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<h1>Add normally distributed errors to simulated kinetic degradation data</h1>
<small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/add_err.R'><code>R/add_err.R</code></a></small>
<div class="hidden name"><code>add_err.Rd</code></div>
</div>
<div class="ref-description">
<p>Normally distributed errors are added to data predicted for a specific
degradation model using <code><a href='mkinpredict.html'>mkinpredict</a></code>. The variance of the error
may depend on the predicted value and is specified as a standard deviation.</p>
</div>
<pre class="usage"><span class='fu'>add_err</span><span class='op'>(</span>
<span class='va'>prediction</span>,
<span class='va'>sdfunc</span>,
secondary <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span>,
n <span class='op'>=</span> <span class='fl'>1000</span>,
LOD <span class='op'>=</span> <span class='fl'>0.1</span>,
reps <span class='op'>=</span> <span class='fl'>2</span>,
digits <span class='op'>=</span> <span class='fl'>1</span>,
seed <span class='op'>=</span> <span class='cn'>NA</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>prediction</th>
<td><p>A prediction from a kinetic model as produced by
<code><a href='mkinpredict.html'>mkinpredict</a></code>.</p></td>
</tr>
<tr>
<th>sdfunc</th>
<td><p>A function taking the predicted value as its only argument and
returning a standard deviation that should be used for generating the
random error terms for this value.</p></td>
</tr>
<tr>
<th>secondary</th>
<td><p>The names of state variables that should have an initial
value of zero</p></td>
</tr>
<tr>
<th>n</th>
<td><p>The number of datasets to be generated.</p></td>
</tr>
<tr>
<th>LOD</th>
<td><p>The limit of detection (LOD). Values that are below the LOD after
adding the random error will be set to NA.</p></td>
</tr>
<tr>
<th>reps</th>
<td><p>The number of replicates to be generated within the datasets.</p></td>
</tr>
<tr>
<th>digits</th>
<td><p>The number of digits to which the values will be rounded.</p></td>
</tr>
<tr>
<th>seed</th>
<td><p>The seed used for the generation of random numbers. If NA, the
seed is not set.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>A list of datasets compatible with <code><a href='mmkin.html'>mmkin</a></code>, i.e. the
components of the list are datasets compatible with <code><a href='mkinfit.html'>mkinfit</a></code>.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Ranke J and Lehmann R (2015) To t-test or not to t-test, that is
the question. XV Symposium on Pesticide Chemistry 2-4 September 2015,
Piacenza, Italy
https://jrwb.de/posters/piacenza_2015.pdf</p>
<h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
<p>Johannes Ranke</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'>
<span class='co'># The kinetic model</span>
<span class='va'>m_SFO_SFO</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"M1"</span><span class='op'>)</span>,
M1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
<span class='co'># Generate a prediction for a specific set of parameters</span>
<span class='va'>sampling_times</span> <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span><span class='op'>)</span>
<span class='co'># This is the prediction used for the "Type 2 datasets" on the Piacenza poster</span>
<span class='co'># from 2015</span>
<span class='va'>d_SFO_SFO</span> <span class='op'><-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>m_SFO_SFO</span>,
<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='fl'>0.1</span>, f_parent_to_M1 <span class='op'>=</span> <span class='fl'>0.5</span>,
k_M1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>log</a></span><span class='op'>(</span><span class='fl'>2</span><span class='op'>)</span><span class='op'>/</span><span class='fl'>1000</span><span class='op'>)</span>,
<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span>, M1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>,
<span class='va'>sampling_times</span><span class='op'>)</span>
<span class='co'># Add an error term with a constant (independent of the value) standard deviation</span>
<span class='co'># of 10, and generate three datasets</span>
<span class='va'>d_SFO_SFO_err</span> <span class='op'><-</span> <span class='fu'>add_err</span><span class='op'>(</span><span class='va'>d_SFO_SFO</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fl'>10</span>, n <span class='op'>=</span> <span class='fl'>3</span>, seed <span class='op'>=</span> <span class='fl'>123456789</span> <span class='op'>)</span>
<span class='co'># Name the datasets for nicer plotting</span>
<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>d_SFO_SFO_err</span><span class='op'>)</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"Dataset"</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>3</span><span class='op'>)</span>
<span class='co'># Name the model in the list of models (with only one member in this case) for</span>
<span class='co'># nicer plotting later on. Be quiet and use only one core not to offend CRAN</span>
<span class='co'># checks</span>
<span class='co'># \dontrun{</span>
<span class='va'>f_SFO_SFO</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"SFO-SFO"</span> <span class='op'>=</span> <span class='va'>m_SFO_SFO</span><span class='op'>)</span>,
<span class='va'>d_SFO_SFO_err</span>, cores <span class='op'>=</span> <span class='fl'>1</span>,
quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_SFO_SFO</span><span class='op'>)</span>
</div><div class='img'><img src='add_err-1.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='co'># We would like to inspect the fit for dataset 3 more closely</span>
<span class='co'># Using double brackets makes the returned object an mkinfit object</span>
<span class='co'># instead of a list of mkinfit objects, so plot.mkinfit is used</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_SFO_SFO</span><span class='op'>[[</span><span class='fl'>3</span><span class='op'>]</span><span class='op'>]</span>, show_residuals <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
</div><div class='img'><img src='add_err-2.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='co'># If we use single brackets, we should give two indices (model and dataset),</span>
<span class='co'># and plot.mmkin is used</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_SFO_SFO</span><span class='op'>[</span><span class='fl'>1</span>, <span class='fl'>3</span><span class='op'>]</span><span class='op'>)</span>
</div><div class='img'><img src='add_err-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># }</span>
</div></pre>
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