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.