coda.base

Compositional Bases for Log-Ratio Transformations

This R package provides tools for working with compositional data using log-ratio methodology, following the foundational work of Aitchison and further developments by Egozcue and collaborators.

The package is focused on the construction and use of orthonormal and non-orthonormal bases for the representation of compositions in real coordinates, enabling advanced statistical modeling and interpretation.

Key Functions

• ilr_basis(), alr_basis(), clr_basis() – classical log-ratio bases:

  • ILR/OLR (Isometric/Orthonormal Log-Ratio): orthonormal basis.
  • ALR (Additive Log-Ratio): basis with respect to a reference part.
  • CLR (Centered Log-Ratio): non-orthonormal, but symmetrically treats all parts.

• pc_basis(), pb_basis(), pw_basis() – domain-specific and data-driven bases:

  • PC basis: based on principal component analysis of log-ratio coordinates.
  • PB basis (Principal balances): variability explain by balances.
  • PW (Pairwise Log-Ratios): pairwise comparisons.

• coordinates(x, basis): expresses a composition x in coordinates with respect to a given basis.

• composition(z, basis): reconstructs a composition from coordinates z and the associated basis.

Example

library(coda.base)

# Define a simple 3-part composition
x <- c('a' = 0.2, 'b' = 0.3, 'c' = 0.5)

# Create an ILR basis and express x in ILR coordinates
B <- ilr_basis(x)
h <- coordinates(x, B)  
h

# Recover the original composition
composition(h, B)

Installation

You can install the development version from GitHub:

# Install development version from GitHub
remotes::install_github("mcomas/coda.base")

and the cran version with:

# Install release version from CRAN
install.packages("coda.base")