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+<!-- 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>Fit nonlinear mixed-effects models built from one or more kinetic degradation models and one or more error models — mhmkin • 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" rel="stylesheet"><script src="../deps/headroom-0.11.0/headroom.min.js"></script><script src="../deps/headroom-0.11.0/jQuery.headroom.min.js"></script><script src="../deps/bootstrap-toc-1.0.1/bootstrap-toc.min.js"></script><script src="../deps/clipboard.js-2.0.11/clipboard.min.js"></script><script src="../deps/search-1.0.0/autocomplete.jquery.min.js"></script><script src="../deps/search-1.0.0/fuse.min.js"></script><script src="../deps/search-1.0.0/mark.min.js"></script><!-- pkgdown --><script src="../pkgdown.js"></script><meta property="og:title" content="Fit nonlinear mixed-effects models built from one or more kinetic degradation models and one or more error models — mhmkin"><meta name="description" content="The name of the methods expresses that (multiple) hierarchichal
+(also known as multilevel) multicompartment kinetic models are
+fitted. Our kinetic models are nonlinear, so we can use various nonlinear
+mixed-effects model fitting functions."><meta property="og:description" content="The name of the methods expresses that (multiple) hierarchichal
+(also known as multilevel) multicompartment kinetic models are
+fitted. Our kinetic models are nonlinear, so we can use various nonlinear
+mixed-effects model fitting functions."><meta name="robots" content="noindex"></head><body>
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+ <li><h6 class="dropdown-header" data-toc-skip>Example evaluations with (generalised) nonlinear least squares</h6></li>
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+ <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>
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+ <li><a class="dropdown-item" href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a></li>
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+ <main id="main" class="col-md-9"><div class="page-header">
+
+ <h1>Fit nonlinear mixed-effects models built from one or more kinetic degradation models and one or more error models</h1>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/mhmkin.R" class="external-link"><code>R/mhmkin.R</code></a></small>
+ <div class="d-none name"><code>mhmkin.Rd</code></div>
+ </div>
+
+ <div class="ref-description section level2">
+ <p>The name of the methods expresses that (<strong>m</strong>ultiple) <strong>h</strong>ierarchichal
+(also known as multilevel) <strong>m</strong>ulticompartment <strong>kin</strong>etic models are
+fitted. Our kinetic models are nonlinear, so we can use various nonlinear
+mixed-effects model fitting functions.</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">mhmkin</span><span class="op">(</span><span class="va">objects</span>, <span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># S3 method for class 'mmkin'</span></span>
+<span><span class="fu">mhmkin</span><span class="op">(</span><span class="va">objects</span>, <span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># S3 method for class 'list'</span></span>
+<span><span class="fu">mhmkin</span><span class="op">(</span></span>
+<span> <span class="va">objects</span>,</span>
+<span> backend <span class="op">=</span> <span class="st">"saemix"</span>,</span>
+<span> algorithm <span class="op">=</span> <span class="st">"saem"</span>,</span>
+<span> no_random_effect <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span> <span class="va">...</span>,</span>
+<span> cores <span class="op">=</span> <span class="kw">if</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Sys.info.html" class="external-link">Sys.info</a></span><span class="op">(</span><span class="op">)</span><span class="op">[</span><span class="st">"sysname"</span><span class="op">]</span> <span class="op">==</span> <span class="st">"Windows"</span><span class="op">)</span> <span class="fl">1</span> <span class="kw">else</span> <span class="fu">parallel</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">detectCores</a></span><span class="op">(</span><span class="op">)</span>,</span>
+<span> cluster <span class="op">=</span> <span class="cn">NULL</span></span>
+<span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># S3 method for class 'mhmkin'</span></span>
+<span><span class="va">x</span><span class="op">[</span><span class="va">i</span>, <span class="va">j</span>, <span class="va">...</span>, drop <span class="op">=</span> <span class="cn">FALSE</span><span class="op">]</span></span>
+<span></span>
+<span><span class="co"># S3 method for class 'mhmkin'</span></span>
+<span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">x</span>, <span class="va">...</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-objects">objects<a class="anchor" aria-label="anchor" href="#arg-objects"></a></dt>
+<dd><p>A list of <a href="mmkin.html">mmkin</a> objects containing fits of the same
+degradation models to the same data, but using different error models.
+Alternatively, a single <a href="mmkin.html">mmkin</a> object containing fits of several
+degradation models to the same data</p></dd>
+
+
+<dt id="arg--">...<a class="anchor" aria-label="anchor" href="#arg--"></a></dt>
+<dd><p>Further arguments that will be passed to the nonlinear mixed-effects
+model fitting function.</p></dd>
+
+
+<dt id="arg-backend">backend<a class="anchor" aria-label="anchor" href="#arg-backend"></a></dt>
+<dd><p>The backend to be used for fitting. Currently, only saemix is
+supported</p></dd>
+
+
+<dt id="arg-algorithm">algorithm<a class="anchor" aria-label="anchor" href="#arg-algorithm"></a></dt>
+<dd><p>The algorithm to be used for fitting (currently not used)</p></dd>
+
+
+<dt id="arg-no-random-effect">no_random_effect<a class="anchor" aria-label="anchor" href="#arg-no-random-effect"></a></dt>
+<dd><p>Default is NULL and will be passed to <a href="saem.html">saem</a>. If a
+character vector is supplied, it will be passed to all calls to <a href="saem.html">saem</a>,
+which will exclude random effects for all matching parameters. Alternatively,
+a list of character vectors or an object of class <a href="illparms.html">illparms.mhmkin</a> can be
+specified. They have to have the same dimensions that the return object of
+the current call will have, i.e. the number of rows must match the number
+of degradation models in the mmkin object(s), and the number of columns must
+match the number of error models used in the mmkin object(s).</p></dd>
+
+
+<dt id="arg-cores">cores<a class="anchor" aria-label="anchor" href="#arg-cores"></a></dt>
+<dd><p>The number of cores to be used for multicore processing. This
+is only used when the <code>cluster</code> argument is <code>NULL</code>. On Windows
+machines, cores &gt; 1 is not supported, you need to use the <code>cluster</code>
+argument to use multiple logical processors. Per default, all cores detected
+by <code><a href="https://rdrr.io/r/parallel/detectCores.html" class="external-link">parallel::detectCores()</a></code> are used, except on Windows where the default
+is 1.</p></dd>
+
+
+<dt id="arg-cluster">cluster<a class="anchor" aria-label="anchor" href="#arg-cluster"></a></dt>
+<dd><p>A cluster as returned by makeCluster to be used for
+parallel execution.</p></dd>
+
+
+<dt id="arg-x">x<a class="anchor" aria-label="anchor" href="#arg-x"></a></dt>
+<dd><p>An mhmkin object.</p></dd>
+
+
+<dt id="arg-i">i<a class="anchor" aria-label="anchor" href="#arg-i"></a></dt>
+<dd><p>Row index selecting the fits for specific models</p></dd>
+
+
+<dt id="arg-j">j<a class="anchor" aria-label="anchor" href="#arg-j"></a></dt>
+<dd><p>Column index selecting the fits to specific datasets</p></dd>
+
+
+<dt id="arg-drop">drop<a class="anchor" aria-label="anchor" href="#arg-drop"></a></dt>
+<dd><p>If FALSE, the method always returns an mhmkin object, otherwise
+either a list of fit objects or a single fit object.</p></dd>
+
+</dl></div>
+ <div class="section level2">
+ <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
+ <p>A two-dimensional <a href="https://rdrr.io/r/base/array.html" class="external-link">array</a> of fit objects and/or try-errors that can
+be indexed using the degradation model names for the first index (row index)
+and the error model names for the second index (column index), with class
+attribute 'mhmkin'.</p>
+<p>An object inheriting from <code>mhmkin</code>.</p>
+ </div>
+ <div class="section level2">
+ <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
+ <div class="dont-index"><p><code>[.mhmkin</code> for subsetting mhmkin objects</p></div>
+ </div>
+ <div class="section level2">
+ <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
+ <p>Johannes Ranke</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="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="co"># We start with separate evaluations of all the first six datasets with two</span></span></span>
+<span class="r-in"><span><span class="co"># degradation models and two error models</span></span></span>
+<span class="r-in"><span><span class="va">f_sep_const</span> <span class="op">&lt;-</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/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="st">"FOMC"</span><span class="op">)</span>, <span class="va">ds_fomc</span><span class="op">[</span><span class="fl">1</span><span class="op">:</span><span class="fl">6</span><span class="op">]</span>, cores <span class="op">=</span> <span class="fl">2</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_sep_tc</span> <span class="op">&lt;-</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_sep_const</span>, error_model <span class="op">=</span> <span class="st">"tc"</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="co"># The mhmkin function sets up hierarchical degradation models aka</span></span></span>
+<span class="r-in"><span><span class="co"># nonlinear mixed-effects models for all four combinations, specifying</span></span></span>
+<span class="r-in"><span><span class="co"># uncorrelated random effects for all degradation parameters</span></span></span>
+<span class="r-in"><span><span class="va">f_saem_1</span> <span class="op">&lt;-</span> <span class="fu">mhmkin</span><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><span class="va">f_sep_const</span>, <span class="va">f_sep_tc</span><span class="op">)</span>, cores <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="status.html">status</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> error</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> degradation const tc</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO OK OK</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC OK OK</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> OK: Fit terminated successfully</span>
+<span class="r-in"><span><span class="co"># The 'illparms' function shows that in all hierarchical fits, at least</span></span></span>
+<span class="r-in"><span><span class="co"># one random effect is ill-defined (the confidence interval for the</span></span></span>
+<span class="r-in"><span><span class="co"># random effect expressed as standard deviation includes zero)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> error</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> degradation const tc </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO sd(parent_0) sd(parent_0) </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC sd(log_beta) sd(parent_0), sd(log_beta)</span>
+<span class="r-in"><span><span class="co"># Therefore we repeat the fits, excluding the ill-defined random effects</span></span></span>
+<span class="r-in"><span><span class="va">f_saem_2</span> <span class="op">&lt;-</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_saem_1</span>, no_random_effect <span class="op">=</span> <span class="fu"><a href="illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="status.html">status</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> error</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> degradation const tc</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO OK OK</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC OK OK</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> OK: Fit terminated successfully</span>
+<span class="r-in"><span><span class="fu"><a href="illparms.html">illparms</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> error</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> degradation const tc</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC </span>
+<span class="r-in"><span><span class="co"># Model comparisons show that FOMC with two-component error is preferable,</span></span></span>
+<span class="r-in"><span><span class="co"># and confirms our reduction of the default parameter model</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_1</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Data: 95 observations of 1 variable(s) grouped in 6 datasets</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> npar AIC BIC Lik</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO const 5 574.40 573.35 -282.20</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO tc 6 543.72 542.47 -265.86</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC const 7 489.67 488.22 -237.84</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC tc 8 406.11 404.44 -195.05</span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Data: 95 observations of 1 variable(s) grouped in 6 datasets</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> npar AIC BIC Lik</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO const 4 572.22 571.39 -282.11</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO tc 5 541.63 540.59 -265.81</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC const 6 487.38 486.13 -237.69</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC tc 6 402.12 400.88 -195.06</span>
+<span class="r-in"><span><span class="co"># The convergence plot for the selected model looks fine</span></span></span>
+<span class="r-in"><span><span class="fu">saemix</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">so</span>, plot.type <span class="op">=</span> <span class="st">"convergence"</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="mhmkin-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="co"># The plot of predictions versus data shows that we have a pretty data-rich</span></span></span>
+<span class="r-in"><span><span class="co"># situation with homogeneous distribution of residuals, because we used the</span></span></span>
+<span class="r-in"><span><span class="co"># same degradation model, error model and parameter distribution model that</span></span></span>
+<span class="r-in"><span><span class="co"># was used in the data generation.</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">f_saem_2</span><span class="op">[[</span><span class="st">"FOMC"</span>, <span class="st">"tc"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></span></span>
+<span class="r-plt img"><img src="mhmkin-2.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="co"># We can specify the same parameter model reductions manually</span></span></span>
+<span class="r-in"><span><span class="va">no_ranef</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="st">"parent_0"</span>, <span class="st">"log_beta"</span>, <span class="st">"parent_0"</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">"parent_0"</span>, <span class="st">"log_beta"</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/dim.html" class="external-link">dim</a></span><span class="op">(</span><span class="va">no_ranef</span><span class="op">)</span> <span class="op">&lt;-</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">2</span>, <span class="fl">2</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">f_saem_2m</span> <span class="op">&lt;-</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_saem_1</span>, no_random_effect <span class="op">=</span> <span class="va">no_ranef</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/anova.html" class="external-link">anova</a></span><span class="op">(</span><span class="va">f_saem_2m</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Data: 95 observations of 1 variable(s) grouped in 6 datasets</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> npar AIC BIC Lik</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO const 4 572.22 571.39 -282.11</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> SFO tc 5 541.63 540.59 -265.81</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC const 6 487.38 486.13 -237.69</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> FOMC tc 6 402.12 400.88 -195.06</span>
+<span class="r-in"><span><span class="co"># }</span></span></span>
+</code></pre></div>
+ </div>
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