|The alpha-IT transformation||R Documentation|
The α-IT transformation.
ait(x, a, h = TRUE)
A matrix with the compositional data.
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 α=0 the isometric log-ratio transformation is applied.
A boolean variable. If is TRUE (default value) the multiplication with the Helmert sub-matrix will take place. When α=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.
The α-IT transformation is applied to the compositional data.
A matrix with the α-IT transformed data.
R implementation and documentation: Michail Tsagris email@example.com.
Clarotto L., Allard D. and Menafoglio A. (2022). A new class of α-transformations for the spatial analysis of Compositional Data. Spatial Statistics, 47.
aitdist, ait.knn, alfa, green, alr
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) )
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