ilr. mkin 0.9-41

Usage

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. +

+ +

Description

+ +

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

+ +

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. +

+ +

References

+ +

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

+ +

Examples

# Order matters
+ilr(c(0.1, 1, 10))
+
+[1] -1.628174 -2.820079
+
+ilr(c(10, 1, 0.1))
+
+[1] 1.628174 2.820079
+
+# Equal entries give ilr transformations with zeros as elements
+ilr(c(3, 3, 3))
+
+[1] 0 0
+
+# Almost equal entries give small numbers
+ilr(c(0.3, 0.4, 0.3))
+
+[1] -0.2034219  0.1174457
+
+# Only the ratio between the numbers counts, not their sum
+invilr(ilr(c(0.7, 0.29, 0.01)))
+
+[1] 0.70 0.29 0.01
+
+invilr(ilr(2.1 * c(0.7, 0.29, 0.01)))
+
+[1] 0.70 0.29 0.01
+
+# Inverse transformation of larger numbers gives unequal elements
+invilr(-10)
+
+[1] 7.213536e-07 9.999993e-01
+
+invilr(c(-10, 0))
+
+[1] 7.207415e-07 9.991507e-01 8.486044e-04
+
+# The sum of the elements of the inverse ilr is 1
+sum(invilr(c(-10, 0)))
+
+[1] 1
+
+# 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
+
+[1] 4
+
+ilr(c(b[1:3], 1 - sum(b[1:3]))) # Gives c(0.1, 0.3, 0.5)
+
+[1] 0.1 0.3 0.5
+

+ + +

Author

+ + René Lehmann and Johannes Ranke + + +

+ Function to perform isometric log-ratio transformation +