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,..., orig=gsi.orig(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 |

`orig` |
a compositional object which should be mimicked by the inverse transformation. It is especially used to reconstruct the names of the parts. |

### 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) := \left(\ln x_i - \frac1D \sum_{j=1}^D \ln x_j\right)_i `

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

### 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=".")
```

*compositions*version 2.0-8 Index]