Compositional (version 5.5)

The alpha-IT transformation: The \(\alpha\)-IT transformation

Description

The \(\alpha\)-IT transformation.

Usage

ait(x, a, h = TRUE)

Arguments

x

A matrix with the compositional data.

a

The value of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If \(\alpha=0\) the isometric log-ratio transformation is applied.

h

A boolean variable. If is TRUE (default value) the multiplication with the Helmert sub-matrix will take place. When \(\alpha=0\) and h = FALSE, the result is the centred log-ratio transformation (Aitchison, 1986). In general, when h = FALSE the resulting transformation maps the data onto a singualr space. The sum of the vectors is equal to 0. Hence, from the simplex constraint the data go to another constraint.

Value

A matrix with the \(\alpha\)-IT transformed data.

Details

The \(\alpha\)-IT transformation is applied to the compositional data.

References

Clarotto L., Allard D. and Menafoglio A. (2022). A new class of \(\alpha\)-transformations for the spatial analysis of Compositional Data. Spatial Statistics, 47.

See Also

aitdist, ait.knn, alfa, green, alr

Examples

# NOT RUN {
library(MASS)
x <- as.matrix(fgl[, 2:9])
x <- x / rowSums(x)
y1 <- ait(x, 0.2)
y2 <- ait(x, 1)
rbind( colMeans(y1), colMeans(y2) )
# }