# ait: The alpha-IT transformation In Compositional: Compositional Data Analysis

 The alpha-IT transformation R Documentation

## The α-IT transformation

### Description

The α-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 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.

### Details

The α-IT transformation is applied to the compositional data.

### Value

A matrix with the α-IT transformed data.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### References

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 ```

### Examples

```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) )
```

Compositional documentation built on July 8, 2022, 1:06 a.m.