R: Centered log ratio transform

clr {compositions} | R Documentation

## Centered log ratio transform

### Description

Compute the centered log ratio transform of a (dataset of) composition(s) and its inverse.

### Usage

              clr( x,... )
              clrInv( z,... )

### Arguments

`x` | a composition or a data matrix of compositions, not necessarily closed
`z` | the clr-transform of a composition or a data matrix of clr-transforms of compositions, not necessarily centered (i.e. summing up to zero)
`...` | for generic use only

### Details

The clr-transform maps a composition in the D-part Aitchison-simplex isometrically to a D-dimensonal euclidian vector subspace: consequently, the transformation is not injective. Thus resulting covariance matrices are always singular.
The data can then be analysed in this transformation by all classical multivariate analysis tools not relying on a full rank of the covariance. See `ilr` and `alr` for alternatives. The interpretation of the results is relatively easy since the relation between each original part and a transformed variable is preserved.
The centered logratio transform is given by

clr(x) := (\emph{ln} \bold{x} - mean(\emph{ln} \bold{x}) )

The image of the `clr` is a vector with entries summing to 0. This hyperplane is also called the clr-plane.

### Value

`clr` gives the centered log ratio transform, `clrInv` gives closed compositions with the given clr-transform

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de

### References

Aitchison, J. (1986) The Statistical Analysis of Compositional Data, Monographs on Statistics and Applied Probability. Chapman & Hall Ltd., London (UK). 416p.

### See Also

`ilr`,`alr`,`apt`

### Examples

    (tmp <- clr(c(1,2,3)))
    clrInv(tmp)
    clrInv(tmp) - clo(c(1,2,3)) # 0
    data(Hydrochem)
    cdata <- Hydrochem[,6:19]
    pairs(clr(cdata),pch=".")

[Package compositions version 1.40-5 Index]