The additive log-ratio transformation and its inverse {Compositional}

The additive log-ratio transformation and its inverse

Description

The additive log-ratio transformation and its inverse.

Usage

alr(x)
alrinv(y)

Arguments

x

A numerical matrix with the compositional data.

y

A numerical matrix with data to be closed into the simplex.

Details

The additive log-ratio transformation with the first component being the common divisor is applied. The inverse of this transformation is also available. This means that no zeros are allowed.

Value

A matrix with the alr transformed data (if alr is used) or with the compositional data (if the alrinv is used).

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

See Also

bc, pivot, fp, green, alfa, alfainv

Examples

library(MASS)
x <- as.matrix(fgl[, 2:9])
x <- x / rowSums(x)
y <- alr(x)
x1 <- alrinv(y)