1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
|
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object — plot.mixed.mmkin • mkin</title>
<!-- jquery -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script>
<!-- Bootstrap -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script>
<!-- bootstrap-toc -->
<link rel="stylesheet" href="../bootstrap-toc.css">
<script src="../bootstrap-toc.js"></script>
<!-- Font Awesome icons -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous" />
<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script>
<!-- headroom.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script>
<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>
<meta property="og:title" content="Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object — plot.mixed.mmkin" />
<meta property="og:description" content="Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object" />
<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">1.1.0</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-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>Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object</h1>
<small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/plot.mixed.mmkin.R'><code>R/plot.mixed.mmkin.R</code></a></small>
<div class="hidden name"><code>plot.mixed.mmkin.Rd</code></div>
</div>
<div class="ref-description">
<p>Plot predictions from a fitted nonlinear mixed model obtained via an mmkin row object</p>
</div>
<pre class="usage"><span class='co'># S3 method for mixed.mmkin</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span>
<span class='va'>x</span>,
i <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fu'><a href='https://rdrr.io/r/base/nrow.html'>ncol</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>mmkin</span><span class='op'>)</span>,
obs_vars <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>map</span><span class='op'>)</span>,
standardized <span class='op'>=</span> <span class='cn'>TRUE</span>,
xlab <span class='op'>=</span> <span class='st'>"Time"</span>,
xlim <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/range.html'>range</a></span><span class='op'>(</span><span class='va'>x</span><span class='op'>$</span><span class='va'>data</span><span class='op'>$</span><span class='va'>time</span><span class='op'>)</span>,
resplot <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='st'>"predicted"</span>, <span class='st'>"time"</span><span class='op'>)</span>,
pred_over <span class='op'>=</span> <span class='cn'>NULL</span>,
test_log_parms <span class='op'>=</span> <span class='cn'>FALSE</span>,
conf.level <span class='op'>=</span> <span class='fl'>0.6</span>,
ymax <span class='op'>=</span> <span class='st'>"auto"</span>,
maxabs <span class='op'>=</span> <span class='st'>"auto"</span>,
ncol.legend <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>i</span><span class='op'>)</span> <span class='op'><=</span> <span class='fl'>3</span>, <span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>i</span><span class='op'>)</span> <span class='op'>+</span> <span class='fl'>1</span>, <span class='fu'><a href='https://rdrr.io/r/base/ifelse.html'>ifelse</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>i</span><span class='op'>)</span> <span class='op'><=</span> <span class='fl'>8</span>, <span class='fl'>3</span>, <span class='fl'>4</span><span class='op'>)</span><span class='op'>)</span>,
nrow.legend <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/Round.html'>ceiling</a></span><span class='op'>(</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>i</span><span class='op'>)</span> <span class='op'>+</span> <span class='fl'>1</span><span class='op'>)</span><span class='op'>/</span><span class='va'>ncol.legend</span><span class='op'>)</span>,
rel.height.legend <span class='op'>=</span> <span class='fl'>0.02</span> <span class='op'>+</span> <span class='fl'>0.07</span> <span class='op'>*</span> <span class='va'>nrow.legend</span>,
rel.height.bottom <span class='op'>=</span> <span class='fl'>1.1</span>,
pch_ds <span class='op'>=</span> <span class='fl'>1</span><span class='op'>:</span><span class='fu'><a href='https://rdrr.io/r/base/length.html'>length</a></span><span class='op'>(</span><span class='va'>i</span><span class='op'>)</span>,
col_ds <span class='op'>=</span> <span class='va'>pch_ds</span> <span class='op'>+</span> <span class='fl'>1</span>,
lty_ds <span class='op'>=</span> <span class='va'>col_ds</span>,
frame <span class='op'>=</span> <span class='cn'>TRUE</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>x</th>
<td><p>An object of class <a href='mixed.html'>mixed.mmkin</a>, <a href='saem.html'>saem.mmkin</a> or <a href='nlme.mmkin.html'>nlme.mmkin</a></p></td>
</tr>
<tr>
<th>i</th>
<td><p>A numeric index to select datasets for which to plot the individual predictions,
in case plots get too large</p></td>
</tr>
<tr>
<th>obs_vars</th>
<td><p>A character vector of names of the observed variables for
which the data and the model should be plotted. Defauls to all observed
variables in the model.</p></td>
</tr>
<tr>
<th>standardized</th>
<td><p>Should the residuals be standardized? Only takes effect if
<code>resplot = "time"</code>.</p></td>
</tr>
<tr>
<th>xlab</th>
<td><p>Label for the x axis.</p></td>
</tr>
<tr>
<th>xlim</th>
<td><p>Plot range in x direction.</p></td>
</tr>
<tr>
<th>resplot</th>
<td><p>Should the residuals plotted against time or against
predicted values?</p></td>
</tr>
<tr>
<th>pred_over</th>
<td><p>Named list of alternative predictions as obtained
from <a href='mkinpredict.html'>mkinpredict</a> with a compatible <a href='mkinmod.html'>mkinmod</a>.</p></td>
</tr>
<tr>
<th>test_log_parms</th>
<td><p>Passed to <a href='mean_degparms.html'>mean_degparms</a> in the case of an
<a href='mixed.html'>mixed.mmkin</a> object</p></td>
</tr>
<tr>
<th>conf.level</th>
<td><p>Passed to <a href='mean_degparms.html'>mean_degparms</a> in the case of an
<a href='mixed.html'>mixed.mmkin</a> object</p></td>
</tr>
<tr>
<th>ymax</th>
<td><p>Vector of maximum y axis values</p></td>
</tr>
<tr>
<th>maxabs</th>
<td><p>Maximum absolute value of the residuals. This is used for the
scaling of the y axis and defaults to "auto".</p></td>
</tr>
<tr>
<th>ncol.legend</th>
<td><p>Number of columns to use in the legend</p></td>
</tr>
<tr>
<th>nrow.legend</th>
<td><p>Number of rows to use in the legend</p></td>
</tr>
<tr>
<th>rel.height.legend</th>
<td><p>The relative height of the legend shown on top</p></td>
</tr>
<tr>
<th>rel.height.bottom</th>
<td><p>The relative height of the bottom plot row</p></td>
</tr>
<tr>
<th>pch_ds</th>
<td><p>Symbols to be used for plotting the data.</p></td>
</tr>
<tr>
<th>col_ds</th>
<td><p>Colors used for plotting the observed data and the
corresponding model prediction lines for the different datasets.</p></td>
</tr>
<tr>
<th>lty_ds</th>
<td><p>Line types to be used for the model predictions.</p></td>
</tr>
<tr>
<th>frame</th>
<td><p>Should a frame be drawn around the plots?</p></td>
</tr>
<tr>
<th>...</th>
<td><p>Further arguments passed to <code><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></code>.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>The function is called for its side effect.</p>
<h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
<p>Johannes Ranke</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='va'>ds</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'>experimental_data_for_UBA_2019</span><span class='op'>[</span><span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>]</span>,
<span class='kw'>function</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span> <span class='va'>x</span><span class='op'>$</span><span class='va'>data</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='st'>"name"</span>, <span class='st'>"time"</span>, <span class='st'>"value"</span><span class='op'>)</span><span class='op'>]</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</span><span class='op'>)</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/paste.html'>paste0</a></span><span class='op'>(</span><span class='st'>"ds "</span>, <span class='fl'>6</span><span class='op'>:</span><span class='fl'>10</span><span class='op'>)</span>
<span class='va'>dfop_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='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='st'>"A1"</span><span class='op'>)</span>,
A1 <span class='op'>=</span> <span class='fu'><a href='mkinmod.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='co'># \dontrun{</span>
<span class='va'>f</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>dfop_sfo</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f</span><span class='op'>[</span>, <span class='fl'>3</span><span class='op'>:</span><span class='fl'>4</span><span class='op'>]</span>, standardized <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
</div><div class='img'><img src='plot.mixed.mmkin-1.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='co'># For this fit we need to increase pnlsMaxiter, and we increase the</span>
<span class='co'># tolerance in order to speed up the fit for this example evaluation</span>
<span class='co'># It still takes 20 seconds to run</span>
<span class='va'>f_nlme</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/pkg/nlme/man/nlme.html'>nlme</a></span><span class='op'>(</span><span class='va'>f</span>, control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>pnlsMaxIter <span class='op'>=</span> <span class='fl'>120</span>, tolerance <span class='op'>=</span> <span class='fl'>1e-3</span><span class='op'>)</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlme</span><span class='op'>)</span>
</div><div class='img'><img src='plot.mixed.mmkin-2.png' alt='' width='700' height='433' /></div><div class='input'>
<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</span>, transformations <span class='op'>=</span> <span class='st'>"saemix"</span><span class='op'>)</span>
</div><div class='output co'>#> Running main SAEM algorithm
#> [1] "Thu Sep 16 14:34:31 2021"
#> ....
#> Minimisation finished
#> [1] "Thu Sep 16 14:34:38 2021"</div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem</span><span class='op'>)</span>
</div><div class='img'><img src='plot.mixed.mmkin-3.png' alt='' width='700' height='433' /></div><div class='input'>
<span class='va'>f_obs</span> <span class='op'><-</span> <span class='fu'><a href='mmkin.html'>mmkin</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span><span class='st'>"DFOP-SFO"</span> <span class='op'>=</span> <span class='va'>dfop_sfo</span><span class='op'>)</span>, <span class='va'>ds</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"obs"</span><span class='op'>)</span>
<span class='va'>f_nlmix</span> <span class='op'><-</span> <span class='fu'>nlmix</span><span class='op'>(</span><span class='va'>f_obs</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='error'>Error in nlmix(f_obs): could not find function "nlmix"</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_nlmix</span><span class='op'>)</span>
</div><div class='output co'>#> <span class='error'>Error in plot(f_nlmix): object 'f_nlmix' not found</span></div><div class='input'>
<span class='co'># We can overlay the two variants if we generate predictions</span>
<span class='va'>pred_nlme</span> <span class='op'><-</span> <span class='fu'><a href='mkinpredict.html'>mkinpredict</a></span><span class='op'>(</span><span class='va'>dfop_sfo</span>,
<span class='va'>f_nlme</span><span class='op'>$</span><span class='va'>bparms.optim</span><span class='op'>[</span><span class='op'>-</span><span class='fl'>1</span><span class='op'>]</span>,
<span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='va'>f_nlme</span><span class='op'>$</span><span class='va'>bparms.optim</span><span class='op'>[[</span><span class='fl'>1</span><span class='op'>]</span><span class='op'>]</span>, A1 <span class='op'>=</span> <span class='fl'>0</span><span class='op'>)</span>,
<span class='fu'><a href='https://rdrr.io/r/base/seq.html'>seq</a></span><span class='op'>(</span><span class='fl'>0</span>, <span class='fl'>180</span>, by <span class='op'>=</span> <span class='fl'>0.2</span><span class='op'>)</span><span class='op'>)</span>
<span class='fu'><a href='https://rdrr.io/r/graphics/plot.default.html'>plot</a></span><span class='op'>(</span><span class='va'>f_saem</span>, pred_over <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>nlme <span class='op'>=</span> <span class='va'>pred_nlme</span><span class='op'>)</span><span class='op'>)</span>
</div><div class='img'><img src='plot.mixed.mmkin-4.png' alt='' width='700' height='433' /></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>
|
