\name{robCompositions-package}
\alias{robCompositions-package}
\alias{robCompositions}
\docType{package}
\title{
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). 
}
\details{
\tabular{ll}{
Package: \tab robCompositions\cr
Type: \tab Package\cr
Version: \tab 1.3.3\cr
Date: \tab 2009-11-28\cr
License: \tab GPL 2\cr
LazyLoad: \tab yes\cr
}

}
\author{
Matthias Templ, Peter Filzmoser, Karel Hron, 

Maintainer: Matthias Templ <templ@tuwien.ac.at>
}
\references{
Aitchison, J. (1986) \emph{The Statistical Analysis of Compositional
Data} Monographs on Statistics and Applied Probability. Chapman \&
Hall Ltd., London (UK). 416p. \\

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

Filzmoser, P., Hron, K., Reimann, C. (2009)
Principal Component Analysis for Compositional Data with Outliers. \emph{Environmetrics}, \bold{20} (6), 621--632.

P. Filzmoser, K. Hron, C. Reimann, R. Garrett (2009): Robust Factor Analysis for Compositional Data. 
\emph{Computers and Geosciences}, \bold{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 
\emph{Computational Statistics and Data Analysis}, accepted for publication.

C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter (2008): 
Statistical Data Analysis Explained. 
\emph{Applied Environmental Statistics with R}. 
John Wiley and Sons, Chichester, 2008.
}
\keyword{ package }
\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)
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 <- alr(x, 2)
y <- invalr(x.alr)
invalr(alr(x, 3))
data(expenditures)
x <- expenditures
y <- invalr(alr(x, 5))
head(x)
head(y)
invalr(x.alr, ivar=2, useClassInfo=FALSE)

data(expenditures)
eclr <- clr(expenditures)
inveclr <- invclr(eclr)
head(expenditures)
head(inveclr)
head(invclr(eclr$x.clr))

require(MASS)
Sigma <- matrix(c(5.05,4.95,4.95,5.05), ncol=2, byrow=TRUE)
z <- invilr(mvrnorm(100, mu=c(0,2), Sigma=Sigma))
}