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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:

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