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diff --git a/docs/dev/reference/sigma_twocomp.html b/docs/dev/reference/sigma_twocomp.html new file mode 100644 index 00000000..12af9e8a --- /dev/null +++ b/docs/dev/reference/sigma_twocomp.html @@ -0,0 +1,169 @@ +<!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>Two-component error model — sigma_twocomp • 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 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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> + 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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-reference-topic"> +<div class="row"> + <main id="main" class="col-md-9"><div class="page-header"> + + <h1>Two-component error model</h1> + <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/sigma_twocomp.R" class="external-link"><code>R/sigma_twocomp.R</code></a></small> + <div class="d-none name"><code>sigma_twocomp.Rd</code></div> + </div> + + <div class="ref-description section level2"> + <p>Function describing the standard deviation of the measurement error in +dependence of the measured value \(y\):</p> + </div> + + <div class="section level2"> + <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2> + <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">sigma_twocomp</span><span class="op">(</span><span class="va">y</span>, <span class="va">sigma_low</span>, <span class="va">rsd_high</span><span class="op">)</span></span></code></pre></div> + </div> + + <div class="section level2"> + <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2> + + +<dl><dt id="arg-y">y<a class="anchor" aria-label="anchor" href="#arg-y"></a></dt> +<dd><p>The magnitude of the observed value</p></dd> + + +<dt id="arg-sigma-low">sigma_low<a class="anchor" aria-label="anchor" href="#arg-sigma-low"></a></dt> +<dd><p>The asymptotic minimum of the standard deviation for low +observed values</p></dd> + + +<dt id="arg-rsd-high">rsd_high<a class="anchor" aria-label="anchor" href="#arg-rsd-high"></a></dt> +<dd><p>The coefficient describing the increase of the standard +deviation with the magnitude of the observed value</p></dd> + +</dl></div> + <div class="section level2"> + <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2> + <p>The standard deviation of the response variable.</p> + </div> + <div class="section level2"> + <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2> + <p>$$\sigma = \sqrt{ \sigma_{low}^2 + y^2 * {rsd}_{high}^2}$$ sigma = +sqrt(sigma_low^2 + y^2 * rsd_high^2)</p> +<p>This is the error model used for example by Werner et al. (1978). The model +proposed by Rocke and Lorenzato (1995) can be written in this form as well, +but assumes approximate lognormal distribution of errors for high values of +y.</p> + </div> + <div class="section level2"> + <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2> + <p>Werner, Mario, Brooks, Samuel H., and Knott, Lancaster B. (1978) +Additive, Multiplicative, and Mixed Analytical Errors. Clinical Chemistry +24(11), 1895-1898.</p> +<p>Rocke, David M. and Lorenzato, Stefan (1995) A two-component model for +measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p> +<p>Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical +Degradation Data. <em>Environments</em> 6(12) 124 +<a href="https://doi.org/10.3390/environments6120124" class="external-link">doi:10.3390/environments6120124</a> +.</p> + </div> + + <div class="section level2"> + <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2> + <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="va">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="r-in"><span><span class="va">d_pred</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>time <span class="op">=</span> <span class="va">times</span>, parent <span class="op">=</span> <span class="fl">100</span> <span class="op">*</span> <span class="fu"><a href="https://rdrr.io/r/base/Log.html" class="external-link">exp</a></span><span class="op">(</span><span class="op">-</span> <span class="fl">0.03</span> <span class="op">*</span> <span class="va">times</span><span class="op">)</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">123456</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="va">d_syn</span> <span class="op"><-</span> <span class="fu"><a href="add_err.html">add_err</a></span><span class="op">(</span><span class="va">d_pred</span>, <span class="kw">function</span><span class="op">(</span><span class="va">y</span><span class="op">)</span> <span class="fu">sigma_twocomp</span><span class="op">(</span><span class="va">y</span>, <span class="fl">1</span>, <span class="fl">0.07</span><span class="op">)</span>,</span></span> +<span class="r-in"><span> reps <span class="op">=</span> <span class="fl">2</span>, n <span class="op">=</span> <span class="fl">1</span><span class="op">)</span><span class="op">[[</span><span class="fl">1</span><span class="op">]</span><span class="op">]</span></span></span> +<span class="r-in"><span><span class="va">f_nls</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/nls.html" class="external-link">nls</a></span><span class="op">(</span><span class="va">value</span> <span class="op">~</span> <span class="fu"><a href="https://rdrr.io/r/stats/SSasymp.html" class="external-link">SSasymp</a></span><span class="op">(</span><span class="va">time</span>, <span class="fl">0</span>, <span class="va">parent_0</span>, <span class="va">lrc</span><span class="op">)</span>, data <span class="op">=</span> <span class="va">d_syn</span>,</span></span> +<span class="r-in"><span> start <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>parent_0 <span class="op">=</span> <span class="fl">100</span>, lrc <span class="op">=</span> <span class="op">-</span><span class="fl">3</span><span class="op">)</span><span class="op">)</span></span></span> +<span class="r-in"><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="va"><a href="https://svn.r-project.org/R-packages/trunk/nlme/" class="external-link">nlme</a></span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="va">f_gnls</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/gnls.html" class="external-link">gnls</a></span><span class="op">(</span><span class="va">value</span> <span class="op">~</span> <span class="fu"><a href="https://rdrr.io/r/stats/SSasymp.html" class="external-link">SSasymp</a></span><span class="op">(</span><span class="va">time</span>, <span class="fl">0</span>, <span class="va">parent_0</span>, <span class="va">lrc</span><span class="op">)</span>,</span></span> +<span class="r-in"><span> data <span class="op">=</span> <span class="va">d_syn</span>, na.action <span class="op">=</span> <span class="va">na.omit</span>,</span></span> +<span class="r-in"><span> start <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>parent_0 <span class="op">=</span> <span class="fl">100</span>, lrc <span class="op">=</span> <span class="op">-</span><span class="fl">3</span><span class="op">)</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/length.html" class="external-link">length</a></span><span class="op">(</span><span class="fu">findFunction</span><span class="op">(</span><span class="st">"varConstProp"</span><span class="op">)</span><span class="op">)</span> <span class="op">></span> <span class="fl">0</span><span class="op">)</span> <span class="op">{</span></span></span> +<span class="r-in"><span> <span class="va">f_gnls_tc</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_gnls</span>, weights <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/pkg/nlme/man/varConstProp.html" class="external-link">varConstProp</a></span><span class="op">(</span><span class="op">)</span><span class="op">)</span></span></span> +<span class="r-in"><span> <span class="va">f_gnls_tc_sf</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/update.html" class="external-link">update</a></span><span class="op">(</span><span class="va">f_gnls_tc</span>, control <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>sigma <span class="op">=</span> <span class="fl">1</span><span class="op">)</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="op">}</span></span></span> +<span class="r-in"><span><span class="va">f_mkin</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">d_syn</span>, error_model <span class="op">=</span> <span class="st">"const"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="va">f_mkin_tc</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">d_syn</span>, error_model <span class="op">=</span> <span class="st">"tc"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span> +<span class="r-in"><span><span class="fu"><a href="plot.mkinfit.html">plot_res</a></span><span class="op">(</span><span class="va">f_mkin_tc</span>, standardized <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span> +<span class="r-plt img"><img src="sigma_twocomp-1.png" alt="" width="700" height="433"></span> +<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/AIC.html" class="external-link">AIC</a></span><span class="op">(</span><span class="va">f_nls</span>, <span class="va">f_gnls</span>, <span class="va">f_gnls_tc</span>, <span class="va">f_gnls_tc_sf</span>, <span class="va">f_mkin</span>, <span class="va">f_mkin_tc</span><span class="op">)</span></span></span> +<span class="r-out co"><span class="r-pr">#></span> df AIC</span> +<span class="r-out co"><span class="r-pr">#></span> f_nls 3 114.4817</span> +<span class="r-out co"><span class="r-pr">#></span> f_gnls 3 114.4817</span> +<span class="r-out co"><span class="r-pr">#></span> f_gnls_tc 5 103.6447</span> +<span class="r-out co"><span class="r-pr">#></span> f_gnls_tc_sf 4 101.6447</span> +<span class="r-out co"><span class="r-pr">#></span> f_mkin 3 114.4817</span> +<span class="r-out co"><span class="r-pr">#></span> f_mkin_tc 4 101.6446</span> +</code></pre></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 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