Total variability {Compositional}

Total variability

Description

Total variability.

Usage

totvar(x, a = 0)

Arguments

x

A numerical 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 centred log-ratio transformation is used.

Details

The \alpha-transformation is applied and the sum of the variances of the transformed variables is calculated. This is the total variability. Aitchison (1986) used the centred log-ratio transformation, but we have extended it to cover more geometries, via the \alpha-transformation.

Value

The total variability of the data in a given geometry as dictated by the value of \alpha.

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

alfa, \ link{alfainv,} alfa.profile, alfa.tune

Examples

x <- as.matrix(iris[, 1:4])
x <- x / rowSums(x)
totvar(x)