The method to construct principal balances based on PLS is introduced in the paper "Nesrstová, V, Wilms, I, Palarea-Albaladejo, J, et al. Principal balances of compositional data for regression and classification using partial least squares. Journal of Chemometrics. 2023; 37(12):e3518."

Calculations were performed in following software, using the listed libraries:

• R version: 4.1.3 (2022-03-10) -- "One Push-Up"
• Essential libraries:
  • pls: for PLS; version 2.8-0
  • compositions: to handle compositional data (CoDa); version 2.0-4
  • selbal: version 0.1.0

1. Scripts with functions:

a) Functions for PLS PBs:

fBalChip_PLS.R -> Main function to obtain PLS PBs -> calls the following 3 functions within its code

fBPMaxOrthNewChip_PLS.R

fBalChipman_PLS.R

fBPUpChi_PLS.r

Functions to calculate the original PCA PBs introduced in "J. A. Martín-Fernández, V. Pawlowsky-Glahn, J. J. Egozcue, and R. Tolosona-Delgado. Advances in principal balances for compositional data. Mathematical Geosciences, 50(3):273–298, 2018." are also available at http://www.compositionaldata.com

fBalChip.R -> Main function to obtain PCA PBs -> calls the following 3 functions within its code

fBPMaxOrthNewChip.R

fBalChipman.R

fBPUpChi.r

b) Auxiliary functions: Auxiliary_functions.R

2. Simulation scripts

Each simulation scenario is in a separate script. Each script covers CV and the comparison of first balances in for PCA PBs, PLS PBs and Selbal.

• Sim_1.R: one block of markers
• Sim_2.R: 4 same-sized blocks of markers
• Sim_3.R: different-sized blocks of markers

3. An easy-to-use toy example

Model_example.R

An easy-to-use script, which shows how to use the function fBalChip_PLS to obtain PLS PBs. CoDa data set X is generated via ilr coordinates.