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<meta property="og:title" content="Functions to transform and backtransform kinetic parameters for fitting — transform_odeparms" />

<meta property="og:description" content="The transformations are intended to map parameters that should only take
  on restricted values to the full scale of real numbers. For kinetic rate
  constants and other paramters that can only take on positive values, a
  simple log transformation is used. For compositional parameters, such as
  the formations fractions that should always sum up to 1 and can not be
  negative, the ilr transformation is used.
The transformation of sets of formation fractions is fragile, as it supposes
  the same ordering of the components in forward and backward transformation.
  This is no problem for the internal use in mkinfit." />
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    <h1>Functions to transform and backtransform kinetic parameters for fitting</h1>
    
    <div class="hidden name"><code>transform_odeparms.Rd</code></div>
    </div>

    <div class="ref-description">
    
    <p>The transformations are intended to map parameters that should only take
  on restricted values to the full scale of real numbers. For kinetic rate
  constants and other paramters that can only take on positive values, a
  simple log transformation is used. For compositional parameters, such as
  the formations fractions that should always sum up to 1 and can not be
  negative, the <code><a href='ilr.html'>ilr</a></code> transformation is used.</p>
<p>The transformation of sets of formation fractions is fragile, as it supposes
  the same ordering of the components in forward and backward transformation.
  This is no problem for the internal use in <code><a href='mkinfit.html'>mkinfit</a></code>.</p>
    
    </div>

    <pre class="usage"><span class='fu'>transform_odeparms</span>(<span class='no'>parms</span>, <span class='no'>mkinmod</span>,
                   <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'>backtransform_odeparms</span>(<span class='no'>transparms</span>, <span class='no'>mkinmod</span>,
                       <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</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>parms</th>
      <td><p>Parameters of kinetic models as used in the differential equations.</p></td>
    </tr>
    <tr>
      <th>transparms</th>
      <td><p>Transformed parameters of kinetic models as used in the fitting procedure.</p></td>
    </tr>
    <tr>
      <th>mkinmod</th>
      <td><p>The kinetic model of class <code><a href='mkinmod.html'>mkinmod</a></code>, containing the names of
    the model variables that are needed for grouping the formation fractions
    before <code><a href='ilr.html'>ilr</a></code> transformation, the parameter names and
    the information if the pathway to sink is included in the model.</p></td>
    </tr>
    <tr>
      <th>transform_rates</th>
      <td><p>Boolean specifying if kinetic rate constants should be transformed in the
    model specification used in the fitting for better compliance with the
    assumption of normal distribution of the estimator. If TRUE, also
    alpha and beta parameters of the FOMC model are log-transformed, as well
    as k1 and k2 rate constants for the DFOP and HS models and the break point tb
    of the HS model.</p></td>
    </tr>
    <tr>
      <th>transform_fractions</th>
      <td><p>Boolean specifying if formation fractions constants should be transformed in the
    model specification used in the fitting for better compliance with the
    assumption of normal distribution of the estimator. The default (TRUE) is
    to do transformations. The g parameter of the DFOP and HS models are also
    transformed, as they can also be seen as compositional data. The
    transformation used for these transformations is the <code><a href='ilr.html'>ilr</a></code>
    transformation.</p></td>
    </tr>
    </table>
    
    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>A vector of transformed or backtransformed parameters with the same names
  as the original parameters.</p>
    

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'><span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit.s</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>fit</span>)
<span class='co'># Transformed and backtransformed parameters</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                   Estimate Std. Error Lower  Upper
#&gt; parent_0             99.60     1.5702 96.40 102.79
#&gt; log_k_parent_sink    -3.04     0.0763 -3.19  -2.88
#&gt; log_k_parent_m1      -2.98     0.0403 -3.06  -2.90
#&gt; log_k_m1_sink        -5.25     0.1332 -5.52  -4.98
#&gt; sigma                 3.13     0.3585  2.40   3.85</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;               Estimate se_notrans t value   Pr(&gt;t)    Lower    Upper
#&gt; parent_0      99.59848    1.57022   63.43 2.30e-36 96.40384 102.7931
#&gt; k_parent_sink  0.04792    0.00365   13.11 6.13e-15  0.04103   0.0560
#&gt; k_parent_m1    0.05078    0.00205   24.80 3.27e-23  0.04678   0.0551
#&gt; k_m1_sink      0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
#&gt; sigma          3.12550    0.35852    8.72 2.24e-10  2.39609   3.8549</div><div class='input'>
</div><div class='input'><span class='co'># Compare to the version without transforming rate parameters</span>
<span class='no'>fit.2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit.2.s</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>fit.2</span>)
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.2.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;               Estimate Std. Error    Lower    Upper
#&gt; parent_0      99.59848    1.57022 96.40384 1.03e+02
#&gt; k_parent_sink  0.04792    0.00365  0.04049 5.54e-02
#&gt; k_parent_m1    0.05078    0.00205  0.04661 5.49e-02
#&gt; k_m1_sink      0.00526    0.00070  0.00384 6.69e-03
#&gt; sigma          3.12550    0.35852  2.39609 3.85e+00</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.2.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;               Estimate se_notrans t value   Pr(&gt;t)    Lower    Upper
#&gt; parent_0      99.59848    1.57022   63.43 2.30e-36 96.40384 1.03e+02
#&gt; k_parent_sink  0.04792    0.00365   13.11 6.13e-15  0.04049 5.54e-02
#&gt; k_parent_m1    0.05078    0.00205   24.80 3.27e-23  0.04661 5.49e-02
#&gt; k_m1_sink      0.00526    0.00070    7.51 6.16e-09  0.00384 6.69e-03
#&gt; sigma          3.12550    0.35852    8.72 2.24e-10  2.39609 3.85e+00</div><div class='input'>
<span class='no'>initials</span> <span class='kw'>&lt;-</span> <span class='no'>fit</span>$<span class='no'>start</span>$<span class='no'>value</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/names'>names</a></span>(<span class='no'>initials</span>) <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/colnames'>rownames</a></span>(<span class='no'>fit</span>$<span class='no'>start</span>)
<span class='no'>transformed</span> <span class='kw'>&lt;-</span> <span class='no'>fit</span>$<span class='no'>start_transformed</span>$<span class='no'>value</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/names'>names</a></span>(<span class='no'>transformed</span>) <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/colnames'>rownames</a></span>(<span class='no'>fit</span>$<span class='no'>start_transformed</span>)
<span class='fu'>transform_odeparms</span>(<span class='no'>initials</span>, <span class='no'>SFO_SFO</span>)</div><div class='output co'>#&gt;          parent_0 log_k_parent_sink   log_k_parent_m1     log_k_m1_sink 
#&gt;        100.750000         -2.302585         -2.301586         -2.300587 </div><div class='input'><span class='fu'>backtransform_odeparms</span>(<span class='no'>transformed</span>, <span class='no'>SFO_SFO</span>)</div><div class='output co'>#&gt;      parent_0 k_parent_sink   k_parent_m1     k_m1_sink 
#&gt;      100.7500        0.1000        0.1001        0.1002 </div><div class='input'>
</div><div class='input'><span class='co'># The case of formation fractions</span>
<span class='no'>SFO_SFO.ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>
<span class='no'>fit.ff</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit.ff.s</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>fit.ff</span>)
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.ff.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                Estimate Std. Error   Lower   Upper
#&gt; parent_0         99.598     1.5702 96.4038 102.793
#&gt; log_k_parent     -2.316     0.0409 -2.3988  -2.233
#&gt; log_k_m1         -5.248     0.1332 -5.5184  -4.977
#&gt; f_parent_ilr_1    0.041     0.0631 -0.0875   0.169
#&gt; sigma             3.126     0.3585  2.3961   3.855</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.ff.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;                Estimate se_notrans t value   Pr(&gt;t)    Lower    Upper
#&gt; parent_0       99.59848    1.57022   63.43 2.30e-36 96.40384 102.7931
#&gt; k_parent        0.09870    0.00403   24.47 4.96e-23  0.09082   0.1073
#&gt; k_m1            0.00526    0.00070    7.51 6.16e-09  0.00401   0.0069
#&gt; f_parent_to_m1  0.51448    0.02230   23.07 3.10e-22  0.46912   0.5596
#&gt; sigma           3.12550    0.35852    8.72 2.24e-10  2.39609   3.8549</div><div class='input'><span class='no'>initials</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='st'>"f_parent_to_m1"</span> <span class='kw'>=</span> <span class='fl'>0.5</span>)
<span class='no'>transformed</span> <span class='kw'>&lt;-</span> <span class='fu'>transform_odeparms</span>(<span class='no'>initials</span>, <span class='no'>SFO_SFO.ff</span>)
<span class='fu'>backtransform_odeparms</span>(<span class='no'>transformed</span>, <span class='no'>SFO_SFO.ff</span>)</div><div class='output co'>#&gt; f_parent_to_m1 
#&gt;            0.5 </div><div class='input'>
<span class='co'># And without sink</span>
<span class='no'>SFO_SFO.ff.2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>),
  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
  <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#&gt; <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'>

<span class='no'>fit.ff.2</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>SFO_SFO.ff.2</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit.ff.2.s</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>fit.ff.2</span>)
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.ff.2.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;              Estimate Std. Error Lower Upper
#&gt; parent_0        84.79      3.012 78.67 90.91
#&gt; log_k_parent    -2.76      0.082 -2.92 -2.59
#&gt; log_k_m1        -4.21      0.123 -4.46 -3.96
#&gt; sigma            8.22      0.943  6.31 10.14</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.ff.2.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#&gt;          Estimate se_notrans t value   Pr(&gt;t)   Lower  Upper
#&gt; parent_0  84.7916    3.01203   28.15 1.92e-25 78.6704 90.913
#&gt; k_parent   0.0635    0.00521   12.19 2.91e-14  0.0538  0.075
#&gt; k_m1       0.0148    0.00182    8.13 8.81e-10  0.0115  0.019
#&gt; sigma      8.2229    0.94323    8.72 1.73e-10  6.3060 10.140</div></pre>
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    <h2>Contents</h2>
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      <li><a href="#arguments">Arguments</a></li>
      
      <li><a href="#value">Value</a></li>
      
      <li><a href="#examples">Examples</a></li>
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    <h2>Author</h2>
    <p>Johannes Ranke</p>
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