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diff --git a/docs/loq.html b/docs/loq.html new file mode 100644 index 0000000..352737f --- /dev/null +++ b/docs/loq.html @@ -0,0 +1,191 @@ +<!DOCTYPE html> +<html lang="en"> + <head> + <meta charset="utf-8"> +<title>loq. chemCal 0.1-37</title> +<meta name="viewport" content="width=device-width, initial-scale=1.0"> +<meta name="author" content=""> + +<link href="css/bootstrap.css" rel="stylesheet"> +<link href="css/bootstrap-responsive.css" rel="stylesheet"> +<link href="css/highlight.css" rel="stylesheet"> +<link href="css/staticdocs.css" rel="stylesheet"> + +<!--[if lt IE 9]> + <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script> +<![endif]--> + +<script type="text/x-mathjax-config"> + MathJax.Hub.Config({ + tex2jax: { + inlineMath: [ ['$','$'], ["\\(","\\)"] ], + processEscapes: true + } + }); +</script> +<script type="text/javascript" + src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> +</script> + </head> + + <body> + <div class="navbar"> + <div class="navbar-inner"> + <div class="container"> + <a class="brand" href="index.html">chemCal 0.1-37</a> + <div class="nav"> + <ul class="nav"> + <li><a href="index.html">Home</a></li> + <li><a href="reference.html">Reference</a></li> + </ul> + </div> + </div> + </div> +</div> + + + <div class="container"> + <header> + + </header> + + <h1>Estimate a limit of quantification (LOQ)</h1> + +<div class="row"> + <div class="span8"> + <h2>Usage</h2> + <pre><span class="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">object</span><span class="keyword">,</span> <span class="symbol">...</span><span class="keyword">,</span> <span class="argument">alpha</span> <span class="argument">=</span> <span class="number">0.05</span><span class="keyword">,</span> <span class="argument">k</span> <span class="argument">=</span> <span class="number">3</span><span class="keyword">,</span> <span class="argument">n</span> <span class="argument">=</span> <span class="number">1</span><span class="keyword">,</span> <span class="argument">w.loq</span> <span class="argument">=</span> <span class="string">"auto"</span><span class="keyword">,</span> + <span class="argument">var.loq</span> <span class="argument">=</span> <span class="string">"auto"</span><span class="keyword">,</span> <span class="argument">tol</span> <span class="argument">=</span> <span class="string">"default"</span><span class="keyword">)</span></pre> + + <h2>Arguments</h2> + <dl> + <dt>object</dt> + <dd> + A univariate model object of class <code><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></code> or + <code><a href='http://www.rdocumentation.org/packages/MASS/topics/rlm'>rlm</a></code> + with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>, + optionally from a weighted regression. If weights are specified + in the model, either <code>w.loq</code> or <code>var.loq</code> have to + be specified. + </dd> + <dt>alpha</dt> + <dd> + The error tolerance for the prediction of x values in the calculation. + </dd> + <dt>...</dt> + <dd> + Placeholder for further arguments that might be needed by + future implementations. + </dd> + <dt>k</dt> + <dd> + The inverse of the maximum relative error tolerated at the + desired LOQ. + </dd> + <dt>n</dt> + <dd> + The number of replicate measurements for which the LOQ should be + specified. + </dd> + <dt>w.loq</dt> + <dd> + The weight that should be attributed to the LOQ. Defaults + to one for unweighted regression, and to the mean of the weights + for weighted regression. See <code><a href='massart97ex3.html'>massart97ex3</a></code> for + an example how to take advantage of knowledge about the + variance function. + </dd> + <dt>var.loq</dt> + <dd> + The approximate variance at the LOQ. The default value is + calculated from the model. + </dd> + <dt>tol</dt> + <dd> + The default tolerance for the LOQ on the x scale is the value of the + smallest non-zero standard divided by 1000. Can be set to a + numeric value to override this. + </dd> + </dl> + + <div class="Value"> + <h2>Value</h2> + + <p><dl> + The estimated limit of quantification for a model used for calibration. +</dl></p> + + </div> + + <div class="Description"> + <h2>Description</h2> + + <p>The limit of quantification is the x value, where the relative error + of the quantification given the calibration model reaches a prespecified + value 1/k. Thus, it is the solution of the equation + $$L = k c(L)$$ + where c(L) is half of the length of the confidence interval at the limit L + (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by + <code><a href='inverse.predict.html'>inverse.predict</a></code>, and L is obtained by iteration.</p> + + </div> + + <div class="Note"> + <h2>Note</h2> + + <p>- IUPAC recommends to base the LOQ on the standard deviation of the signal + where x = 0. + - The calculation of a LOQ based on weighted regression is non-standard + and therefore not tested. Feedback is welcome.</p> + + </div> + + <h2 id="examples">Examples</h2> + <pre class="examples"><div class='input'><span class="functioncall"><a href='http://www.rdocumentation.org/packages/utils/topics/data'>data</a></span><span class="keyword">(</span><span class="symbol">massart97ex3</span><span class="keyword">)</span> +<span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/attach'>attach</a></span><span class="keyword">(</span><span class="symbol">massart97ex3</span><span class="keyword">)</span> +<span class="symbol">m</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></span><span class="keyword">(</span><span class="symbol">y</span> <span class="keyword">~</span> <span class="symbol">x</span><span class="keyword">)</span> +<span class="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">)</span></div> +<div class='output'>$x +[1] 13.97764 + +$y + 1 +30.6235 + +</div> +<div class='input'> +<span class="comment"># We can get better by using replicate measurements</span> +<span class="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="argument">n</span> <span class="argument">=</span> <span class="number">3</span><span class="keyword">)</span></div> +<div class='output'>$x +[1] 9.971963 + +$y + 1 +22.68539 + +</div></pre> + </div> + <div class="span4 sidebar"> + <!-- <ul> + <li>loq</li><li>loq.lm</li><li>loq.rlm</li><li>loq.default</li> + </ul> + <ul> + <li>manip</li> + </ul> --> + + <h2>See also</h2> + <p>Examples for <code><a href='din32645.html'>din32645</a></code></p> + + + + + </div> +</div> + + <footer> + <p class="pull-right"><a href="#">Back to top</a></p> +<p>Built by <a href="https://github.com/hadley/staticdocs">staticdocs</a>. 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