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    <h1>Create an nlme model for an mmkin row object</h1>
    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/nlme.mmkin.R'><code>R/nlme.mmkin.R</code></a></small>
    <div class="hidden name"><code>nlme.mmkin.Rd</code></div>
    </div>

    <div class="ref-description">
    <p>This functions sets up a nonlinear mixed effects model for an mmkin row
object. An mmkin row object is essentially a list of mkinfit objects that
have been obtained by fitting the same model to a list of datasets.</p>
    </div>

    <pre class="usage"><span class='co'># S3 method for mmkin</span>
<span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span>
  <span class='va'>model</span>,
  data <span class='op'>=</span> <span class='st'>"auto"</span>,
  fixed <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>as.list</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='fu'><a href='nlme_function.html'>mean_degparms</a></span><span class='op'>(</span><span class='va'>model</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>el</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/eval.html'>eval</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/parse.html'>parse</a></span><span class='op'>(</span>text <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='va'>el</span>, <span class='fl'>1</span>, sep <span class='op'>=</span> <span class='st'>"~"</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span><span class='op'>)</span>,
  random <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/pdDiag.html'>pdDiag</a></span><span class='op'>(</span><span class='va'>fixed</span><span class='op'>)</span>,
  <span class='va'>groups</span>,
  start <span class='op'>=</span> <span class='fu'><a href='nlme_function.html'>mean_degparms</a></span><span class='op'>(</span><span class='va'>model</span>, random <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
  correlation <span class='op'>=</span> <span class='cn'>NULL</span>,
  weights <span class='op'>=</span> <span class='cn'>NULL</span>,
  <span class='va'>subset</span>,
  method <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'>"ML"</span>, <span class='st'>"REML"</span><span class='op'>)</span>,
  na.action <span class='op'>=</span> <span class='va'>na.fail</span>,
  <span class='va'>naPattern</span>,
  control <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='op'>)</span>,
  verbose <span class='op'>=</span> <span class='cn'>FALSE</span>
<span class='op'>)</span>

<span class='co'># S3 method for nlme.mmkin</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, digits <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span><span class='op'>(</span><span class='st'>"digits"</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>3</span><span class='op'>)</span>, <span class='va'>...</span><span class='op'>)</span>

<span class='co'># S3 method for nlme.mmkin</span>
<span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</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>model</th>
      <td><p>An <a href='mmkin.html'>mmkin</a> row object.</p></td>
    </tr>
    <tr>
      <th>data</th>
      <td><p>Ignored, data are taken from the mmkin model</p></td>
    </tr>
    <tr>
      <th>fixed</th>
      <td><p>Ignored, all degradation parameters fitted in the
mmkin model are used as fixed parameters</p></td>
    </tr>
    <tr>
      <th>random</th>
      <td><p>If not specified, correlated random effects are set up
for all optimised degradation model parameters using the log-Cholesky
parameterization <a href='https://rdrr.io/pkg/nlme/man/pdLogChol.html'>nlme::pdLogChol</a> that is also the default of
the generic <a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a> method.</p></td>
    </tr>
    <tr>
      <th>groups</th>
      <td><p>See the documentation of nlme</p></td>
    </tr>
    <tr>
      <th>start</th>
      <td><p>If not specified, mean values of the fitted degradation
parameters taken from the mmkin object are used</p></td>
    </tr>
    <tr>
      <th>correlation</th>
      <td><p>See the documentation of nlme</p></td>
    </tr>
    <tr>
      <th>weights</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>subset</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>method</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>na.action</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>naPattern</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>control</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>verbose</th>
      <td><p>passed to nlme</p></td>
    </tr>
    <tr>
      <th>x</th>
      <td><p>An nlme.mmkin object to print</p></td>
    </tr>
    <tr>
      <th>digits</th>
      <td><p>Number of digits to use for printing</p></td>
    </tr>
    <tr>
      <th>...</th>
      <td><p>Update specifications passed to update.nlme</p></td>
    </tr>
    <tr>
      <th>object</th>
      <td><p>An nlme.mmkin object to update</p></td>
    </tr>
    </table>

    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>Upon success, a fitted 'nlme.mmkin' object, which is an nlme object
with additional elements. It also inherits from 'mixed.mmkin'.</p>
    <h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>

    <p>Note that the convergence of the nlme algorithms depends on the quality
of the data. In degradation kinetics, we often only have few datasets
(e.g. data for few soils) and complicated degradation models, which may
make it impossible to obtain convergence with nlme.</p>
    <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>

    <p>As the object inherits from <a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme::nlme</a>, there is a wealth of
methods that will automatically work on 'nlme.mmkin' objects, such as
<code><a href='https://rdrr.io/pkg/nlme/man/intervals.html'>nlme::intervals()</a></code>, <code><a href='https://rdrr.io/pkg/nlme/man/anova.lme.html'>nlme::anova.lme()</a></code> and <code><a href='https://rdrr.io/pkg/nlme/man/coef.lme.html'>nlme::coef.lme()</a></code>.</p>
    <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>

    <div class='dont-index'><p><code><a href='nlme_function.html'>nlme_function()</a></code>, <a href='plot.mixed.mmkin.html'>plot.mixed.mmkin</a>, <a href='summary.nlme.mmkin.html'>summary.nlme.mmkin</a></p></div>

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'><span class='va'>ds</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
 <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</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='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span>, <span class='va'>name</span> <span class='op'>==</span> <span class='st'>"parent"</span><span class='op'>)</span><span class='op'>)</span>
<span class='va'>f</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'>c</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span>
<span class='kw'><a href='https://rdrr.io/r/base/library.html'>library</a></span><span class='op'>(</span><span class='va'><a href='https://svn.r-project.org/R-packages/trunk/nlme/'>nlme</a></span><span class='op'>)</span>
<span class='va'>f_nlme_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='op'>]</span><span class='op'>)</span>

<span class='co'># \dontrun{</span>

  <span class='va'>f_nlme_dfop</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span><span class='st'>"DFOP"</span>, <span class='op'>]</span><span class='op'>)</span>
  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo</span>, <span class='va'>f_nlme_dfop</span><span class='op'>)</span>
</div><div class='output co'>#&gt;             Model df      AIC      BIC    logLik   Test  L.Ratio p-value
#&gt; f_nlme_sfo      1  5 625.0539 637.5529 -307.5269                        
#&gt; f_nlme_dfop     2  9 495.1270 517.6253 -238.5635 1 vs 2 137.9269  &lt;.0001</div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Kinetic nonlinear mixed-effects model fit by maximum likelihood
#&gt; 
#&gt; Structural model:
#&gt; d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#&gt;            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#&gt;            * parent
#&gt; 
#&gt; Data:
#&gt; 90 observations of 1 variable(s) grouped in 5 datasets
#&gt; 
#&gt; Log-likelihood: -238.6
#&gt; 
#&gt; Fixed effects:
#&gt;  list(parent_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1) 
#&gt; parent_0   log_k1   log_k2 g_qlogis 
#&gt;  94.1702  -1.8002  -4.1474   0.0324 
#&gt; 
#&gt; Random effects:
#&gt;  Formula: list(parent_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)
#&gt;  Level: ds
#&gt;  Structure: Diagonal
#&gt;         parent_0 log_k1 log_k2 g_qlogis Residual
#&gt; StdDev:    2.488 0.8447   1.33   0.4652    2.321
#&gt; </div><div class='input'>  <span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop</span><span class='op'>)</span>
</div><div class='img'><img src='nlme.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'>  <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop</span><span class='op'>)</span>
</div><div class='output co'>#&gt; $distimes
#&gt;            DT50     DT90 DT50back  DT50_k1  DT50_k2
#&gt; parent 10.79857 100.7937 30.34193 4.193938 43.85443
#&gt; </div><div class='input'>
  <span class='va'>ds_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
   <span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>data</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='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</span><span class='op'>)</span>
  <span class='va'>m_sfo_sfo</span> <span class='op'>&lt;-</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='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
    A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.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'>"min"</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
  <span class='va'>m_sfo_sfo_ff</span> <span class='op'>&lt;-</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='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
    A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.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>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
  <span class='va'>m_dfop_sfo</span> <span class='op'>&lt;-</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='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
    A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>

  <span class='va'>f_2</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/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='st'>"SFO-SFO-ff"</span> <span class='op'>=</span> <span class='va'>m_sfo_sfo_ff</span>,
   <span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>m_dfop_sfo</span><span class='op'>)</span>,
    <span class='va'>ds_2</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>

  <span class='va'>f_nlme_sfo_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='op'>]</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_nlme_sfo_sfo</span><span class='op'>)</span>
</div><div class='img'><img src='nlme.mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'>
  <span class='co'># With formation fractions this does not coverge with defaults</span>
  <span class='co'># f_nlme_sfo_sfo_ff &lt;- nlme(f_2["SFO-SFO-ff", ])</span>
  <span class='co'>#plot(f_nlme_sfo_sfo_ff)</span>

  <span class='co'># For the following, we need to increase pnlsMaxIter and the tolerance</span>
  <span class='co'># to get convergence</span>
  <span class='va'>f_nlme_dfop_sfo</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='op'>]</span>,
    control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>pnlsMaxIter <span class='op'>=</span> <span class='fl'>120</span>, tolerance <span class='op'>=</span> <span class='fl'>5e-4</span><span class='op'>)</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_nlme_dfop_sfo</span><span class='op'>)</span>
</div><div class='img'><img src='nlme.mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'>
  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span>, <span class='va'>f_nlme_sfo_sfo</span><span class='op'>)</span>
</div><div class='output co'>#&gt;                 Model df       AIC       BIC    logLik   Test  L.Ratio p-value
#&gt; f_nlme_dfop_sfo     1 13  843.8548  884.6201 -408.9274                        
#&gt; f_nlme_sfo_sfo      2  9 1085.1821 1113.4043 -533.5910 1 vs 2 249.3273  &lt;.0001</div><div class='input'>
  <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo_sfo</span><span class='op'>)</span>
</div><div class='output co'>#&gt; $ff
#&gt; parent_sink   parent_A1     A1_sink 
#&gt;   0.5912432   0.4087568   1.0000000 
#&gt; 
#&gt; $distimes
#&gt;            DT50     DT90
#&gt; parent 19.13518  63.5657
#&gt; A1     66.02155 219.3189
#&gt; </div><div class='input'>  <span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span><span class='op'>)</span>
</div><div class='output co'>#&gt; $ff
#&gt;   parent_A1 parent_sink 
#&gt;   0.2768575   0.7231425 
#&gt; 
#&gt; $distimes
#&gt;             DT50     DT90 DT50back  DT50_k1  DT50_k2
#&gt; parent  11.07091 104.6320 31.49737 4.462384 46.20825
#&gt; A1     162.30492 539.1653       NA       NA       NA
#&gt; </div><div class='input'>
  <span class='kw'>if</span> <span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>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'>&gt;</span> <span class='fl'>0</span><span class='op'>)</span> <span class='op'>{</span> <span class='co'># tc error model for nlme available</span>
    <span class='co'># Attempts to fit metabolite kinetics with the tc error model are possible,</span>
    <span class='co'># but need tweeking of control values and sometimes do not converge</span>

    <span class='va'>f_tc</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'>c</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"DFOP"</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
    <span class='va'>f_nlme_sfo_tc</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_tc</span><span class='op'>[</span><span class='st'>"SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
    <span class='va'>f_nlme_dfop_tc</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_tc</span><span class='op'>[</span><span class='st'>"DFOP"</span>, <span class='op'>]</span><span class='op'>)</span>
    <span class='fu'><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo</span>, <span class='va'>f_nlme_sfo_tc</span>, <span class='va'>f_nlme_dfop</span>, <span class='va'>f_nlme_dfop_tc</span><span class='op'>)</span>
    <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_tc</span><span class='op'>)</span>
  <span class='op'>}</span>
</div><div class='output co'>#&gt; Kinetic nonlinear mixed-effects model fit by maximum likelihood
#&gt; 
#&gt; Structural model:
#&gt; d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
#&gt;            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
#&gt;            * parent
#&gt; 
#&gt; Data:
#&gt; 90 observations of 1 variable(s) grouped in 5 datasets
#&gt; 
#&gt; Log-likelihood: -238.4
#&gt; 
#&gt; Fixed effects:
#&gt;  list(parent_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1) 
#&gt; parent_0   log_k1   log_k2 g_qlogis 
#&gt; 94.04774 -1.82340 -4.16716  0.05686 
#&gt; 
#&gt; Random effects:
#&gt;  Formula: list(parent_0 ~ 1, log_k1 ~ 1, log_k2 ~ 1, g_qlogis ~ 1)
#&gt;  Level: ds
#&gt;  Structure: Diagonal
#&gt;         parent_0 log_k1 log_k2 g_qlogis Residual
#&gt; StdDev:    2.474   0.85  1.337   0.4659        1
#&gt; 
#&gt; Variance function:
#&gt;  Structure: Constant plus proportion of variance covariate
#&gt;  Formula: ~fitted(.) 
#&gt;  Parameter estimates:
#&gt;      const       prop 
#&gt; 2.23223147 0.01262395 </div><div class='input'>
  <span class='va'>f_2_obs</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>f_2</span>, error_model <span class='op'>=</span> <span class='st'>"obs"</span><span class='op'>)</span>
  <span class='va'>f_nlme_sfo_sfo_obs</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2_obs</span><span class='op'>[</span><span class='st'>"SFO-SFO"</span>, <span class='op'>]</span><span class='op'>)</span>
  <span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>f_nlme_sfo_sfo_obs</span><span class='op'>)</span>
</div><div class='output co'>#&gt; Kinetic nonlinear mixed-effects model fit by maximum likelihood
#&gt; 
#&gt; Structural model:
#&gt; d_parent/dt = - k_parent_sink * parent - k_parent_A1 * parent
#&gt; d_A1/dt = + k_parent_A1 * parent - k_A1_sink * A1
#&gt; 
#&gt; Data:
#&gt; 170 observations of 2 variable(s) grouped in 5 datasets
#&gt; 
#&gt; Log-likelihood: -473
#&gt; 
#&gt; Fixed effects:
#&gt;  list(parent_0 ~ 1, log_k_parent_sink ~ 1, log_k_parent_A1 ~ 1,      log_k_A1_sink ~ 1) 
#&gt;          parent_0 log_k_parent_sink   log_k_parent_A1     log_k_A1_sink 
#&gt;            87.976            -3.670            -4.164            -4.645 
#&gt; 
#&gt; Random effects:
#&gt;  Formula: list(parent_0 ~ 1, log_k_parent_sink ~ 1, log_k_parent_A1 ~ 1,      log_k_A1_sink ~ 1)
#&gt;  Level: ds
#&gt;  Structure: Diagonal
#&gt;         parent_0 log_k_parent_sink log_k_parent_A1 log_k_A1_sink Residual
#&gt; StdDev:    3.992             1.777           1.055        0.4821    6.483
#&gt; 
#&gt; Variance function:
#&gt;  Structure: Different standard deviations per stratum
#&gt;  Formula: ~1 | name 
#&gt;  Parameter estimates:
#&gt;    parent        A1 
#&gt; 1.0000000 0.2049995 </div><div class='input'>  <span class='va'>f_nlme_dfop_sfo_obs</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f_2_obs</span><span class='op'>[</span><span class='st'>"DFOP-SFO"</span>, <span class='op'>]</span>,
    control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>pnlsMaxIter <span class='op'>=</span> <span class='fl'>120</span>, tolerance <span class='op'>=</span> <span class='fl'>5e-4</span><span class='op'>)</span><span class='op'>)</span>

  <span class='va'>f_2_tc</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/update.html'>update</a></span><span class='op'>(</span><span class='va'>f_2</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
  <span class='co'># f_nlme_sfo_sfo_tc &lt;- nlme(f_2_tc["SFO-SFO", ]) # No convergence with 50 iterations</span>
  <span class='co'># f_nlme_dfop_sfo_tc &lt;- nlme(f_2_tc["DFOP-SFO", ],</span>
  <span class='co'>#  control = list(pnlsMaxIter = 120, tolerance = 5e-4)) # Error in X[, fmap[[nm]]] &lt;- gradnm</span>

  <span class='fu'><a href='https://rdrr.io/r/stats/anova.html'>anova</a></span><span class='op'>(</span><span class='va'>f_nlme_dfop_sfo</span>, <span class='va'>f_nlme_dfop_sfo_obs</span><span class='op'>)</span>
</div><div class='output co'>#&gt;                     Model df      AIC      BIC    logLik   Test  L.Ratio
#&gt; f_nlme_dfop_sfo         1 13 843.8548 884.6201 -408.9274                
#&gt; f_nlme_dfop_sfo_obs     2 14 817.5338 861.4350 -394.7669 1 vs 2 28.32093
#&gt;                     p-value
#&gt; f_nlme_dfop_sfo            
#&gt; f_nlme_dfop_sfo_obs  &lt;.0001</div><div class='input'>
<span class='co'># }</span>
</div></pre>
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