inv_ilr {intervalpsych}R Documentation

Inverse Log-Ratio transformations for interval responses

Description

Transform unbounded data back to the simplex space using either Isometric Log-Ratio (ILR) or Sum Log-Ratio (SLR) inverse transformations, as described by Smithson & Broomell (2024). These transformations are the inverse transformations of ilr() and slr().

Inverse ILR

The inverse ILR transformation equations are:

x_1 = \frac{\exp(\sqrt{2} x_{loc})}{\exp(\sqrt{2} x_{loc}) + \exp(\sqrt{\frac{3}{2}} x_{wid} + \frac{x_{loc}}{\sqrt{2}}) + 1}

x_2 = \frac{\exp(\sqrt{\frac{3}{2}} x_{wid} + \frac{x_{loc}}{\sqrt{2}})}{\exp(\sqrt{2} x_{loc}) + \exp(\sqrt{\frac{3}{2}} x_{wid} + \frac{x_{loc}}{\sqrt{2}}) + 1}

x_3 = \frac{1}{\exp(\sqrt{2} x_{loc}) + \exp(\sqrt{\frac{3}{2}} x_{wid} + \frac{x_{loc}}{\sqrt{2}}) + 1}

Inverse SLR

The inverse SLR transformation equations are:

x_1 = \frac{\exp(x_{loc})}{(\exp(x_{loc}) + 1)(\exp(x_{wid}) + 1)}

x_2 = \frac{\exp(x_{wid})}{\exp(x_{wid}) + 1}

x_3 = \frac{1}{(\exp(x_{loc}) + 1)(\exp(x_{wid}) + 1)}

where (x_{loc}, x_{wid}) are the unbounded interval location and width and (x_1, x_2, x_3) is the resulting interval response in the simplex format.

Usage

inv_ilr(bvn)

inv_slr(bvn)

Arguments

bvn

A numeric vector containing an unbounded interval location and width or a dataframe where each of the rows consists of such a vector.

Value

A numeric vector containing a 2-simplex or a dataframe where each of the rows consists of such a vector.

References

Smithson, M., & Broomell, S. B. (2024). Compositional data analysis tutorial. Psychological Methods, 29(2), 362–378.

See Also

ilr(), slr()

Examples

# Generate some unbounded data
bvn <- data.frame(rbind(c(0, .2), c(-2, .4)))

# Inverse ILR transformation
inv_ilr(bvn)

# Inverse SLR transformation
inv_slr(bvn)



[Package intervalpsych version 0.1.0 Index]