Additive Log-Ratios (ALR)

Computes ALR transformation.

Usage

transform_alr(object, ...)

# S4 method for class 'CompositionMatrix'
transform_alr(object, j = ncol(object), weights = FALSE)

# S4 method for class 'GroupedComposition'
transform_alr(object, j = ncol(object), weights = FALSE)

# S4 method for class 'CLR'
transform_alr(object, j = ncol(object))

# S4 method for class 'GroupedCLR'
transform_alr(object, j = ncol(object), weights = FALSE)

Arguments

object

A CompositionMatrix object.

...

Currently not used.

j

An integer giving the index of the rationing part (denominator).

weights

A logical scalar: should varying weights (column means) be computed? If FALSE (the default), equally-weighted parts are used. Alternatively, a positive numeric vector of weights can be specified (will be rescaled to sum to \(1\)). Weights will be used internally by other methods (e.g. variance()).

Value

An ALR object.

Details

The ALR transformation is the logratio of a pair of parts with respect to a fixed part.

References

Aitchison, J. (1986). The Statistical Analysis of Compositional Data. London: Chapman and Hall.

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_clr(), transform_ilr(), transform_inverse(), transform_lr(), transform_plr()

Author

N. Frerebeau

Examples

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

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

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

## Inverse transformation
inv_alr <- transform_inverse(alr)
all.equal(coda, inv_alr)
#> [1] TRUE