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<h1>Calibration data from Massart et al. (1997), example 3</h1>
<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>
<pre class="usage"><span class='no'>massart97ex3</span></pre>
<h2 class="hasAnchor" id="format"><a class="anchor" href="#format"></a>Format</h2>
<p>A dataframe containing 6 levels of x values with 5
observations of y for each level.</p>
<h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>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>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'># For reproducing the results for replicate standard measurements in example 8,</span>
<span class='co'># we need to do the calibration on the means when using chemCal > 0.2</span>
<span class='no'>weights</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/with.html'>with</a></span>(<span class='no'>massart97ex3</span>, {
<span class='no'>yx</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/split.html'>split</a></span>(<span class='no'>y</span>, <span class='no'>x</span>)
<span class='no'>ybar</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>sapply</a></span>(<span class='no'>yx</span>, <span class='no'>mean</span>)
<span class='no'>s</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>sapply</a></span>(<span class='no'>yx</span>, <span class='no'>sd</span>), <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>2</span>)
<span class='no'>w</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>round</a></span>(<span class='fl'>1</span> / (<span class='no'>s</span>^<span class='fl'>2</span>), <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>3</span>)
})
<span class='no'>massart97ex3.means</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/aggregate.html'>aggregate</a></span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='no'>massart97ex3</span>, <span class='no'>mean</span>)
<span class='no'>m3.means</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>w</span> <span class='kw'>=</span> <span class='no'>weights</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>massart97ex3.means</span>)
<span class='co'># The following concords with the book p. 200</span>
<span class='fu'><a href='inverse.predict.html'>inverse.predict</a></span>(<span class='no'>m3.means</span>, <span class='fl'>15</span>, <span class='kw'>ws</span> <span class='kw'>=</span> <span class='fl'>1.67</span>) <span class='co'># 5.9 +- 2.5</span></div><div class='output co'>#> $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='fu'><a href='inverse.predict.html'>inverse.predict</a></span>(<span class='no'>m3.means</span>, <span class='fl'>90</span>, <span class='kw'>ws</span> <span class='kw'>=</span> <span class='fl'>0.145</span>) <span class='co'># 44.1 +- 7.9</span></div><div class='output co'>#> $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='co'># The LOD is only calculated for models from unweighted regression</span>
<span class='co'># with this version of chemCal</span>
<span class='no'>m0</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>massart97ex3</span>)
<span class='fu'><a href='lod.html'>lod</a></span>(<span class='no'>m0</span>)</div><div class='output co'>#> $x
#> [1] 5.407085
#>
#> $y
#> [1] 13.63911
#> </div><div class='input'>
<span class='co'># Limit of quantification from unweighted regression</span>
<span class='fu'><a href='loq.html'>loq</a></span>(<span class='no'>m0</span>)</div><div class='output co'>#> $x
#> [1] 9.627349
#>
#> $y
#> [1] 22.00246
#> </div><div class='input'>
<span class='co'># For calculating the limit of quantification from a model from weighted</span>
<span class='co'># regression, we need to supply weights, internally used for inverse.predict</span>
<span class='co'># If we are not using a variance function, we can use the weight from</span>
<span class='co'># the above example as a first approximation (x = 15 is close to our</span>
<span class='co'># loq approx 14 from above).</span>
<span class='fu'><a href='loq.html'>loq</a></span>(<span class='no'>m3.means</span>, <span class='kw'>w.loq</span> <span class='kw'>=</span> <span class='fl'>1.67</span>)</div><div class='output co'>#> $x
#> [1] 7.346195
#>
#> $y
#> [1] 17.90777
#> </div><div class='input'># The weight for the loq should therefore be derived at x = 7.3 instead
# of 15, but the graphical procedure of Massart (p. 201) to derive the
# variances on which the weights are based is quite inaccurate anyway.
</div></pre>
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