aboutsummaryrefslogtreecommitdiff
path: root/docs/reference/transform_odeparms.html
blob: 66253bba646bf8c1b852192c6c9747eaf64af885 (plain) (blame)
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
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html>
  <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>transform_odeparms. mkin</title>

<!-- jquery -->
<script src="https://code.jquery.com/jquery-3.1.0.min.js" integrity="sha384-nrOSfDHtoPMzJHjVTdCopGqIqeYETSXhZDFyniQ8ZHcVy08QesyHcnOUpMpqnmWq" crossorigin="anonymous"></script>

<!-- Bootstrap -->
<link href="https://maxcdn.bootstrapcdn.com/bootswatch/3.3.7/cerulean/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous">

<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>

<!-- Font Awesome icons -->
<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" integrity="sha384-T8Gy5hrqNKT+hzMclPo118YTQO6cYprQmhrYwIiQ/3axmI1hQomh7Ud2hPOy8SP1" crossorigin="anonymous">


<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>

<!-- mathjax -->
<script src='https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></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>
    <div class="container">
      <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">
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
      </button>
      <a class="navbar-brand" href="../index.html">mkin</a>
    </div>
    <div id="navbar" class="navbar-collapse collapse">
      <ul class="nav navbar-nav">
        <li>
  <a href="../index.html">Home</a>
</li>
<li>
  <a href="../reference/index.html">Reference</a>
</li>
      </ul>
      <ul class="nav navbar-nav navbar-right">
        <li>
  <a href="https://github.com/jranke/mkin">
    <span class="fa fa-github fa-lg"></span>
     
  </a>
</li>
      </ul>
    </div><!--/.nav-collapse -->
  </div><!--/.container -->
</div><!--/.navbar -->
      
      </header>

      <div class="page-header">
  <h1>
</h1>
</div>

<div class="row">
  <div class="col-md-9">
    
    <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>ilr</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>mkinfit</code>.</p>
    

    <pre><span class='fu'>transform_odeparms</span>(<span class='no'>parms</span>, <span class='no'>mkinmod</span>,
                   <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'>backtransform_odeparms</span>(<span class='no'>transparms</span>, <span class='no'>mkinmod</span>,
                       <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</pre>
    
    <h2>Arguments</h2>
    <dl class="dl-horizontal">
      <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>mkinmod</code>, containing the names of
    the model variables that are needed for grouping the formation fractions
    before <code>ilr</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>ilr</code>
    transformation.
  </dd>
    </dl>
    
    <div class="Value">
      <h2>Value</h2>

      <p>A vector of transformed or backtransformed parameters with the same names
  as the original parameters.</p>
    </div>
    
    <h2 id="examples">Examples</h2>
    <pre class="examples"><div class='input'><span class='no'>SFO_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinmod</span>(
  <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'>list</span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output'><strong class='text-info'>Successfully compiled differential equation model from auto-generated C code.</strong></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span>
<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'>summary</span>(<span class='no'>fit</span>, <span class='kw'>data</span><span class='kw'>=</span><span class='fl'>FALSE</span>) <span class='co'># See transformed and backtransformed parameters</span></div><div class='output co'>#&gt; mkin version:    0.9.44.9000 
#&gt; R version:       3.3.1 
#&gt; Date of fit:     Thu Oct  6 10:47:45 2016 
#&gt; Date of summary: Thu Oct  6 10:47:45 2016 
#&gt; 
#&gt; Equations:
#&gt; d_parent = - k_parent_sink * parent - k_parent_m1 * parent
#&gt; d_m1 = + k_parent_m1 * parent - k_m1_sink * m1
#&gt; 
#&gt; Model predictions using solution type deSolve 
#&gt; 
#&gt; Fitted with method Port using 153 model solutions performed in 0.638 s
#&gt; 
#&gt; Weighting: none
#&gt; 
#&gt; Starting values for parameters to be optimised:
#&gt;                  value   type
#&gt; parent_0      100.7500  state
#&gt; k_parent_sink   0.1000 deparm
#&gt; k_parent_m1     0.1001 deparm
#&gt; k_m1_sink       0.1002 deparm
#&gt; 
#&gt; Starting values for the transformed parameters actually optimised:
#&gt;                        value lower upper
#&gt; parent_0          100.750000  -Inf   Inf
#&gt; log_k_parent_sink  -2.302585  -Inf   Inf
#&gt; log_k_parent_m1    -2.301586  -Inf   Inf
#&gt; log_k_m1_sink      -2.300587  -Inf   Inf
#&gt; 
#&gt; Fixed parameter values:
#&gt;      value  type
#&gt; m1_0     0 state
#&gt; 
#&gt; Optimised, transformed parameters with symmetric confidence intervals:
#&gt;                   Estimate Std. Error  Lower   Upper
#&gt; parent_0            99.600    1.61400 96.330 102.900
#&gt; log_k_parent_sink   -3.038    0.07826 -3.197  -2.879
#&gt; log_k_parent_m1     -2.980    0.04124 -3.064  -2.897
#&gt; log_k_m1_sink       -5.248    0.13610 -5.523  -4.972
#&gt; 
#&gt; Parameter correlation:
#&gt;                   parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
#&gt; parent_0           1.00000            0.6075        -0.06625       -0.1701
#&gt; log_k_parent_sink  0.60752            1.0000        -0.08740       -0.6253
#&gt; log_k_parent_m1   -0.06625           -0.0874         1.00000        0.4716
#&gt; log_k_m1_sink     -0.17006           -0.6253         0.47163        1.0000
#&gt; 
#&gt; Residual standard error: 3.211 on 36 degrees of freedom
#&gt; 
#&gt; Backtransformed parameters:
#&gt; Confidence intervals for internally transformed parameters are asymmetric.
#&gt; t-test (unrealistically) based on the assumption of normal distribution
#&gt; for estimators of untransformed parameters.
#&gt;                Estimate t value    Pr(&gt;t)     Lower     Upper
#&gt; parent_0      99.600000  61.720 2.024e-38 96.330000 1.029e+02
#&gt; k_parent_sink  0.047920  12.780 3.050e-15  0.040890 5.616e-02
#&gt; k_parent_m1    0.050780  24.250 3.407e-24  0.046700 5.521e-02
#&gt; k_m1_sink      0.005261   7.349 5.758e-09  0.003992 6.933e-03
#&gt; 
#&gt; Chi2 error levels in percent:
#&gt;          err.min n.optim df
#&gt; All data   6.398       4 15
#&gt; parent     6.827       3  6
#&gt; m1         4.490       1  9
#&gt; 
#&gt; Resulting formation fractions:
#&gt;                 ff
#&gt; parent_sink 0.4855
#&gt; parent_m1   0.5145
#&gt; m1_sink     1.0000
#&gt; 
#&gt; Estimated disappearance times:
#&gt;           DT50   DT90
#&gt; parent   7.023  23.33
#&gt; m1     131.761 437.70
#&gt; </div><div class='input'>
<span class='co'>## Not run: ------------------------------------</span>
<span class='co'># fit.2 &lt;- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE)</span>
<span class='co'># summary(fit.2, data=FALSE) </span>
<span class='co'>## ---------------------------------------------</span>

<span class='no'>initials</span> <span class='kw'>&lt;-</span> <span class='no'>fit</span>$<span class='no'>start</span>$<span class='no'>value</span>
<span class='fu'>names</span>(<span class='no'>initials</span>) <span class='kw'>&lt;-</span> <span class='fu'>rownames</span>(<span class='no'>fit</span>$<span class='no'>start</span>)
<span class='no'>transformed</span> <span class='kw'>&lt;-</span> <span class='no'>fit</span>$<span class='no'>start_transformed</span>$<span class='no'>value</span>
<span class='fu'>names</span>(<span class='no'>transformed</span>) <span class='kw'>&lt;-</span> <span class='fu'>rownames</span>(<span class='no'>fit</span>$<span class='no'>start_transformed</span>)
<span class='fu'>transform_odeparms</span>(<span class='no'>initials</span>, <span class='no'>SFO_SFO</span>)</div><div class='output co'>#&gt;          parent_0 log_k_parent_sink   log_k_parent_m1     log_k_m1_sink 
#&gt;        100.750000         -2.302585         -2.301586         -2.300587 
#&gt; </div><div class='input'><span class='fu'>backtransform_odeparms</span>(<span class='no'>transformed</span>, <span class='no'>SFO_SFO</span>)</div><div class='output co'>#&gt;      parent_0 k_parent_sink   k_parent_m1     k_m1_sink 
#&gt;      100.7500        0.1000        0.1001        0.1002 
#&gt; </div><div class='input'>
<span class='co'>## Not run: ------------------------------------</span>
<span class='co'># # The case of formation fractions</span>
<span class='co'># SFO_SFO.ff &lt;- mkinmod(</span>
<span class='co'>#   parent = list(type = "SFO", to = "m1", sink = TRUE),</span>
<span class='co'>#   m1 = list(type = "SFO"),</span>
<span class='co'>#   use_of_ff = "max")</span>
<span class='co'># </span>
<span class='co'># fit.ff &lt;- mkinfit(SFO_SFO.ff, FOCUS_2006_D)</span>
<span class='co'># summary(fit.ff, data = FALSE)</span>
<span class='co'># initials &lt;- c("f_parent_to_m1" = 0.5)</span>
<span class='co'># transformed &lt;- transform_odeparms(initials, SFO_SFO.ff)</span>
<span class='co'># backtransform_odeparms(transformed, SFO_SFO.ff)</span>
<span class='co'># </span>
<span class='co'># # And without sink</span>
<span class='co'># SFO_SFO.ff.2 &lt;- mkinmod(</span>
<span class='co'>#   parent = list(type = "SFO", to = "m1", sink = FALSE),</span>
<span class='co'>#   m1 = list(type = "SFO"),</span>
<span class='co'>#   use_of_ff = "max")</span>
<span class='co'># </span>
<span class='co'># </span>
<span class='co'># fit.ff.2 &lt;- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D)</span>
<span class='co'># summary(fit.ff.2, data = FALSE)</span>
<span class='co'>## ---------------------------------------------</span></div></pre>
  </div>
  <div class="col-md-3">
    <h2>Author</h2>
    
  Johannes Ranke

  </div>
</div>

      <footer>
      <p>Built by <a href="http://hadley.github.io/pkgdown/">pkgdown</a>. Styled with <a href="http://getbootstrap.com">Bootstrap 3</a>.</p>
      </footer>
   </div>

  </body>
</html>

Contact - Imprint