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<meta property="og:description" content="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
inverse.predict, and L is obtained by iteration." />
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<h1>Estimate a limit of quantification (LOQ)</h1>
<div class="hidden name"><code>loq.Rd</code></div>
</div>
<div class="ref-description">
<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>
<pre class="usage"><span class='fu'>loq</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span>, alpha <span class='op'>=</span> <span class='fl'>0.05</span>, k <span class='op'>=</span> <span class='fl'>3</span>, n <span class='op'>=</span> <span class='fl'>1</span>, w.loq <span class='op'>=</span> <span class='st'>"auto"</span>,
var.loq <span class='op'>=</span> <span class='st'>"auto"</span>, tol <span class='op'>=</span> <span class='st'>"default"</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>object</th>
<td><p>A univariate model object of class <code><a href='https://rdrr.io/r/stats/lm.html'>lm</a></code> or
<code><a href='https://rdrr.io/pkg/MASS/man/rlm.html'>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.</p></td>
</tr>
<tr>
<th>alpha</th>
<td><p>The error tolerance for the prediction of x values in the calculation.</p></td>
</tr>
<tr>
<th>...</th>
<td><p>Placeholder for further arguments that might be needed by
future implementations.</p></td>
</tr>
<tr>
<th>k</th>
<td><p>The inverse of the maximum relative error tolerated at the
desired LOQ.</p></td>
</tr>
<tr>
<th>n</th>
<td><p>The number of replicate measurements for which the LOQ should be
specified.</p></td>
</tr>
<tr>
<th>w.loq</th>
<td><p>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.</p></td>
</tr>
<tr>
<th>var.loq</th>
<td><p>The approximate variance at the LOQ. The default value is
calculated from the model.</p></td>
</tr>
<tr>
<th>tol</th>
<td><p>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.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>The estimated limit of quantification for a model used for calibration.</p>
<h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>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>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p>Examples for <code><a href='din32645.html'>din32645</a></code></p></div>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='va'>m</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span><span class='op'>(</span><span class='va'>y</span> <span class='op'>~</span> <span class='va'>x</span>, data <span class='op'>=</span> <span class='va'>massart97ex1</span><span class='op'>)</span>
<span class='fu'>loq</span><span class='op'>(</span><span class='va'>m</span><span class='op'>)</span>
</div><div class='output co'>#> $x
#> [1] 13.97764
#>
#> $y
#> [1] 30.6235
#> </div><div class='input'>
<span class='co'># We can get better by using replicate measurements</span>
<span class='fu'>loq</span><span class='op'>(</span><span class='va'>m</span>, n <span class='op'>=</span> <span class='fl'>3</span><span class='op'>)</span>
</div><div class='output co'>#> $x
#> [1] 9.971963
#>
#> $y
#> [1] 22.68539
#> </div></pre>
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