ilr_basis {coda.base}

Isometric/Orthonormal log-ratio basis for log-transformed compositions.

Description

By default the basis of the clr-given by Egozcue et al., 2013 Build an isometric log-ratio basis for a composition with k+1 parts

h_i = \sqrt{\frac{i}{i+1}} \log\frac{\sqrt[i]{\prod_{j=1}^i x_j}}{x_{i+1}}

for i \in 1\ldots k.

Usage

ilr_basis(dim, type = "default")

olr_basis(dim, type = "default")

Arguments

dim

number of components

type

if different than 'pivot' (pivot balances) or 'cdp' (codapack balances) default balances are returned, which computes a triangular Helmert matrix as defined by Egozcue et al., 2013.

Details

Modifying parameter type (pivot or cdp) other ilr/olr basis can be generated

Value

matrix

References

Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G. and Barceló-Vidal C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3) 279-300

Examples

ilr_basis(5)