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<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'><-</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'>#> <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'><-</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'>#> <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'><-</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>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 99.60 1.5702 96.40 102.79
#> log_k_parent_sink -3.04 0.0763 -3.19 -2.88
#> log_k_parent_m1 -2.98 0.0403 -3.06 -2.90
#> log_k_m1_sink -5.25 0.1332 -5.52 -4.98
#> sigma 3.13 0.3585 2.40 3.85</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 102.7931
#> k_parent_sink 0.04792 0.00365 13.11 6.13e-15 0.04103 0.0560
#> k_parent_m1 0.05078 0.00205 24.80 3.27e-23 0.04678 0.0551
#> k_m1_sink 0.00526 0.00070 7.51 6.16e-09 0.00401 0.0069
#> 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'><-</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'>#> <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'><-</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>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 99.59848 1.57022 96.40384 1.03e+02
#> k_parent_sink 0.04792 0.00365 0.04049 5.54e-02
#> k_parent_m1 0.05078 0.00205 0.04661 5.49e-02
#> k_m1_sink 0.00526 0.00070 0.00384 6.69e-03
#> sigma 3.12550 0.35852 2.39609 3.85e+00</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.2.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 1.03e+02
#> k_parent_sink 0.04792 0.00365 13.11 6.13e-15 0.04049 5.54e-02
#> k_parent_m1 0.05078 0.00205 24.80 3.27e-23 0.04661 5.49e-02
#> k_m1_sink 0.00526 0.00070 7.51 6.16e-09 0.00384 6.69e-03
#> 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'><-</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'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/colnames'>rownames</a></span>(<span class='no'>fit</span>$<span class='no'>start</span>)
<span class='no'>transformed</span> <span class='kw'><-</span> <span class='no'>fit</span>$<span class='no'>start_transformed</span>$<span class='no'>value</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/names'>names</a></span>(<span class='no'>transformed</span>) <span class='kw'><-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/colnames'>rownames</a></span>(<span class='no'>fit</span>$<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'>#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
#> 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'>#> parent_0 k_parent_sink k_parent_m1 k_m1_sink
#> 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'><-</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'>#> <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'><-</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'>#> <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'><-</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>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 99.598 1.5702 96.4038 102.793
#> log_k_parent -2.316 0.0409 -2.3988 -2.233
#> log_k_m1 -5.248 0.1332 -5.5184 -4.977
#> f_parent_ilr_1 0.041 0.0631 -0.0875 0.169
#> sigma 3.126 0.3585 2.3961 3.855</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.ff.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 102.7931
#> k_parent 0.09870 0.00403 24.47 4.96e-23 0.09082 0.1073
#> k_m1 0.00526 0.00070 7.51 6.16e-09 0.00401 0.0069
#> f_parent_to_m1 0.51448 0.02230 23.07 3.10e-22 0.46912 0.5596
#> 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'><-</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'><-</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'>#> f_parent_to_m1
#> 0.5 </div><div class='input'>
<span class='co'># And without sink</span>
<span class='no'>SFO_SFO.ff.2</span> <span class='kw'><-</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'>#> <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'><-</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'>#> <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'><-</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>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 84.79 3.012 78.67 90.91
#> log_k_parent -2.76 0.082 -2.92 -2.59
#> log_k_m1 -4.21 0.123 -4.46 -3.96
#> sigma 8.22 0.943 6.31 10.14</div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='no'>fit.ff.2.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate se_notrans t value Pr(>t) Lower Upper
#> parent_0 84.7916 3.01203 28.15 1.92e-25 78.6704 90.913
#> k_parent 0.0635 0.00521 12.19 2.91e-14 0.0538 0.075
#> k_m1 0.0148 0.00182 8.13 8.81e-10 0.0115 0.019
#> 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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