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      <h1>Estimate a limit of quantification (LOQ)</h1>

<div class="row">
  <div class="span8">
    <h2>Usage</h2>
    <pre><div>loq(object, ..., alpha&nbsp;=&nbsp;0.05, k&nbsp;=&nbsp;3, n&nbsp;=&nbsp;1, w.loq&nbsp;=&nbsp;"auto", var.loq&nbsp;=&nbsp;"auto", tol&nbsp;=&nbsp;"default")</div></pre>
    
    <h2>Arguments</h2>
    <dl>
      <dt>object</dt>
      <dd>
    A univariate model object of class <code><a href='http://www.inside-r.org/r-doc/stats/lm'>lm</a></code> or 
    <code><a href='http://www.inside-r.org/r-doc/MASS/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'>data(massart97ex3)
attach(massart97ex3)
m &lt;- lm(y ~ x)
loq(m)
</div>
<div class='output'>$x
[1] 13.97764

$y
      1 
30.6235 

</div>
<div class='input'>
# We can get better by using replicate measurements
loq(m, n = 3)
</div>
<div class='output'>$x
[1] 9.971963

$y
       1 
22.68539 

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

        
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