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Compositional (version 5.5)

Total variability: 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.

Value

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

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.

References

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

See Also

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

Examples

Run this code
# NOT RUN {
x <- as.matrix(iris[, 1:4])
x <- x / rowSums(x)
totvar(x)
# }

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