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<h1>Functions to transform and backtransform kinetic parameters for fitting</h1>
<small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/transform_odeparms.R'><code>R/transform_odeparms.R</code></a></small>
<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>
</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>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>
<tr>
<th>transparms</th>
<td><p>Transformed parameters of kinetic models as used in the
fitting procedure.</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="details"><a class="anchor" href="#details"></a>Details</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 <code><a href='mkinfit.html'>mkinfit</a></code>.</p>
<h2 class="hasAnchor" id="functions"><a class="anchor" href="#functions"></a>Functions</h2>
<ul>
<li><p><code>backtransform_odeparms</code>: Backtransform the set of transformed parameters</p></li>
</ul>
<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://rdrr.io/r/base/list.html'>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://rdrr.io/r/base/list.html'>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://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit</span>)
<span class='co'># Transformed and backtransformed parameters</span>
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 99.598 1.5702 96.4038 102.793
#> log_k_parent -2.316 0.0409 -2.3988 -2.233
#> log_k_m1 -5.248 0.1332 -5.5184 -4.977
#> f_parent_ilr_1 0.041 0.0631 -0.0875 0.169
#> sigma 3.126 0.3585 2.3961 3.855</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.s</span>$<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 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='co'># \dontrun{</span>
<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='output co'>#> <span class='error'>Error in if (cost < cost.current) { assign("cost.current", cost, inherits = TRUE) if (!quiet) cat(ifelse(OLS, "Sum of squared residuals", "Negative log-likelihood"), " at call ", calls, ": ", cost.current, "\n", sep = "")}: Fehlender Wert, wo TRUE/FALSE nötig ist</span></div><div class='output co'>#> <span class='message'>Timing stopped at: 0.002 0 0.003</span></div><div class='input'><span class='no'>fit.2.s</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit.2</span>)</div><div class='output co'>#> <span class='error'>Error in summary(fit.2): Objekt 'fit.2' nicht gefunden</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.2.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> <span class='error'>Error in print(fit.2.s$par, 3): Objekt 'fit.2.s' nicht gefunden</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.2.s</span>$<span class='no'>bpar</span>, <span class='fl'>3</span>)</div><div class='output co'>#> <span class='error'>Error in print(fit.2.s$bpar, 3): Objekt 'fit.2.s' nicht gefunden</span></div><div class='input'><span class='co'># }</span>
<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://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>initials</span>) <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/colnames.html'>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>$<span class='no'>value</span>
<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>transformed</span>) <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/colnames.html'>rownames</a></span>(<span class='no'>fit</span>$<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 log_k_m1 f_parent_ilr_1
#> 100.750000 -2.302585 -2.301586 0.000000 </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 k_m1 f_parent_to_m1
#> 100.7500 0.1000 0.1001 0.5000 </div><div class='input'>
<span class='co'># \dontrun{</span>
<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://rdrr.io/r/base/list.html'>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://rdrr.io/r/base/list.html'>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://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit.ff</span>)
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.ff.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 99.598 1.5702 96.4038 102.793
#> log_k_parent -2.316 0.0409 -2.3988 -2.233
#> log_k_m1 -5.248 0.1332 -5.5184 -4.977
#> f_parent_ilr_1 0.041 0.0631 -0.0875 0.169
#> sigma 3.126 0.3585 2.3961 3.855</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.ff.s</span>$<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://rdrr.io/r/base/c.html'>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://rdrr.io/r/base/list.html'>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://rdrr.io/r/base/list.html'>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://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit.ff.2</span>)
<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.ff.2.s</span>$<span class='no'>par</span>, <span class='fl'>3</span>)</div><div class='output co'>#> Estimate Std. Error Lower Upper
#> parent_0 84.79 3.012 78.67 90.91
#> log_k_parent -2.76 0.082 -2.92 -2.59
#> log_k_m1 -4.21 0.123 -4.46 -3.96
#> sigma 8.22 0.943 6.31 10.14</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='no'>fit.ff.2.s</span>$<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><div class='input'># }
</div></pre>
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