ilr {intervalpsych} | R Documentation |
Log-Ratio transformations for interval responses
Description
Transform interval responses from the simplex space to the unbounded space
using either Isometric Log-Ratio (ILR) or Sum Log-Ratio (SLR)
transformations, as described by Smithson & Broomell (2024).
These transformations preserve the dimensional conceptualization of the
interval responses in terms of a location and a width.
See also inv_ilr()
, inv_slr()
for the inverse transformations.
ILR
The ILR transformation equations are:
x_{loc} = \sqrt{\frac{1}{2}} \log\left(\frac{x_1}{x_3}\right)
x_{wid} = \sqrt{\frac{2}{3}} \log\left(\frac{x_2}{\sqrt{x_1 x_3}}\right)
SLR
The SLR transformation equations are:
x_{loc} = \log\left(\frac{x_1}{x_3}\right)
x_{wid} = \log\left(\frac{x_2}{x_1 + x_3}\right)
where (x_1, x_2, x_3)
is the interval response in the simplex format
and (x_{loc}, x_{wid})
are the transformed values representing the
unbounded location and width.
Usage
ilr(simplex)
slr(simplex)
Arguments
simplex |
A numeric vector that is a 2-simplex (3 elements that sum to 1) or a dataframe where each of the rows is a 2-simplex. |
Value
A numeric vector with 2 elements, the unbounded interval location and width, or a dataframe where each of the rows is a numeric vector with these 2 elements.
References
Smithson, M., & Broomell, S. B. (2024). Compositional data analysis tutorial. Psychological Methods, 29(2), 362–378.
See Also
Examples
# Generate some simplex data
simplex <- data.frame(rbind(c(.1, .2, .7), c(.4, .5, .1)))
# ILR transformation
ilr(simplex)
# SLR transformation
slr(simplex)