ilr {compositions} | R Documentation |

## Isometric log ratio transform

### Description

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

### Usage

```
ilr( x , V = ilrBase(x) ,...)
ilrInv( z , V = ilrBase(z=z),..., orig=gsi.orig(z))
```

### Arguments

`x` |
a composition, not necessarily closed |

`z` |
the ilr-transform of a composition |

`V` |
a matrix, with columns giving the chosen basis of the clr-plane |

`...` |
generic arguments. not used. |

`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 ilr-transform maps a composition in the D-part Aitchison-simplex
isometrically to a D-1 dimensonal euclidian vector. The data can then
be analysed in this transformation by all classical multivariate
analysis tools. However the interpretation of the results may be
difficult, since there is no one-to-one relation between the original parts
and the transformed variables.

The isometric logratio transform is given by

` ilr(x) := V^t clr(x) `

with `clr`

(x) the centred log ratio transform and
`V\in R^{d \times (d-1)}`

a matrix which columns form an orthonormal
basis of the clr-plane. A default matrix `V`

is given by
`ilrBase(`

.
`D`)

### Value

`ilr`

gives the isometric log ratio transform,
`ilrInv`

gives closed compositions with the given ilr-transforms

### Author(s)

K.Gerald v.d. Boogaart http://www.stat.boogaart.de, Raimon Tolosana-Delgado

### References

Egozcue J.J., V. Pawlowsky-Glahn, G. Mateu-Figueras and
C. Barcel'o-Vidal (2003) Isometric logratio transformations for
compositional data analysis. *Mathematical Geology*, **35**(3)
279-300

Aitchison, J, C. Barcel'o-Vidal, J.J. Egozcue, V. Pawlowsky-Glahn
(2002) A consise guide to the algebraic geometric structure of the
simplex, the sample space for compositional data analysis, *Terra
Nostra*, Schriften der Alfred Wegener-Stiftung, 03/2003

https://ima.udg.edu/Activitats/CoDaWork03/

### See Also

### Examples

```
(tmp <- ilr(c(1,2,3)))
ilrInv(tmp)
ilrInv(tmp) - clo(c(1,2,3)) # 0
data(Hydrochem)
cdata <- Hydrochem[,6:19]
pairs(ilr(cdata))
ilrBase(D=3)
```

*compositions*version 2.0-8 Index]