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restricted values to the full scale of real numbers. For kinetic rate
constants and other parameters 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,
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<img src="" class="logo" alt=""><h1>Functions to transform and backtransform kinetic parameters for fitting</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/transform_odeparms.R" class="external-link"><code>R/transform_odeparms.R</code></a></small>
<div class="d-none name"><code>transform_odeparms.Rd</code></div>
</div>
<div class="ref-description section level2">
<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 parameters 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 <a href="ilr.html">ilr</a> transformation is used.</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">transform_odeparms</span><span class="op">(</span></span>
<span> <span class="va">parms</span>,</span>
<span> <span class="va">mkinmod</span>,</span>
<span> transform_rates <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> transform_fractions <span class="op">=</span> <span class="cn">TRUE</span></span>
<span><span class="op">)</span></span>
<span></span>
<span><span class="fu">backtransform_odeparms</span><span class="op">(</span></span>
<span> <span class="va">transparms</span>,</span>
<span> <span class="va">mkinmod</span>,</span>
<span> transform_rates <span class="op">=</span> <span class="cn">TRUE</span>,</span>
<span> transform_fractions <span class="op">=</span> <span class="cn">TRUE</span></span>
<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>parms</dt>
<dd><p>Parameters of kinetic models as used in the differential
equations.</p></dd>
<dt>mkinmod</dt>
<dd><p>The kinetic model of class <a href="mkinmod.html">mkinmod</a>, containing
the names of the model variables that are needed for grouping the
formation fractions before <a href="ilr.html">ilr</a> transformation, the parameter
names and the information if the pathway to sink is included in the model.</p></dd>
<dt>transform_rates</dt>
<dd><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></dd>
<dt>transform_fractions</dt>
<dd><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 model is also seen as a fraction.
If a single fraction is transformed (g parameter of DFOP or only a single
target variable e.g. a single metabolite plus a pathway to sink), a
logistic transformation is used <code><a href="https://rdrr.io/r/stats/Logistic.html" class="external-link">stats::qlogis()</a></code>. In other cases, i.e. if
two or more formation fractions need to be transformed whose sum cannot
exceed one, the <a href="ilr.html">ilr</a> transformation is used.</p></dd>
<dt>transparms</dt>
<dd><p>Transformed parameters of kinetic models as used in the
fitting procedure.</p></dd>
</dl></div>
<div class="section level2">
<h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
<p>A vector of transformed or backtransformed parameters</p>
</div>
<div class="section level2">
<h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
<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 <a href="mkinfit.html">mkinfit</a>.</p>
</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></span>
<span class="r-in"><span><span class="va">SFO_SFO</span> <span class="op"><-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span></span></span>
<span class="r-in"><span> parent <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>type <span class="op">=</span> <span class="st">"SFO"</span>, to <span class="op">=</span> <span class="st">"m1"</span>, sink <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> m1 <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>type <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><span class="op">)</span></span></span>
<span class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># Fit the model to the FOCUS example dataset D using defaults</span></span></span>
<span class="r-in"><span><span class="va">FOCUS_D</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">FOCUS_2006_D</span>, <span class="va">value</span> <span class="op">!=</span> <span class="fl">0</span><span class="op">)</span> <span class="co"># remove zero values to avoid warning</span></span></span>
<span class="r-in"><span><span class="va">fit</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</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">fit.s</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="co"># Transformed and backtransformed parameters</span></span></span>
<span class="r-in"><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">fit.s</span><span class="op">$</span><span class="va">par</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 99.60 1.5702 96.40 102.79</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_parent_sink -3.04 0.0763 -3.19 -2.88</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_parent_m1 -2.98 0.0403 -3.06 -2.90</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1_sink -5.25 0.1332 -5.52 -4.98</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 3.13 0.3585 2.40 3.85</span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">fit.s</span><span class="op">$</span><span class="va">bpar</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate se_notrans t value Pr(>t) Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 102.7931</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent_sink 0.04792 0.00365 13.11 6.13e-15 0.04103 0.0560</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent_m1 0.05078 0.00205 24.80 3.27e-23 0.04678 0.0551</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1_sink 0.00526 0.00070 7.51 6.16e-09 0.00401 0.0069</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 3.12550 0.35852 8.72 2.24e-10 2.39609 3.8549</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
<span class="r-in"><span><span class="co"># Compare to the version without transforming rate parameters (does not work</span></span></span>
<span class="r-in"><span><span class="co"># with analytical solution, we get NA values for m1 in predictions)</span></span></span>
<span class="r-in"><span><span class="va">fit.2</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO</span>, <span class="va">FOCUS_D</span>, transform_rates <span class="op">=</span> <span class="cn">FALSE</span>,</span></span>
<span class="r-in"><span> solution_type <span class="op">=</span> <span class="st">"deSolve"</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">fit.2.s</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit.2</span><span class="op">)</span></span></span>
<span class="r-in"><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">fit.2.s</span><span class="op">$</span><span class="va">par</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 99.59848 1.57022 96.40384 1.03e+02</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent_sink 0.04792 0.00365 0.04049 5.54e-02</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent_m1 0.05078 0.00205 0.04661 5.49e-02</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1_sink 0.00526 0.00070 0.00384 6.69e-03</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 3.12550 0.35852 2.39609 3.85e+00</span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">fit.2.s</span><span class="op">$</span><span class="va">bpar</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate se_notrans t value Pr(>t) Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40384 1.03e+02</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent_sink 0.04792 0.00365 13.11 6.13e-15 0.04049 5.54e-02</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent_m1 0.05078 0.00205 24.80 3.27e-23 0.04661 5.49e-02</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1_sink 0.00526 0.00070 7.51 6.16e-09 0.00384 6.69e-03</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 3.12550 0.35852 8.72 2.24e-10 2.39609 3.85e+00</span>
<span class="r-in"><span><span class="co"># }</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">initials</span> <span class="op"><-</span> <span class="va">fit</span><span class="op">$</span><span class="va">start</span><span class="op">$</span><span class="va">value</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">initials</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">fit</span><span class="op">$</span><span class="va">start</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">transformed</span> <span class="op"><-</span> <span class="va">fit</span><span class="op">$</span><span class="va">start_transformed</span><span class="op">$</span><span class="va">value</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/names.html" class="external-link">names</a></span><span class="op">(</span><span class="va">transformed</span><span class="op">)</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/colnames.html" class="external-link">rownames</a></span><span class="op">(</span><span class="va">fit</span><span class="op">$</span><span class="va">start_transformed</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu">transform_odeparms</span><span class="op">(</span><span class="va">initials</span>, <span class="va">SFO_SFO</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink </span>
<span class="r-out co"><span class="r-pr">#></span> 100.750000 -2.302585 -2.301586 -2.300587 </span>
<span class="r-in"><span><span class="fu">backtransform_odeparms</span><span class="op">(</span><span class="va">transformed</span>, <span class="va">SFO_SFO</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 k_parent_sink k_parent_m1 k_m1_sink </span>
<span class="r-out co"><span class="r-pr">#></span> 100.7500 0.1000 0.1001 0.1002 </span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
<span class="r-in"><span><span class="co"># The case of formation fractions (this is now the default)</span></span></span>
<span class="r-in"><span><span class="va">SFO_SFO.ff</span> <span class="op"><-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span></span></span>
<span class="r-in"><span> parent <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>type <span class="op">=</span> <span class="st">"SFO"</span>, to <span class="op">=</span> <span class="st">"m1"</span>, sink <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> m1 <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>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></span>
<span class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">fit.ff</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO.ff</span>, <span class="va">FOCUS_D</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">fit.ff.s</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit.ff</span><span class="op">)</span></span></span>
<span class="r-in"><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">fit.ff.s</span><span class="op">$</span><span class="va">par</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 99.5985 1.5702 96.404 102.79</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_parent -2.3157 0.0409 -2.399 -2.23</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -5.2475 0.1332 -5.518 -4.98</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_qlogis 0.0579 0.0893 -0.124 0.24</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 3.1255 0.3585 2.396 3.85</span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">fit.ff.s</span><span class="op">$</span><span class="va">bpar</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate se_notrans t value Pr(>t) Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 99.59848 1.57022 63.43 2.30e-36 96.40383 102.7931</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent 0.09870 0.00403 24.47 4.96e-23 0.09082 0.1073</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1 0.00526 0.00070 7.51 6.16e-09 0.00401 0.0069</span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 0.51448 0.02230 23.07 3.10e-22 0.46912 0.5596</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 3.12550 0.35852 8.72 2.24e-10 2.39609 3.8549</span>
<span class="r-in"><span><span class="va">initials</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">"f_parent_to_m1"</span> <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">transformed</span> <span class="op"><-</span> <span class="fu">transform_odeparms</span><span class="op">(</span><span class="va">initials</span>, <span class="va">SFO_SFO.ff</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="fu">backtransform_odeparms</span><span class="op">(</span><span class="va">transformed</span>, <span class="va">SFO_SFO.ff</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> f_parent_to_m1 </span>
<span class="r-out co"><span class="r-pr">#></span> 0.5 </span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># And without sink</span></span></span>
<span class="r-in"><span><span class="va">SFO_SFO.ff.2</span> <span class="op"><-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span></span></span>
<span class="r-in"><span> parent <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>type <span class="op">=</span> <span class="st">"SFO"</span>, to <span class="op">=</span> <span class="st">"m1"</span>, sink <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> m1 <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>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>,</span></span>
<span class="r-in"><span> use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></span>
<span class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="va">fit.ff.2</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">SFO_SFO.ff.2</span>, <span class="va">FOCUS_D</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">fit.ff.2.s</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/saemix/man/summary-methods.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">fit.ff.2</span><span class="op">)</span></span></span>
<span class="r-in"><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">fit.ff.2.s</span><span class="op">$</span><span class="va">par</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 84.79 3.012 78.67 90.91</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_parent -2.76 0.082 -2.92 -2.59</span>
<span class="r-out co"><span class="r-pr">#></span> log_k_m1 -4.21 0.123 -4.46 -3.96</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 8.22 0.943 6.31 10.14</span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="va">fit.ff.2.s</span><span class="op">$</span><span class="va">bpar</span>, <span class="fl">3</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Estimate se_notrans t value Pr(>t) Lower Upper</span>
<span class="r-out co"><span class="r-pr">#></span> parent_0 84.7916 3.01203 28.15 1.92e-25 78.6704 90.913</span>
<span class="r-out co"><span class="r-pr">#></span> k_parent 0.0635 0.00521 12.19 2.91e-14 0.0538 0.075</span>
<span class="r-out co"><span class="r-pr">#></span> k_m1 0.0148 0.00182 8.13 8.81e-10 0.0115 0.019</span>
<span class="r-out co"><span class="r-pr">#></span> sigma 8.2229 0.94323 8.72 1.73e-10 6.3060 10.140</span>
<span class="r-in"><span><span class="co"># }</span></span></span>
<span class="r-in"><span></span></span>
</code></pre></div>
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