ilr: Function to perform isometric log-ratio transformation In mkin: Kinetic Evaluation of Chemical Degradation Data

Description

This implementation is a special case of the class of isometric log-ratio transformations.

Usage

 ```1 2``` ``` ilr(x) invilr(x) ```

Arguments

 `x` A numeric vector. Naturally, the forward transformation is only sensible for vectors with all elements being greater than zero.

Value

The result of the forward or backward transformation. The returned components always sum to 1 for the case of the inverse log-ratio transformation.

Author(s)

René Lehmann and Johannes Ranke

References

Peter Filzmoser, Karel Hron (2008) Outlier Detection for Compositional Data Using Robust Methods. Math Geosci 40 233-248

Another implementation can be found in R package `robCompositions`.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# Order matters ilr(c(0.1, 1, 10)) ilr(c(10, 1, 0.1)) # Equal entries give ilr transformations with zeros as elements ilr(c(3, 3, 3)) # Almost equal entries give small numbers ilr(c(0.3, 0.4, 0.3)) # Only the ratio between the numbers counts, not their sum invilr(ilr(c(0.7, 0.29, 0.01))) invilr(ilr(2.1 * c(0.7, 0.29, 0.01))) # Inverse transformation of larger numbers gives unequal elements invilr(-10) invilr(c(-10, 0)) # The sum of the elements of the inverse ilr is 1 sum(invilr(c(-10, 0))) # This is why we do not need all elements of the inverse transformation to go back: a <- c(0.1, 0.3, 0.5) b <- invilr(a) length(b) # Four elements ilr(c(b[1:3], 1 - sum(b[1:3]))) # Gives c(0.1, 0.3, 0.5) ```

Example output

```Loading required package: minpack.lm
[1] -1.628174 -2.820079
[1] 1.628174 2.820079
[1] 0 0
[1] -0.2034219  0.1174457
[1] 0.70 0.29 0.01
[1] 0.70 0.29 0.01
[1] 7.213536e-07 9.999993e-01
[1] 7.207415e-07 9.991507e-01 8.486044e-04
[1] 1
[1] 4
[1] 0.1 0.3 0.5
```

mkin documentation built on Feb. 9, 2018, 6:08 a.m.