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authorJohannes Ranke <jranke@uni-bremen.de>2015-11-09 09:05:15 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2015-11-09 09:05:15 +0100
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+ René Lehmann and Johannes Ranke
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+ <header>
+
+ </header>
+
+ <h1>
+ Function to perform isometric log-ratio transformation
+</h1>
+
+<div class="row">
+ <div class="span8">
+ <h2>Usage</h2>
+ <pre><div>ilr(x) invilr(x)</div></pre>
+
+ <h2>Arguments</h2>
+ <dl>
+ <dt>x</dt>
+ <dd>
+ A numeric vector. Naturally, the forward transformation is only sensible for
+ vectors with all elements being greater than zero.
+ </dd>
+ </dl>
+
+ <div class="Description">
+ <h2>Description</h2>
+
+ <p>This implementation is a special case of the class of isometric log-ratio transformations.</p>
+
+ </div>
+
+ <div class="Value">
+ <h2>Value</h2>
+
+ <p><dl>
+ The result of the forward or backward transformation. The returned components always
+ sum to 1 for the case of the inverse log-ratio transformation.
+</dl></p>
+
+ </div>
+
+ <div class="References">
+ <h2>References</h2>
+
+ <p>Peter Filzmoser, Karel Hron (2008) Outlier Detection for Compositional Data Using Robust Methods. Math Geosci 40 233-248</p>
+
+ </div>
+
+ <h2 id="examples">Examples</h2>
+ <pre class="examples"><div class='input'># Order matters
+ilr(c(0.1, 1, 10))
+</div>
+<div class='output'>[1] -1.628174 -2.820079
+</div>
+<div class='input'>ilr(c(10, 1, 0.1))
+</div>
+<div class='output'>[1] 1.628174 2.820079
+</div>
+<div class='input'># Equal entries give ilr transformations with zeros as elements
+ilr(c(3, 3, 3))
+</div>
+<div class='output'>[1] 0 0
+</div>
+<div class='input'># Almost equal entries give small numbers
+ilr(c(0.3, 0.4, 0.3))
+</div>
+<div class='output'>[1] -0.2034219 0.1174457
+</div>
+<div class='input'># Only the ratio between the numbers counts, not their sum
+invilr(ilr(c(0.7, 0.29, 0.01)))
+</div>
+<div class='output'>[1] 0.70 0.29 0.01
+</div>
+<div class='input'>invilr(ilr(2.1 * c(0.7, 0.29, 0.01)))
+</div>
+<div class='output'>[1] 0.70 0.29 0.01
+</div>
+<div class='input'># Inverse transformation of larger numbers gives unequal elements
+invilr(-10)
+</div>
+<div class='output'>[1] 7.213536e-07 9.999993e-01
+</div>
+<div class='input'>invilr(c(-10, 0))
+</div>
+<div class='output'>[1] 7.207415e-07 9.991507e-01 8.486044e-04
+</div>
+<div class='input'># The sum of the elements of the inverse ilr is 1
+sum(invilr(c(-10, 0)))
+</div>
+<div class='output'>[1] 1
+</div>
+<div class='input'># This is why we do not need all elements of the inverse transformation to go back:
+a &lt;- c(0.1, 0.3, 0.5)
+b &lt;- invilr(a)
+length(b) # Four elements
+</div>
+<div class='output'>[1] 4
+</div>
+<div class='input'>ilr(c(b[1:3], 1 - sum(b[1:3]))) # Gives c(0.1, 0.3, 0.5)
+</div>
+<div class='output'>[1] 0.1 0.3 0.5
+</div></pre>
+ </div>
+ <div class="span4">
+ <!-- <ul>
+ <li>ilr</li><li>invilr</li>
+ </ul>
+ <ul>
+ <li> manip </li>
+ </ul> -->
+
+ <h2>See also</h2>
+
+ Another implementation can be found in R package <code>robCompositions</code>.
+
+
+ <h2>Author</h2>
+
+ René Lehmann and Johannes Ranke
+
+
+ </div>
+</div>
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