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<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>
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<h2>See also</h2>
<p>Examples for <code><a href='din32645.html'>din32645</a></code></p>
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