`coda.base` features' enumeration
In coda.base: A Basic Set of Functions for Compositional Data Analysis

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(coda.base)

Main functions

Simulated data set:

nP = 6
nO = 8
set.seed(1)
X = matrix(rlnorm(nP * nO), ncol = nP, nrow = nO)
colnames(X) = paste0('P', 1:nP)
rownames(X) = paste0('O', 1:nO)
X

Descriptive statistics

Center:

center(X)

Variation array:

variation_array(X)

Aitchison distances between compositions

stats::dist() is rewritten to include the Aitchison distance between compositions:

dist(X, method = 'aitchison')

Log-ratio coordinates. `coordinates()`

coordinates(X)

By default, coda.base uses the isometric log-ratio coordinates defined in Egozcue et al. 2003.

coordinates(X, 'ilr'): isometric log-ratio coordinates (Egozcue et al. 2003, defaults)
coordinates(X, 'olr'): orthonormal log-ratio coordinates (equivalent to ilr)
coordinates(X, 'alr'): additive log-ratio coordinates
coordinates(X, 'clr'): centered log-ratio coordinates
coordinates(X, 'pw'): pairwise log-ratio coordinates
coordinates(X, 'pc'): principal component coordinates
coordinates(X, 'pb'): principal balance coordinates
coordinates(X, 'cdp'): balanced isometric log-ratio coordinates

To reduce typing, alr_c(), clr_c(), ilr_c() and olr_c() are functions that call coordinates() function with the option given by their name.

coordinates(X, B) accepts a log-contrast matrix $B$ to build the log-ratio coordinates. Different log-contrast matrices $B$ can be constructed (following section).

Functions to build log-contrast matrices

ilr_basis(nP)

all.equal(as.numeric(coordinates(X, 'ilr')),
          as.numeric(log(X) %*% ilr_basis(nP)))

Log-ratio matrix transformations:

ilr_basis(nP) or olr_basis(nP) (Egozcue et al. 2003, defaults)
ilr_basis(nP, type = 'pivot') or olr_basis(nP, type = 'pivot') to pivot log-ratio coordinates
ilr_basis(nP, type = 'cdp') or olr_basis(nP, type = 'cdp') to balanced log-ratio coordinates (CoDaPack's default)
alr_basis(nP) to additive-log ratio coordinates. Numerator order and denominator can be modified. For example, alr_basis(nP, denominator = 1, numerator = nP:2).
clr_basis(nP) to centered log-ratio coordinates.
pc_basis(X) to principal components log-ratio coordinates.
cc_basis(X, X2) to canonical correlations log-ratio coordinates.
pb_basis(X, method = 'exact') to principal balances using the exact algorithm.
pb_basis(X, method = 'constrained') to principal balances using pca constrained algorithm.
pb_basis(X, method = 'cluster') to principal balances obtained using parts clustering algorithm.
pairwise_basis(nP) to pairwise log-ratio coordinates.
sbp_basis(b0 = b1~b2, b1 = P1~P2+P3, b2 = P4~P5+P6, data=X)