transform_ilr {nexus}

Isometric Log-Ratios (ILR)

Description

Computes ILR transformations.

Usage

transform_ilr(object, base, ...)

## S4 method for signature 'CompositionMatrix,missing'
transform_ilr(object)

## S4 method for signature 'CompositionMatrix,matrix'
transform_ilr(object, base)

Arguments

object

A CompositionMatrix object.

base

A matrix giving the base of the transformation.

...

Currently not used.

Details

The ILR transformation provides the coordinates of any composition with respect to a given orthonormal basis. transform_ilr() uses the orthonormal basis (Helmert matrix) originally defined by Egozcue et al. (2003).

Value

An ILR object.

Author(s)

N. Frerebeau

References

Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G. & Barceló-Vidal, C. (2003). Isometric Logratio Transformations for Compositional Data Analysis. Mathematical Geology, 35(3), 279-300. doi:10.1023/A:1023818214614.

Greenacre, M. J. (2019). Compositional Data Analysis in Practice. Boca Raton: CRC Press.

Greenacre, M. J. (2021). Compositional Data Analysis. Annual Review of Statistics and Its Application, 8(1): 271-299. doi:10.1146/annurev-statistics-042720-124436.

See Also

Other log-ratio transformations: transform_alr(), transform_clr(), transform_inverse(), transform_lr(), transform_plr()

Examples

## Data from Aitchison 1986
data("hongite")

## Coerce to compositional data
coda <- as_composition(hongite)

## Pairwise log-ratio
lr <- transform_lr(coda)

## Centered log-ratio
clr <- transform_clr(coda)

## Additive log-ratio
alr <- transform_alr(coda)

## Isometric log-ratio
ilr <- transform_ilr(coda)
plr <- transform_plr(coda)

## Inverse transformation
inv_clr <- transform_inverse(clr)
all.equal(coda, inv_clr)

inv_alr <- transform_inverse(alr)
all.equal(coda, inv_alr)

inv_ilr <- transform_inverse(ilr)
all.equal(coda, inv_ilr)

inv_plr <- transform_inverse(plr)
all.equal(coda, inv_plr)