bpc: Backwards pivot coordinates and their inverse

In robCompositions: Compositional Data Analysis

Backwards pivot coordinates and their inverse

Description

Backwards pivot coordinate representation of a set of compositional ventors as a special case of isometric logratio coordinates and their inverse mapping.

Usage

bpc(X, base = exp(1))

Arguments

X	object of class data.frame. Positive values only.
base	a positive number: the base with respect to which logarithms are computed. Defaults to exp(1).

Details

bpc

Backwards pivot coordinates map D-part compositional data from the simplex into a (D-1)-dimensional real space isometrically. The first coordinate has form of pairwise logratio log(x2/x1) and serves as an alternative to additive logratio transformation with part x1 being the rationing element. The remaining coordinates are structured as detailed in Nesrstova et al. (2023). Consequently, when a specific pairwise logratio is of the main interest, the respective columns have to be placed at the first (the compositional part in denominator of the logratio, the rationing element) and the second position (the compositional part in numerator) in the data matrix X.

Value

Coordinates	array of orthonormal coordinates.
Coordinates.ortg	array of orthogonal coordinates (without the normalising constant sqrt(i/i+1).
Contrast.matrix	contrast matrix corresponding to the orthonormal coordinates.
Base	the base with respect to which logarithms are computed.
Levels	the order of compositional parts.

Author(s)

Kamila Facevicova

References

Hron, K., Coenders, G., Filzmoser, P., Palarea-Albaladejo, J., Famera, M., Matys Grygar, M. (2022). Analysing pairwise logratios revisited. Mathematical Geosciences 53, 1643 - 1666.

Nesrstova, V., Jaskova, P., Pavlu, I., Hron, K., Palarea-Albaladejo, J., Gaba, A., Pelclova, J., Facevicova, K. (2023). Simple enough, but not simpler: Reconsidering additive logratio coordinates in compositional analysis. Submitted

See Also

bpcTab bpcTabWrapper bpcPca bpcReg

Examples

data(expenditures)

# default setting with ln()
bpc(expenditures)

# logarithm of base 2
bpc(expenditures, base = 2)

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.