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diff --git a/vignettes/examples.tex b/vignettes/examples.tex deleted file mode 100644 index 4d92a06..0000000 --- a/vignettes/examples.tex +++ /dev/null @@ -1,657 +0,0 @@ -% $Id: $ -%%\VignetteIndexEntry{Examples for kinetic evaluations using kinfit} -%%\usepackage{Sweave} -\documentclass[12pt,a4paper]{article} -\usepackage{a4wide} -%%\usepackage[lists,heads]{endfloat} -\input{header} -\hypersetup{ - pdftitle = {Examples for kinetic evaluations using kinfit}, - 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 kinfit} -\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{mkin} package \citep{pkg:mkin}. The datasets are from Appendix 3, -of the FOCUS kinetics report \citep{FOCUS2006, FOCUSkinetics2011}. - -\subsection{Laboratory Data L1} - -The following code defines an object containing the example dataset L1 from the -FOCUS kinetics report, p. 284 - -\begin{Schunk} -\begin{Sinput} -R> library("kinfit") -R> FOCUS_2006_L1 = kinobject("Parent", "Degradation data", "") -R> FOCUS_2006_L1$data = data.frame( -+ t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2), -+ parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6, -+ 72.0, 71.9, 50.3, 59.4, 47.0, 45.1, -+ 27.7, 27.3, 10.0, 10.4, 2.9, 4.0)) -\end{Sinput} -\end{Schunk} - -The following two lines fit the model and produce the summary report -of the model fit. This covers the numerical analyses given in the -FOCUS report. - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L1$fits <- kinfit(FOCUS_2006_L1$data, -+ kinmodels = c("SFO", "FOMC", "DFOP")) -R> FOCUS_2006_L1$results <- kinresults(FOCUS_2006_L1$fits) -R> kinreport(FOCUS_2006_L1) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:07:59 2013 - -Data: - t parent -1 0 88.3 -2 0 91.4 -3 1 85.6 -4 1 84.5 -5 2 78.9 -6 2 77.6 -7 3 72.0 -8 3 71.9 -9 5 50.3 -10 5 59.4 -11 7 47.0 -12 7 45.1 -13 14 27.7 -14 14 27.3 -15 21 10.0 -16 21 10.4 -17 30 2.9 -18 30 4.0 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 92.4710 1.36830 67.6 0.00e+00 -k 0.0956 0.00388 24.6 1.87e-14 - -Chi2 error estimation: 3.42 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 7.2 24.1 -\end{Soutput} -\end{Schunk} - -Obviously, the FOMC model and the DFOP model were not fitted. As discussed in the -kinfit vignette of this package, this occurs when the SFO model fits very well. - -We can try to force the FOMC fit using the parameters obtained using mkin. - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L1$fits <- kinfit(FOCUS_2006_L1$data, -+ kinmodels = c("SFO", "FOMC", "DFOP"), -+ start.FOMC = list(parent.0 = 92.47, alpha = 1.35e11, beta = 1.41e12)) -R> FOCUS_2006_L1$results <- kinresults(FOCUS_2006_L1$fits) -R> kinreport(FOCUS_2006_L1) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:08:00 2013 - -Data: - t parent -1 0 88.3 -2 0 91.4 -3 1 85.6 -4 1 84.5 -5 2 78.9 -6 2 77.6 -7 3 72.0 -8 3 71.9 -9 5 50.3 -10 5 59.4 -11 7 47.0 -12 7 45.1 -13 14 27.7 -14 14 27.3 -15 21 10.0 -16 21 10.4 -17 30 2.9 -18 30 4.0 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 92.4710 1.36830 67.6 0.00e+00 -k 0.0956 0.00388 24.6 1.87e-14 - -Chi2 error estimation: 3.42 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 7.2 24.1 -\end{Soutput} -\end{Schunk} - -It still does not converge. As discussed in the kinfit vignette, the FOMC model usually -is not returned by kinfit when the SFO model fits very well. This should be seen as -a feature, not a bug, as the FOMC model is ill-defined in such cases. - -A plot of the fit is obtained with the kinplot function. - -\begin{Schunk} -\begin{Sinput} -R> kinplot(FOCUS_2006_L1, ylab = "Observed") -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L1_SFO_plot} - -The residual plot can be easily obtained by - -\begin{Schunk} -\begin{Sinput} -R> kinresplot(FOCUS_2006_L1, "SFO", ylab = "Observed") -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L1_SFO_residuals} - -\subsection{Laboratory Data L2} - -The following code defines example dataset L2 from the FOCUS kinetics -report, p. 287 - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L2 = kinobject("Parent", "Degradation data", "") -R> FOCUS_2006_L2$data = 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)) -\end{Sinput} -\end{Schunk} - -Again, the SFO, FOMC and DFOP models are fitted and a report is printed. - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L2$fits <- kinfit(FOCUS_2006_L2$data, -+ kinmodels = c("SFO", "FOMC", "DFOP")) -R> FOCUS_2006_L2$results <- kinresults(FOCUS_2006_L2$fits) -R> kinreport(FOCUS_2006_L2) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:08:00 2013 - -Data: - t parent -1 0 96.1 -2 0 91.8 -3 1 41.4 -4 1 38.7 -5 3 19.3 -6 3 22.3 -7 7 4.6 -8 7 4.6 -9 14 2.6 -10 14 1.2 -11 28 0.3 -12 28 0.6 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 91.466 3.8065 24.03 1.77e-10 -k 0.663 0.0712 9.31 1.52e-06 - -Chi2 error estimation: 14.38 % - - - ---- -Nonlinear least squares fit of the FOMC model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 93.77 1.856 50.51 1.17e-12 -alpha 1.37 0.257 5.36 2.30e-04 -beta 1.23 0.363 3.40 3.95e-03 - -Chi2 error estimation: 6.2 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 1.0 3.5 -FOMC 0.8 5.4 -\end{Soutput} -\end{Schunk} - -Here, only the DFOP did not converge using default parameters. The DFOP fit can be -obtained using refined starting parameters: - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L2$fits <- kinfit(FOCUS_2006_L2$data, -+ kinmodels = c("SFO", "FOMC", "DFOP"), -+ start.DFOP = list(parent.0 = 94, g = 0.4, k1 = 142, k2 = 0.34)) -R> FOCUS_2006_L2$results <- kinresults(FOCUS_2006_L2$fits) -R> kinreport(FOCUS_2006_L2) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:08:00 2013 - -Data: - t parent -1 0 96.1 -2 0 91.8 -3 1 41.4 -4 1 38.7 -5 3 19.3 -6 3 22.3 -7 7 4.6 -8 7 4.6 -9 14 2.6 -10 14 1.2 -11 28 0.3 -12 28 0.6 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 91.466 3.8065 24.03 1.77e-10 -k 0.663 0.0712 9.31 1.52e-06 - -Chi2 error estimation: 14.38 % - - - ---- -Nonlinear least squares fit of the FOMC model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 93.77 1.856 50.51 1.17e-12 -alpha 1.37 0.257 5.36 2.30e-04 -beta 1.23 0.363 3.40 3.95e-03 - -Chi2 error estimation: 6.2 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 1.0 3.5 -FOMC 0.8 5.4 -\end{Soutput} -\end{Schunk} - -Again, even with starting parameters very close to the optimum obtained using mkin, -there is no convergence with kinfit. However, when looking at the fit obtained using -mkin plotted in the mkin vignette, it is clear that the point where the break point -of the curve, caused by the large difference between k1 and k2, is not clearly defined -by the data. Therefore, it should be seen as a desirable feature of the -underlying nls() function that no solution is returned. - -Comparison of $\chi^2$ error levels of the two models shows that the FOMC model allows -for a better representation of the data. This is also obvious from the plot -of the fits. - -\begin{Schunk} -\begin{Sinput} -R> kinplot(FOCUS_2006_L2, ylab = "Observed") -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L2_plot} - -Residual plots are obtained using kinresplot. - -\begin{Schunk} -\begin{Sinput} -R> par(mfrow=c(2,1)) -R> kinresplot(FOCUS_2006_L2, "SFO", ylab = "Observed") -R> kinresplot(FOCUS_2006_L2, "FOMC", ylab = "Observed") -\end{Sinput} -\end{Schunk} -\includegraphics{examples-L2_resplot} - -\subsection{Laboratory Data L3} - -The following code defines example dataset L3 from the FOCUS kinetics -report, p. 290 and attempts to fit the SFO, FOMC and DFOP models. - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L3 = kinobject("Parent", "Degradation data", "") -R> FOCUS_2006_L3$data = data.frame( -+ t = c(0, 3, 7, 14, 30, 60, 91, 120), -+ parent = c(97.8, 60, 51, 43, 35, 22, 15, 12)) -R> FOCUS_2006_L3$fits <- kinfit(FOCUS_2006_L3$data, -+ kinmodels = c("SFO", "FOMC", "DFOP")) -R> FOCUS_2006_L3$results <- kinresults(FOCUS_2006_L3$fits) -R> kinreport(FOCUS_2006_L3) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:08:00 2013 - -Data: - t parent -1 0 97.8 -2 3 60.0 -3 7 51.0 -4 14 43.0 -5 30 35.0 -6 60 22.0 -7 91 15.0 -8 120 12.0 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 74.8718 8.45736 8.85 5.78e-05 -k 0.0253 0.00824 3.07 1.10e-02 - -Chi2 error estimation: 21.24 % - - - ---- -Nonlinear least squares fit of the DFOP model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 97.7460 1.438160 68.0 1.40e-07 -k1 0.5162 0.068841 7.5 8.46e-04 -k2 0.0138 0.000812 16.9 3.56e-05 -g 0.4566 0.017970 25.4 7.12e-06 - -Chi2 error estimation: 2.22 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 27.4 91.1 -DFOP 7.5 123.0 -\end{Soutput} -\end{Schunk} - -In this case, the FOMC model does not return a solution using kinfit. Trying with -closer starting parameters gives success this time. - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L3$fits <- kinfit(FOCUS_2006_L3$data, -+ kinmodels = c("SFO", "FOMC", "DFOP"), -+ start.FOMC = list(parent.0 = 100, alpha = 0.5, beta = 2)) -R> FOCUS_2006_L3$results <- kinresults(FOCUS_2006_L3$fits) -R> kinreport(FOCUS_2006_L3) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:08:00 2013 - -Data: - t parent -1 0 97.8 -2 3 60.0 -3 7 51.0 -4 14 43.0 -5 30 35.0 -6 60 22.0 -7 91 15.0 -8 120 12.0 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 74.8718 8.45736 8.85 5.78e-05 -k 0.0253 0.00824 3.07 1.10e-02 - -Chi2 error estimation: 21.24 % - - - ---- -Nonlinear least squares fit of the FOMC model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 96.974 4.550 21.31 2.11e-06 -alpha 0.422 0.072 5.87 1.02e-03 -beta 1.858 0.881 2.11 4.44e-02 - -Chi2 error estimation: 7.32 % - - - ---- -Nonlinear least squares fit of the DFOP model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 97.7460 1.438160 68.0 1.40e-07 -k1 0.5162 0.068841 7.5 8.46e-04 -k2 0.0138 0.000812 16.9 3.56e-05 -g 0.4566 0.017970 25.4 7.12e-06 - -Chi2 error estimation: 2.22 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 27.4 91.1 -FOMC 7.7 431.2 -DFOP 7.5 123.0 -\end{Soutput} -\begin{Sinput} -R> kinplot(FOCUS_2006_L3, ylab = "Observed") -\end{Sinput} -\end{Schunk} -\includegraphics{examples-FOCUS_2006_L3_2} - -Based on the $\chi^2$ error level criterion and the visual analysis of the -fits, the DFOP model would be the best-fit model of choice for laboratory data -L3. - -\subsection{Laboratory Data L4} - -The following code defines example dataset L4 from the FOCUS kinetics -report, p. 293 and attempts to fit the SFO, FOMC and DFOP models. - -\begin{Schunk} -\begin{Sinput} -R> FOCUS_2006_L4 = kinobject("Parent", "Degradation data", "") -R> FOCUS_2006_L4$data = data.frame( -+ t = c(0, 3, 7, 14, 30, 60, 91, 120), -+ parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0)) -R> FOCUS_2006_L4$fits <- kinfit(FOCUS_2006_L4$data, -+ kinmodels = c("SFO", "FOMC", "DFOP")) -R> FOCUS_2006_L4$results <- kinresults(FOCUS_2006_L4$fits) -R> kinreport(FOCUS_2006_L4) -\end{Sinput} -\begin{Soutput} -Parent compound: Parent -Study type: Degradation data -System: -kinfit version: 1.1.10 -R version: 2.15.2 -Report generated: Sun Feb 17 21:08:00 2013 - -Data: - t parent -1 0 96.6 -2 3 96.3 -3 7 94.3 -4 14 88.8 -5 30 74.9 -6 60 59.9 -7 91 53.5 -8 120 49.0 - - - ---- -Nonlinear least squares fit of the SFO model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 96.44152 1.948781 49.5 2.28e-09 -k 0.00654 0.000523 12.5 8.01e-06 - -Chi2 error estimation: 3.29 % - - - ---- -Nonlinear least squares fit of the FOMC model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 99.143 1.680 59.02 1.32e-08 -alpha 0.704 0.262 2.68 2.18e-02 -beta 64.980 36.617 1.77 6.81e-02 - -Chi2 error estimation: 2.03 % - - - ---- -Nonlinear least squares fit of the DFOP model - -Parameter estimation: - Estimate Std. Error t value Pr(>t) -parent.0 98.7514 1.33707 73.857 1.01e-07 -k1 0.0105 0.00449 2.348 3.93e-02 -k2 -0.0112 0.01884 -0.596 7.08e-01 -g 0.9390 0.18530 5.068 3.57e-03 - -Chi2 error estimation: 1.63 % - - - ---- -Endpoint estimates - - DT50 DT90 -SFO 106.0 352.0 -FOMC 108.9 1644.1 -DFOP 118.7 122.8 -\end{Soutput} -\begin{Sinput} -R> kinplot(FOCUS_2006_L4, ylab = "Observed") -\end{Sinput} -\end{Schunk} -\includegraphics{examples-FOCUS_2006_L4} - -Although the $\chi^2$ error level is slightly smaller for the DFOP model and also -for the FOMC model, the differences are small, and the SFO model may appear to -be a suitable choice. The better fit of the DFOP model depends very much on the -last three data points. - -\bibliographystyle{plainnat} -\bibliography{references} - -\end{document} -% vim: set foldmethod=syntax: |