The alpha-transformation {Compositional} | R Documentation |
The α-transformation.
alfa(x, a, h = TRUE) alef(x, a)
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 α=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 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-transformation is applied to the compositional data. The command "alef" is the same as
"alfa(x, a, h = FALSE)", but reurns a different element as well and is necessary for the functions a.est
, a.mle
and alpha.mle
.
A list including:
sa |
The logarithm of the Jacobian determinant of the α-transformation. This is used in the "profile" function to speed up the computations. |
sk |
If the "alef" was called, this will return the sum of the α-power transformed data, prior to being normalised to sum to 1. If α=0, this will not be returned. |
aff |
The α-transformed data. |
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.
Tsagris Michail and Stewart Connie (2020). A folded model for compositional data analysis. Australian and New Zealand Journal of Statistics, 62(2): 249-277. https://arxiv.org/pdf/1802.07330.pdf
Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. https://arxiv.org/pdf/1106.1451.pdf
Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.
alfainv, pivot, alfa.profile, alfa.tune
a.est, alpha.mle, alr, bc, fp, green
library(MASS) x <- as.matrix(fgl[, 2:9]) x <- x / rowSums(x) y1 <- alfa(x, 0.2)$aff y2 <- alfa(x, 1)$aff rbind( colMeans(y1), colMeans(y2) ) y3 <- alfa(x, 0.2)$aff dim(y1) ; dim(y3) rowSums(y1) rowSums(y3)