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diff --git a/docs/dev/articles/mkin.html b/docs/dev/articles/mkin.html new file mode 100644 index 00000000..30b2182f --- /dev/null +++ b/docs/dev/articles/mkin.html @@ -0,0 +1,414 @@ +<!DOCTYPE html> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<meta charset="utf-8"> +<meta http-equiv="X-UA-Compatible" content="IE=edge"> +<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<title>Short introduction to mkin • mkin</title> +<script src="../deps/jquery-3.6.0/jquery-3.6.0.min.js"></script><meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> +<link href="../deps/bootstrap-5.3.1/bootstrap.min.css" rel="stylesheet"> +<script src="../deps/bootstrap-5.3.1/bootstrap.bundle.min.js"></script><link href="../deps/font-awesome-6.5.2/css/all.min.css" rel="stylesheet"> +<link href="../deps/font-awesome-6.5.2/css/v4-shims.min.css" 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data-bs-placement="bottom" title="In-development version">1.2.10</small> + + + <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbar" aria-controls="navbar" aria-expanded="false" aria-label="Toggle navigation"> + <span class="navbar-toggler-icon"></span> + </button> + + <div id="navbar" class="collapse navbar-collapse ms-3"> + <ul class="navbar-nav me-auto"> +<li class="nav-item"><a class="nav-link" href="../reference/index.html">Reference</a></li> +<li class="active nav-item dropdown"> + <button class="nav-link dropdown-toggle" type="button" id="dropdown-articles" data-bs-toggle="dropdown" aria-expanded="false" aria-haspopup="true">Articles</button> + <ul class="dropdown-menu" aria-labelledby="dropdown-articles"> +<li><a class="dropdown-item" href="../articles/mkin.html">Introduction to mkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li> + <li><a class="dropdown-item" href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a></li> + <li><a class="dropdown-item" href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a></li> + <li><a class="dropdown-item" href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with hierarchical models (nonlinear mixed-effects models)</h6></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a></li> + <li><a class="dropdown-item" href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a></li> + <li><a class="dropdown-item" href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a></li> + <li><a class="dropdown-item" href="../articles/web_only/multistart.html">Short demo of the multistart method</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Performance</h6></li> + <li><a class="dropdown-item" href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a></li> + <li><a class="dropdown-item" href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a></li> + <li><a class="dropdown-item" href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a></li> + <li><hr class="dropdown-divider"></li> + <li><h6 class="dropdown-header" data-toc-skip>Miscellaneous</h6></li> + <li><a class="dropdown-item" href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li> + <li><a class="dropdown-item" href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a></li> + </ul> +</li> +<li class="nav-item"><a class="nav-link" href="../coverage/coverage.html">Test coverage</a></li> +<li class="nav-item"><a class="nav-link" href="../news/index.html">News</a></li> + </ul> +<ul class="navbar-nav"> +<li class="nav-item"><form class="form-inline" role="search"> + <input class="form-control" type="search" name="search-input" id="search-input" autocomplete="off" aria-label="Search site" placeholder="Search for" data-search-index="../search.json"> +</form></li> +<li class="nav-item"><a class="external-link nav-link" href="https://github.com/jranke/mkin/" aria-label="GitHub"><span class="fa fab fa-github fa-lg"></span></a></li> + </ul> +</div> + + + </div> +</nav><div class="container template-article"> + + + + +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Short introduction to mkin</h1> + <h4 data-toc-skip class="author">Johannes +Ranke</h4> + + <h4 data-toc-skip class="date">Last change 18 May 2023 +(rebuilt 2025-02-14)</h4> + + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/vignettes/mkin.rmd" class="external-link"><code>vignettes/mkin.rmd</code></a></small> + <div class="d-none name"><code>mkin.rmd</code></div> + </div> + + + +<p><a href="https://www.jrwb.de" class="external-link">Wissenschaftlicher Berater, Kronacher +Str. 12, 79639 Grenzach-Wyhlen, Germany</a><br> Privatdozent at the +University of Freiburg</p> +<div class="section level2"> +<h2 id="abstract">Abstract<a class="anchor" aria-label="anchor" href="#abstract"></a> +</h2> +<p>In the regulatory evaluation of chemical substances like plant +protection products (pesticides), biocides and other chemicals, +degradation data play an important role. For the evaluation of pesticide +degradation experiments, detailed guidance has been developed, based on +nonlinear optimisation. The <code>R</code> add-on package +<code>mkin</code> implements fitting some of the models recommended in +this guidance from within R and calculates some statistical measures for +data series within one or more compartments, for parent and +metabolites.</p> +<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r"> +<code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="st"><a href="https://pkgdown.jrwb.de/mkin/">"mkin"</a></span>, quietly <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span><span class="co"># Define the kinetic model</span></span> +<span><span class="va">m_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M1"</span><span class="op">)</span>,</span> +<span> M1 <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"M2"</span><span class="op">)</span>,</span> +<span> M2 <span class="op">=</span> <span class="fu"><a href="../reference/mkinmod.html">mkinsub</a></span><span class="op">(</span><span class="st">"SFO"</span><span class="op">)</span>,</span> +<span> use_of_ff <span class="op">=</span> <span class="st">"max"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span></span> +<span></span> +<span><span class="co"># Produce model predictions using some arbitrary parameters</span></span> +<span><span class="va">sampling_times</span> <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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> +<span><span class="va">d_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinpredict.html">mkinpredict</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>,</span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span>k_parent <span class="op">=</span> <span class="fl">0.03</span>,</span> +<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" class="external-link">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">100</span>,</span> +<span> f_M1_to_M2 <span class="op">=</span> <span class="fl">0.9</span>, k_M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">log</a></span><span class="op">(</span><span class="fl">2</span><span class="op">)</span><span class="op">/</span><span class="fl">50</span><span class="op">)</span>,</span> +<span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">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>, M2 <span class="op">=</span> <span class="fl">0</span><span class="op">)</span>,</span> +<span> <span class="va">sampling_times</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># Generate a dataset by adding normally distributed errors with</span></span> +<span><span class="co"># standard deviation 3, for two replicates at each sampling time</span></span> +<span><span class="va">d_SFO_SFO_SFO_err</span> <span class="op"><-</span> <span class="fu"><a href="../reference/add_err.html">add_err</a></span><span class="op">(</span><span class="va">d_SFO_SFO_SFO</span>, reps <span class="op">=</span> <span class="fl">2</span>,</span> +<span> sdfunc <span class="op">=</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fl">3</span>,</span> +<span> n <span class="op">=</span> <span class="fl">1</span>, seed <span class="op">=</span> <span class="fl">123456789</span> <span class="op">)</span></span> +<span></span> +<span><span class="co"># Fit the model to the dataset</span></span> +<span><span class="va">f_SFO_SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="../reference/mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_SFO_SFO_SFO</span>, <span class="va">d_SFO_SFO_SFO_err</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span> +<span></span> +<span><span class="co"># Plot the results separately for parent and metabolites</span></span> +<span><span class="fu"><a href="../reference/plot.mkinfit.html">plot_sep</a></span><span class="op">(</span><span class="va">f_SFO_SFO_SFO</span>, lpos <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"topright"</span>, <span class="st">"bottomright"</span>, <span class="st">"bottomright"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div> +<p><img src="mkin_files/figure-html/unnamed-chunk-2-1.png" width="768"></p> +</div> +<div class="section level2"> +<h2 id="background">Background<a class="anchor" aria-label="anchor" href="#background"></a> +</h2> +<p>The <code>mkin</code> package <span class="citation">(J. Ranke +2021)</span> implements the approach to degradation kinetics recommended +in the kinetics report provided by the FOrum for Co-ordination of +pesticide fate models and their USe <span class="citation">(FOCUS Work +Group on Degradation Kinetics 2006, 2014)</span>. It covers data series +describing the decline of one compound, data series with transformation +products (commonly termed metabolites) and data series for more than one +compartment. It is possible to include back reactions. Therefore, +equilibrium reactions and equilibrium partitioning can be specified, +although this often leads to an overparameterisation of the model.</p> +<p>When the first <code>mkin</code> code was published in 2010, the most +commonly used tools for fitting more complex kinetic degradation models +to experimental data were KinGUI <span class="citation">(Schäfer et al. +2007)</span>, a MATLAB based tool with a graphical user interface that +was specifically tailored to the task and included some output as +proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general +purpose compartment based tool providing infrastructure for fitting +dynamic simulation models based on differential equations to data.</p> +<p>The ‘mkin’ code was first uploaded to the BerliOS development +platform. When this was taken down, the version control history was +imported into the R-Forge site (see <em>e.g.</em> <a href="https://cgit.jrwb.de/mkin/commit/?id=30cbb4092f6d2d3beff5800603374a0d009ad770" class="external-link">the +initial commit on 11 May 2010</a>), where the code is still being +updated.</p> +<p>At that time, the R package <code>FME</code> (Flexible Modelling +Environment) <span class="citation">(Soetaert and Petzoldt 2010)</span> +was already available, and provided a good basis for developing a +package specifically tailored to the task. The remaining challenge was +to make it as easy as possible for the users (including the author of +this vignette) to specify the system of differential equations and to +include the output requested by the FOCUS guidance, such as the +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msup><mi>χ</mi><mn>2</mn></msup><annotation encoding="application/x-tex">\chi^2</annotation></semantics></math> +error level as defined in this guidance.</p> +<p>Also, <code>mkin</code> introduced using analytical solutions for +parent only kinetics for improved optimization speed. Later, Eigenvalue +based solutions were introduced to <code>mkin</code> for the case of +linear differential equations (<em>i.e.</em> where the FOMC or DFOP +models were not used for the parent compound), greatly improving the +optimization speed for these cases. This, has become somehow obsolete, +as the use of compiled code described below gives even faster execution +times.</p> +<p>The possibility to specify back-reactions and a biphasic model +(SFORB) for metabolites were present in <code>mkin</code> from the very +beginning.</p> +<div class="section level3"> +<h3 id="derived-software-tools">Derived software tools<a class="anchor" aria-label="anchor" href="#derived-software-tools"></a> +</h3> +<p>Soon after the publication of <code>mkin</code>, two derived tools +were published, namely KinGUII (developed at Bayer Crop Science) and +CAKE (commissioned to Tessella by Syngenta), which added a graphical +user interface (GUI), and added fitting by iteratively reweighted least +squares (IRLS) and characterisation of likely parameter distributions by +Markov Chain Monte Carlo (MCMC) sampling.</p> +<p>CAKE focuses on a smooth use experience, sacrificing some flexibility +in the model definition, originally allowing only two primary +metabolites in parallel. The current version 3.4 of CAKE released in May +2020 uses a scheme for up to six metabolites in a flexible arrangement +and supports biphasic modelling of metabolites, but does not support +back-reactions (non-instantaneous equilibria).</p> +<p>KinGUI offers an even more flexible widget for specifying complex +kinetic models. Back-reactions (non-instantaneous equilibria) were +supported early on, but until 2014, only simple first-order models could +be specified for transformation products. Starting with KinGUII version +2.1, biphasic modelling of metabolites was also available in +KinGUII.</p> +<p>A further graphical user interface (GUI) that has recently been +brought to a decent degree of maturity is the browser based GUI named +<code>gmkin</code>. Please see its <a href="https://pkgdown.jrwb.de/gmkin/" class="external-link">documentation page</a> and <a href="https://pkgdown.jrwb.de/gmkin/articles/gmkin_manual.html" class="external-link">manual</a> +for further information.</p> +<p>A comparison of scope, usability and numerical results obtained with +these tools has been recently been published by <span class="citation">Johannes Ranke, Wöltjen, and Meinecke +(2018)</span>.</p> +</div> +</div> +<div class="section level2"> +<h2 id="unique-features">Unique features<a class="anchor" aria-label="anchor" href="#unique-features"></a> +</h2> +<p>Currently, the main unique features available in <code>mkin</code> +are</p> +<ul> +<li>the <a href="https://pkgdown.jrwb.de/mkin/articles/web_only/compiled_models.html">speed +increase</a> by using compiled code when a compiler is present,</li> +<li>parallel model fitting on multicore machines using the <a href="https://pkgdown.jrwb.de/mkin/reference/mmkin.html"><code>mmkin</code> +function</a>,</li> +<li>the estimation of parameter confidence intervals based on +transformed parameters (see below) and</li> +<li>the possibility to use the <a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component +error model</a> +</li> +</ul> +<p>The iteratively reweighted least squares fitting of different +variances for each variable as introduced by <span class="citation">Gao +et al. (2011)</span> has been available in mkin since <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-22-2013-10-26">version +0.9-22</a>. With <a href="https://pkgdown.jrwb.de/mkin/news/index.html#mkin-0-9-49-5-2019-07-04">release +0.9.49.5</a>, the IRLS algorithm has been complemented by direct or +step-wise maximisation of the likelihood function, which makes it +possible not only to fit the variance by variable error model but also a +<a href="https://pkgdown.jrwb.de/mkin/reference/sigma_twocomp.html">two-component +error model</a> inspired by error models developed in analytical +chemistry <span class="citation">(Johannes Ranke and Meinecke +2019)</span>.</p> +</div> +<div class="section level2"> +<h2 id="internal-parameter-transformations">Internal parameter transformations<a class="anchor" aria-label="anchor" href="#internal-parameter-transformations"></a> +</h2> +<p>For rate constants, the log transformation is used, as proposed by +Bates and Watts <span class="citation">(1988, 77, 149)</span>. +Approximate intervals are constructed for the transformed rate constants +<span class="citation">(compare Bates and Watts 1988, 135)</span>, +<em>i.e.</em> for their logarithms. Confidence intervals for the rate +constants are then obtained using the appropriate backtransformation +using the exponential function.</p> +<p>In the first version of <code>mkin</code> allowing for specifying +models using formation fractions, a home-made reparameterisation was +used in order to ensure that the sum of formation fractions would not +exceed unity.</p> +<p>This method is still used in the current version of KinGUII (v2.1 +from April 2014), with a modification that allows for fixing the pathway +to sink to zero. CAKE uses penalties in the objective function in order +to enforce this constraint.</p> +<p>In 2012, an alternative reparameterisation of the formation fractions +was proposed together with René Lehmann <span class="citation">(J. Ranke +and Lehmann 2012)</span>, based on isometric logratio transformation +(ILR). The aim was to improve the validity of the linear approximation +of the objective function during the parameter estimation procedure as +well as in the subsequent calculation of parameter confidence intervals. +In the current version of mkin, a logit transformation is used for +parameters that are bound between 0 and 1, such as the g parameter of +the DFOP model.</p> +<div class="section level3"> +<h3 id="confidence-intervals-based-on-transformed-parameters">Confidence intervals based on transformed parameters<a class="anchor" aria-label="anchor" href="#confidence-intervals-based-on-transformed-parameters"></a> +</h3> +<p>In the first attempt at providing improved parameter confidence +intervals introduced to <code>mkin</code> in 2013, confidence intervals +obtained from FME on the transformed parameters were simply all +backtransformed one by one to yield asymmetric confidence intervals for +the backtransformed parameters.</p> +<p>However, while there is a 1:1 relation between the rate constants in +the model and the transformed parameters fitted in the model, the +parameters obtained by the isometric logratio transformation are +calculated from the set of formation fractions that quantify the paths +to each of the compounds formed from a specific parent compound, and no +such 1:1 relation exists.</p> +<p>Therefore, parameter confidence intervals for formation fractions +obtained with this method only appear valid for the case of a single +transformation product, where currently the logit transformation is used +for the formation fraction.</p> +<p>The confidence intervals obtained by backtransformation for the cases +where a 1:1 relation between transformed and original parameter exist +are considered by the author of this vignette to be more accurate than +those obtained using a re-estimation of the Hessian matrix after +backtransformation, as implemented in the FME package.</p> +</div> +<div class="section level3"> +<h3 id="parameter-t-test-based-on-untransformed-parameters">Parameter t-test based on untransformed parameters<a class="anchor" aria-label="anchor" href="#parameter-t-test-based-on-untransformed-parameters"></a> +</h3> +<p>The standard output of many nonlinear regression software packages +includes the results from a test for significant difference from zero +for all parameters. Such a test is also recommended to check the +validity of rate constants in the FOCUS guidance <span class="citation">(FOCUS Work Group on Degradation Kinetics 2014, +96ff)</span>.</p> +<p>It has been argued that the precondition for this test, <em>i.e.</em> +normal distribution of the estimator for the parameters, is not +fulfilled in the case of nonlinear regression <span class="citation">(J. +Ranke and Lehmann 2015)</span>. However, this test is commonly used by +industry, consultants and national authorities in order to decide on the +reliability of parameter estimates, based on the FOCUS guidance +mentioned above. Therefore, the results of this one-sided t-test are +included in the summary output from <code>mkin</code>.</p> +<p>As it is not reasonable to test for significant difference of the +transformed parameters (<em>e.g.</em> +<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>o</mi><mi>g</mi><mrow><mo stretchy="true" form="prefix">(</mo><mi>k</mi><mo stretchy="true" form="postfix">)</mo></mrow></mrow><annotation encoding="application/x-tex">log(k)</annotation></semantics></math>) +from zero, the t-test is calculated based on the model definition before +parameter transformation, <em>i.e.</em> in a similar way as in packages +that do not apply such an internal parameter transformation. A note is +included in the <code>mkin</code> output, pointing to the fact that the +t-test is based on the unjustified assumption of normal distribution of +the parameter estimators.</p> +</div> +</div> +<div class="section level2"> +<h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a> +</h2> +<!-- vim: set foldmethod=syntax: --> +<div id="refs" class="references csl-bib-body hanging-indent"> +<div id="ref-bates1988" class="csl-entry"> +Bates, D., and D. Watts. 1988. <em>Nonlinear Regression and Its +Applications</em>. Wiley-Interscience. +</div> +<div id="ref-FOCUS2006" class="csl-entry"> +FOCUS Work Group on Degradation Kinetics. 2006. <em>Guidance Document on +Estimating Persistence and Degradation Kinetics from Environmental Fate +Studies on Pesticides in EU Registration. Report of the FOCUS Work Group +on Degradation Kinetics</em>. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. +</div> +<div id="ref-FOCUSkinetics2014" class="csl-entry"> +———. 2014. <em>Generic Guidance for Estimating Persistence and +Degradation Kinetics from Environmental Fate Studies on Pesticides in EU +Registration</em>. 1.1 ed. <a href="http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics" class="external-link">http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a>. +</div> +<div id="ref-gao11" class="csl-entry"> +Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. +<span>“Improving Uncertainty Analysis in Kinetic Evaluations Using +Iteratively Reweighted Least Squares.”</span> Journal. <em>Environmental +Science and Technology</em> 45: 4429–37. +</div> +<div id="ref-pkg:mkin" class="csl-entry"> +Ranke, J. 2021. <em>‘<span class="nocase">mkin</span>‘: +<span>K</span>inetic Evaluation of Chemical Degradation Data</em>. <a href="https://CRAN.R-project.org/package=mkin" class="external-link">https://CRAN.R-project.org/package=mkin</a>. +</div> +<div id="ref-ranke2012" class="csl-entry"> +Ranke, J., and R. Lehmann. 2012. <span>“Parameter Reliability in Kinetic +Evaluation of Environmental Metabolism Data - Assessment and the +Influence of Model Specification.”</span> In <em>SETAC World 20-24 +May</em>. Berlin. <a href="https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf" class="external-link">https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf</a>. +</div> +<div id="ref-ranke2015" class="csl-entry"> +———. 2015. <span>“To t-Test or Not to t-Test, That Is the +Question.”</span> In <em>XV Symposium on Pesticide Chemistry 2-4 +September 2015</em>. Piacenza. <a href="https://jrwb.de/posters/piacenza_2015.pdf" class="external-link">https://jrwb.de/posters/piacenza_2015.pdf</a>. +</div> +<div id="ref-ranke2019" class="csl-entry"> +Ranke, Johannes, and Stefan Meinecke. 2019. <span>“Error Models for the +Kinetic Evaluation of Chemical Degradation Data.”</span> +<em>Environments</em> 6 (12). <a href="https://doi.org/10.3390/environments6120124" class="external-link">https://doi.org/10.3390/environments6120124</a>. +</div> +<div id="ref-ranke2018" class="csl-entry"> +Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. +<span>“Comparison of Software Tools for Kinetic Evaluation of Chemical +Degradation Data.”</span> <em>Environmental Sciences Europe</em> 30 (1): +17. <a href="https://doi.org/10.1186/s12302-018-0145-1" class="external-link">https://doi.org/10.1186/s12302-018-0145-1</a>. +</div> +<div id="ref-schaefer2007" class="csl-entry"> +Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. +<span>“<span>KinGUI</span>: A New Kinetic Software Tool for Evaluations +According to <span>FOCUS</span> Degradation Kinetics.”</span> In +<em>Proceedings of the XIII Symposium Pesticide Chemistry</em>, edited +by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. +Piacenza. +</div> +<div id="ref-soetaert2010" class="csl-entry"> +Soetaert, Karline, and Thomas Petzoldt. 2010. <span>“Inverse Modelling, +Sensitivity and Monte Carlo Analysis in <span>R</span> Using Package +<span>FME</span>.”</span> <em>Journal of Statistical Software</em> 33 +(3): 1–28. <a href="https://doi.org/10.18637/jss.v033.i03" class="external-link">https://doi.org/10.18637/jss.v033.i03</a>. +</div> +</div> +</div> + </main><aside class="col-md-3"><nav id="toc" aria-label="Table of contents"><h2>On this page</h2> + </nav></aside> +</div> + + + + <footer><div class="pkgdown-footer-left"> + <p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown-footer-right"> + <p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.1.1.</p> +</div> + + </footer> +</div> + + + + + + </body> +</html> |