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
|
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>transform_odeparms. mkin 0.9.43</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="author" content="
Johannes Ranke
">
<link href="css/bootstrap.css" rel="stylesheet">
<link href="css/bootstrap-responsive.css" rel="stylesheet">
<link href="css/highlight.css" rel="stylesheet">
<link href="css/staticdocs.css" rel="stylesheet">
<!--[if lt IE 9]>
<script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
<![endif]-->
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
processEscapes: true
}
});
</script>
<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
</head>
<body>
<div class="navbar">
<div class="navbar-inner">
<div class="container">
<a class="brand" href="#">mkin 0.9.43</a>
<div class="nav">
<ul class="nav">
<li><a href="index.html"><i class="icon-home icon-white"></i> Index</a></li>
</ul>
</div>
</div>
</div>
</div>
<div class="container">
<header>
</header>
<h1>
Functions to transform and backtransform kinetic parameters for fitting
</h1>
<div class="row">
<div class="span8">
<h2>Usage</h2>
<pre><div>transform_odeparms(parms, mkinmod, transform_rates = TRUE, transform_fractions = TRUE)
backtransform_odeparms(transparms, mkinmod, transform_rates = TRUE, transform_fractions = TRUE)</div></pre>
<h2>Arguments</h2>
<dl>
<dt>parms</dt>
<dd>
Parameters of kinetic models as used in the differential equations.
</dd>
<dt>transparms</dt>
<dd>
Transformed parameters of kinetic models as used in the fitting procedure.
</dd>
<dt>mkinmod</dt>
<dd>
The kinetic model of class <code><a href='mkinmod.html'>mkinmod</a></code>, containing the names of
the model variables that are needed for grouping the formation fractions
before <code><a href='ilr.html'>ilr</a></code> transformation, the parameter names and
the information if the pathway to sink is included in the model.
</dd>
<dt>transform_rates</dt>
<dd>
Boolean specifying if kinetic rate constants should be transformed in the
model specification used in the fitting for better compliance with the
assumption of normal distribution of the estimator. If TRUE, also
alpha and beta parameters of the FOMC model are log-transformed, as well
as k1 and k2 rate constants for the DFOP and HS models and the break point tb
of the HS model.
</dd>
<dt>transform_fractions</dt>
<dd>
Boolean specifying if formation fractions constants should be transformed in the
model specification used in the fitting for better compliance with the
assumption of normal distribution of the estimator. The default (TRUE) is
to do transformations. The g parameter of the DFOP and HS models are also
transformed, as they can also be seen as compositional data. The
transformation used for these transformations is the <code><a href='ilr.html'>ilr</a></code>
transformation.
</dd>
</dl>
<div class="Description">
<h2>Description</h2>
<p>The transformations are intended to map parameters that should only take
on restricted values to the full scale of real numbers. For kinetic rate
constants and other paramters that can only take on positive values, a
simple log transformation is used. For compositional parameters, such as
the formations fractions that should always sum up to 1 and can not be
negative, the <code><a href='ilr.html'>ilr</a></code> transformation is used.</p>
<p>The transformation of sets of formation fractions is fragile, as it supposes
the same ordering of the components in forward and backward transformation.
This is no problem for the internal use in <code><a href='mkinfit.html'>mkinfit</a></code>.</p>
</div>
<div class="Value">
<h2>Value</h2>
<p><dl>
A vector of transformed or backtransformed parameters with the same names
as the original parameters.
</dl></p>
</div>
<h2 id="examples">Examples</h2>
<pre class="examples"><div class='input'>SFO_SFO <- mkinmod(
parent = list(type = "SFO", to = "m1", sink = TRUE),
m1 = list(type = "SFO"))
</div>
<strong class='message'>Successfully compiled differential equation model from auto-generated C code.</strong>
<div class='input'># Fit the model to the FOCUS example dataset D using defaults
fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
summary(fit, data=FALSE) # See transformed and backtransformed parameters
</div>
<div class='output'>mkin version: 0.9.43
R version: 3.3.1
Date of fit: Tue Jun 28 01:32:50 2016
Date of summary: Tue Jun 28 01:32:50 2016
Equations:
d_parent = - k_parent_sink * parent - k_parent_m1 * parent
d_m1 = + k_parent_m1 * parent - k_m1_sink * m1
Model predictions using solution type deSolve
Fitted with method Port using 153 model solutions performed in 1.694 s
Weighting: none
Starting values for parameters to be optimised:
value type
parent_0 100.7500 state
k_parent_sink 0.1000 deparm
k_parent_m1 0.1001 deparm
k_m1_sink 0.1002 deparm
Starting values for the transformed parameters actually optimised:
value lower upper
parent_0 100.750000 -Inf Inf
log_k_parent_sink -2.302585 -Inf Inf
log_k_parent_m1 -2.301586 -Inf Inf
log_k_m1_sink -2.300587 -Inf Inf
Fixed parameter values:
value type
m1_0 0 state
Optimised, transformed parameters with symmetric confidence intervals:
Estimate Std. Error Lower Upper
parent_0 99.600 1.61400 96.330 102.900
log_k_parent_sink -3.038 0.07826 -3.197 -2.879
log_k_parent_m1 -2.980 0.04124 -3.064 -2.897
log_k_m1_sink -5.248 0.13610 -5.523 -4.972
Parameter correlation:
parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
parent_0 1.00000 0.6075 -0.06625 -0.1701
log_k_parent_sink 0.60752 1.0000 -0.08740 -0.6253
log_k_parent_m1 -0.06625 -0.0874 1.00000 0.4716
log_k_m1_sink -0.17006 -0.6253 0.47163 1.0000
Residual standard error: 3.211 on 36 degrees of freedom
Backtransformed parameters:
Confidence intervals for internally transformed parameters are asymmetric.
t-test (unrealistically) based on the assumption of normal distribution
for estimators of untransformed parameters.
Estimate t value Pr(>t) Lower Upper
parent_0 99.600000 61.720 2.024e-38 96.330000 1.029e+02
k_parent_sink 0.047920 12.780 3.050e-15 0.040890 5.616e-02
k_parent_m1 0.050780 24.250 3.407e-24 0.046700 5.521e-02
k_m1_sink 0.005261 7.349 5.758e-09 0.003992 6.933e-03
Chi2 error levels in percent:
err.min n.optim df
All data 6.398 4 15
parent 6.827 3 6
m1 4.490 1 9
Resulting formation fractions:
ff
parent_sink 0.4855
parent_m1 0.5145
m1_sink 1.0000
Estimated disappearance times:
DT50 DT90
parent 7.023 23.33
m1 131.761 437.70
</div>
<div class='input'>
## Not run:
# fit.2 <- mkinfit(SFO_SFO, FOCUS_2006_D, transform_rates = FALSE)
# summary(fit.2, data=FALSE)
# ## End(Not run)
initials <- fit$start$value
names(initials) <- rownames(fit$start)
transformed <- fit$start_transformed$value
names(transformed) <- rownames(fit$start_transformed)
transform_odeparms(initials, SFO_SFO)
</div>
<div class='output'> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
100.750000 -2.302585 -2.301586 -2.300587
</div>
<div class='input'>backtransform_odeparms(transformed, SFO_SFO)
</div>
<div class='output'> parent_0 k_parent_sink k_parent_m1 k_m1_sink
100.7500 0.1000 0.1001 0.1002
</div>
<div class='input'>
## Not run:
# # The case of formation fractions
# SFO_SFO.ff <- mkinmod(
# parent = list(type = "SFO", to = "m1", sink = TRUE),
# m1 = list(type = "SFO"),
# use_of_ff = "max")
#
# fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_2006_D)
# summary(fit.ff, data = FALSE)
# initials <- c("f_parent_to_m1" = 0.5)
# transformed <- transform_odeparms(initials, SFO_SFO.ff)
# backtransform_odeparms(transformed, SFO_SFO.ff)
#
# # And without sink
# SFO_SFO.ff.2 <- mkinmod(
# parent = list(type = "SFO", to = "m1", sink = FALSE),
# m1 = list(type = "SFO"),
# use_of_ff = "max")
#
#
# fit.ff.2 <- mkinfit(SFO_SFO.ff.2, FOCUS_2006_D)
# summary(fit.ff.2, data = FALSE)
# ## End(Not run)
</div></pre>
</div>
<div class="span4">
<!-- <ul>
<li>transform_odeparms</li><li>backtransform_odeparms</li>
</ul>
<ul>
<li> manip </li>
</ul> -->
<h2>Author</h2>
Johannes Ranke
</div>
</div>
<footer>
<p class="pull-right"><a href="#">Back to top</a></p>
<p>Built by <a href="https://github.com/hadley/staticdocs">staticdocs</a>. Styled with <a href="http://twitter.github.com/bootstrap">bootstrap</a>.</p>
</footer>
</div>
</body>
</html>
|
