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-<title>transform_odeparms. mkin 0.9.44.9000</title>
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- Johannes Ranke
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-
- <h1>
- Functions to transform and backtransform kinetic parameters for fitting
-</h1>
-
-<div class="row">
- <div class="span8">
- <h2>Usage</h2>
- <pre><div>transform_odeparms(parms, mkinmod, transform_rates&nbsp;=&nbsp;TRUE, transform_fractions&nbsp;=&nbsp;TRUE)
-backtransform_odeparms(transparms, mkinmod, transform_rates&nbsp;=&nbsp;TRUE, transform_fractions&nbsp;=&nbsp;TRUE)</div></pre>
-
- <h2>Arguments</h2>
- <dl>
- <dt>parms</dt>
- <dd>
- Parameters of kinetic models as used in the differential equations.
- </dd>
- <dt>transparms</dt>
- <dd>
- Transformed parameters of kinetic models as used in the fitting procedure.
- </dd>
- <dt>mkinmod</dt>
- <dd>
- 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.
- </dd>
- <dt>transform_rates</dt>
- <dd>
- 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.
- </dd>
- <dt>transform_fractions</dt>
- <dd>
- 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.
- </dd>
- </dl>
-
- <div class="Description">
- <h2>Description</h2>
-
- <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>
-
- <div class="Value">
- <h2>Value</h2>
-
- <p><dl>
- A vector of transformed or backtransformed parameters with the same names
- as the original parameters.
-</dl></p>
-
- </div>
-
- <h2 id="examples">Examples</h2>
- <pre class="examples"><div class='input'>SFO_SFO &lt;- mkinmod(
- parent = list(type = &quot;SFO&quot;, to = &quot;m1&quot;, sink = TRUE),
- m1 = list(type = &quot;SFO&quot;))
-</div>
-<strong class='message'>Successfully compiled differential equation model from auto-generated C code.</strong>
-<div class='input'># Fit the model to the FOCUS example dataset D using defaults
-fit &lt;- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
-summary(fit, data=FALSE) # See transformed and backtransformed parameters
-</div>
-<div class='output'>mkin version: 0.9.44.9000
-R version: 3.3.1
-Date of fit: Sat Sep 10 05:19:46 2016
-Date of summary: Sat Sep 10 05:19:46 2016
-
-Equations:
-d_parent = - k_parent_sink * parent - k_parent_m1 * parent
-d_m1 = + k_parent_m1 * parent - k_m1_sink * m1
-
-Model predictions using solution type deSolve
-
-Fitted with method Port using 153 model solutions performed in 0.681 s
-
-Weighting: none
-
-Starting values for parameters to be optimised:
- value type
-parent_0 100.7500 state
-k_parent_sink 0.1000 deparm
-k_parent_m1 0.1001 deparm
-k_m1_sink 0.1002 deparm
-
-Starting values for the transformed parameters actually optimised:
- value lower upper
-parent_0 100.750000 -Inf Inf
-log_k_parent_sink -2.302585 -Inf Inf
-log_k_parent_m1 -2.301586 -Inf Inf
-log_k_m1_sink -2.300587 -Inf Inf
-
-Fixed parameter values:
- value type
-m1_0 0 state
-
-Optimised, transformed parameters with symmetric confidence intervals:
- Estimate Std. Error Lower Upper
-parent_0 99.600 1.61400 96.330 102.900
-log_k_parent_sink -3.038 0.07826 -3.197 -2.879
-log_k_parent_m1 -2.980 0.04124 -3.064 -2.897
-log_k_m1_sink -5.248 0.13610 -5.523 -4.972
-
-Parameter correlation:
- parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
-parent_0 1.00000 0.6075 -0.06625 -0.1701
-log_k_parent_sink 0.60752 1.0000 -0.08740 -0.6253
-log_k_parent_m1 -0.06625 -0.0874 1.00000 0.4716
-log_k_m1_sink -0.17006 -0.6253 0.47163 1.0000
-
-Residual standard error: 3.211 on 36 degrees of freedom
-
-Backtransformed parameters:
-Confidence intervals for internally transformed parameters are asymmetric.
-t-test (unrealistically) based on the assumption of normal distribution
-for estimators of untransformed parameters.
- Estimate t value Pr(&gt;t) Lower Upper
-parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02
-k_parent_sink 0.047920 12.780 3.050e-15 0.040890 5.616e-02
-k_parent_m1 0.050780 24.250 3.407e-24 0.046700 5.521e-02
-k_m1_sink 0.005261 7.349 5.758e-09 0.003992 6.933e-03
-
-Chi2 error levels in percent:
- err.min n.optim df
-All data 6.398 4 15
-parent 6.827 3 6
-m1 4.490 1 9
-
-Resulting formation fractions:
- ff
-parent_sink 0.4855
-parent_m1 0.5145
-m1_sink 1.0000
-
-Estimated disappearance times:
- DT50 DT90
-parent 7.023 23.33
-m1 131.761 437.70
-</div>
-<div class='input'>
-## Not run:
-# fit.2 &lt;- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE)
-# summary(fit.2, data=FALSE)
-# ## End(Not run)
-
-initials &lt;- fit$start$value
-names(initials) &lt;- rownames(fit$start)
-transformed &lt;- fit$start_transformed$value
-names(transformed) &lt;- rownames(fit$start_transformed)
-transform_odeparms(initials, SFO_SFO)
-</div>
-<div class='output'> 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'>backtransform_odeparms(transformed, SFO_SFO)
-</div>
-<div class='output'> parent_0 k_parent_sink k_parent_m1 k_m1_sink
- 100.7500 0.1000 0.1001 0.1002
-</div>
-<div class='input'>
-## Not run:
-# # The case of formation fractions
-# SFO_SFO.ff &lt;- mkinmod(
-# parent = list(type = &quot;SFO&quot;, to = &quot;m1&quot;, sink = TRUE),
-# m1 = list(type = &quot;SFO&quot;),
-# use_of_ff = &quot;max&quot;)
-#
-# fit.ff &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D)
-# summary(fit.ff, data = FALSE)
-# initials &lt;- c(&quot;f_parent_to_m1&quot; = 0.5)
-# transformed &lt;- transform_odeparms(initials, SFO_SFO.ff)
-# backtransform_odeparms(transformed, SFO_SFO.ff)
-#
-# # And without sink
-# SFO_SFO.ff.2 &lt;- mkinmod(
-# parent = list(type = &quot;SFO&quot;, to = &quot;m1&quot;, sink = FALSE),
-# m1 = list(type = &quot;SFO&quot;),
-# use_of_ff = &quot;max&quot;)
-#
-#
-# fit.ff.2 &lt;- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D)
-# summary(fit.ff.2, data = FALSE)
-# ## End(Not run)
-</div></pre>
- </div>
- <div class="span4">
- <!-- <ul>
- <li>transform_odeparms</li><li>backtransform_odeparms</li>
- </ul>
- <ul>
- <li> manip </li>
- </ul> -->
-
-
- <h2>Author</h2>
-
- Johannes Ranke
-
-
- </div>
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