Compositional (version 5.5)

Alpha generalised correlations between two compositional datasets: \(\alpha\) generalised correlations between two compositional datasets

Description

\(\alpha\) generalised correlations between two compositional datasets.

Usage

acor(y, x, a, type = "dcor")

Arguments

y

A matrix with the compositional data.

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 \(\alpha=0\) the isometric log-ratio transformation is applied. If more than one valuesare supplied the distance or canonical correlation are computed for all values.

type

The type of correlation to compute, the distance correlation ("edist"), the canonical correlation ("cancor") or "both".

Value

A vector or a matrix depending on the length of the values of \(\alpha\) and the type of the correlation to be computed.

Details

The \(\alpha\)-transformation is applied to each composition and then the distance correlation or the canonical correlation is computed. If one value of \(\alpha\) is supplied the type="cancor" will return all eigenvalues. If more than one values of \(\alpha\) are provided then the first eigenvalue only will be returned.

References

G.J. Szekely, M.L. Rizzo and N. K. Bakirov (2007). Measuring and Testing Independence by Correlation of Distances. Annals of Statistics, 35(6): 2769-2794.

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

See Also

acor.tune, aeqdist.etest, alfa, alfa.profile

Examples

# NOT RUN {
y <- rdiri(30, runif(3) )
x <- rdiri(30, runif(4) )
acor(y, x, a = 0.4)
# }