ilr. mkin 0.9.44.9000

Usage

ilr(x) invilr(x)

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Arguments

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

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Description

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

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Value

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

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References

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

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Examples

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

- - René Lehmann and Johannes Ranke - - -

- Function to perform isometric log-ratio transformation -