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| author | Johannes Ranke <jranke@uni-bremen.de> | 2020-11-08 02:59:07 +0100 | 
|---|---|---|
| committer | Johannes Ranke <jranke@uni-bremen.de> | 2020-11-08 02:59:07 +0100 | 
| commit | 1c647363430e0db732c23feebe4293dc48978608 (patch) | |
| tree | ff7e6933a851b449e533df083b741898d724ee67 /docs/dev/reference/summary.saem.mmkin.html | |
| parent | 279a1d83d7cbe39a953467762629eb1abb9addf4 (diff) | |
Update static docs
Diffstat (limited to 'docs/dev/reference/summary.saem.mmkin.html')
| -rw-r--r-- | docs/dev/reference/summary.saem.mmkin.html | 436 | 
1 files changed, 436 insertions, 0 deletions
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Optionally +(default is FALSE), the data are listed in full." /> + + +<meta name="robots" content="noindex"> + +<!-- mathjax --> +<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script> +<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script> + +<!--[if lt IE 9]> +<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> +<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> +<![endif]--> + + + +  </head> + +  <body data-spy="scroll" data-target="#toc"> +    <div class="container template-reference-topic"> +      <header> +      <div class="navbar navbar-default navbar-fixed-top" role="navigation"> +  <div class="container"> +    <div class="navbar-header"> +      <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> +        <span class="sr-only">Toggle navigation</span> +        <span class="icon-bar"></span> +        <span class="icon-bar"></span> +        <span class="icon-bar"></span> +      </button> +      <span class="navbar-brand"> +        <a class="navbar-link" href="../index.html">mkin</a> +        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span> +      </span> +    </div> + +    <div id="navbar" class="navbar-collapse collapse"> +      <ul class="nav navbar-nav"> +        <li> +  <a href="../reference/index.html">Functions and data</a> +</li> +<li class="dropdown"> +  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false"> +    Articles +      +    <span class="caret"></span> +  </a> +  <ul class="dropdown-menu" role="menu"> +    <li> +      <a href="../articles/mkin.html">Introduction to mkin</a> +    </li> +    <li> +      <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> +    </li> +    <li> +      <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> +    </li> +    <li> +      <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> +    </li> +    <li> +      <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> +    </li> +    <li> +      <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> +    </li> +    <li> +      <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> +    </li> +    <li> +      <a href="../articles/web_only/benchmarks.html">Some benchmark timings</a> +    </li> +  </ul> +</li> +<li> +  <a href="../news/index.html">News</a> +</li> +      </ul> +      <ul class="nav navbar-nav navbar-right"> +        <li> +  <a href="https://github.com/jranke/mkin/"> +    <span class="fab fa fab fa-github fa-lg"></span> +      +  </a> +</li> +      </ul> +       +    </div><!--/.nav-collapse --> +  </div><!--/.container --> +</div><!--/.navbar --> + +       + +      </header> + +<div class="row"> +  <div class="col-md-9 contents"> +    <div class="page-header"> +    <h1>Summary method for class "saem.mmkin"</h1> +    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/summary.saem.mmkin.R'><code>R/summary.saem.mmkin.R</code></a></small> +    <div class="hidden name"><code>summary.saem.mmkin.Rd</code></div> +    </div> + +    <div class="ref-description"> +    <p>Lists model equations, initial parameter values, optimised parameters +for fixed effects (population), random effects (deviations from the +population mean) and residual error model, as well as the resulting +endpoints such as formation fractions and DT50 values. Optionally +(default is FALSE), the data are listed in full.</p> +    </div> + +    <pre class="usage"><span class='co'># S3 method for saem.mmkin</span> +<span class='fu'><a href='https://rdrr.io/pkg/saemix/man/summary-methods.html'>summary</a></span><span class='op'>(</span><span class='va'>object</span>, data <span class='op'>=</span> <span class='cn'>FALSE</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span>, distimes <span class='op'>=</span> <span class='cn'>TRUE</span>, <span class='va'>...</span><span class='op'>)</span> + +<span class='co'># S3 method for summary.saem.mmkin</span> +<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span><span class='op'>(</span><span class='va'>x</span>, digits <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Extremes.html'>max</a></span><span class='op'>(</span><span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/options.html'>getOption</a></span><span class='op'>(</span><span class='st'>"digits"</span><span class='op'>)</span> <span class='op'>-</span> <span class='fl'>3</span><span class='op'>)</span>, verbose <span class='op'>=</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>verbose</span>, <span class='va'>...</span><span class='op'>)</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>object</th> +      <td><p>an object of class <a href='saem.html'>saem.mmkin</a></p></td> +    </tr> +    <tr> +      <th>data</th> +      <td><p>logical, indicating whether the full data should be included in +the summary.</p></td> +    </tr> +    <tr> +      <th>verbose</th> +      <td><p>Should the summary be verbose?</p></td> +    </tr> +    <tr> +      <th>distimes</th> +      <td><p>logical, indicating whether DT50 and DT90 values should be +included.</p></td> +    </tr> +    <tr> +      <th>...</th> +      <td><p>optional arguments passed to methods like <code>print</code>.</p></td> +    </tr> +    <tr> +      <th>x</th> +      <td><p>an object of class summary.saem.mmkin</p></td> +    </tr> +    <tr> +      <th>digits</th> +      <td><p>Number of digits to use for printing</p></td> +    </tr> +    </table> + +    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2> + +    <p>The summary function returns a list based on the <a href='https://rdrr.io/pkg/saemix/man/SaemixObject-class.html'>saemix::SaemixObject</a> +obtained in the fit, with at least the following additional components</p> +<dt>saemixversion, mkinversion, Rversion</dt><dd><p>The saemix, mkin and R versions used</p></dd> +<dt>date.fit, date.summary</dt><dd><p>The dates where the fit and the summary were +produced</p></dd> +<dt>diffs</dt><dd><p>The differential equations used in the degradation model</p></dd> +<dt>use_of_ff</dt><dd><p>Was maximum or minimum use made of formation fractions</p></dd> +<dt>data</dt><dd><p>The data</p></dd> +<dt>confint_trans</dt><dd><p>Transformed parameters as used in the optimisation, with confidence intervals</p></dd> +<dt>confint_back</dt><dd><p>Backtransformed parameters, with confidence intervals if available</p></dd> +<dt>ff</dt><dd><p>The estimated formation fractions derived from the fitted +model.</p></dd> +<dt>distimes</dt><dd><p>The DT50 and DT90 values for each observed variable.</p></dd> +<dt>SFORB</dt><dd><p>If applicable, eigenvalues of SFORB components of the model.</p></dd> +The print method is called for its side effect, i.e. printing the summary. + +    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2> + +    <p>Johannes Ranke for the mkin specific parts +saemix authors for the parts inherited from saemix.</p> + +    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2> +    <pre class="examples"><div class='input'><span class='co'># Generate five datasets following SFO kinetics</span> +<span class='va'>sampling_times</span> <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>1</span>, <span class='fl'>3</span>, <span class='fl'>7</span>, <span class='fl'>14</span>, <span class='fl'>28</span>, <span class='fl'>60</span>, <span class='fl'>90</span>, <span class='fl'>120</span><span class='op'>)</span> +<span class='va'>dt50_sfo_in_pop</span> <span class='op'><-</span> <span class='fl'>50</span> +<span class='va'>k_in_pop</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>log</a></span><span class='op'>(</span><span class='fl'>2</span><span class='op'>)</span> <span class='op'>/</span> <span class='va'>dt50_sfo_in_pop</span> +<span class='fu'><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></span><span class='op'>(</span><span class='fl'>1234</span><span class='op'>)</span> +<span class='va'>k_in</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/Lognormal.html'>rlnorm</a></span><span class='op'>(</span><span class='fl'>5</span>, <span class='fu'><a href='https://rdrr.io/r/base/Log.html'>log</a></span><span class='op'>(</span><span class='va'>k_in_pop</span><span class='op'>)</span>, <span class='fl'>0.5</span><span class='op'>)</span> +<span class='va'>SFO</span> <span class='op'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</span> + +<span class='va'>pred_sfo</span> <span class='op'><-</span> <span class='kw'>function</span><span class='op'>(</span><span class='va'>k</span><span class='op'>)</span> <span class='op'>{</span> +  <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>SFO</span>, +    <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>k_parent <span class='op'>=</span> <span class='va'>k</span><span class='op'>)</span>, +    <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fl'>100</span><span class='op'>)</span>, +    <span class='va'>sampling_times</span><span class='op'>)</span> +<span class='op'>}</span> + +<span class='va'>ds_sfo_mean</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>k_in</span>, <span class='va'>pred_sfo</span><span class='op'>)</span> +<span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>ds_sfo_mean</span><span class='op'>)</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste</a></span><span class='op'>(</span><span class='st'>"ds"</span>, <span class='fl'>1</span><span class='op'>:</span><span class='fl'>5</span><span class='op'>)</span> + +<span class='va'>ds_sfo_syn</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>lapply</a></span><span class='op'>(</span><span class='va'>ds_sfo_mean</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>ds</span><span class='op'>)</span> <span class='op'>{</span> +  <span class='fu'><a href='add_err.html'>add_err</a></span><span class='op'>(</span><span class='va'>ds</span>, +    sdfunc <span class='op'>=</span> <span class='kw'>function</span><span class='op'>(</span><span class='va'>value</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/base/MathFun.html'>sqrt</a></span><span class='op'>(</span><span class='fl'>1</span><span class='op'>^</span><span class='fl'>2</span> <span class='op'>+</span> <span class='va'>value</span><span class='op'>^</span><span class='fl'>2</span> <span class='op'>*</span> <span class='fl'>0.07</span><span class='op'>^</span><span class='fl'>2</span><span class='op'>)</span>, +    n <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span><span class='op'>[[</span><span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span> +<span class='op'>}</span><span class='op'>)</span> + +<span class='co'># \dontrun{</span> +<span class='co'># Evaluate using mmkin and saem</span> +<span class='va'>f_mmkin</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>ds_sfo_syn</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>, cores <span class='op'>=</span> <span class='fl'>1</span><span class='op'>)</span> +<span class='va'>f_saem</span> <span class='op'><-</span> <span class='fu'><a href='saem.html'>saem</a></span><span class='op'>(</span><span class='va'>f_mmkin</span><span class='op'>)</span> +</div><div class='output co'>#> Running main SAEM algorithm +#> [1] "Sun Nov  8 02:58:03 2020" +#> .... +#>     Minimisation finished +#> [1] "Sun Nov  8 02:58:07 2020"</div><div class='input'><span class='fu'><a href='https://rdrr.io/pkg/saemix/man/summary-methods.html'>summary</a></span><span class='op'>(</span><span class='va'>f_saem</span>, data <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span> +</div><div class='output co'>#> saemix version used for fitting:      3.1.9000  +#> mkin version used for pre-fitting:  0.9.50.4  +#> R version used for fitting:         4.0.3  +#> Date of fit:     Sun Nov  8 02:58:07 2020  +#> Date of summary: Sun Nov  8 02:58:07 2020  +#>  +#> Equations: +#> d_parent/dt = - k_parent * parent +#>  +#> Data: +#> 90 observations of 1 variable(s) grouped in 5 datasets +#>  +#> Model predictions using solution type analytical  +#>  +#> Fitted in 4.175 s using 300, 100 iterations +#>  +#> Variance model: Two-component variance function  +#>  +#> Mean of starting values for individual parameters: +#>     parent_0 log_k_parent  +#>    97.849556    -4.455036  +#>  +#> Fixed degradation parameter values: +#> None +#>  +#> Results: +#>  +#> Likelihood computed by importance sampling +#>        AIC      BIC    logLik +#>   555.6718 553.3284 -271.8359 +#>  +#> Optimised, transformed parameters with symmetric confidence intervals: +#>                   est.     lower      upper +#> parent_0     97.840291 94.701895 100.978686 +#> log_k_parent -4.464246 -5.001413  -3.927078 +#>  +#> Correlation:  +#>              prnt_0 +#> log_k_parent 0.022  +#>  +#> Random effects: +#>                      est.     lower     upper +#> SD.parent_0     3.0805465 0.4960170 5.6650760 +#> SD.log_k_parent 0.6109508 0.2301398 0.9917617 +#>  +#> Variance model: +#>           est.      lower      upper +#> a.1 1.06249961 0.23012265 1.89487657 +#> b.1 0.04649661 0.03060849 0.06238473 +#>  +#> Backtransformed parameters with asymmetric confidence intervals: +#>                 est.        lower        upper +#> parent_0 97.84029088 94.701895315 100.97868644 +#> k_parent  0.01151338  0.006728434   0.01970115 +#>  +#> Estimated disappearance times: +#>        DT50 DT90 +#> parent 60.2  200 +#>  +#> Data: +#>    ds   name time observed predicted   residual standardized +#>  ds 1 parent    0    103.6    97.303   6.297361     -1.12720 +#>  ds 1 parent    0     95.9    97.303  -1.402639      0.25107 +#>  ds 1 parent    1     95.4    96.599  -1.198705      0.21583 +#>  ds 1 parent    1     95.3    96.599  -1.298705      0.23383 +#>  ds 1 parent    3     91.6    95.206  -3.606076      0.65693 +#>  ds 1 parent    3     94.5    95.206  -0.706076      0.12863 +#>  ds 1 parent    7     88.1    92.481  -4.380761      0.81692 +#>  ds 1 parent    7     89.6    92.481  -2.880761      0.53720 +#>  ds 1 parent   14     90.3    87.898   2.402166     -0.46649 +#>  ds 1 parent   14     96.0    87.898   8.102166     -1.57340 +#>  ds 1 parent   28     80.2    79.402   0.797948     -0.16783 +#>  ds 1 parent   28     77.9    79.402  -1.502052      0.31593 +#>  ds 1 parent   60     59.3    62.940  -3.639829      0.91247 +#>  ds 1 parent   60     59.6    62.940  -3.339829      0.83726 +#>  ds 1 parent   90     59.4    50.620   8.779547     -2.56999 +#>  ds 1 parent   90     51.0    50.620   0.379547     -0.11110 +#>  ds 1 parent  120     38.8    40.712  -1.912380      0.64706 +#>  ds 1 parent  120     38.9    40.712  -1.812380      0.61323 +#>  ds 2 parent    0    103.2    97.185   6.015158     -1.07774 +#>  ds 2 parent    0     95.1    97.185  -2.084842      0.37354 +#>  ds 2 parent    1     88.3    95.609  -7.309466      1.32706 +#>  ds 2 parent    1    102.4    95.609   6.790534     -1.23285 +#>  ds 2 parent    3     88.4    92.535  -4.134911      0.77071 +#>  ds 2 parent    3     95.2    92.535   2.665089     -0.49675 +#>  ds 2 parent    7     83.5    86.679  -3.179231      0.62426 +#>  ds 2 parent    7     96.4    86.679   9.720769     -1.90873 +#>  ds 2 parent   14     77.3    77.309  -0.009268      0.00199 +#>  ds 2 parent   14     76.0    77.309  -1.309268      0.28113 +#>  ds 2 parent   28     61.7    61.499   0.201491     -0.05137 +#>  ds 2 parent   28     56.5    61.499  -4.998509      1.27449 +#>  ds 2 parent   60     35.1    36.454  -1.353571      0.49087 +#>  ds 2 parent   60     32.2    36.454  -4.253571      1.54256 +#>  ds 2 parent   90     21.2    22.326  -1.125996      0.53604 +#>  ds 2 parent   90     23.3    22.326   0.974004     -0.46368 +#>  ds 2 parent  120     14.1    13.674   0.426440     -0.25110 +#>  ds 2 parent  120     16.9    13.674   3.226440     -1.89983 +#>  ds 3 parent    0     92.4    93.838  -1.437848      0.26501 +#>  ds 3 parent    0     94.0    93.838   0.162152     -0.02989 +#>  ds 3 parent    1     95.7    91.709   3.991384     -0.74932 +#>  ds 3 parent    1     90.8    91.709  -0.908616      0.17058 +#>  ds 3 parent    3     86.7    87.594  -0.893997      0.17409 +#>  ds 3 parent    3     85.8    87.594  -1.793997      0.34934 +#>  ds 3 parent    7     77.1    79.910  -2.810299      0.58817 +#>  ds 3 parent    7     81.5    79.910   1.589701     -0.33271 +#>  ds 3 parent   14     69.1    68.050   1.050102     -0.24845 +#>  ds 3 parent   14     62.4    68.050  -5.649898      1.33675 +#>  ds 3 parent   28     49.1    49.349  -0.248837      0.07412 +#>  ds 3 parent   28     47.2    49.349  -2.148837      0.64010 +#>  ds 3 parent   60     21.9    23.676  -1.775776      0.82085 +#>  ds 3 parent   60     23.6    23.676  -0.075776      0.03503 +#>  ds 3 parent   90     12.4    11.892   0.507660     -0.31425 +#>  ds 3 parent   90     13.8    11.892   1.907660     -1.18088 +#>  ds 3 parent  120      4.9     5.974  -1.073521      0.80099 +#>  ds 3 parent  120      7.5     5.974   1.526479     -1.13895 +#>  ds 4 parent    0     91.8   102.087 -10.287197      1.77084 +#>  ds 4 parent    0    104.6   102.087   2.512803     -0.43256 +#>  ds 4 parent    1    117.5   101.632  15.867689     -2.74145 +#>  ds 4 parent    1     99.3   101.632  -2.332311      0.40295 +#>  ds 4 parent    3     94.0   100.729  -6.728610      1.17100 +#>  ds 4 parent    3     98.7   100.729  -2.028610      0.35304 +#>  ds 4 parent    7    109.2    98.945  10.254756     -1.81080 +#>  ds 4 parent    7     89.2    98.945  -9.745244      1.72083 +#>  ds 4 parent   14    103.3    95.900   7.400009     -1.34021 +#>  ds 4 parent   14    103.0    95.900   7.100009     -1.28588 +#>  ds 4 parent   28     90.8    90.088   0.712227     -0.13563 +#>  ds 4 parent   28     88.7    90.088  -1.387773      0.26427 +#>  ds 4 parent   60     74.8    78.091  -3.291273      0.70124 +#>  ds 4 parent   60     75.3    78.091  -2.791273      0.59471 +#>  ds 4 parent   90     71.1    68.300   2.800407     -0.66075 +#>  ds 4 parent   90     78.0    68.300   9.700407     -2.28880 +#>  ds 4 parent  120     59.1    59.736  -0.635668      0.16554 +#>  ds 4 parent  120     53.8    59.736  -5.935668      1.54574 +#>  ds 5 parent    0     94.9    98.353  -3.452694      0.61266 +#>  ds 5 parent    0    101.8    98.353   3.447306     -0.61171 +#>  ds 5 parent    1     96.1    96.722  -0.621996      0.11187 +#>  ds 5 parent    1     97.1    96.722   0.378004     -0.06799 +#>  ds 5 parent    3     93.8    93.541   0.258738     -0.04781 +#>  ds 5 parent    3     85.8    93.541  -7.741262      1.43043 +#>  ds 5 parent    7     87.6    87.490   0.109848     -0.02141 +#>  ds 5 parent    7     94.0    87.490   6.509848     -1.26885 +#>  ds 5 parent   14     82.5    77.827   4.672679     -0.99818 +#>  ds 5 parent   14     81.7    77.827   3.872679     -0.82728 +#>  ds 5 parent   28     60.0    61.585  -1.585419      0.40382 +#>  ds 5 parent   28     61.0    61.585  -0.585419      0.14911 +#>  ds 5 parent   60     32.5    36.068  -3.568284      1.30251 +#>  ds 5 parent   60     35.5    36.068  -0.568284      0.20744 +#>  ds 5 parent   90     21.8    21.842  -0.042136      0.02028 +#>  ds 5 parent   90     24.4    21.842   2.557864     -1.23088 +#>  ds 5 parent  120     14.1    13.227   0.872898     -0.52035 +#>  ds 5 parent  120     12.1    13.227  -1.127102      0.67189</div><div class='input'><span class='co'># }</span> + +</div></pre> +  </div> +  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> +    <nav id="toc" data-toggle="toc" class="sticky-top"> +      <h2 data-toc-skip>Contents</h2> +    </nav> +  </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> 1.6.1.</p> +</div> + +      </footer> +   </div> + +   + + +  </body> +</html> + + | 
