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- Updated the staticdoc documentation



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-% $Id: examples.Rnw 66 2010-09-03 08:50:26Z jranke $
-%%\VignetteIndexEntry{Examples for kinetic evaluations using mkin}
-%%VignetteDepends{FME}
-%%\usepackage{Sweave}
-\documentclass[12pt,a4paper]{article}
-\usepackage{a4wide}
-%%\usepackage[lists,heads]{endfloat}
-\input{header}
-\hypersetup{  
-  pdftitle = {Examples for kinetic evaluations using mkin},
-  pdfsubject = {Manuscript},
-  pdfauthor = {Johannes Ranke},
-  colorlinks = {true},
-  linkcolor = {blue},
-  citecolor = {blue},
-  urlcolor = {red},
-  hyperindex = {true},
-  linktocpage = {true},
-}
-
-\begin{document}
-\title{Examples for kinetic evaluations using mkin}
-\author{\textbf{Johannes Ranke} \\[0.5cm]
-%EndAName
-Eurofins Regulatory AG\\
-Weidenweg 15, CH--4310 Rheinfelden, Switzerland\\[0.5cm]
-and\\[0.5cm]
-University of Bremen\\
-}
-\maketitle
-
-%\begin{abstract}
-%\end{abstract}
-
-
-\thispagestyle{empty} \setcounter{page}{0}
-
-\clearpage
-
-\tableofcontents
-
-\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
-
-\section{Kinetic evaluations for parent compounds}
-\label{intro}
-
-These examples are also evaluated in a parallel vignette of the
-\Rpackage{kinfit} package \citep{pkg:kinfit}. The datasets are from Appendix 3,
-of the FOCUS kinetics report \citep{FOCUS2006, FOCUSkinetics2011}.
-
-\subsection{Laboratory Data L1}
-
-The following code defines example dataset L1 from the FOCUS kinetics
-report, p. 284
-
-\begin{Schunk}
-\begin{Sinput}
-R> library("mkin")
-R> FOCUS_2006_L1 = data.frame(
-+   t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
-+   parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, 
-+              72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
-+              27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
-R> FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
-\end{Sinput}
-\end{Schunk}
-
-The next step is to set up the models used for the kinetic analysis. Note that
-the model definitions contain the names of the observed variables in the data.
-In this case, there is only one variable called \Robject{parent}.
-
-\begin{Schunk}
-\begin{Sinput}
-R> SFO <- mkinmod(parent = list(type = "SFO"))
-R> FOMC <- mkinmod(parent = list(type = "FOMC"))
-R> DFOP <- mkinmod(parent = list(type = "DFOP"))
-\end{Sinput}
-\end{Schunk}
-
-The three models cover the first assumption of simple first order (SFO),
-the case of declining rate constant over time (FOMC) and the case of two
-different phases of the kinetics (DFOP). For a more detailed discussion
-of the models, please see the FOCUS kinetics report.
-
-The following two lines fit the model and produce the summary report
-of the model fit. This covers the numerical analysis given in the 
-FOCUS report.
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
-R> summary(m.L1.SFO)
-\end{Sinput}
-\begin{Soutput}
-mkin version:    0.9.10 
-R version:       2.15.2 
-Date of fit:     Sat Feb 16 21:38:15 2013 
-Date of summary: Sat Feb 16 21:38:15 2013 
-
-Equations:
-[1] d_parent = - k_parent_sink * parent
-
-Starting values for optimised parameters:
-              initial   type transformed
-parent_0        100.0  state  100.000000
-k_parent_sink     0.1 deparm   -2.302585
-
-Fixed parameter values:
-None
-
-Optimised, transformed parameters:
-              Estimate Std. Error
-parent_0        92.471      1.368
-k_parent_sink   -2.347      0.041
-
-Backtransformed parameters:
-              Estimate
-parent_0        92.471
-k_parent_sink    0.096
-
-Residual standard error: 2.948 on 16 degrees of freedom
-
-Chi2 error levels in percent:
-         err.min n.optim df
-All data   3.424       2  7
-parent     3.424       2  7
-
-Estimated disappearance times:
-        DT50  DT90
-parent 7.249 24.08
-
-Estimated formation fractions:
-            ff
-parent_sink  1
-
-Parameter correlation:
-              parent_0 k_parent_sink
-parent_0        1.0000        0.6248
-k_parent_sink   0.6248        1.0000
-
-Data:
- time variable observed predicted residual
-    0   parent     88.3    92.471  -4.1710
-    0   parent     91.4    92.471  -1.0710
-    1   parent     85.6    84.039   1.5610
-    1   parent     84.5    84.039   0.4610
-    2   parent     78.9    76.376   2.5241
-    2   parent     77.6    76.376   1.2241
-    3   parent     72.0    69.412   2.5884
-    3   parent     71.9    69.412   2.4884
-    5   parent     50.3    57.330  -7.0301
-    5   parent     59.4    57.330   2.0699
-    7   parent     47.0    47.352  -0.3515
-    7   parent     45.1    47.352  -2.2515
-   14   parent     27.7    24.247   3.4527
-   14   parent     27.3    24.247   3.0527
-   21   parent     10.0    12.416  -2.4163
-   21   parent     10.4    12.416  -2.0163
-   30   parent      2.9     5.251  -2.3513
-   30   parent      4.0     5.251  -1.2513
-\end{Soutput}
-\end{Schunk}
-
-A plot of the fit is obtained with the plot function for mkinfit objects.
-
-\begin{Schunk}
-\begin{Sinput}
-R> plot(m.L1.SFO)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L1_SFO_plot}
-
-The residual plot can be obtained using the information contained in the
-mkinfit object, which is in fact a derivative of an modFit object defined by
-the \Rpackage{FME} package.
-
-\begin{Schunk}
-\begin{Sinput}
-R> plot(m.L1.SFO$data$time, m.L1.SFO$data$residual,
-+   xlab = "Time", ylab = "Residual", ylim = c(-8, 8))
-R> abline(h = 0, lty = 2)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L1_SFO_residuals}
-
-For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
-is checked.
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
-R> s.m.L1.FOMC <- summary(m.L1.FOMC)
-R> s.m.L1.FOMC$errmin
-\end{Sinput}
-\begin{Soutput}
-            err.min n.optim df
-All data 0.03618911       3  6
-parent   0.03618911       3  6
-\end{Soutput}
-\end{Schunk}
-
-Due to the higher number of parameters, and the lower number of degrees of freedom
-of the fit, the $\chi^2$ error level is actually higher for the FOMC model (3.6\%) than 
-for the SFO model (3.4\%).
-
-\subsection{Laboratory Data L2}
-
-The following code defines example dataset L2 from the FOCUS kinetics
-report, p. 287
-
-\begin{Schunk}
-\begin{Sinput}
-R> library("mkin")
-R> FOCUS_2006_L2 = data.frame(
-+   t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
-+   parent = c(96.1, 91.8, 41.4, 38.7,
-+              19.3, 22.3, 4.6, 4.6,
-+              2.6, 1.2, 0.3, 0.6))
-R> FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
-\end{Sinput}
-\end{Schunk}
-
-Again, the SFO model is fitted and a summary is obtained.
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
-R> summary(m.L2.SFO)
-\end{Sinput}
-\begin{Soutput}
-mkin version:    0.9.10 
-R version:       2.15.2 
-Date of fit:     Sat Feb 16 21:38:15 2013 
-Date of summary: Sat Feb 16 21:38:15 2013 
-
-Equations:
-[1] d_parent = - k_parent_sink * parent
-
-Starting values for optimised parameters:
-              initial   type transformed
-parent_0        100.0  state  100.000000
-k_parent_sink     0.1 deparm   -2.302585
-
-Fixed parameter values:
-None
-
-Optimised, transformed parameters:
-              Estimate Std. Error
-parent_0       91.4656      3.807
-k_parent_sink  -0.4112      0.107
-
-Backtransformed parameters:
-              Estimate
-parent_0        91.466
-k_parent_sink    0.663
-
-Residual standard error: 5.51 on 10 degrees of freedom
-
-Chi2 error levels in percent:
-         err.min n.optim df
-All data   14.38       2  4
-parent     14.38       2  4
-
-Estimated disappearance times:
-        DT50  DT90
-parent 1.046 3.474
-
-Estimated formation fractions:
-            ff
-parent_sink  1
-
-Parameter correlation:
-              parent_0 k_parent_sink
-parent_0        1.0000        0.4295
-k_parent_sink   0.4295        1.0000
-
-Data:
- time variable observed     predicted residual
-    0   parent     96.1 91.4656079103   4.6344
-    0   parent     91.8 91.4656079103   0.3344
-    1   parent     41.4 47.1395280371  -5.7395
-    1   parent     38.7 47.1395280371  -8.4395
-    3   parent     19.3 12.5210295280   6.7790
-    3   parent     22.3 12.5210295280   9.7790
-    7   parent      4.6  0.8833842647   3.7166
-    7   parent      4.6  0.8833842647   3.7166
-   14   parent      2.6  0.0085318162   2.5915
-   14   parent      1.2  0.0085318162   1.1915
-   28   parent      0.3  0.0000007958   0.3000
-   28   parent      0.6  0.0000007958   0.6000
-\end{Soutput}
-\end{Schunk}
-
-The $\chi^2$ error level of 14\% suggests that the model does not fit very well.
-This is also obvious from the plots of the fit and the residuals.
-
-\begin{Schunk}
-\begin{Sinput}
-R> plot(m.L2.SFO)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L2_SFO_plot}
-
-In the FOCUS kinetics report, it is stated that there is no apparent systematic
-error observed from the residual plot up to the measured DT90 (approximately at
-day 5), and there is an underestimation beyond that point.
-
-\begin{Schunk}
-\begin{Sinput}
-R> plot(m.L2.SFO$data$time, m.L2.SFO$data$residual,
-+   xlab = "Time", ylab = "Residual", ylim = c(-10, 10))
-R> abline(h = 0, lty = 2)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L2_SFO_residuals}
-
-We may add that it is difficult to judge the random nature of the residuals just 
-from the three samplings at days 0, 1 and 3. Also, it is not clear why a
-consistent underestimation after the approximate DT90 should be irrelevant.
-
-For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
-is checked.
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet=TRUE)
-R> plot(m.L2.FOMC)
-R> s.m.L2.FOMC <- summary(m.L2.FOMC)
-R> s.m.L2.FOMC$errmin
-\end{Sinput}
-\begin{Soutput}
-            err.min n.optim df
-All data 0.06204245       3  3
-parent   0.06204245       3  3
-\end{Soutput}
-\end{Schunk}
-\includegraphics{examples-L2_FOMC}
-
-The error level at which the $\chi^2$ test passes is much lower in this case.
-Therefore, the FOMC model provides a better description of the data, as less
-experimental error has to be assumed in order to explain the data.
-
-Fitting the four parameter DFOP model does not further reduce the 
-$\chi^2$ error level. 
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet=TRUE)
-R> plot(m.L2.DFOP)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L2_DFOP}
-
-Here, the default starting parameters for the DFOP model obviously do not lead
-to a reasonable solution. Therefore the fit is repeated with different starting
-parameters.
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, 
-+   parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
-+   quiet=TRUE)
-R> plot(m.L2.DFOP)
-R> summary(m.L2.DFOP)
-\end{Sinput}
-\begin{Soutput}
-mkin version:    0.9.10 
-R version:       2.15.2 
-Date of fit:     Sat Feb 16 21:38:16 2013 
-Date of summary: Sat Feb 16 21:38:16 2013 
-
-Equations:
-[1] d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time))) * parent
-
-Starting values for optimised parameters:
-         initial   type transformed
-parent_0   1e+02  state 100.0000000
-k1         1e+00 deparm   0.0000000
-k2         1e-02 deparm  -4.6051702
-g          8e-01 deparm   0.9802581
-
-Fixed parameter values:
-None
-
-Optimised, transformed parameters:
-         Estimate Std. Error
-parent_0  93.9500         NA
-k1         4.9589         NA
-k2        -1.0880         NA
-g         -0.2821         NA
-
-Backtransformed parameters:
-         Estimate
-parent_0   93.950
-k1        142.434
-k2          0.337
-g           0.402
-
-Residual standard error: 1.732 on 8 degrees of freedom
-
-Chi2 error levels in percent:
-         err.min n.optim df
-All data   2.529       4  2
-parent     2.529       4  2
-
-Estimated disappearance times:
-       DT50 DT90
-parent   NA   NA
-
-Estimated formation fractions:
-[1] ff
-<0 rows> (or 0-length row.names)
-
-Data:
- time variable observed predicted residual
-    0   parent     96.1 93.950000   2.1500
-    0   parent     91.8 93.950000  -2.1500
-    1   parent     41.4 40.143423   1.2566
-    1   parent     38.7 40.143423  -1.4434
-    3   parent     19.3 20.464500  -1.1645
-    3   parent     22.3 20.464500   1.8355
-    7   parent      4.6  5.318322  -0.7183
-    7   parent      4.6  5.318322  -0.7183
-   14   parent      2.6  0.503070   2.0969
-   14   parent      1.2  0.503070   0.6969
-   28   parent      0.3  0.004501   0.2955
-   28   parent      0.6  0.004501   0.5955
-\end{Soutput}
-\begin{Sinput}
-R> s.m.L2.DFOP <- summary(m.L2.DFOP)
-R> s.m.L2.DFOP$errmin
-\end{Sinput}
-\begin{Soutput}
-            err.min n.optim df
-All data 0.02528763       4  2
-parent   0.02528763       4  2
-\end{Soutput}
-\end{Schunk}
-\includegraphics{examples-L2_DFOP_2}
-
-Therefore, the FOMC model is clearly the best-fit model based on the 
-$\chi^2$ error level criterion.
-
-\subsection{Laboratory Data L3}
-
-The following code defines example dataset L3 from the FOCUS kinetics
-report, p. 290
-
-\begin{Schunk}
-\begin{Sinput}
-R> library("mkin")
-R> FOCUS_2006_L3 = data.frame(
-+   t = c(0, 3, 7, 14, 30, 60, 91, 120),
-+   parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
-R> FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
-\end{Sinput}
-\end{Schunk}
-
-SFO model, summary and plot:
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet=TRUE)
-R> summary(m.L3.SFO)
-\end{Sinput}
-\begin{Soutput}
-mkin version:    0.9.10 
-R version:       2.15.2 
-Date of fit:     Sat Feb 16 21:38:16 2013 
-Date of summary: Sat Feb 16 21:38:16 2013 
-
-Equations:
-[1] d_parent = - k_parent_sink * parent
-
-Starting values for optimised parameters:
-              initial   type transformed
-parent_0        100.0  state  100.000000
-k_parent_sink     0.1 deparm   -2.302585
-
-Fixed parameter values:
-None
-
-Optimised, transformed parameters:
-              Estimate Std. Error
-parent_0        74.873      8.458
-k_parent_sink   -3.678      0.326
-
-Backtransformed parameters:
-              Estimate
-parent_0        74.873
-k_parent_sink    0.025
-
-Residual standard error: 12.91 on 6 degrees of freedom
-
-Chi2 error levels in percent:
-         err.min n.optim df
-All data   21.24       2  6
-parent     21.24       2  6
-
-Estimated disappearance times:
-        DT50  DT90
-parent 27.43 91.12
-
-Estimated formation fractions:
-            ff
-parent_sink  1
-
-Parameter correlation:
-              parent_0 k_parent_sink
-parent_0        1.0000        0.5484
-k_parent_sink   0.5484        1.0000
-
-Data:
- time variable observed predicted  residual
-    0   parent     97.8    74.873  22.92734
-    3   parent     60.0    69.407  -9.40654
-    7   parent     51.0    62.734 -11.73403
-   14   parent     43.0    52.563  -9.56336
-   30   parent     35.0    35.083  -0.08281
-   60   parent     22.0    16.439   5.56137
-   91   parent     15.0     7.510   7.48961
-  120   parent     12.0     3.609   8.39083
-\end{Soutput}
-\begin{Sinput}
-R> plot(m.L3.SFO)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L3_SFO}
-
-The $\chi^2$ error level of 22\% as well as the plot suggest that the model
-does not fit very well. 
-
-The FOMC model performs better:
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet=TRUE)
-R> plot(m.L3.FOMC)
-R> s.m.L3.FOMC <- summary(m.L3.FOMC)
-R> s.m.L3.FOMC$errmin
-\end{Sinput}
-\begin{Soutput}
-            err.min n.optim df
-All data 0.07321867       3  5
-parent   0.07321867       3  5
-\end{Soutput}
-\begin{Sinput}
-R> endpoints(m.L3.FOMC)
-\end{Sinput}
-\begin{Soutput}
-$distimes
-           DT50     DT90
-parent 7.729478 431.2428
-
-$ff
-logical(0)
-
-$SFORB
-logical(0)
-\end{Soutput}
-\end{Schunk}
-\includegraphics{examples-L3_FOMC}
-
-The error level at which the $\chi^2$ test passes is 7\% in this case.
-
-Fitting the four parameter DFOP model further reduces the $\chi^2$ error level
-considerably:
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet=TRUE)
-R> plot(m.L3.DFOP)
-R> s.m.L3.DFOP <- summary(m.L3.DFOP)
-R> s.m.L3.DFOP$errmin
-\end{Sinput}
-\begin{Soutput}
-            err.min n.optim df
-All data 0.02223992       4  4
-parent   0.02223992       4  4
-\end{Soutput}
-\end{Schunk}
-\includegraphics{examples-L3_DFOP}
-
-Therefore, the DFOP model is the best-fit model based on the $\chi^2$ error
-level criterion for laboratory data L3.
-
-\subsection{Laboratory Data L4}
-
-The following code defines example dataset L4 from the FOCUS kinetics
-report, p. 293
-
-\begin{Schunk}
-\begin{Sinput}
-R> library("mkin")
-R> FOCUS_2006_L4 = data.frame(
-+   t = c(0, 3, 7, 14, 30, 60, 91, 120),
-+   parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
-R> FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
-\end{Sinput}
-\end{Schunk}
-
-SFO model, summary and plot:
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet=TRUE)
-R> summary(m.L4.SFO)
-\end{Sinput}
-\begin{Soutput}
-mkin version:    0.9.10 
-R version:       2.15.2 
-Date of fit:     Sat Feb 16 21:38:17 2013 
-Date of summary: Sat Feb 16 21:38:17 2013 
-
-Equations:
-[1] d_parent = - k_parent_sink * parent
-
-Starting values for optimised parameters:
-              initial   type transformed
-parent_0        100.0  state  100.000000
-k_parent_sink     0.1 deparm   -2.302585
-
-Fixed parameter values:
-None
-
-Optimised, transformed parameters:
-              Estimate Std. Error
-parent_0         96.44      1.949
-k_parent_sink    -5.03      0.080
-
-Backtransformed parameters:
-              Estimate
-parent_0        96.442
-k_parent_sink    0.007
-
-Residual standard error: 3.651 on 6 degrees of freedom
-
-Chi2 error levels in percent:
-         err.min n.optim df
-All data   3.288       2  6
-parent     3.288       2  6
-
-Estimated disappearance times:
-       DT50 DT90
-parent  106  352
-
-Estimated formation fractions:
-            ff
-parent_sink  1
-
-Parameter correlation:
-              parent_0 k_parent_sink
-parent_0        1.0000        0.5865
-k_parent_sink   0.5865        1.0000
-
-Data:
- time variable observed predicted residual
-    0   parent     96.6     96.44   0.1585
-    3   parent     96.3     94.57   1.7324
-    7   parent     94.3     92.13   2.1744
-   14   parent     88.8     88.00   0.7972
-   30   parent     74.9     79.26  -4.3589
-   60   parent     59.9     65.14  -5.2376
-   91   parent     53.5     53.18   0.3167
-  120   parent     49.0     43.99   5.0054
-\end{Soutput}
-\begin{Sinput}
-R> plot(m.L4.SFO)
-\end{Sinput}
-\end{Schunk}
-\includegraphics{examples-L4_SFO}
-
-The $\chi^2$ error level of 3.3\% as well as the plot suggest that the model
-fits very well. 
-
-The FOMC model for comparison
-
-\begin{Schunk}
-\begin{Sinput}
-R> m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet=TRUE)
-R> plot(m.L4.FOMC)
-R> s.m.L4.FOMC <- summary(m.L4.FOMC)
-R> s.m.L4.FOMC$errmin
-\end{Sinput}
-\begin{Soutput}
-            err.min n.optim df
-All data 0.02027643       3  5
-parent   0.02027643       3  5
-\end{Soutput}
-\end{Schunk}
-\includegraphics{examples-L4_FOMC}
-
-The error level at which the $\chi^2$ test passes is slightly lower for the FOMC 
-model. However, the difference appears negligible.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-\end{document}
-% vim: set foldmethod=syntax: