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the Port algorithm nlminb, and the specified initial or fixed
parameters and starting values. In each step of the optimsation, the kinetic
model is solved using the function mkinpredict. The parameters
of the selected error model are fitted simultaneously with the degradation
model parameters, as both of them are arguments of the likelihood function.
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<h1>Fit a kinetic model to data with one or more state variables</h1>
<div class="hidden name"><code>mkinfit.Rd</code></div>
</div>
<div class="ref-description">
<p>This function maximises the likelihood of the observed data using
the Port algorithm <code><a href='https://www.rdocumentation.org/packages/stats/topics/nlminb'>nlminb</a></code>, and the specified initial or fixed
parameters and starting values. In each step of the optimsation, the kinetic
model is solved using the function <code><a href='mkinpredict.html'>mkinpredict</a></code>. The parameters
of the selected error model are fitted simultaneously with the degradation
model parameters, as both of them are arguments of the likelihood function.</p>
<p>Per default, parameters in the kinetic models are internally transformed in
order to better satisfy the assumption of a normal distribution of their
estimators.</p>
</div>
<pre class="usage"><span class='fu'>mkinfit</span>(<span class='no'>mkinmod</span>, <span class='no'>observed</span>,
<span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
<span class='kw'>state.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
<span class='kw'>err.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
<span class='kw'>fixed_parms</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>fixed_initials</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/names'>names</a></span>(<span class='no'>mkinmod</span>$<span class='no'>diffs</span>)[-<span class='fl'>1</span>],
<span class='kw'>from_max_mean</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
<span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='st'>"auto"</span>, <span class='st'>"analytical"</span>, <span class='st'>"eigen"</span>, <span class='st'>"deSolve"</span>),
<span class='kw'>method.ode</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>,
<span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
<span class='kw'>control</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/list'>list</a></span>(<span class='kw'>eval.max</span> <span class='kw'>=</span> <span class='fl'>300</span>, <span class='kw'>iter.max</span> <span class='kw'>=</span> <span class='fl'>200</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='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
<span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-8</span>, <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>, <span class='kw'>n.outtimes</span> <span class='kw'>=</span> <span class='fl'>100</span>,
<span class='kw'>error_model</span> <span class='kw'>=</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/c'>c</a></span>(<span class='st'>"const"</span>, <span class='st'>"obs"</span>, <span class='st'>"tc"</span>),
<span class='kw'>trace_parms</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='no'>...</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>mkinmod</th>
<td><p>A list of class <code><a href='mkinmod.html'>mkinmod</a></code>, containing the kinetic model to be
fitted to the data, or one of the shorthand names ("SFO", "FOMC", "DFOP",
"HS", "SFORB", "IORE"). If a shorthand name is given, a parent only degradation
model is generated for the variable with the highest value in
<code>observed</code>.</p></td>
</tr>
<tr>
<th>observed</th>
<td><p>A dataframe with the observed data. The first column called "name" must
contain the name of the observed variable for each data point. The second
column must contain the times of observation, named "time". The third
column must be named "value" and contain the observed values. Zero values
in the "value" column will be removed, with a warning, in order to
avoid problems with fitting the two-component error model. This is not
expected to be a problem, because in general, values of zero are not
observed in degradation data, because there is a lower limit of detection.</p></td>
</tr>
<tr>
<th>parms.ini</th>
<td><p>A named vector of initial values for the parameters, including parameters
to be optimised and potentially also fixed parameters as indicated by
<code>fixed_parms</code>. If set to "auto", initial values for rate constants
are set to default values. Using parameter names that are not in the model
gives an error.</p>
<p>It is possible to only specify a subset of the parameters that the model
needs. You can use the parameter lists "bparms.ode" from a previously
fitted model, which contains the differential equation parameters from this
model. This works nicely if the models are nested. An example is given
below.</p></td>
</tr>
<tr>
<th>state.ini</th>
<td><p>A named vector of initial values for the state variables of the model. In
case the observed variables are represented by more than one model
variable, the names will differ from the names of the observed variables
(see <code>map</code> component of <code><a href='mkinmod.html'>mkinmod</a></code>). The default is to set
the initial value of the first model variable to the mean of the time zero
values for the variable with the maximum observed value, and all others to 0.
If this variable has no time zero observations, its initial value is set to 100.</p></td>
</tr>
<tr>
<th>err.ini</th>
<td><p>A named vector of initial values for the error model parameters to be
optimised. If set to "auto", initial values are set to default values.
Otherwise, inital values for all error model parameters must be
given.</p></td>
</tr>
<tr>
<th>fixed_parms</th>
<td><p>The names of parameters that should not be optimised but rather kept at the
values specified in <code>parms.ini</code>.</p></td>
</tr>
<tr>
<th>fixed_initials</th>
<td><p>The names of model variables for which the initial state at time 0 should
be excluded from the optimisation. Defaults to all state variables except
for the first one.</p></td>
</tr>
<tr>
<th>from_max_mean</th>
<td><p>If this is set to TRUE, and the model has only one observed variable, then
data before the time of the maximum observed value (after averaging for each
sampling time) are discarded, and this time is subtracted from all
remaining time values, so the time of the maximum observed mean value is
the new time zero.</p></td>
</tr>
<tr>
<th>solution_type</th>
<td><p>If set to "eigen", the solution of the system of differential equations is
based on the spectral decomposition of the coefficient matrix in cases that
this is possible. If set to "deSolve", a numerical ode solver from package
<code>deSolve</code> is used. If set to "analytical", an analytical
solution of the model is used. This is only implemented for simple
degradation experiments with only one state variable, i.e. with no
metabolites. The default is "auto", which uses "analytical" if possible,
otherwise "deSolve" if a compiler is present, and "eigen" if no
compiler is present and the model can be expressed using eigenvalues and
eigenvectors. This argument is passed on to the helper function
<code><a href='mkinpredict.html'>mkinpredict</a></code>.</p></td>
</tr>
<tr>
<th>method.ode</th>
<td><p>The solution method passed via <code><a href='mkinpredict.html'>mkinpredict</a></code> to
<code>ode</code> in case the solution type is "deSolve". The default
"lsoda" is performant, but sometimes fails to converge.</p></td>
</tr>
<tr>
<th>use_compiled</th>
<td><p>If set to <code>FALSE</code>, no compiled version of the <code><a href='mkinmod.html'>mkinmod</a></code>
model is used in the calls to <code><a href='mkinpredict.html'>mkinpredict</a></code> even if a compiled
version is present.</p></td>
</tr>
<tr>
<th>control</th>
<td><p>A list of control arguments passed to <code><a href='https://www.rdocumentation.org/packages/stats/topics/nlminb'>nlminb</a></code>.</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. If FALSE, zero is used as a lower bound for the rates
in the optimisation.</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. If TRUE, 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>quiet</th>
<td><p>Suppress printing out the current value of the negative log-likelihood
after each improvement?</p></td>
</tr>
<tr>
<th>atol</th>
<td><p>Absolute error tolerance, passed to <code>ode</code>. Default is 1e-8,
lower than in <code>lsoda</code>.</p></td>
</tr>
<tr>
<th>rtol</th>
<td><p>Absolute error tolerance, passed to <code>ode</code>. Default is 1e-10,
much lower than in <code>lsoda</code>.</p></td>
</tr>
<tr>
<th>n.outtimes</th>
<td><p>The length of the dataseries that is produced by the model prediction
function <code><a href='mkinpredict.html'>mkinpredict</a></code>. This impacts the accuracy of
the numerical solver if that is used (see <code>solution_type</code> argument.
The default value is 100.</p></td>
</tr>
<tr>
<th>error_model</th>
<td><p>If the error model is "const", a constant standard deviation
is assumed.</p>
<p>If the error model is "obs", each observed variable is assumed to have its
own variance.</p>
<p>If the error model is "tc" (two-component error model), a two component
error model similar to the one described by Rocke and Lorenzato (1995) is
used for setting up the likelihood function. Note that this model deviates
from the model by Rocke and Lorenzato, as their model implies that the
errors follow a lognormal distribution for large values, not a normal
distribution as assumed by this method.</p></td>
</tr>
<tr>
<th>trace_parms</th>
<td><p>Should a trace of the parameter values be listed?</p></td>
</tr>
<tr>
<th>…</th>
<td><p>Further arguments that will be passed on to <code>deSolve</code>.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>A list with "mkinfit" in the class attribute. A summary can be obtained by
<code><a href='summary.mkinfit.html'>summary.mkinfit</a></code>.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p>Plotting methods <code><a href='plot.mkinfit.html'>plot.mkinfit</a></code> and <code><a href='mkinparplot.html'>mkinparplot</a></code>.</p>
<p>Comparisons of models fitted to the same data can be made using <code><a href='https://www.rdocumentation.org/packages/stats/topics/AIC'>AIC</a></code>
by virtue of the method <code><a href='logLik.mkinfit.html'>logLik.mkinfit</a></code>.</p>
<p>Fitting of several models to several datasets in a single call to
<code><a href='mmkin.html'>mmkin</a></code>.</p></div>
<h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>
<p>When using the "IORE" submodel for metabolites, fitting with
"transform_rates = TRUE" (the default) often leads to failures of the
numerical ODE solver. In this situation it may help to switch off the
internal rate transformation.</p>
<h2 class="hasAnchor" id="source"><a class="anchor" href="#source"></a>Source</h2>
<p>Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for
measurement error in analytical chemistry. Technometrics 37(2), 176-184.</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='co'># Use shorthand notation for parent only degradation</span>
<span class='no'>fit</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.49.4
#> R version used for fitting: 3.6.0
#> Date of fit: Thu May 2 17:41:11 2019
#> Date of summary: Thu May 2 17:41:11 2019
#>
#> Equations:
#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
#>
#> Model predictions using solution type analytical
#>
#> Fitted using 221 model solutions performed in 0.455 s
#>
#> Error model:
#> Constant variance
#>
#> Starting values for parameters to be optimised:
#> value type
#> parent_0 85.100000 state
#> alpha 1.000000 deparm
#> beta 10.000000 deparm
#> sigma 1.857444 error
#>
#> Starting values for the transformed parameters actually optimised:
#> value lower upper
#> parent_0 85.100000 -Inf Inf
#> log_alpha 0.000000 -Inf Inf
#> log_beta 2.302585 -Inf Inf
#> sigma 1.857444 0 Inf
#>
#> Fixed parameter values:
#> None
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> Estimate Std. Error Lower Upper
#> parent_0 85.87000 1.8070 81.23000 90.5200
#> log_alpha 0.05192 0.1353 -0.29580 0.3996
#> log_beta 0.65100 0.2287 0.06315 1.2390
#> sigma 1.85700 0.4378 0.73200 2.9830
#>
#> Parameter correlation:
#> parent_0 log_alpha log_beta sigma
#> parent_0 1.000e+00 -1.565e-01 -3.142e-01 -1.317e-07
#> log_alpha -1.565e-01 1.000e+00 9.564e-01 -2.640e-07
#> log_beta -3.142e-01 9.564e-01 1.000e+00 -2.205e-07
#> sigma -1.317e-07 -2.640e-07 -2.205e-07 1.000e+00
#>
#> 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(>t) Lower Upper
#> parent_0 85.870 47.530 3.893e-08 81.2300 90.520
#> alpha 1.053 7.393 3.562e-04 0.7439 1.491
#> beta 1.917 4.373 3.601e-03 1.0650 3.451
#> sigma 1.857 4.243 4.074e-03 0.7320 2.983
#>
#> FOCUS Chi2 error levels in percent:
#> err.min n.optim df
#> All data 6.657 3 6
#> parent 6.657 3 6
#>
#> Estimated disappearance times:
#> DT50 DT90 DT50back
#> parent 1.785 15.15 4.56
#>
#> Data:
#> time variable observed predicted residual
#> 0 parent 85.1 85.875 -0.7749
#> 1 parent 57.9 55.191 2.7091
#> 3 parent 29.9 31.845 -1.9452
#> 7 parent 14.6 17.012 -2.4124
#> 14 parent 9.7 9.241 0.4590
#> 28 parent 6.6 4.754 1.8460
#> 63 parent 4.0 2.102 1.8977
#> 91 parent 3.9 1.441 2.4590
#> 119 parent 0.6 1.092 -0.4919</div><div class='input'>
<span class='co'># One parent compound, one metabolite, both single first order.</span>
<span class='co'># Use mkinsub for convenience in model formulation. Pathway to sink included per default.</span>
<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='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
<span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></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='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/system.time'>system.time</a></span>(<span class='no'>fit</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>,
<span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"eigen"</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'>#> User System verstrichen
#> 1.54 0.00 1.54 </div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/stats/topics/coef'>coef</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#> NULL</div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#> $ff
#> parent_sink parent_m1 m1_sink
#> 0.485524 0.514476 1.000000
#>
#> $SFORB
#> logical(0)
#>
#> $distimes
#> DT50 DT90
#> parent 7.022928 23.32966
#> m1 131.760715 437.69962
#> </div><div class='input'><span class='co'># deSolve is slower when no C compiler (gcc) was available during model generation</span>
<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/print'>print</a></span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/system.time'>system.time</a></span>(<span class='no'>fit.deSolve</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>,
<span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</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'>#> Sum of squared residuals at call 1: 18915.53
#> Sum of squared residuals at call 2: 18915.53
#> Sum of squared residuals at call 6: 11424.02
#> Sum of squared residuals at call 10: 11424
#> Sum of squared residuals at call 13: 2367.052
#> Sum of squared residuals at call 14: 2367.05
#> Sum of squared residuals at call 19: 1314.716
#> Sum of squared residuals at call 22: 1314.714
#> Sum of squared residuals at call 25: 991.8311
#> Sum of squared residuals at call 28: 991.8305
#> Sum of squared residuals at call 30: 893.6462
#> Sum of squared residuals at call 33: 893.6457
#> Sum of squared residuals at call 35: 569.4049
#> Sum of squared residuals at call 38: 569.4047
#> Sum of squared residuals at call 40: 565.0651
#> Sum of squared residuals at call 41: 565.065
#> Sum of squared residuals at call 42: 565.0637
#> Sum of squared residuals at call 45: 428.0188
#> Sum of squared residuals at call 46: 428.0185
#> Sum of squared residuals at call 50: 406.732
#> Sum of squared residuals at call 52: 406.732
#> Sum of squared residuals at call 55: 398.9115
#> Sum of squared residuals at call 57: 398.9113
#> Sum of squared residuals at call 60: 394.5943
#> Sum of squared residuals at call 62: 394.5943
#> Sum of squared residuals at call 66: 385.26
#> Sum of squared residuals at call 67: 385.2599
#> Sum of squared residuals at call 69: 385.2599
#> Sum of squared residuals at call 70: 385.2597
#> Sum of squared residuals at call 71: 374.7604
#> Sum of squared residuals at call 72: 374.7603
#> Sum of squared residuals at call 76: 373.199
#> Sum of squared residuals at call 79: 373.199
#> Sum of squared residuals at call 80: 373.199
#> Sum of squared residuals at call 81: 372.3772
#> Sum of squared residuals at call 84: 372.3772
#> Sum of squared residuals at call 86: 371.2615
#> Sum of squared residuals at call 89: 371.2615
#> Sum of squared residuals at call 90: 371.2615
#> Sum of squared residuals at call 92: 371.2439
#> Sum of squared residuals at call 93: 371.2439
#> Sum of squared residuals at call 94: 371.2439
#> Sum of squared residuals at call 97: 371.2198
#> Sum of squared residuals at call 98: 371.2198
#> Sum of squared residuals at call 102: 371.2174
#> Sum of squared residuals at call 104: 371.2174
#> Sum of squared residuals at call 107: 371.2147
#> Sum of squared residuals at call 110: 371.2147
#> Sum of squared residuals at call 111: 371.2147
#> Sum of squared residuals at call 112: 371.2145
#> Sum of squared residuals at call 113: 371.2145
#> Sum of squared residuals at call 116: 371.2145
#> Sum of squared residuals at call 119: 371.2135
#> Sum of squared residuals at call 121: 371.2135
#> Sum of squared residuals at call 124: 371.2135
#> Sum of squared residuals at call 126: 371.2135
#> Sum of squared residuals at call 127: 371.2135
#> Sum of squared residuals at call 133: 371.2134
#> Sum of squared residuals at call 135: 371.2134
#> Sum of squared residuals at call 138: 371.2134
#> Sum of squared residuals at call 142: 371.2134
#> Negative log-likelihood at call 152: 97.22429
#> Optimisation successfully terminated.
#> User System verstrichen
#> 1.1 0.0 1.1 </div><div class='input'><span class='fu'><a href='https://www.rdocumentation.org/packages/stats/topics/coef'>coef</a></span>(<span class='no'>fit.deSolve</span>)</div><div class='output co'>#> NULL</div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.deSolve</span>)</div><div class='output co'>#> $ff
#> parent_sink parent_m1 m1_sink
#> 0.485524 0.514476 1.000000
#>
#> $SFORB
#> logical(0)
#>
#> $distimes
#> DT50 DT90
#> parent 7.022928 23.32966
#> m1 131.760710 437.69961
#> </div><div class='input'>
# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
</div><div class='input'><span class='no'>FOMC_SFO</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(
<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"FOMC"</span>, <span class='st'>"m1"</span>),
<span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>))</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
<span class='no'>fit.FOMC_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='co'># Use starting parameters from parent only FOMC fit</span>
<span class='no'>fit.FOMC</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='no'>fit.FOMC_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
<span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.FOMC</span>$<span class='no'>bparms.ode</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='co'># Use stepwise fitting, using optimised parameters from parent only fit, SFORB</span>
<span class='no'>SFORB_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'>"SFORB"</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.SFORB_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_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.SFORB_SFO.deSolve</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</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='co'># Use starting parameters from parent only SFORB fit (not really needed in this case)</span>
<span class='no'>fit.SFORB</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='st'>"SFORB"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='no'>fit.SFORB_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.SFORB</span>$<span class='no'>bparms.ode</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'>
</div><div class='input'><span class='co'># Weighted fits, including IRLS</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='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
<span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></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'>f.noweight</span> <span class='kw'><-</span> <span class='fu'>mkinfit</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='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>f.noweight</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.49.4
#> R version used for fitting: 3.6.0
#> Date of fit: Thu May 2 17:41:27 2019
#> Date of summary: Thu May 2 17:41:27 2019
#>
#> Equations:
#> d_parent/dt = - k_parent * parent
#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
#>
#> Model predictions using solution type deSolve
#>
#> Fitted using 404 model solutions performed in 1.067 s
#>
#> Error model:
#> Constant variance
#>
#> Starting values for parameters to be optimised:
#> value type
#> parent_0 100.750000 state
#> k_parent 0.100000 deparm
#> k_m1 0.100100 deparm
#> f_parent_to_m1 0.500000 deparm
#> sigma 3.125504 error
#>
#> Starting values for the transformed parameters actually optimised:
#> value lower upper
#> parent_0 100.750000 -Inf Inf
#> log_k_parent -2.302585 -Inf Inf
#> log_k_m1 -2.301586 -Inf Inf
#> f_parent_ilr_1 0.000000 -Inf Inf
#> sigma 3.125504 0 Inf
#>
#> Fixed parameter values:
#> value type
#> m1_0 0 state
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> Estimate Std. Error Lower Upper
#> parent_0 99.60000 1.57000 96.40000 102.8000
#> log_k_parent -2.31600 0.04087 -2.39900 -2.2330
#> log_k_m1 -5.24800 0.13320 -5.51800 -4.9770
#> f_parent_ilr_1 0.04096 0.06312 -0.08746 0.1694
#> sigma 3.12600 0.35850 2.39600 3.8550
#>
#> Parameter correlation:
#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma
#> parent_0 1.000e+00 5.174e-01 -1.688e-01 -5.471e-01 -5.940e-09
#> log_k_parent 5.174e-01 1.000e+00 -3.263e-01 -5.426e-01 -1.406e-08
#> log_k_m1 -1.688e-01 -3.263e-01 1.000e+00 7.478e-01 -2.306e-08
#> f_parent_ilr_1 -5.471e-01 -5.426e-01 7.478e-01 1.000e+00 -6.664e-09
#> sigma -5.940e-09 -1.406e-08 -2.306e-08 -6.664e-09 1.000e+00
#>
#> 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(>t) Lower Upper
#> parent_0 99.600000 63.430 2.298e-36 96.400000 1.028e+02
#> k_parent 0.098700 24.470 4.955e-23 0.090820 1.073e-01
#> k_m1 0.005261 7.510 6.165e-09 0.004012 6.898e-03
#> f_parent_to_m1 0.514500 23.070 3.104e-22 0.469100 5.596e-01
#> sigma 3.126000 8.718 2.235e-10 2.396000 3.855e+00
#>
#> FOCUS Chi2 error levels in percent:
#> err.min n.optim df
#> All data 6.398 4 15
#> parent 6.459 2 7
#> m1 4.690 2 8
#>
#> Resulting formation fractions:
#> ff
#> parent_m1 0.5145
#> parent_sink 0.4855
#>
#> Estimated disappearance times:
#> DT50 DT90
#> parent 7.023 23.33
#> m1 131.761 437.70
#>
#> Data:
#> time variable observed predicted residual
#> 0 parent 99.46 99.59848 -1.385e-01
#> 0 parent 102.04 99.59848 2.442e+00
#> 1 parent 93.50 90.23787 3.262e+00
#> 1 parent 92.50 90.23787 2.262e+00
#> 3 parent 63.23 74.07320 -1.084e+01
#> 3 parent 68.99 74.07320 -5.083e+00
#> 7 parent 52.32 49.91207 2.408e+00
#> 7 parent 55.13 49.91207 5.218e+00
#> 14 parent 27.27 25.01257 2.257e+00
#> 14 parent 26.64 25.01257 1.627e+00
#> 21 parent 11.50 12.53462 -1.035e+00
#> 21 parent 11.64 12.53462 -8.946e-01
#> 35 parent 2.85 3.14787 -2.979e-01
#> 35 parent 2.91 3.14787 -2.379e-01
#> 50 parent 0.69 0.71624 -2.624e-02
#> 50 parent 0.63 0.71624 -8.624e-02
#> 75 parent 0.05 0.06074 -1.074e-02
#> 75 parent 0.06 0.06074 -7.382e-04
#> 1 m1 4.84 4.80296 3.704e-02
#> 1 m1 5.64 4.80296 8.370e-01
#> 3 m1 12.91 13.02400 -1.140e-01
#> 3 m1 12.96 13.02400 -6.400e-02
#> 7 m1 22.97 25.04476 -2.075e+00
#> 7 m1 24.47 25.04476 -5.748e-01
#> 14 m1 41.69 36.69002 5.000e+00
#> 14 m1 33.21 36.69002 -3.480e+00
#> 21 m1 44.37 41.65310 2.717e+00
#> 21 m1 46.44 41.65310 4.787e+00
#> 35 m1 41.22 43.31312 -2.093e+00
#> 35 m1 37.95 43.31312 -5.363e+00
#> 50 m1 41.19 41.21831 -2.831e-02
#> 50 m1 40.01 41.21831 -1.208e+00
#> 75 m1 40.09 36.44703 3.643e+00
#> 75 m1 33.85 36.44703 -2.597e+00
#> 100 m1 31.04 31.98163 -9.416e-01
#> 100 m1 33.13 31.98163 1.148e+00
#> 120 m1 25.15 28.78984 -3.640e+00
#> 120 m1 33.31 28.78984 4.520e+00</div><div class='input'><span class='no'>f.obs</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"obs"</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='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>f.obs</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.49.4
#> R version used for fitting: 3.6.0
#> Date of fit: Thu May 2 17:41:28 2019
#> Date of summary: Thu May 2 17:41:28 2019
#>
#> Equations:
#> d_parent/dt = - k_parent * parent
#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
#>
#> Model predictions using solution type deSolve
#>
#> Fitted using 558 model solutions performed in 1.447 s
#>
#> Error model:
#> Variance unique to each observed variable
#>
#> Starting values for parameters to be optimised:
#> value type
#> parent_0 100.7500 state
#> k_parent 0.1000 deparm
#> k_m1 0.1001 deparm
#> f_parent_to_m1 0.5000 deparm
#> sigma_parent 3.0000 error
#> sigma_m1 3.0000 error
#>
#> Starting values for the transformed parameters actually optimised:
#> value lower upper
#> parent_0 100.750000 -Inf Inf
#> log_k_parent -2.302585 -Inf Inf
#> log_k_m1 -2.301586 -Inf Inf
#> f_parent_ilr_1 0.000000 -Inf Inf
#> sigma_parent 3.000000 0 Inf
#> sigma_m1 3.000000 0 Inf
#>
#> Fixed parameter values:
#> value type
#> m1_0 0 state
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> Estimate Std. Error Lower Upper
#> parent_0 99.65000 1.70200 96.19000 103.1000
#> log_k_parent -2.31300 0.04376 -2.40200 -2.2240
#> log_k_m1 -5.25000 0.12430 -5.50400 -4.9970
#> f_parent_ilr_1 0.03861 0.06171 -0.08708 0.1643
#> sigma_parent 3.40100 0.56820 2.24400 4.5590
#> sigma_m1 2.85500 0.45240 1.93400 3.7770
#>
#> Parameter correlation:
#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_parent
#> parent_0 1.00000 0.51078 -0.19133 -0.59997 0.035671
#> log_k_parent 0.51078 1.00000 -0.37458 -0.59239 0.069834
#> log_k_m1 -0.19133 -0.37458 1.00000 0.74398 -0.026158
#> f_parent_ilr_1 -0.59997 -0.59239 0.74398 1.00000 -0.041369
#> sigma_parent 0.03567 0.06983 -0.02616 -0.04137 1.000000
#> sigma_m1 -0.03385 -0.06627 0.02482 0.03926 -0.004628
#> sigma_m1
#> parent_0 -0.033847
#> log_k_parent -0.066265
#> log_k_m1 0.024822
#> f_parent_ilr_1 0.039256
#> sigma_parent -0.004628
#> sigma_m1 1.000000
#>
#> 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(>t) Lower Upper
#> parent_0 99.650000 58.560 2.004e-34 96.190000 1.031e+02
#> k_parent 0.098970 22.850 1.099e-21 0.090530 1.082e-01
#> k_m1 0.005245 8.046 1.732e-09 0.004072 6.756e-03
#> f_parent_to_m1 0.513600 23.560 4.352e-22 0.469300 5.578e-01
#> sigma_parent 3.401000 5.985 5.662e-07 2.244000 4.559e+00
#> sigma_m1 2.855000 6.311 2.215e-07 1.934000 3.777e+00
#>
#> FOCUS Chi2 error levels in percent:
#> err.min n.optim df
#> All data 6.398 4 15
#> parent 6.464 2 7
#> m1 4.682 2 8
#>
#> Resulting formation fractions:
#> ff
#> parent_m1 0.5136
#> parent_sink 0.4864
#>
#> Estimated disappearance times:
#> DT50 DT90
#> parent 7.003 23.26
#> m1 132.154 439.01
#>
#> Data:
#> time variable observed predicted residual
#> 0 parent 99.46 99.65417 -1.942e-01
#> 0 parent 102.04 99.65417 2.386e+00
#> 1 parent 93.50 90.26333 3.237e+00
#> 1 parent 92.50 90.26333 2.237e+00
#> 3 parent 63.23 74.05306 -1.082e+01
#> 3 parent 68.99 74.05306 -5.063e+00
#> 7 parent 52.32 49.84325 2.477e+00
#> 7 parent 55.13 49.84325 5.287e+00
#> 14 parent 27.27 24.92971 2.340e+00
#> 14 parent 26.64 24.92971 1.710e+00
#> 21 parent 11.50 12.46890 -9.689e-01
#> 21 parent 11.64 12.46890 -8.289e-01
#> 35 parent 2.85 3.11925 -2.692e-01
#> 35 parent 2.91 3.11925 -2.092e-01
#> 50 parent 0.69 0.70679 -1.679e-02
#> 50 parent 0.63 0.70679 -7.679e-02
#> 75 parent 0.05 0.05952 -9.523e-03
#> 75 parent 0.06 0.05952 4.772e-04
#> 1 m1 4.84 4.81075 2.925e-02
#> 1 m1 5.64 4.81075 8.292e-01
#> 3 m1 12.91 13.04197 -1.320e-01
#> 3 m1 12.96 13.04197 -8.197e-02
#> 7 m1 22.97 25.06847 -2.098e+00
#> 7 m1 24.47 25.06847 -5.985e-01
#> 14 m1 41.69 36.70308 4.987e+00
#> 14 m1 33.21 36.70308 -3.493e+00
#> 21 m1 44.37 41.65115 2.719e+00
#> 21 m1 46.44 41.65115 4.789e+00
#> 35 m1 41.22 43.29465 -2.075e+00
#> 35 m1 37.95 43.29465 -5.345e+00
#> 50 m1 41.19 41.19948 -9.482e-03
#> 50 m1 40.01 41.19948 -1.189e+00
#> 75 m1 40.09 36.44036 3.650e+00
#> 75 m1 33.85 36.44036 -2.590e+00
#> 100 m1 31.04 31.98774 -9.477e-01
#> 100 m1 33.13 31.98774 1.142e+00
#> 120 m1 25.15 28.80430 -3.654e+00
#> 120 m1 33.31 28.80430 4.506e+00</div><div class='input'><span class='no'>f.tc</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</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='fu'><a href='https://www.rdocumentation.org/packages/base/topics/summary'>summary</a></span>(<span class='no'>f.tc</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.49.4
#> R version used for fitting: 3.6.0
#> Date of fit: Thu May 2 17:41:32 2019
#> Date of summary: Thu May 2 17:41:32 2019
#>
#> Equations:
#> d_parent/dt = - k_parent * parent
#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
#>
#> Model predictions using solution type deSolve
#>
#> Fitted using 844 model solutions performed in 3.407 s
#>
#> Error model:
#> Two-component variance function
#>
#> Starting values for parameters to be optimised:
#> value type
#> parent_0 100.7500 state
#> k_parent 0.1000 deparm
#> k_m1 0.1001 deparm
#> f_parent_to_m1 0.5000 deparm
#> sigma_low 3.0000 error
#> rsd_high 0.0100 error
#>
#> Starting values for the transformed parameters actually optimised:
#> value lower upper
#> parent_0 100.750000 -Inf Inf
#> log_k_parent -2.302585 -Inf Inf
#> log_k_m1 -2.301586 -Inf Inf
#> f_parent_ilr_1 0.000000 -Inf Inf
#> sigma_low 3.000000 0 Inf
#> rsd_high 0.010000 0 Inf
#>
#> Fixed parameter values:
#> value type
#> m1_0 0 state
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> Estimate Std. Error Lower Upper
#> parent_0 100.70000 2.621000 95.400000 106.10000
#> log_k_parent -2.29700 0.008862 -2.315000 -2.27900
#> log_k_m1 -5.26600 0.091310 -5.452000 -5.08000
#> f_parent_ilr_1 0.02374 0.055300 -0.088900 0.13640
#> sigma_low 0.00305 0.004829 -0.006786 0.01289
#> rsd_high 0.07928 0.009418 0.060100 0.09847
#>
#> Parameter correlation:
#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_low rsd_high
#> parent_0 1.00000 0.67644 -0.10215 -0.76822 0.14294 -0.08783
#> log_k_parent 0.67644 1.00000 -0.15102 -0.59491 0.34611 -0.08125
#> log_k_m1 -0.10215 -0.15102 1.00000 0.51808 -0.05236 0.01240
#> f_parent_ilr_1 -0.76822 -0.59491 0.51808 1.00000 -0.13900 0.03248
#> sigma_low 0.14294 0.34611 -0.05236 -0.13900 1.00000 -0.16546
#> rsd_high -0.08783 -0.08125 0.01240 0.03248 -0.16546 1.00000
#>
#> 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(>t) Lower Upper
#> parent_0 1.007e+02 38.4300 1.180e-28 95.400000 1.061e+02
#> k_parent 1.006e-01 112.8000 1.718e-43 0.098760 1.024e-01
#> k_m1 5.167e-03 10.9500 1.171e-12 0.004290 6.223e-03
#> f_parent_to_m1 5.084e-01 26.0100 2.146e-23 0.468600 5.481e-01
#> sigma_low 3.050e-03 0.6314 2.661e-01 -0.006786 1.289e-02
#> rsd_high 7.928e-02 8.4170 6.418e-10 0.060100 9.847e-02
#>
#> FOCUS Chi2 error levels in percent:
#> err.min n.optim df
#> All data 6.475 4 15
#> parent 6.573 2 7
#> m1 4.671 2 8
#>
#> Resulting formation fractions:
#> ff
#> parent_m1 0.5084
#> parent_sink 0.4916
#>
#> Estimated disappearance times:
#> DT50 DT90
#> parent 6.893 22.9
#> m1 134.156 445.7
#>
#> Data:
#> time variable observed predicted residual
#> 0 parent 99.46 100.73434 -1.274339
#> 0 parent 102.04 100.73434 1.305661
#> 1 parent 93.50 91.09751 2.402486
#> 1 parent 92.50 91.09751 1.402486
#> 3 parent 63.23 74.50141 -11.271410
#> 3 parent 68.99 74.50141 -5.511410
#> 7 parent 52.32 49.82880 2.491201
#> 7 parent 55.13 49.82880 5.301201
#> 14 parent 27.27 24.64809 2.621908
#> 14 parent 26.64 24.64809 1.991908
#> 21 parent 11.50 12.19232 -0.692315
#> 21 parent 11.64 12.19232 -0.552315
#> 35 parent 2.85 2.98327 -0.133266
#> 35 parent 2.91 2.98327 -0.073266
#> 50 parent 0.69 0.66013 0.029874
#> 50 parent 0.63 0.66013 -0.030126
#> 75 parent 0.05 0.05344 -0.003438
#> 75 parent 0.06 0.05344 0.006562
#> 1 m1 4.84 4.88645 -0.046451
#> 1 m1 5.64 4.88645 0.753549
#> 3 m1 12.91 13.22867 -0.318669
#> 3 m1 12.96 13.22867 -0.268669
#> 7 m1 22.97 25.36417 -2.394167
#> 7 m1 24.47 25.36417 -0.894167
#> 14 m1 41.69 37.00974 4.680263
#> 14 m1 33.21 37.00974 -3.799737
#> 21 m1 44.37 41.90133 2.468668
#> 21 m1 46.44 41.90133 4.538668
#> 35 m1 41.22 43.45691 -2.236914
#> 35 m1 37.95 43.45691 -5.506914
#> 50 m1 41.19 41.34199 -0.151986
#> 50 m1 40.01 41.34199 -1.331986
#> 75 m1 40.09 36.61471 3.475294
#> 75 m1 33.85 36.61471 -2.764706
#> 100 m1 31.04 32.20082 -1.160824
#> 100 m1 33.13 32.20082 0.929176
#> 120 m1 25.15 29.04130 -3.891305
#> 120 m1 33.31 29.04130 4.268695</div><div class='input'>
</div></pre>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
<h2>Contents</h2>
<ul class="nav nav-pills nav-stacked">
<li><a href="#arguments">Arguments</a></li>
<li><a href="#value">Value</a></li>
<li><a href="#see-also">See also</a></li>
<li><a href="#note">Note</a></li>
<li><a href="#source">Source</a></li>
<li><a href="#examples">Examples</a></li>
</ul>
<h2>Author</h2>
<p>Johannes Ranke</p>
</div>
</div>
<footer>
<div class="copyright">
<p>Developed by Johannes Ranke.</p>
</div>
<div class="pkgdown">
<p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.3.0.9000.</p>
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