ilr_basis function

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

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

for $i \in 1\ldots k$.

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.

Returns

matrix

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

for $i \in 1\ldots k$.

Details

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

Examples

ilr_basis(5)

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