot(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 of Compositional 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 are transformed 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 nor longer of diagonal form. This kind of factor analysis is designed for centered log-ratio transformed compositional data. However, if the covariance is not specified, the covariance is estimated from isometric log-ratio transformed data internally, but the data used for factor analysis are 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 Statistics with R. John Wiley and Sons, Chichester, 2008.

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

Examples

data(expenditures)
x <- expenditures
res.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 splitted by 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 simplex into a (D-1)-dimensional real space isometrically. From our choice of pivot coordinates, 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 compositional data 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 variable
pivotCoord(expenditures)
## third variable as pivot variable
pivotCoord(expenditures, 3) 

x <- exp(mvrnorm(2000, mu=rep(1,10), diag(10)))
system.time(pivotCoord(x))
system.time(pivotCoord(x, fast=TRUE))

## without normalizing constant
pivotCoord(expenditures, norm = "orthogonal") # or:
pivotCoord(expenditures, norm = "1")
## other normalization
pivotCoord(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 in order to see how the imputated values are distributed in comparison with the original 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 the imputed values another plot symbol and color is used in order to highlight them. Currently, the ggpairs functions from the GGally package is used.

Plot 2 is a parallel coordinate plot in which imputed values in certain variables are highlighted. In parallel coordinate plots, the variables are represented by parallel axes. Each observation of the scaled data is shown as a line. If interactive is TRUE, the variables to be used for highlighting can be selected interactively. Observations which includes imputed values in any of the selected variables will be highlighted. A variable can be added to the selection by clicking on a coordinate axis. If a variable is already selected, clicking on its coordinate axis will remove it from the selection. Clicking anywhere outside the plot region quits the interactive 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 of the values are missing in the unimputed data set.

Value

None (invisible NULL).

Author(s)

Matthias Templ

References

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

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

See Also

impCoda, impKNNa

Examples

data(expenditures)
expenditures[1,3]
expenditures[1,3] <- NA
xi <- impKNNa(expenditures)
xi
summary(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 for Compositional 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

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

• springnumeric vector on counts for different level of precipitation

• summernumeric vector on counts for different level of precipitation

• autumnnumeric vector on counts for different level of precipitation

• winternumeric vector on counts for different level of precipitation

Author(s)

Matthias Templ matthias.templ@tuwien.ac.at

References

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

Examples

data(precipitation)
precipitation
str(precipitation)

Print method for objects of class imp

Description

The function returns a few information about how many missing values are imputed and possible other information about the amount of iterations, for example.

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)
xi
summary(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 Templ matthias.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

Details

Method “rmultinom” generate multinomially distributed samples from the independent probability table, which is estimated from x using geometric mean marginals. The relative simplicial deviance of the original data are then compared to the generated ones.

Method “permutation” permutes the entries of x and compares the relative simplicial deviance estimated from the original data to the ones of the permuted data (the independence table is unchanged and originates on x).

Method “rmultinom” should be preferred, while method “permutation” can be used for comparisons.

Value

A list with class “htest” containing the following components:

• statisticthe value of the relative simplicial deviance (test statistic).

• methoda character string indicating what type of rSDev.test was performed.

• p.valuethe p-value for the test.

Author(s)

Matthias Templ, Karel Hron

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

rSDev

Examples

data(precipitation)
rSDev.test(precipitation)

codes for UNIDO tables

Description

• ISOCNISOCN codes

• OPERATOROperator

• ADESCCountry

• CCODECountry code

• CDESCCountry destination

• ACODECountry destination code

Usage

data(rcodes)

Format

A data.frame with 2717 rows and 6 columns.

Examples

data(rcodes)
str(rcodes)

relative difference between covariance matrices

Description

The sample covariance matrices are computed from compositions expressed in the same isometric logratio coordinates.

Usage

rdcm(x, y)

Arguments

Details

The difference in covariance structure is based on the Euclidean distance between both covariance estimations.

Value

the error measures value

Author(s)

Matthias Templ

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, 54 (12), 3095-3107.

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

rdcm

Examples

data(expenditures)
x <- expenditures
x[1,3] <- NA
xi <- impKNNa(x)$xImp
rdcm(expenditures, xi)

saffron compositions

Description

Stable isotope ratio and trace metal cncentration data for saffron samples.

Format

A data frame with 53 observations on the following 36 variables.

• Sample adulterated honey, Honey or Syrup

• Country group information

• Batch detailed group information

• Region less detailed group information

• d2H region

• d13C chemical element

• d15N chemical element

• Li chemical element

• B chemical element

• Na chemical element

• Mg chemical element

• Al chemical element

• Kchemical element

• Ca chemical element

• V chemical element

• Mn chemical element

• Fe chemical element

• Co chemical element

• Ni chemical element

• Cu chemical element

• Zn chemical element

• Ga chemical element

• As chemical element

• Rb chemical element

• Sr chemical element

• Y chemical element

• Mo chemical element

• Cd chemical element

• Cs chemical element

• Ba chemical element

• Ce chemical element

• Pr chemical element

• Nd chemical element

• Sm chemical element

• Gd chemical element

• Pb chemical element

Note

In the original paper, the authors applied lda for classifying the observations.

Source

Mendeley Data, contributed by Russell Frew and translated to R by Matthias Templ

References

Frew, Russell (2019), Data for: CHEMICAL PROFILING OF SAFFRON FOR AUTHENTICATION OF ORIGIN, Mendeley Data, V1, doi:10.17632/5544tn9v6c.1

Examples

data(saffron)

aphyric skye lavas data

Description

AFM compositions of 23 aphyric Skye lavas. This data set can be found on page 360 of the Aitchison book (see reference).

Usage

data(skyeLavas)

Format

A data frame with 23 observations on the following 3 variables.

Details

• sodium-potassium a numeric vector of percentages of Na2O+K2O

• iron a numeric vector of percentages of Fe2O3

• magnesium a numeric vector of percentages of MgO

Author(s)

Matthias Templ matthias.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(skyeLavas)
str(skyeLavas)
summary(skyeLavas)
rowSums(skyeLavas)

Estimate density from histogram

Description

Given raw (discretized) distributional observations, smoothSplines computes the density function that 'best' fits data, in a trade-off between smooth and least squares approximation, using B-spline basis functions.

Usage

smoothSplines(
  k,
  l,
  alpha,
  data,
  xcp,
  knots,
  weights = matrix(1, dim(data)[1], dim(data)[2]),
  num_points = 100,
  prior = "default",
  cores = 1,
  fast = 0
)

Arguments

Details

The original discretized densities are not directly smoothed, but instead the centred logratio transformation is first applied, to deal with the unit integral constraint related to density functions.
Then the constrained variational problem is set. This minimization problem for the optimal density is a compromise between staying close to the given data, at the corresponding xcp, and obtaining a smooth function. The non-smoothness measure takes into account the lth derivative, while the fidelity term is weigthed by alpha.
The solution is a natural spline. The vector of its coefficients is obtained by the minimum norm solution of a linear system. The resulting splines can be either back-transformed to the original Bayes space of density functions (in order to provide their smoothed counterparts for vizualization and interpretation purposes), or retained for further statistical analysis in the clr space.

Value

An object of class smoothSpl, containing among the other the following variables:

Author(s)

Alessia Di Blasi, Federico Pavone, Gianluca Zeni, Matthias Templ

References

J. Machalova, K. Hron & G.S. Monti (2016): Preprocessing of centred logratio transformed density functions using smoothing splines. Journal of Applied Statistics, 43:8, 1419-1435.

Examples

SepalLengthCm <- iris$Sepal.Length
Species <- iris$Species

iris1 <- SepalLengthCm[iris$Species==levels(iris$Species)[1]]
h1 <- hist(iris1, nclass = 12, plot = FALSE)

midx1 <- h1$mids
midy1 <- matrix(h1$density, nrow=1, ncol = length(h1$density), byrow=TRUE)
knots <- 7
## Not run: 
sol1 <- smoothSplines(k=3,l=2,alpha=1000,midy1,midx1,knots)
plot(sol1)

h1 <- hist(iris1, freq = FALSE, nclass = 12, xlab = "Sepal Length     [cm]", main = "Iris setosa")
# black line: kernel method; red line: smoothSplines result
lines(density(iris1), col = "black", lwd = 1.5)
xx1 <- seq(sol1$Xcp[1],tail(sol1$Xcp,n=1),length.out = sol1$NumPoints)
lines(xx1,sol1$Y[1,], col = 'red', lwd = 2)

## End(Not run)

Estimate density from histogram - for different alpha

Description

As smoothSplines, smoothSplinesVal computes the density function that 'best' fits discretized distributional data, using B-spline basis functions, for different alpha.
Comparing and choosing an appropriate alpha is the ultimate goal.

Usage

smoothSplinesVal(
  k,
  l,
  alpha,
  data,
  xcp,
  knots,
  weights = matrix(1, dim(data)[1], dim(data)[2]),
  prior = "default",
  cores = 1
)

Arguments

Details

See smoothSplines for the description of the algorithm.

Value

A list of three objects:

Author(s)

Alessia Di Blasi, Federico Pavone, Gianluca Zeni, Matthias Templ

References

J. Machalova, K. Hron & G.S. Monti (2016): Preprocessing of centred logratio transformed density functions using smoothing splines. Journal of Applied Statistics, 43:8, 1419-1435.

Examples

SepalLengthCm <- iris$Sepal.Length
Species <- iris$Species

iris1 <- SepalLengthCm[iris$Species==levels(iris$Species)[1]]
h1 <- hist(iris1, nclass = 12, plot = FALSE)

## Not run: 
midx1 <- h1$mids
midy1 <- matrix(h1$density, nrow=1, ncol = length(h1$density), byrow=TRUE)
knots <- 7
sol1 <- smoothSplinesVal(k=3,l=2,alpha=10^seq(-4,4,by=1),midy1,midx1,knots,cores=1)

## End(Not run)

social expenditures

Description

Social expenditures according to source (public or private) and three important branches (health, old age, incapacity related) in selected OECD countries in 2010. Expenditures are always provided in the respective currency.

Usage

data(socExp)

Format

A data frame with 20 observations on the following 8 variables (country + currency + row-wise sorted cells of 2x3 compositional table).

Details

• country Country of origin

• currency Currency unit (in Million)

• health-public Health from the public

• old-public Old age expenditures from the public

• incap-public Incapacity related expenditures from the public

• health-private Health from private sources

• old-private Old age expenditures from private sources

• incap-private Incapacity related expenditures from private sources

Author(s)

conversion to R by Karel Hron Karel Hron and modifications by Matthias Templ matthias.templ@tuwien.ac.at

References

OECD

Examples

data(socExp)
str(socExp)
rowSums(socExp[, 3:ncol(socExp)])

Classical estimates for tables

Description

Some standard/classical (non-compositional) statistics

Usage

stats(
  x,
  margins = NULL,
  statistics = c("phi", "cramer", "chisq", "yates"),
  maggr = mean
)

Arguments

Details

statistics ‘phi’ is the values of the table divided by the product of margins. ‘cramer’ normalize these values according to the dimension of the table. ‘chisq’ are the expected values according to Pearson while ‘yates’ according to Yates.

For the maggr function argument, arithmetic means (mean) should be chosen to obtain the classical results. Any other user-provided functions should be take with care since the classical estimations relies on the arithmetic mean.

Value

List containing all statistics

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)
stats(precipitation)
stats(precipitation, statistics = "cramer")
stats(precipitation, statistics = "chisq")
stats(precipitation, statistics = "yates")

## take with care 
## (the provided statistics are not designed for that case):
stats(precipitation, statistics = "chisq", maggr = gmean)

Summary method for objects of class imp

Description

A short comparison of the original data and the imputed data is given.

Usage

## S3 method for class 'imp'
summary(object, ...)

Arguments

Details

Note that this function will be enhanced with more sophisticated methods in future versions of the package. It is very rudimental in its present form.

Value

None (invisible NULL).

Author(s)

Matthias Templ

See Also

impCoda, impKNNa

Examples

data(expenditures)
expenditures[1,3]
expenditures[1,3] <- NA
xi <- impKNNa(expenditures)
xi
summary(xi)
# plot(xi, which=1:2)

Coordinate representation of compositional tables and a sample of compositional tables

Description

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

tabCoordWrapper: For each compositional table in the sample tabCoordWrapper 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

tabCoord(
  x = NULL,
  row.factor = NULL,
  col.factor = NULL,
  value = NULL,
  SBPr = NULL,
  SBPc = NULL,
  pivot = FALSE,
  print.res = FALSE
)

tabCoordWrapper(
  X,
  obs.ID = NULL,
  row.factor = NULL,
  col.factor = NULL,
  value = NULL,
  SBPr = NULL,
  SBPc = NULL,
  pivot = FALSE,
  test = FALSE,
  n.boot = 1000
)

Arguments

Details

tabCoord

This transformation moves the IJ-part compositional tables from the simplex into a (IJ-1)-dimensional real space isometrically with respect to its two-factorial nature. The coordinate system is formed by two types of coordinates - balances and log odds-ratios.

tabCoordWrapper: Each of n IJ-part compositional tables from the sample is with respect to its two-factorial nature isometrically transformed from the simplex into a (IJ-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., Hron, K., Todorov, V. and M. Templ (2018) General approach to coordinate representation of compositional tables. Scandinavian Journal of Statistics, 45(4), 879–899.

See Also

cubeCoord cubeCoordWrapper

Examples

###################
### Coordinate representation of a CoDa Table

# example from Fa\v cevicov\'a (2018):
data(manu_abs)
manu_USA <- manu_abs[which(manu_abs$country=='USA'),]
manu_USA$output <- factor(manu_USA$output, levels=c('LAB', 'SUR', 'INP'))

# pivot coordinates
tabCoord(manu_USA, row.factor = 'output', col.factor = 'isic', value='value')

# SBPs defined in paper
r <- rbind(c(-1,-1,1), c(-1,1,0))
c <- rbind(c(-1,-1,-1,-1,1), c(-1,-1,-1,1,0), c(-1,-1,1,0,0), c(-1,1,0,0,0))
tabCoord(manu_USA, row.factor = 'output', col.factor = 'isic', value='value', SBPr=r, SBPc=c)

###################
### Analysis of a sample of CoDa Tables

# example from Fa\v cevicov\'a (2018):
data(manu_abs)

### Compositional tables approach,
### analysis of the relative structure.
### An example from Facevi\v cov\'a (2018)

manu_abs$output <- factor(manu_abs$output, levels=c('LAB', 'SUR', 'INP'))

# pivot coordinates
tabCoordWrapper(manu_abs, obs.ID='country',
row.factor = 'output', col.factor = 'isic', value='value')

# SBPs defined in paper
r <- rbind(c(-1,-1,1), c(-1,1,0))
c <- rbind(c(-1,-1,-1,-1,1), c(-1,-1,-1,1,0), 
c(-1,-1,1,0,0), c(-1,1,0,0,0))
tabCoordWrapper(manu_abs, obs.ID='country',row.factor = 'output', 
col.factor = 'isic', value='value', SBPr=r, SBPc=c, test=TRUE)

### Classical approach,
### generalized linear mixed effect model.

## Not run: 
library(lme4)
glmer(value~output*as.factor(isic)+(1|country),data=manu_abs,family=poisson)

## End(Not run)

teaching stuff

Description

Teaching stuff in selected countries

Format

A (tidy) data frame with 1216 observations on the following 4 variables.

• country Country of origin

• subject school type: primary, lower secondary, higher secondary and tertiary

• year Year

• value Number of stuff

Details

Teaching staff include professional personnel directly involved in teaching students, including classroom teachers, special education teachers and other teachers who work with students as a whole class, in small groups, or in one-to-one teaching. Teaching staff also include department chairs of whose duties include some teaching, but it does not include non-professional personnel who support teachers in providing instruction to students, such as teachers' aides and other paraprofessional personnel. Academic staff include personnel whose primary assignment is instruction, research or public service, holding an academic rank with such titles as professor, associate professor, assistant professor, instructor, lecturer, or the equivalent of any of these academic ranks. The category includes personnel with other titles (e.g. dean, director, associate dean, assistant dean, chair or head of department), if their principal activity is instruction or research.

Author(s)

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

Source

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

References

OECD (2017), Teaching staff (indicator). doi: 10.1787/6a32426b-en (Accessed on 27 March 2017)

Examples

data(teachingStuff)
str(teachingStuff)

Ternary diagram

Description

This plot shows the relative proportions of three variables (compositional parts) in one diagramm. Before plotting, the data are scaled.

Usage

ternaryDiag(
  x,
  name = colnames(x),
  text = NULL,
  grid = TRUE,
  gridCol = grey(0.6),
  mcex = 1.2,
  line = "none",
  robust = TRUE,
  group = NULL,
  tol = 0.975,
  ...
)

Arguments

Details

The relative proportions of each variable are plotted.

Author(s)

Peter Filzmoser <P.Filzmoser@tuwien.ac.at>, Matthias Templ <matthias.templ@fhnw.ch>

References

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

Examples

data(arcticLake)
ternaryDiag(arcticLake)

data(coffee)
x <- coffee[,2:4]
grp <- as.integer(coffee[,1])
ternaryDiag(x, col=grp, pch=grp)
ternaryDiag(x, grid=FALSE, col=grp, pch=grp)
legend("topright", legend=unique(coffee[,4]), pch=1:2, col=1:2)

ternaryDiag(x, grid=FALSE, col=grp, pch=grp, line="ellipse", tol=c(0.975,0.9), lty=2)
ternaryDiag(x, grid=FALSE, line="pca")
ternaryDiag(x, grid=FALSE, col=grp, pch=grp, line="pca", lty=2, lwd=2)

Adds a line to a ternary diagram.

Description

A low-level plot function which adds a line to a high-level ternary diagram.

Usage

ternaryDiagAbline(x, ...)

Arguments

Details

This is a small utility function which helps to add a line in a ternary plot from two given points in an isometric transformed space.

Value

no values are returned.

Author(s)

Matthias Templ

See Also

ternaryDiag

Examples

data(coffee)
x <- coffee[,2:4]
ternaryDiag(x, grid=FALSE)
ternaryDiagAbline(data.frame(z1=c(0.01,0.5), z2=c(0.4,0.8)), col="red")

Adds tolerance ellipses to a ternary diagram.

Description

Low-level plot function which add tolerance ellipses to a high-level plot of a ternary diagram.

Usage

ternaryDiagEllipse(x, tolerance = c(0.9, 0.95, 0.975), locscatt = "MCD", ...)

Arguments

Value

no values are returned.

Author(s)

Peter Filzmoser, Matthias Templ

See Also

ternaryDiag

Examples

data(coffee)
x <- coffee[,2:4]
ternaryDiag(x, grid=FALSE)
ternaryDiagEllipse(x)
## or directly:
ternaryDiag(x, grid=FALSE, line="ellipse")

Add points or lines to a given ternary diagram.

Description

Low-level plot function to add points or lines to a ternary high-level plot.

Usage

ternaryDiagPoints(x, ...)

Arguments

Value

no values are returned.

Author(s)

Matthias Templ

References

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

See Also

ternaryDiag

Examples

data(coffee)
x <- coffee[,2:4]
ternaryDiag(x, grid=FALSE)
ternaryDiagPoints(x+1, col="red", pch=2)

Trapezoidal formula for numerical integration

Description

Numerical integration via trapezoidal formula.

Usage

trapzc(step, f)