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<h1>Calibration data from Massart et al. (1997), example 3</h1>
<div class="row">
<div class="span8">
<h2>Usage</h2>
<pre><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></pre>
<div class="Description">
<h2>Description</h2>
<p>Sample dataset from p. 188 to test the package.</p>
</div>
<div class="Format">
<h2>Format</h2>
<p>A dataframe containing 6 levels of x values with 5
observations of y for each level.</p>
</div>
<div class="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>
<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></div>
<strong class='message'>The following objects are masked from massart97ex3 (pos = 3):
x, y
</strong>
<div class='input'><span class="symbol">yx</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/split'>split</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="symbol">ybar</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/lapply'>sapply</a></span><span class="keyword">(</span><span class="symbol">yx</span><span class="keyword">,</span> <span class="symbol">mean</span><span class="keyword">)</span>
<span class="symbol">s</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/Round'>round</a></span><span class="keyword">(</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/lapply'>sapply</a></span><span class="keyword">(</span><span class="symbol">yx</span><span class="keyword">,</span> <span class="symbol">sd</span><span class="keyword">)</span><span class="keyword">,</span> <span class="argument">digits</span> <span class="argument">=</span> <span class="number">2</span><span class="keyword">)</span>
<span class="symbol">w</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/Round'>round</a></span><span class="keyword">(</span><span class="number">1</span> <span class="keyword">/</span> <span class="keyword">(</span><span class="symbol">s</span><span class="keyword">^</span><span class="number">2</span><span class="keyword">)</span><span class="keyword">,</span> <span class="argument">digits</span> <span class="argument">=</span> <span class="number">3</span><span class="keyword">)</span>
<span class="symbol">weights</span> <span class="assignement"><-</span> <span class="symbol">w</span><span class="keyword">[</span><span class="functioncall"><a href='http://www.rdocumentation.org/packages/base/topics/factor'>factor</a></span><span class="keyword">(</span><span class="symbol">x</span><span class="keyword">)</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="argument">w</span> <span class="argument">=</span> <span class="symbol">weights</span><span class="keyword">)</span>
<span class="functioncall"><a href='calplot.lm.html'>calplot</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">)</span></div>
<strong class='warning'>Warning message:
Assuming constant prediction variance even though model fit is weighted
</strong>
<p><img src='massart97ex3-5.png' alt='' width='540' height='400' /></p>
<div class='input'>
<span class="comment"># The following concords with the book p. 200</span>
<span class="functioncall"><a href='inverse.predict.html'>inverse.predict</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="number">15</span><span class="keyword">,</span> <span class="argument">ws</span> <span class="argument">=</span> <span class="number">1.67</span><span class="keyword">)</span> <span class="comment"># 5.9 +- 2.5</span></div>
<div class='output'>$Prediction
[1] 5.865367
$`Standard Error`
[1] 0.8926109
$Confidence
[1] 2.478285
$`Confidence Limits`
[1] 3.387082 8.343652
</div>
<div class='input'><span class="functioncall"><a href='inverse.predict.html'>inverse.predict</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="number">90</span><span class="keyword">,</span> <span class="argument">ws</span> <span class="argument">=</span> <span class="number">0.145</span><span class="keyword">)</span> <span class="comment"># 44.1 +- 7.9</span></div>
<div class='output'>$Prediction
[1] 44.06025
$`Standard Error`
[1] 2.829162
$Confidence
[1] 7.855012
$`Confidence Limits`
[1] 36.20523 51.91526
</div>
<div class='input'>
<span class="comment"># The LOD is only calculated for models from unweighted regression</span>
<span class="comment"># with this version of chemCal</span>
<span class="symbol">m0</span> <span class="assignement"><-</span> <span class="functioncall"><a href='http://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></span><span class="keyword">(</span><span class="symbol">y</span> <span class="keyword">~</span> <span class="symbol">x</span><span class="keyword">)</span>
<span class="functioncall"><a href='lod.html'>lod</a></span><span class="keyword">(</span><span class="symbol">m0</span><span class="keyword">)</span></div>
<div class='output'>$x
[1] 5.407085
$y
1
13.63911
</div>
<div class='input'>
<span class="comment"># Limit of quantification from unweighted regression</span>
<span class="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">m0</span><span class="keyword">)</span></div>
<div class='output'>$x
[1] 13.97764
$y
1
30.6235
</div>
<div class='input'>
<span class="comment"># For calculating the limit of quantification from a model from weighted</span>
<span class="comment"># regression, we need to supply weights, internally used for inverse.predict</span>
<span class="comment"># If we are not using a variance function, we can use the weight from</span>
<span class="comment"># the above example as a first approximation (x = 15 is close to our</span>
<span class="comment"># loq approx 14 from above).</span>
<span class="functioncall"><a href='loq.html'>loq</a></span><span class="keyword">(</span><span class="symbol">m</span><span class="keyword">,</span> <span class="argument">w.loq</span> <span class="argument">=</span> <span class="number">1.67</span><span class="keyword">)</span></div>
<div class='output'>$x
[1] 7.346195
$y
1
17.90777
</div>
<div class='input'><span class="comment"># The weight for the loq should therefore be derived at x = 7.3 instead</span>
<span class="comment"># of 15, but the graphical procedure of Massart (p. 201) to derive the </span>
<span class="comment"># variances on which the weights are based is quite inaccurate anyway. </span></div></pre>
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