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<!DOCTYPE html>
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<h1>Calibration data from Massart et al. (1997), example 3</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/chemCal-package.R" class="external-link"><code>R/chemCal-package.R</code></a></small>
<div class="hidden name"><code>massart97ex3.Rd</code></div>
</div>
<div class="ref-description">
<p>Sample dataset from p. 188 to test the package.</p>
</div>
<div id="format">
<h2>Format</h2>
<p>A dataframe containing 6 levels of x values with 5 observations of y
for each level.</p>
</div>
<div id="source">
<h2>Source</h2>
<p>Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S.,
Lewi, P.J., Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and
Qualimetrics: Part A, Chapter 8.</p>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span>
<span class="r-in"><span class="co"># For reproducing the results for replicate standard measurements in example 8,</span></span>
<span class="r-in"><span class="co"># we need to do the calibration on the means when using chemCal > 0.2</span></span>
<span class="r-in"><span class="va">weights</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/with.html" class="external-link">with</a></span><span class="op">(</span><span class="va">massart97ex3</span>, <span class="op">{</span></span>
<span class="r-in"> <span class="va">yx</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/split.html" class="external-link">split</a></span><span class="op">(</span><span class="va">y</span>, <span class="va">x</span><span class="op">)</span></span>
<span class="r-in"> <span class="va">ybar</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">yx</span>, <span class="va">mean</span><span class="op">)</span></span>
<span class="r-in"> <span class="va">s</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/lapply.html" class="external-link">sapply</a></span><span class="op">(</span><span class="va">yx</span>, <span class="va">sd</span><span class="op">)</span>, digits <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span>
<span class="r-in"> <span class="va">w</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="fl">1</span> <span class="op">/</span> <span class="op">(</span><span class="va">s</span><span class="op">^</span><span class="fl">2</span><span class="op">)</span>, digits <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span>
<span class="r-in"><span class="op">}</span><span class="op">)</span></span>
<span class="r-in"></span>
<span class="r-in"><span class="va">massart97ex3.means</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/aggregate.html" class="external-link">aggregate</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, <span class="va">massart97ex3</span>, <span class="va">mean</span><span class="op">)</span></span>
<span class="r-in"></span>
<span class="r-in"><span class="va">m3.means</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, w <span class="op">=</span> <span class="va">weights</span>, data <span class="op">=</span> <span class="va">massart97ex3.means</span><span class="op">)</span></span>
<span class="r-in"></span>
<span class="r-in"><span class="co"># The following concords with the book p. 200</span></span>
<span class="r-in"><span class="fu"><a href="inverse.predict.html">inverse.predict</a></span><span class="op">(</span><span class="va">m3.means</span>, <span class="fl">15</span>, ws <span class="op">=</span> <span class="fl">1.67</span><span class="op">)</span> <span class="co"># 5.9 +- 2.5</span></span>
<span class="r-out co"><span class="r-pr">#></span> $Prediction</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 5.865367</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $`Standard Error`</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 0.8926109</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $Confidence</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 2.478285</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $`Confidence Limits`</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 3.387082 8.343652</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"><span class="fu"><a href="inverse.predict.html">inverse.predict</a></span><span class="op">(</span><span class="va">m3.means</span>, <span class="fl">90</span>, ws <span class="op">=</span> <span class="fl">0.145</span><span class="op">)</span> <span class="co"># 44.1 +- 7.9</span></span>
<span class="r-out co"><span class="r-pr">#></span> $Prediction</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 44.06025</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $`Standard Error`</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 2.829162</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $Confidence</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 7.855012</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $`Confidence Limits`</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 36.20523 51.91526</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"></span>
<span class="r-in"><span class="co"># The LOD is only calculated for models from unweighted regression</span></span>
<span class="r-in"><span class="co"># with this version of chemCal</span></span>
<span class="r-in"><span class="va">m0</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">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">massart97ex3</span><span class="op">)</span> </span>
<span class="r-in"><span class="fu"><a href="lod.html">lod</a></span><span class="op">(</span><span class="va">m0</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> $x</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 5.407085</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $y</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 13.63911</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"></span>
<span class="r-in"><span class="co"># Limit of quantification from unweighted regression</span></span>
<span class="r-in"><span class="fu"><a href="loq.html">loq</a></span><span class="op">(</span><span class="va">m0</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> $x</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 9.627349</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $y</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 22.00246</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"></span>
<span class="r-in"><span class="co"># For calculating the limit of quantification from a model from weighted</span></span>
<span class="r-in"><span class="co"># regression, we need to supply weights, internally used for inverse.predict</span></span>
<span class="r-in"><span class="co"># If we are not using a variance function, we can use the weight from</span></span>
<span class="r-in"><span class="co"># the above example as a first approximation (x = 15 is close to our</span></span>
<span class="r-in"><span class="co"># loq approx 14 from above).</span></span>
<span class="r-in"><span class="fu"><a href="loq.html">loq</a></span><span class="op">(</span><span class="va">m3.means</span>, w.loq <span class="op">=</span> <span class="fl">1.67</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> $x</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 7.346195</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> $y</span>
<span class="r-out co"><span class="r-pr">#></span> [1] 17.90777</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"><span class="co"># The weight for the loq should therefore be derived at x = 7.3 instead</span></span>
<span class="r-in"><span class="co"># of 15, but the graphical procedure of Massart (p. 201) to derive the </span></span>
<span class="r-in"><span class="co"># variances on which the weights are based is quite inaccurate anyway. </span></span>
<span class="r-in"></span>
</code></pre></div>
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