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<h1>Add normally distributed errors to simulated kinetic degradation data</h1>
</div>
<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>
<pre class="usage"><span class='fu'>add_err</span>(<span class='no'>prediction</span>, <span class='no'>sdfunc</span>, <span class='kw'>secondary</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>),
<span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>1000</span>, <span class='kw'>LOD</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>reps</span> <span class='kw'>=</span> <span class='fl'>2</span>,
<span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>NA</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
http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf</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='no'>m_SFO_SFO</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"M1"</span>),
<span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</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='no'>sampling_times</span> <span class='kw'>=</span> <span class='fu'>c</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='co'># This is the prediction used for the "Type 2 datasets" on the Piacenza poster</span>
<span class='co'># from 2015</span>
<span class='no'>d_SFO_SFO</span> <span class='kw'><-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span>(<span class='no'>m_SFO_SFO</span>,
<span class='fu'>c</span>(<span class='kw'>k_parent</span> <span class='kw'>=</span> <span class='fl'>0.1</span>, <span class='kw'>f_parent_to_M1</span> <span class='kw'>=</span> <span class='fl'>0.5</span>,
<span class='kw'>k_M1</span> <span class='kw'>=</span> <span class='fu'>log</span>(<span class='fl'>2</span>)/<span class='fl'>1000</span>),
<span class='fu'>c</span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fl'>100</span>, <span class='kw'>M1</span> <span class='kw'>=</span> <span class='fl'>0</span>),
<span class='no'>sampling_times</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='no'>d_SFO_SFO_err</span> <span class='kw'><-</span> <span class='fu'>add_err</span>(<span class='no'>d_SFO_SFO</span>, <span class='kw'>function</span>(<span class='no'>x</span>) <span class='fl'>10</span>, <span class='kw'>n</span> <span class='kw'>=</span> <span class='fl'>3</span>, <span class='kw'>seed</span> <span class='kw'>=</span> <span class='fl'>123456789</span> )
<span class='co'># Name the datasets for nicer plotting</span>
<span class='fu'>names</span>(<span class='no'>d_SFO_SFO_err</span>) <span class='kw'><-</span> <span class='fu'>paste</span>(<span class='st'>"Dataset"</span>, <span class='fl'>1</span>:<span class='fl'>3</span>)
<span class='co'># Name the model in the list of models (with only one member in this case)</span>
<span class='co'># for nicer plotting later on.</span>
<span class='co'># Be quiet and use the faster Levenberg-Marquardt algorithm, as the datasets</span>
<span class='co'># are easy and examples are run often. Use only one core not to offend CRAN</span>
<span class='co'># checks</span>
<span class='no'>f_SFO_SFO</span> <span class='kw'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span>(<span class='fu'>list</span>(<span class='st'>"SFO-SFO"</span> <span class='kw'>=</span> <span class='no'>m_SFO_SFO</span>),
<span class='no'>d_SFO_SFO_err</span>, <span class='kw'>cores</span> <span class='kw'>=</span> <span class='fl'>1</span>,
<span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>method.modFit</span> <span class='kw'>=</span> <span class='st'>"Marq"</span>)
<span class='fu'>plot</span>(<span class='no'>f_SFO_SFO</span>)</div><div class='img'><img src='add_err-1.png' alt='' width='700' height='432.632880098887' /></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'>plot</span>(<span class='no'>f_SFO_SFO</span><span class='kw'>[[</span><span class='fl'>3</span>]], <span class='kw'>show_residuals</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='img'><img src='add_err-2.png' alt='' width='700' height='432.632880098887' /></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'>plot</span>(<span class='no'>f_SFO_SFO</span>[<span class='fl'>1</span>, <span class='fl'>3</span>])</div><div class='img'><img src='add_err-3.png' alt='' width='700' height='432.632880098887' /></div><div class='input'>
</div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#value">Value</a></li>
<li><a href="#references">References</a></li>
<li><a href="#examples">Examples</a></li>
</ul>
<h2>Author</h2>
Johannes Ranke
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