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authorJohannes Ranke <jranke@uni-bremen.de>2013-11-17 16:13:13 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2013-11-17 16:13:13 +0100
commitebc6f65e4c8b865fb9207ab11dc43cf4ac122c72 (patch)
tree25329171e98a014beafdd1f8db25be21bbe7ce07 /vignettes
parentd8dbf2ad866fb9d34cd1100000b9c116219ecef6 (diff)
Change vignette format to knitr (see ChangeLog)
Diffstat (limited to 'vignettes')
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diff --git a/vignettes/FOCUS_L.Rmd b/vignettes/FOCUS_L.Rmd
new file mode 100644
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--- /dev/null
+++ b/vignettes/FOCUS_L.Rmd
@@ -0,0 +1,243 @@
+<!--
+%\VignetteEngine{knitr::knitr}
+%\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3}
+-->
+
+# Example evaluation of FOCUS Laboratory Data L1 to L3
+
+## Laboratory Data L1
+
+The following code defines example dataset L1 from the FOCUS kinetics
+report, p. 284
+
+```{r}
+library("mkin")
+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))
+FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
+```
+
+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 `parent`.
+
+```{r}
+SFO <- mkinmod(parent = list(type = "SFO"))
+FOMC <- mkinmod(parent = list(type = "FOMC"))
+DFOP <- mkinmod(parent = list(type = "DFOP"))
+```
+
+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.
+
+```{r}
+m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
+summary(m.L1.SFO)
+```
+
+A plot of the fit is obtained with the plot function for mkinfit objects.
+
+```{r fig.width=7, fig.height = 5}
+plot(m.L1.SFO)
+```
+The residual plot can be easily obtained by
+
+```{r fig.width=7, fig.height = 5}
+mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
+```
+
+For comparison, the FOMC model is fitted as well, and the chi^2 error level
+is checked.
+
+```{r}
+m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
+summary(m.L1.FOMC, data = FALSE)
+```
+
+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%). Additionally, the covariance
+matrix can not be obtained, indicating overparameterisation of the model.
+As a consequence, no standard errors for transformed parameters nor
+confidence intervals for backtransformed parameters are available.
+
+The chi^2 error levels reported in Appendix 3 and Appendix 7 to the FOCUS
+kinetics report are rounded to integer percentages and partly deviate by one
+percentage point from the results calculated by mkin. The reason for
+this is not known. However, mkin gives the same chi^2 error levels
+as the kinfit package.
+
+Furthermore, the calculation routines of the kinfit package have been extensively
+compared to the results obtained by the KinGUI software, as documented in the
+kinfit package vignette. KinGUI is a widely used standard package in this field.
+Therefore, the reason for the difference was not investigated further.
+
+## Laboratory Data L2
+
+The following code defines example dataset L2 from the FOCUS kinetics
+report, p. 287
+
+```{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))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
+```
+
+Again, the SFO model is fitted and a summary is obtained.
+
+```{r}
+m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
+summary(m.L2.SFO)
+```
+
+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.
+
+```{r fig.height = 8}
+par(mfrow = c(2, 1))
+plot(m.L2.SFO)
+mkinresplot(m.L2.SFO)
+```
+
+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.
+
+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 _a
+priori_ why a consistent underestimation after the approximate DT90 should be
+irrelevant. However, this can be rationalised by the fact that the FOCUS fate
+models generally only implement SFO kinetics.
+
+For comparison, the FOMC model is fitted as well, and the chi^2 error level
+is checked.
+
+```{r fig.height = 8}
+m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
+par(mfrow = c(2, 1))
+plot(m.L2.FOMC)
+mkinresplot(m.L2.FOMC)
+summary(m.L2.FOMC, data = FALSE)
+```
+
+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 further reduces the chi^2 error level.
+
+```{r fig.height = 5}
+m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.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.
+
+```{r fig.height = 5}
+m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin,
+ parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
+ quiet=TRUE)
+plot(m.L2.DFOP)
+summary(m.L2.DFOP, data = FALSE)
+```
+
+Here, the DFOP model is clearly the best-fit model for dataset L2 based on the
+chi^2 error level criterion. However, the failure to calculate the covariance
+matrix indicates that the parameter estimates correlate excessively. Therefore,
+the FOMC model may be preferred for this dataset.
+
+## Laboratory Data L3
+
+The following code defines example dataset L3 from the FOCUS kinetics report,
+p. 290.
+
+```{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))
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
+```
+
+SFO model, summary and plot:
+
+```{r fig.height = 5}
+m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.SFO)
+summary(m.L3.SFO)
+```
+
+The chi^2 error level of 21% as well as the plot suggest that the model
+does not fit very well.
+
+The FOMC model performs better:
+
+```{r fig.height = 5}
+m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.FOMC)
+summary(m.L3.FOMC, data = FALSE)
+```
+
+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:
+
+```{r fig.height = 5}
+m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.DFOP)
+summary(m.L3.DFOP, data = FALSE)
+```
+
+Here, a look to the model plot, the confidence intervals of the parameters
+and the correlation matrix suggest that the parameter estimates are reliable, and
+the DFOP model can be used as the best-fit model based on the chi^2 error
+level criterion for laboratory data L3.
+
+## Laboratory Data L4
+
+The following code defines example dataset L4 from the FOCUS kinetics
+report, p. 293
+
+```{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))
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
+```
+
+SFO model, summary and plot:
+
+```{r fig.height = 5}
+m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.SFO)
+summary(m.L4.SFO, data = FALSE)
+```
+
+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
+
+```{r fig.height = 5}
+m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.FOMC)
+summary(m.L4.FOMC, data = FALSE)
+```
+
+The error level at which the chi^2 test passes is slightly lower for the FOMC
+model. However, the difference appears negligible.
+
diff --git a/vignettes/FOCUS_L.md b/vignettes/FOCUS_L.md
new file mode 100644
index 0000000..6c43889
--- /dev/null
+++ b/vignettes/FOCUS_L.md
@@ -0,0 +1,931 @@
+<!--
+%\VignetteEngine{knitr::knitr}
+%\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3}
+-->
+
+# Example evaluation of FOCUS Laboratory Data L1 to L3
+
+## Laboratory Data L1
+
+The following code defines example dataset L1 from the FOCUS kinetics
+report, p. 284
+
+
+```r
+library("mkin")
+```
+
+```
+## Loading required package: FME
+## Loading required package: deSolve
+## Loading required package: rootSolve
+## Loading required package: minpack.lm
+## Loading required package: MASS
+## Loading required package: coda
+## Loading required package: lattice
+```
+
+```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, 71.9, 50.3, 59.4, 47,
+ 45.1, 27.7, 27.3, 10, 10.4, 2.9, 4))
+FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
+```
+
+
+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 `parent`.
+
+
+```r
+SFO <- mkinmod(parent = list(type = "SFO"))
+FOMC <- mkinmod(parent = list(type = "FOMC"))
+DFOP <- mkinmod(parent = list(type = "DFOP"))
+```
+
+
+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.
+
+
+```r
+m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet = TRUE)
+summary(m.L1.SFO)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:54 2013
+## Date of summary: Sun Nov 17 15:02:54 2013
+##
+## Equations:
+## [1] d_parent = - k_parent_sink * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100.0 state 100.000
+## k_parent_sink 0.1 deparm -2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 92.50 1.3700 89.60 95.40
+## k_parent_sink -2.35 0.0406 -2.43 -2.26
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 92.5000 89.6000 95.400
+## k_parent_sink 0.0956 0.0877 0.104
+##
+## Residual standard error: 2.95 on 16 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 3.42 2 7
+## parent 3.42 2 7
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 7.25 24.1
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 k_parent_sink
+## parent_0 1.000 0.625
+## k_parent_sink 0.625 1.000
+##
+## Data:
+## time variable observed predicted residual
+## 0 parent 88.3 92.47 -4.171
+## 0 parent 91.4 92.47 -1.071
+## 1 parent 85.6 84.04 1.561
+## 1 parent 84.5 84.04 0.461
+## 2 parent 78.9 76.38 2.524
+## 2 parent 77.6 76.38 1.224
+## 3 parent 72.0 69.41 2.588
+## 3 parent 71.9 69.41 2.488
+## 5 parent 50.3 57.33 -7.030
+## 5 parent 59.4 57.33 2.070
+## 7 parent 47.0 47.35 -0.352
+## 7 parent 45.1 47.35 -2.252
+## 14 parent 27.7 24.25 3.453
+## 14 parent 27.3 24.25 3.053
+## 21 parent 10.0 12.42 -2.416
+## 21 parent 10.4 12.42 -2.016
+## 30 parent 2.9 5.25 -2.351
+## 30 parent 4.0 5.25 -1.251
+```
+
+
+A plot of the fit is obtained with the plot function for mkinfit objects.
+
+
+```r
+plot(m.L1.SFO)
+```
+
+![plot of chunk unnamed-chunk-4](figure/unnamed-chunk-4.png)
+
+The residual plot can be easily obtained by
+
+
+```r
+mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
+```
+
+![plot of chunk unnamed-chunk-5](figure/unnamed-chunk-5.png)
+
+
+For comparison, the FOMC model is fitted as well, and the chi^2 error level
+is checked.
+
+
+```r
+m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet = TRUE)
+summary(m.L1.FOMC, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:55 2013
+## Date of summary: Sun Nov 17 15:02:55 2013
+##
+## Equations:
+## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100 state 100.000
+## alpha 1 deparm 0.000
+## beta 10 deparm 2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 92.5 NA NA NA
+## alpha 25.6 NA NA NA
+## beta 28.0 NA NA NA
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 9.25e+01 NA NA
+## alpha 1.35e+11 NA NA
+## beta 1.41e+12 NA NA
+##
+## Residual standard error: 3.05 on 15 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 3.62 3 6
+## parent 3.62 3 6
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 7.25 24.1
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## Could not estimate covariance matrix; singular system:
+```
+
+
+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%). Additionally, the covariance
+matrix can not be obtained, indicating overparameterisation of the model.
+As a consequence, no standard errors for transformed parameters nor
+confidence intervals for backtransformed parameters are available.
+
+The chi^2 error levels reported in Appendix 3 and Appendix 7 to the FOCUS
+kinetics report are rounded to integer percentages and partly deviate by one
+percentage point from the results calculated by mkin. The reason for
+this is not known. However, mkin gives the same chi^2 error levels
+as the kinfit package.
+
+Furthermore, the calculation routines of the kinfit package have been extensively
+compared to the results obtained by the KinGUI software, as documented in the
+kinfit package vignette. KinGUI is a widely used standard package in this field.
+Therefore, the reason for the difference was not investigated further.
+
+## Laboratory Data L2
+
+The following code defines example dataset L2 from the FOCUS kinetics
+report, p. 287
+
+
+```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))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
+```
+
+
+Again, the SFO model is fitted and a summary is obtained.
+
+
+```r
+m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet = TRUE)
+summary(m.L2.SFO)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:55 2013
+## Date of summary: Sun Nov 17 15:02:55 2013
+##
+## Equations:
+## [1] d_parent = - k_parent_sink * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100.0 state 100.000
+## k_parent_sink 0.1 deparm -2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 91.500 3.810 83.000 99.900
+## k_parent_sink -0.411 0.107 -0.651 -0.172
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 91.500 83.000 99.900
+## k_parent_sink 0.663 0.522 0.842
+##
+## Residual standard error: 5.51 on 10 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 14.4 2 4
+## parent 14.4 2 4
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 1.05 3.47
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 k_parent_sink
+## parent_0 1.00 0.43
+## k_parent_sink 0.43 1.00
+##
+## Data:
+## time variable observed predicted residual
+## 0 parent 96.1 9.15e+01 4.634
+## 0 parent 91.8 9.15e+01 0.334
+## 1 parent 41.4 4.71e+01 -5.740
+## 1 parent 38.7 4.71e+01 -8.440
+## 3 parent 19.3 1.25e+01 6.779
+## 3 parent 22.3 1.25e+01 9.779
+## 7 parent 4.6 8.83e-01 3.717
+## 7 parent 4.6 8.83e-01 3.717
+## 14 parent 2.6 8.53e-03 2.591
+## 14 parent 1.2 8.53e-03 1.191
+## 28 parent 0.3 7.96e-07 0.300
+## 28 parent 0.6 7.96e-07 0.600
+```
+
+
+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.
+
+
+```r
+par(mfrow = c(2, 1))
+plot(m.L2.SFO)
+mkinresplot(m.L2.SFO)
+```
+
+![plot of chunk unnamed-chunk-9](figure/unnamed-chunk-9.png)
+
+
+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.
+
+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 _a
+priori_ why a consistent underestimation after the approximate DT90 should be
+irrelevant. However, this can be rationalised by the fact that the FOCUS fate
+models generally only implement SFO kinetics.
+
+For comparison, the FOMC model is fitted as well, and the chi^2 error level
+is checked.
+
+
+```r
+m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
+par(mfrow = c(2, 1))
+plot(m.L2.FOMC)
+mkinresplot(m.L2.FOMC)
+```
+
+![plot of chunk unnamed-chunk-10](figure/unnamed-chunk-10.png)
+
+```r
+summary(m.L2.FOMC, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:56 2013
+## Date of summary: Sun Nov 17 15:02:56 2013
+##
+## Equations:
+## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100 state 100.000
+## alpha 1 deparm 0.000
+## beta 10 deparm 2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 93.800 1.860 89.600 98.000
+## alpha 0.318 0.187 -0.104 0.740
+## beta 0.210 0.294 -0.456 0.876
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 93.80 89.600 98.0
+## alpha 1.37 0.901 2.1
+## beta 1.23 0.634 2.4
+##
+## Residual standard error: 2.63 on 9 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 6.2 3 3
+## parent 6.2 3 3
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 0.809 5.36
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 alpha beta
+## parent_0 1.0000 -0.0955 -0.186
+## alpha -0.0955 1.0000 0.976
+## beta -0.1863 0.9757 1.000
+```
+
+
+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 further reduces the chi^2 error level.
+
+
+```r
+m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP)
+```
+
+![plot of chunk unnamed-chunk-11](figure/unnamed-chunk-11.png)
+
+
+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.
+
+
+```r
+m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, parms.ini = c(k1 = 1, k2 = 0.01,
+ g = 0.8), quiet = TRUE)
+plot(m.L2.DFOP)
+```
+
+![plot of chunk unnamed-chunk-12](figure/unnamed-chunk-12.png)
+
+```r
+summary(m.L2.DFOP, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:57 2013
+## Date of summary: Sun Nov 17 15:02:57 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
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 1e+02 state 100.0000
+## k1 1e+00 deparm 0.0000
+## k2 1e-02 deparm -4.6052
+## g 8e-01 deparm 0.9803
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 93.900 NA NA NA
+## k1 4.960 NA NA NA
+## k2 -1.090 NA NA NA
+## g -0.282 NA NA NA
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 93.900 NA NA
+## k1 142.000 NA NA
+## k2 0.337 NA NA
+## g 0.402 NA NA
+##
+## Residual standard error: 1.73 on 8 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 2.53 4 2
+## parent 2.53 4 2
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent NA NA
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## Could not estimate covariance matrix; singular system:
+```
+
+
+Here, the DFOP model is clearly the best-fit model for dataset L2 based on the
+chi^2 error level criterion. However, the failure to calculate the covariance
+matrix indicates that the parameter estimates correlate excessively. Therefore,
+the FOMC model may be preferred for this dataset.
+
+## Laboratory Data L3
+
+The following code defines example dataset L3 from the FOCUS kinetics report,
+p. 290.
+
+
+```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))
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
+```
+
+
+SFO model, summary and plot:
+
+
+```r
+m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.SFO)
+```
+
+![plot of chunk unnamed-chunk-14](figure/unnamed-chunk-14.png)
+
+```r
+summary(m.L3.SFO)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:57 2013
+## Date of summary: Sun Nov 17 15:02:57 2013
+##
+## Equations:
+## [1] d_parent = - k_parent_sink * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100.0 state 100.000
+## k_parent_sink 0.1 deparm -2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 74.90 8.460 54.20 95.60
+## k_parent_sink -3.68 0.326 -4.48 -2.88
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 74.9000 54.2000 95.6000
+## k_parent_sink 0.0253 0.0114 0.0561
+##
+## Residual standard error: 12.9 on 6 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 21.2 2 6
+## parent 21.2 2 6
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 27.4 91.1
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 k_parent_sink
+## parent_0 1.000 0.548
+## k_parent_sink 0.548 1.000
+##
+## Data:
+## time variable observed predicted residual
+## 0 parent 97.8 74.87 22.9273
+## 3 parent 60.0 69.41 -9.4065
+## 7 parent 51.0 62.73 -11.7340
+## 14 parent 43.0 52.56 -9.5634
+## 30 parent 35.0 35.08 -0.0828
+## 60 parent 22.0 16.44 5.5614
+## 91 parent 15.0 7.51 7.4896
+## 120 parent 12.0 3.61 8.3908
+```
+
+
+The chi^2 error level of 21% as well as the plot suggest that the model
+does not fit very well.
+
+The FOMC model performs better:
+
+
+```r
+m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.FOMC)
+```
+
+![plot of chunk unnamed-chunk-15](figure/unnamed-chunk-15.png)
+
+```r
+summary(m.L3.FOMC, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:57 2013
+## Date of summary: Sun Nov 17 15:02:57 2013
+##
+## Equations:
+## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100 state 100.000
+## alpha 1 deparm 0.000
+## beta 10 deparm 2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 97.000 4.550 85.3 109.000
+## alpha -0.862 0.170 -1.3 -0.424
+## beta 0.619 0.474 -0.6 1.840
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 97.000 85.300 109.000
+## alpha 0.422 0.273 0.655
+## beta 1.860 0.549 6.290
+##
+## Residual standard error: 4.57 on 5 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 7.32 3 5
+## parent 7.32 3 5
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 7.73 431
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 alpha beta
+## parent_0 1.000 -0.151 -0.427
+## alpha -0.151 1.000 0.911
+## beta -0.427 0.911 1.000
+```
+
+
+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:
+
+
+```r
+m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
+plot(m.L3.DFOP)
+```
+
+![plot of chunk unnamed-chunk-16](figure/unnamed-chunk-16.png)
+
+```r
+summary(m.L3.DFOP, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:58 2013
+## Date of summary: Sun Nov 17 15:02:58 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
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 1e+02 state 100.000
+## k1 1e-01 deparm -2.303
+## k2 1e-02 deparm -4.605
+## g 5e-01 deparm 0.000
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 97.700 1.4400 93.800 102.0000
+## k1 -0.661 0.1330 -1.030 -0.2910
+## k2 -4.290 0.0590 -4.450 -4.1200
+## g -0.123 0.0512 -0.265 0.0193
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 97.7000 93.8000 102.0000
+## k1 0.5160 0.3560 0.7480
+## k2 0.0138 0.0117 0.0162
+## g 0.4570 0.4070 0.5070
+##
+## Residual standard error: 1.44 on 4 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 2.23 4 4
+## parent 2.23 4 4
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 7.46 123
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 k1 k2 g
+## parent_0 1.0000 0.164 0.0131 0.425
+## k1 0.1640 1.000 0.4648 -0.553
+## k2 0.0131 0.465 1.0000 -0.663
+## g 0.4253 -0.553 -0.6631 1.000
+```
+
+
+Here, a look to the model plot, the confidence intervals of the parameters
+and the correlation matrix suggest that the parameter estimates are reliable, and
+the DFOP model can be used as the best-fit model based on the chi^2 error
+level criterion for laboratory data L3.
+
+## Laboratory Data L4
+
+The following code defines example dataset L4 from the FOCUS kinetics
+report, p. 293
+
+
+```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))
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
+```
+
+
+SFO model, summary and plot:
+
+
+```r
+m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.SFO)
+```
+
+![plot of chunk unnamed-chunk-18](figure/unnamed-chunk-18.png)
+
+```r
+summary(m.L4.SFO, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:58 2013
+## Date of summary: Sun Nov 17 15:02:58 2013
+##
+## Equations:
+## [1] d_parent = - k_parent_sink * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100.0 state 100.000
+## k_parent_sink 0.1 deparm -2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 96.40 1.95 91.70 101.00
+## k_parent_sink -5.03 0.08 -5.23 -4.83
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 96.40000 91.70000 1.01e+02
+## k_parent_sink 0.00654 0.00538 7.95e-03
+##
+## Residual standard error: 3.65 on 6 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 3.29 2 6
+## parent 3.29 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 1.000 0.587
+## k_parent_sink 0.587 1.000
+```
+
+
+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
+
+
+```r
+m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
+plot(m.L4.FOMC)
+```
+
+![plot of chunk unnamed-chunk-19](figure/unnamed-chunk-19.png)
+
+```r
+summary(m.L4.FOMC, data = FALSE)
+```
+
+```
+## mkin version: 0.9.25
+## R version: 3.0.2
+## Date of fit: Sun Nov 17 15:02:59 2013
+## Date of summary: Sun Nov 17 15:02:59 2013
+##
+## Equations:
+## [1] d_parent = - (alpha/beta) * ((time/beta) + 1)^-1 * parent
+##
+## Method used for solution of differential equation system:
+## analytical
+##
+## Weighting: none
+##
+## Starting values for optimised parameters:
+## value type transformed
+## parent_0 100 state 100.000
+## alpha 1 deparm 0.000
+## beta 10 deparm 2.303
+##
+## Fixed parameter values:
+## None
+##
+## Optimised, transformed parameters:
+## Estimate Std. Error Lower Upper
+## parent_0 99.100 1.680 94.80 103.000
+## alpha -0.351 0.372 -1.31 0.607
+## beta 4.170 0.564 2.73 5.620
+##
+## Backtransformed parameters:
+## Estimate Lower Upper
+## parent_0 99.100 94.80 103.00
+## alpha 0.704 0.27 1.83
+## beta 65.000 15.30 277.00
+##
+## Residual standard error: 2.31 on 5 degrees of freedom
+##
+## Chi2 error levels in percent:
+## err.min n.optim df
+## All data 2.03 3 5
+## parent 2.03 3 5
+##
+## Estimated disappearance times:
+## DT50 DT90
+## parent 109 1644
+##
+## Estimated formation fractions:
+## ff
+## parent_sink 1
+##
+## Parameter correlation:
+## parent_0 alpha beta
+## parent_0 1.000 -0.536 -0.608
+## alpha -0.536 1.000 0.991
+## beta -0.608 0.991 1.000
+```
+
+
+The error level at which the chi^2 test passes is slightly lower for the FOMC
+model. However, the difference appears negligible.
+
diff --git a/vignettes/FOCUS_Z.Rnw b/vignettes/FOCUS_Z.Rnw
new file mode 100644
index 0000000..44cfa46
--- /dev/null
+++ b/vignettes/FOCUS_Z.Rnw
@@ -0,0 +1,261 @@
+%\VignetteIndexEntry{Examples evaluation of FOCUS dataset Z}
+%\VignetteEngine{knitr::knitr}
+\documentclass[12pt,a4paper]{article}
+\usepackage{a4wide}
+\input{header}
+\hypersetup{
+ pdftitle = {Example evaluation of FOCUS dataset Z},
+ pdfsubject = {Manuscript},
+ pdfauthor = {Johannes Ranke},
+ colorlinks = {true},
+ linkcolor = {blue},
+ citecolor = {blue},
+ urlcolor = {red},
+ hyperindex = {true},
+ linktocpage = {true},
+}
+
+\begin{document}
+
+<<include=FALSE>>=
+require(knitr)
+opts_chunk$set(engine='R', tidy=FALSE)
+@
+
+\title{Example evaluation of FOCUS dataset Z}
+\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
+
+\thispagestyle{empty} \setcounter{page}{0}
+
+\clearpage
+
+\tableofcontents
+
+\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
+
+\section{The data}
+
+The following code defines the example dataset from Appendix 7 to the FOCUS kinetics
+report \citep{FOCUSkinetics2011}, p.350.
+
+<<FOCUS_2006_Z_data, echo=TRUE, eval=TRUE>>=
+require(mkin)
+LOD = 0.5
+FOCUS_2006_Z = data.frame(
+ t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21,
+ 42, 61, 96, 124),
+ Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8,
+ 2.9, 3.5, 5.3, 4.4, 1.2, 0.7),
+ Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1,
+ 1.6, 0.6, 0.5 * LOD, NA, NA, NA),
+ Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5,
+ 0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA),
+ Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5,
+ 25.2, 17.2, 4.8, 4.5, 2.8, 4.4))
+
+FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)
+@
+
+\section{Parent compound and one metabolite}
+
+The next step is to set up the models used for the kinetic analysis. As the
+simultaneous fit of parent and the first metabolite is usually straightforward,
+Step 1 (SFO for parent only) is skipped here. We start with the model 2a,
+with formation and decline of metabolite Z1 and the pathway from parent
+directly to sink included (default in mkin).
+
+<<FOCUS_2006_Z_fits_1, echo=TRUE, fig.height=4>>=
+Z.2a <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),
+ Z1 = list(type = "SFO"))
+m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot(m.Z.2a)
+summary(m.Z.2a, data = FALSE)
+@
+
+As obvious from the summary, the kinetic rate constant from parent compound Z to sink
+is negligible. Accordingly, the exact magnitude of the fitted parameter
+\texttt{log k\_Z\_sink} is ill-defined and the covariance matrix is not returned.
+This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify
+the model by removing the pathway to sink.
+
+A similar result can be obtained when formation fractions are used in the model formulation:
+
+<<FOCUS_2006_Z_fits_2, echo=TRUE, fig.height=4>>=
+Z.2a.ff <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),
+ Z1 = list(type = "SFO"),
+ use_of_ff = "max")
+
+m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot(m.Z.2a.ff)
+summary(m.Z.2a.ff, data = FALSE)
+@
+
+Here, the ilr transformed formation fraction fitted in the model takes a very large value,
+and the backtransformed formation fraction from parent Z to Z1 is practically unity. Again,
+the covariance matrix is not returned as the model is overparameterised.
+
+The simplified model is obtained by setting the list component \texttt{sink} to
+\texttt{FALSE}. This model definition is not supported when formation fractions
+are used.
+
+<<FOCUS_2006_Z_fits_3, echo=TRUE, fig.height=4>>=
+Z.3 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO"))
+m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot(m.Z.3)
+summary(m.Z.3, data = FALSE)
+@
+
+\section{Including metabolites Z2 and Z3}
+
+As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as
+well in the next step. While this step appears questionable on the basis of the above results, it
+is followed here for the purpose of comparison. Also, in the FOCUS report, it is
+assumed that there is additional empirical evidence that Z1 quickly and exclusively
+hydrolyses to Z2.
+
+<<FOCUS_2006_Z_fits_5, echo=TRUE, fig.height=4>>=
+Z.5 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
+ Z2 = list(type = "SFO"))
+m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot(m.Z.5)
+summary(m.Z.5, data = FALSE)
+@
+
+Finally, metabolite Z3 is added to the model. The fit is accellerated
+by using the starting parameters from the previous fit.
+
+<<FOCUS_2006_Z_fits_6, echo=TRUE, fig.height=4>>=
+Z.FOCUS <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
+ Z2 = list(type = "SFO", to = "Z3"),
+ Z3 = list(type = "SFO"))
+m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
+ parms.ini = m.Z.5$bparms.ode,
+ quiet = TRUE)
+plot(m.Z.FOCUS)
+summary(m.Z.FOCUS, data = FALSE)
+@
+
+This is the fit corresponding to the final result chosen in Appendix 7 of the
+FOCUS report. The residual plots can be obtained by
+
+<<FOCUS_2006_Z_residuals_6, echo=TRUE>>=
+par(mfrow = c(2, 2))
+mkinresplot(m.Z.FOCUS, "Z0", lpos = "bottomright")
+mkinresplot(m.Z.FOCUS, "Z1", lpos = "bottomright")
+mkinresplot(m.Z.FOCUS, "Z2", lpos = "bottomright")
+mkinresplot(m.Z.FOCUS, "Z3", lpos = "bottomright")
+@
+
+\section{Using the SFORB model for parent and metabolites}
+
+As the FOCUS report states, there is a certain tailing of the time course of metabolite
+Z3. Also, the time course of the parent compound is not fitted very well using the
+SFO model, as residues at a certain low level remain.
+
+Therefore, an additional model is offered here, using the single first-order
+reversible binding (SFORB) model for metabolite Z3. As expected, the $\chi^2$
+error level is lower for metabolite Z3 using this model and the graphical
+fit for Z3 is improved. However, the covariance matrix is not returned.
+
+<<FOCUS_2006_Z_fits_7, echo=TRUE, fig.height=4>>=
+Z.mkin.1 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
+ Z2 = list(type = "SFO", to = "Z3"),
+ Z3 = list(type = "SFORB"))
+m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin,
+ parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.3),
+ quiet = TRUE)
+plot(m.Z.mkin.1)
+summary(m.Z.mkin.1, data = FALSE)
+@
+
+Therefore, a further stepwise model building is performed starting from the
+stage of parent and one metabolite, starting from the assumption that the model
+fit for the parent compound can be improved by using the SFORB model.
+
+<<FOCUS_2006_Z_fits_8, echo=TRUE, fig.height=4>>=
+Z.mkin.2 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO"))
+m.Z.mkin.2 <- mkinfit(Z.mkin.2, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot(m.Z.mkin.2)
+summary(m.Z.mkin.2, data = FALSE)
+@
+
+When metabolite Z2 is added, the additional sink for Z1 is turned off again,
+for the same reasons as in the original analysis.
+
+<<FOCUS_2006_Z_fits_9, echo=TRUE, fig.height=4>>=
+Z.mkin.3 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO", to = "Z2"),
+ Z2 = list(type = "SFO"))
+m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot(m.Z.mkin.3)
+summary(m.Z.mkin.3, data = FALSE)
+@
+
+This results in a much better representation of the behaviour of the parent
+compound Z0.
+
+Finally, Z3 is added as well. This model appears overparameterised (no
+covariance matrix returned) if the sink for Z1 is left in the model.
+
+<<FOCUS_2006_Z_fits_10, echo=TRUE, fig.height=4>>=
+Z.mkin.4 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
+ Z2 = list(type = "SFO", to = "Z3"),
+ Z3 = list(type = "SFO"))
+m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
+ parms.ini = c(k_Z1_Z2 = 0.05),
+ quiet = TRUE)
+plot(m.Z.mkin.4)
+summary(m.Z.mkin.4, data = FALSE)
+@
+
+The error level of the fit, but especially of metabolite Z3, can be improved if
+the SFORB model is chosen for this metabolite, as this model is capable of
+representing the tailing of the metabolite decline phase.
+
+<<FOCUS_2006_Z_fits_11, echo=TRUE, fig.height=4>>=
+Z.mkin.5 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
+ Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
+ Z2 = list(type = "SFO", to = "Z3"),
+ Z3 = list(type = "SFORB"))
+m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+ parms.ini = m.Z.mkin.4$bparms.ode[1:5],
+ quiet = TRUE)
+plot(m.Z.mkin.5)
+summary(m.Z.mkin.5, data = FALSE)
+@
+
+Looking at the confidence intervals of the SFORB model parameters of Z3, it is
+clear that nothing can be said about the degradation rate of Z3 towards the end
+of the experiment. However, this appears to be a feature of the data.
+
+<<FOCUS_2006_Z_residuals_11>>=
+par(mfrow = c(2, 2))
+mkinresplot(m.Z.mkin.5, "Z0", lpos = "bottomright")
+mkinresplot(m.Z.mkin.5, "Z1", lpos = "bottomright")
+mkinresplot(m.Z.mkin.5, "Z2", lpos = "bottomright")
+mkinresplot(m.Z.mkin.5, "Z3", lpos = "bottomright")
+@
+
+As expected, the residual plots are much more random than in the case of the
+all SFO model for which they were shown above. In conclusion, the model
+\texttt{Z.mkin.5} is proposed as the best-fit model for the dataset from
+Appendix 7 of the FOCUS report.
+
+\bibliographystyle{plainnat}
+\bibliography{references}
+
+\end{document}
+% vim: set foldmethod=syntax:
diff --git a/vignettes/FOCUS_Z.pdf b/vignettes/FOCUS_Z.pdf
new file mode 100644
index 0000000..ca67191
--- /dev/null
+++ b/vignettes/FOCUS_Z.pdf
Binary files differ
diff --git a/vignettes/examples.Rnw b/vignettes/examples.Rnw
deleted file mode 100644
index f876d14..0000000
--- a/vignettes/examples.Rnw
+++ /dev/null
@@ -1,524 +0,0 @@
-% $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},
-}
-\SweaveOpts{engine=R, eps=FALSE, keep.source = TRUE}
-<<setup, echo = FALSE, results = hide>>=
-options(prompt = "R> ")
-options(width = 70)
-options(SweaveHooks = list(
- cex = function() par(cex.lab = 1.3, cex.axis = 1.3)))
-@
-\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}
-
-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
-
-<<FOCUS_2006_L1_data, echo=TRUE, eval=TRUE>>=
-library("mkin")
-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))
-FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
-@
-
-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 \texttt{parent}.
-
-<<Simple_models, echo=TRUE>>=
-SFO <- mkinmod(parent = list(type = "SFO"))
-FOMC <- mkinmod(parent = list(type = "FOMC"))
-DFOP <- mkinmod(parent = list(type = "DFOP"))
-@
-
-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.
-
-<<L1_SFO, echo=TRUE>>=
-m.L1.SFO <- mkinfit(SFO, FOCUS_2006_L1_mkin, quiet=TRUE)
-summary(m.L1.SFO)
-@
-
-A plot of the fit is obtained with the plot function for mkinfit objects.
-
-<<L1_SFO_plot, fig=TRUE, echo=TRUE, height=4>>=
-plot(m.L1.SFO)
-@
-
-The residual plot can be easily obtained by
-
-<<L1_SFO_residuals, fig=TRUE, echo=TRUE, height=4>>=
-mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
-@
-
-For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
-is checked.
-
-<<L1_FOMC, echo=TRUE>>=
-m.L1.FOMC <- mkinfit(FOMC, FOCUS_2006_L1_mkin, quiet=TRUE)
-summary(m.L1.FOMC)
-@
-
-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\%). Additionally, the covariance matrix can not be obtained,
-indicating overparameterisation of the model.
-
-The $\chi^2$ error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics
-report are rounded to integer percentages and partly deviate by one percentage point
-from the results calculated by \texttt{mkin}. The reason for this is not known. However,
-\texttt{mkin} gives the same $\chi^2$ error levels as the \Rpackage{kinfit} package.
-Furthermore, the calculation routines of the kinfit package have been extensively
-compared to the results obtained by the KinGUI software, as documented in the
-kinfit package vignette. KinGUI is a widely used standard package in this field.
-Therefore, the reason for the difference was not investigated further.
-
-\subsection{Laboratory Data L2}
-
-The following code defines example dataset L2 from the FOCUS kinetics
-report, p. 287
-
-<<FOCUS_2006_L2_data, echo=TRUE, eval=TRUE>>=
-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))
-FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
-@
-
-Again, the SFO model is fitted and a summary is obtained.
-
-<<L2_SFO, echo=TRUE>>=
-m.L2.SFO <- mkinfit(SFO, FOCUS_2006_L2_mkin, quiet=TRUE)
-summary(m.L2.SFO)
-@
-
-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.
-
-<<L2_SFO_plot, fig=TRUE, echo=TRUE, height=8>>=
-par(mfrow = c(2, 1))
-plot(m.L2.SFO)
-mkinresplot(m.L2.SFO)
-@
-
-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.
-
-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 \textit{a
-priori} why a consistent underestimation after the approximate DT90 should be
-irrelevant. However, this can be rationalised by the fact that the FOCUS fate
-models generally only implement SFO kinetics.
-
-For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level
-is checked.
-
-<<L2_FOMC, echo=TRUE, fig=TRUE, height=8>>=
-m.L2.FOMC <- mkinfit(FOMC, FOCUS_2006_L2_mkin, quiet = TRUE)
-par(mfrow = c(2, 1))
-plot(m.L2.FOMC)
-mkinresplot(m.L2.FOMC)
-summary(m.L2.FOMC, data = FALSE)
-@
-
-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 further reduces the $\chi^2$ error level.
-
-<<L2_DFOP, echo=TRUE, fig=TRUE, height=4>>=
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.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.
-
-<<L2_DFOP_2, echo=TRUE, fig=TRUE, height=4>>=
-m.L2.DFOP <- mkinfit(DFOP, FOCUS_2006_L2_mkin,
- parms.ini = c(k1 = 1, k2 = 0.01, g = 0.8),
- quiet=TRUE)
-plot(m.L2.DFOP)
-summary(m.L2.DFOP, data = FALSE)
-@
-
-Here, the DFOP model is clearly the best-fit model for dataset L2 based on the
-$\chi^2$ error level criterion. However, the failure to calculate the covariance
-matrix indicates that the parameter estimates correlate excessively. Therefore,
-the FOMC model may be preferred for this dataset.
-
-\subsection{Laboratory Data L3}
-
-The following code defines example dataset L3 from the FOCUS kinetics report,
-p. 290.
-
-<<FOCUS_2006_L3_data, echo=TRUE, eval=TRUE>>=
-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))
-FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
-@
-
-SFO model, summary and plot:
-
-<<L3_SFO, echo=TRUE, fig=TRUE, height=4>>=
-m.L3.SFO <- mkinfit(SFO, FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.SFO)
-summary(m.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:
-
-<<L3_FOMC, echo=TRUE, fig=TRUE, height=4>>=
-m.L3.FOMC <- mkinfit(FOMC, FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.FOMC)
-summary(m.L3.FOMC, data = FALSE)
-@
-
-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:
-
-<<L3_DFOP, echo=TRUE, fig=TRUE, height=4>>=
-m.L3.DFOP <- mkinfit(DFOP, FOCUS_2006_L3_mkin, quiet = TRUE)
-plot(m.L3.DFOP)
-summary(m.L3.DFOP, data = FALSE)
-@
-
-Here, a look to the model plot, the confidence intervals of the parameters
-and the correlation matrix suggest that the parameter estimates are reliable, and
-the DFOP model can be used as 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
-
-<<FOCUS_2006_L4_data, echo=TRUE, eval=TRUE>>=
-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))
-FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
-@
-
-SFO model, summary and plot:
-
-<<L4_SFO, echo=TRUE, fig=TRUE, height=4>>=
-m.L4.SFO <- mkinfit(SFO, FOCUS_2006_L4_mkin, quiet = TRUE)
-plot(m.L4.SFO)
-summary(m.L4.SFO, data = FALSE)
-@
-
-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
-
-<<L4_FOMC, echo=TRUE, fig=TRUE, height=4>>=
-m.L4.FOMC <- mkinfit(FOMC, FOCUS_2006_L4_mkin, quiet = TRUE)
-plot(m.L4.FOMC)
-summary(m.L4.FOMC, data = FALSE)
-@
-
-The error level at which the $\chi^2$ test passes is slightly lower for the FOMC
-model. However, the difference appears negligible.
-
-\section{Kinetic evaluations for parent and metabolites}
-
-\subsection{Laboratory Data for example compound Z}
-
-The following code defines the example dataset from Appendix 7 to the FOCUS kinetics
-report, p.350
-
-<<FOCUS_2006_Z_data, echo=TRUE, eval=TRUE>>=
-LOD = 0.5
-FOCUS_2006_Z = data.frame(
- t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21,
- 42, 61, 96, 124),
- Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8,
- 2.9, 3.5, 5.3, 4.4, 1.2, 0.7),
- Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1,
- 1.6, 0.6, 0.5 * LOD, NA, NA, NA),
- Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5,
- 0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA),
- Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5,
- 25.2, 17.2, 4.8, 4.5, 2.8, 4.4))
-
-FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)
-@
-
-The next step is to set up the models used for the kinetic analysis. As the
-simultaneous fit of parent and the first metabolite is usually straightforward,
-Step 1 (SFO for parent only) is skipped here. We start with the model 2a,
-with formation and decline of metabolite Z1 and the pathway from parent
-directly to sink included (default in mkin).
-
-<<FOCUS_2006_Z_fits_1, echo=TRUE, fig=TRUE, height=4>>=
-Z.2a <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),
- Z1 = list(type = "SFO"))
-m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.2a)
-summary(m.Z.2a, data = FALSE)
-@
-
-As obvious from the summary, the kinetic rate constant from parent compound Z to sink
-is negligible. Accordingly, the exact magnitude of the fitted parameter
-\texttt{log k\_Z\_sink} is ill-defined and the covariance matrix is not returned.
-This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify
-the model by removing the pathway to sink.
-
-A similar result can be obtained when formation fractions are used in the model formulation:
-
-<<FOCUS_2006_Z_fits_2, echo=TRUE, fig=TRUE, height=4>>=
-Z.2a.ff <- mkinmod(Z0 = list(type = "SFO", to = "Z1"),
- Z1 = list(type = "SFO"), use_of_ff = "max")
-
-m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.2a.ff)
-summary(m.Z.2a.ff, data = FALSE)
-@
-
-Here, the ilr transformed formation fraction fitted in the model takes a very large value,
-and the backtransformed formation fraction from parent Z to Z1 is practically unity. Again,
-the covariance matrix is not returned as the model is overparameterised.
-
-The simplified model is obtained by setting the list component \texttt{sink} to
-\texttt{FALSE}. This model definition is not supported when formation fractions
-are used.
-
-<<FOCUS_2006_Z_fits_3, echo=TRUE, fig=TRUE, height=4>>=
-Z.3 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO"))
-m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, parms.ini = c(k_Z0_Z1 = 0.5),
- quiet = TRUE)
-#m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, solution_type = "deSolve")
-plot(m.Z.3)
-summary(m.Z.3, data = FALSE)
-@
-
-The first attempt to fit the model failed, as the default solution type chosen
-by mkinfit is based on eigenvalues, and the system defined by the starting
-parameters is identified as being singular to the solver. This is caused by the
-fact that the rate constants for both state variables are the same using the
-default starting paramters. Setting a different starting value for one of the
-parameters overcomes this. Alternatively, the \Rpackage{deSolve} based model
-solution can be chosen, at the cost of a bit more computing time.
-
-<<FOCUS_2006_Z_fits_4, echo=TRUE, fig=TRUE, height=4>>=
-Z.4a <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2"),
- Z2 = list(type = "SFO"))
-m.Z.4a <- mkinfit(Z.4a, FOCUS_2006_Z_mkin, parms.ini = c(k_Z0_Z1 = 0.5),
- quiet = TRUE)
-plot(m.Z.4a)
-summary(m.Z.4a, data = FALSE)
-@
-
-As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as
-well in the next step. While this step appears questionable on the basis of the above results, it
-is followed here for the purpose of comparison. Also, in the FOCUS report, it is
-assumed that there is additional empirical evidence that Z1 quickly and exclusively
-hydrolyses to Z2. Again, in order to avoid a singular system when using default starting
-parameters, the starting parameter for the pathway without sink term has to be adapted.
-
-<<FOCUS_2006_Z_fits_5, echo=TRUE, fig=TRUE, height=4>>=
-Z.5 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO"))
-m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.2), quiet = TRUE)
-plot(m.Z.5)
-summary(m.Z.5, data = FALSE)
-@
-
-Finally, metabolite Z3 is added to the model.
-
-<<FOCUS_2006_Z_fits_6, echo=TRUE, fig=TRUE, height=4>>=
-Z.FOCUS <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFO"))
-m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.2, k_Z2_Z3 = 0.3),
- quiet = TRUE)
-plot(m.Z.FOCUS)
-summary(m.Z.FOCUS, data = FALSE)
-@
-
-This is the fit corresponding to the final result chosen in Appendix 7 of the
-FOCUS report. The residual plots can be obtained by
-
-<<FOCUS_2006_Z_residuals_6, echo=TRUE, fig=TRUE>>=
-par(mfrow = c(2, 2))
-mkinresplot(m.Z.FOCUS, "Z0", lpos = "bottomright")
-mkinresplot(m.Z.FOCUS, "Z1", lpos = "bottomright")
-mkinresplot(m.Z.FOCUS, "Z2", lpos = "bottomright")
-mkinresplot(m.Z.FOCUS, "Z3", lpos = "bottomright")
-@
-
-As the FOCUS report states, there is a certain tailing of the time course of metabolite
-Z3. Also, the time course of the parent compound is not fitted very well using the
-SFO model, as residues at a certain low level remain.
-
-Therefore, an additional model is offered here, using the single first-order
-reversible binding (SFORB) model for metabolite Z3. As expected, the $\chi^2$
-error level is lower for metabolite Z3 using this model and the graphical
-fit for Z3 is improved. However, the covariance matrix is not returned.
-
-<<FOCUS_2006_Z_fits_7, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.1 <- mkinmod(Z0 = list(type = "SFO", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFORB"))
-m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z0_Z1 = 0.5, k_Z1_Z2 = 0.3),
- quiet = TRUE)
-plot(m.Z.mkin.1)
-summary(m.Z.mkin.1, data = FALSE)
-@
-
-Therefore, a further stepwise model building is performed starting from the
-stage of parent and one metabolite, starting from the assumption that the model
-fit for the parent compound can be improved by using the SFORB model.
-
-<<FOCUS_2006_Z_fits_8, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.2 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO"))
-m.Z.mkin.2 <- mkinfit(Z.mkin.2, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.mkin.2)
-summary(m.Z.mkin.2, data = FALSE)
-@
-
-When metabolite Z2 is added, the additional sink for Z1 is turned off again,
-for the same reasons as in the original analysis.
-
-<<FOCUS_2006_Z_fits_9, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.3 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2"),
- Z2 = list(type = "SFO"))
-m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
-plot(m.Z.mkin.3)
-summary(m.Z.mkin.3, data = FALSE)
-@
-
-This results in a much better representation of the behaviour of the parent
-compound Z0.
-
-Finally, Z3 is added as well. This model appears overparameterised (no
-covariance matrix returned) if the sink for Z1 is left in the model.
-
-<<FOCUS_2006_Z_fits_10, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.4 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFO"))
-m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z1_Z2 = 0.05), quiet = TRUE)
-plot(m.Z.mkin.4)
-summary(m.Z.mkin.4, data = FALSE)
-@
-
-The error level of the fit, but especially of metabolite Z3, can be improved if
-the SFORB model is chosen for this metabolite, as this model is capable of
-representing the tailing of the metabolite decline phase.
-
-Using the SFORB additionally for Z1 or Z2 did not further improve the result.
-
-<<FOCUS_2006_Z_fits_11, echo=TRUE, fig=TRUE, height=4>>=
-Z.mkin.5 <- mkinmod(Z0 = list(type = "SFORB", to = "Z1", sink = FALSE),
- Z1 = list(type = "SFO", to = "Z2", sink = FALSE),
- Z2 = list(type = "SFO", to = "Z3"),
- Z3 = list(type = "SFORB"))
-m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
- parms.ini = c(k_Z1_Z2 = 0.2), quiet = TRUE)
-plot(m.Z.mkin.5)
-summary(m.Z.mkin.5, data = FALSE)
-@
-
-Looking at the confidence intervals of the SFORB model parameters of Z3, it is
-clear that nothing can be said about the degradation rate of Z3 towards the end
-of the experiment. However, this appears to be a feature of the data.
-
-<<FOCUS_2006_Z_residuals_11, fig=TRUE>>=
-par(mfrow = c(2, 2))
-mkinresplot(m.Z.mkin.5, "Z0", lpos = "bottomright")
-mkinresplot(m.Z.mkin.5, "Z1", lpos = "bottomright")
-mkinresplot(m.Z.mkin.5, "Z2", lpos = "bottomright")
-mkinresplot(m.Z.mkin.5, "Z3", lpos = "bottomright")
-@
-
-As expected, the residual plots are much more random than in the case of the
-all SFO model for which they were shown above. In conclusion, the model
-\texttt{Z.mkin.5} is proposed as the best-fit model for the dataset from
-Appendix 7 of the FOCUS report.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-
-\end{document}
-% vim: set foldmethod=syntax:
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diff --git a/vignettes/header.tex b/vignettes/header.tex
index 707997c..476415e 100644
--- a/vignettes/header.tex
+++ b/vignettes/header.tex
@@ -21,11 +21,3 @@
\RequirePackage{graphicx,ae,fancyvrb}
\IfFileExists{upquote.sty}{\RequirePackage{upquote}}{}
\usepackage{relsize}
-
-\DefineVerbatimEnvironment{Sinput}{Verbatim}{baselinestretch=1.05}
-\DefineVerbatimEnvironment{Soutput}{Verbatim}{fontfamily=courier,
- baselinestretch=1.05,
- fontshape=it,
- fontsize=\relsize{-1}}
-\DefineVerbatimEnvironment{Scode}{Verbatim}{}
-\newenvironment{Schunk}{}{}
diff --git a/vignettes/mkin.Rnw b/vignettes/mkin.Rnw
index 5c71e8b..398b541 100644
--- a/vignettes/mkin.Rnw
+++ b/vignettes/mkin.Rnw
@@ -1,168 +1,74 @@
-% $Id: mkin.Rnw 66 2010-09-03 08:50:26Z jranke $
-%%\VignetteIndexEntry{Routines for fitting kinetic models with one or more state variables to chemical degradation data}
-%%VignetteDepends{FME}
-%%\usepackage{Sweave}
-\documentclass[12pt,a4paper]{article}
-\usepackage{a4wide}
-%%\usepackage[lists,heads]{endfloat}
-\input{header}
-\hypersetup{
- pdftitle = {mkin - Routines for fitting kinetic models with one or more state variables to chemical degradation data},
- pdfsubject = {Manuscript},
- pdfauthor = {Johannes Ranke},
- colorlinks = {true},
- linkcolor = {blue},
- citecolor = {blue},
- urlcolor = {red},
- hyperindex = {true},
- linktocpage = {true},
-}
-\SweaveOpts{engine=R, eps=FALSE, keep.source = TRUE}
-<<setup, echo = FALSE, results = hide>>=
-options(prompt = "R> ")
-options(SweaveHooks = list(
- cex = function() par(cex.lab = 1.3, cex.axis = 1.3)))
-@
-\begin{document}
-\title{mkin -\\
-Routines for fitting kinetic models with one or more state variables to chemical degradation data}
-\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}
-In the regulatory evaluation of chemical substances like plant protection
-products (pesticides), biocides and other chemicals, degradation data play an
-important role. For the evaluation of pesticide degradation experiments,
-detailed guidance has been developed, based on nonlinear optimisation.
-The \RR{} add-on package \Rpackage{mkin} implements fitting some of the models
-recommended in this guidance from within R and calculates some statistical
-measures for data series within one or more compartments, for parent and
-metabolites.
-\end{abstract}
-
-
-\thispagestyle{empty} \setcounter{page}{0}
-
-\clearpage
-
-\tableofcontents
-
-\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
-
-\section{Introduction}
-\label{intro}
-
-Many approaches are possible regarding the evaluation of chemical degradation
-data. The \Rpackage{kinfit} package \citep{pkg:kinfit} in \RR{}
-\citep{rcore2013} implements the approach recommended in the kinetics report
-provided by the FOrum for Co-ordination of pesticide fate models and their
-USe \citep{FOCUS2006, FOCUSkinetics2011} for simple data series for one parent
-compound in one compartment.
-
-The \Rpackage{mkin} package \citep{pkg:mkin} extends this approach to data series
-with metabolites and more than one compartment and includes the possibility
-for back reactions.
-
-\section{Example}
-\label{exam}
-
-In the following, requirements for data formatting are explained. Then the
-procedure for fitting the four kinetic models recommended by the FOCUS group
-to an example dataset for parent only given in the FOCUS kinetics report is
-illustrated. The explanations are kept rather verbose in order to lower the
-barrier for \RR{} newcomers.
-
-\subsection{Data format}
-
-The following listing shows example dataset C from the FOCUS kinetics
-report as distributed with the \Rpackage{mkin} package
-
-<<FOCUS_2006_C_data, echo=TRUE, eval=TRUE>>=
-library("mkin")
-FOCUS_2006_C
-@
-
-Note that the data needs to be in the format of a data frame containing a
-variable \Robject{name} specifying the observed variable, indicating the
-compound name and, if applicable, the compartment, a variable \Robject{time}
-containing sampling times, and a numeric variable \Robject{value} specifying
-the observed value of the variable. If a further variable \Robject{error}
-is present, this will be used to give different weights to the data points
-(the higher the error, the lower the weight, see the help page of the
-\Robject{modCost} function of the \Rpackage{FME} package \citep{soetaert10}).
-Replicate measurements are not recorded in extra columns but simply appended,
-leading to multiple occurrences of the sampling times \Robject{time}.
-
-Small to medium size dataset can be conveniently entered directly as \RR{} code
-as shown in the following listing
-
-<<data_format, echo=TRUE>>=
-example_data <- data.frame(
- name = rep("parent", 9),
- time = c(0, 1, 3, 7, 14, 28, 63, 91, 119),
- value = c(85.1, 57.9, 29.9, 14.6, 9.7, 6.6, 4, 3.9, 0.6)
-)
-@
-
-\subsection{Model definition}
-
-The next task is to define the model to be fitted to the data. In order to
-facilitate this task, a convenience function \Robject{mkinmod} is available.
-
-<<model_definition, echo=TRUE>>=
-SFO <- mkinmod(parent = list(type = "SFO"))
-SFORB <- mkinmod(parent = list(type = "SFORB"))
-SFO_SFO <- mkinmod(
- parent = list(type = "SFO", to = "m1", sink = TRUE),
- m1 = list(type = "SFO"))
-SFORB_SFO <- mkinmod(
- parent = list(type = "SFORB", to = "m1", sink = TRUE),
- m1 = list(type = "SFO"))
-@
-
-The model definitions given above define sets of linear first-order ordinary
-differential equations. In these cases, a coefficient matrix is also returned.
-
-Other models that include time on the right-hand side of the differential
-equation are the first-order multi-compartment (FOMC) model and the
-Hockey-Stick (HS) model. At present, these models can only be used only for the
-parent compound.
-
-\subsection{Fitting the model}
-
-Then the model parameters should be fitted to the data. The function
-\Robject{mkinfit} internally creates a cost function using \Robject{modCost}
-from the \Rpackage{FME} package and then produces a fit using \Robject{modFit}
-from the same package. In cases of linear first-order differential
-equations, the solution used for calculating the cost function is based
-on the fundamental system of the coefficient matrix, as proposed by
-\citet{bates88}.
-
-<<model_fitting, echo=TRUE>>=
-SFO.fit <- mkinfit(SFO, FOCUS_2006_C)
-summary(SFO.fit)
-SFORB.fit <- mkinfit(SFORB, FOCUS_2006_C)
-summary(SFORB.fit)
-SFO_SFO.fit <- mkinfit(SFO_SFO, FOCUS_2006_D)
-summary(SFO_SFO.fit, data=FALSE)
-SFORB_SFO.fit <- mkinfit(SFORB_SFO, FOCUS_2006_D)
-summary(SFORB_SFO.fit, data=FALSE)
-@
-
-\section{Acknowledgements}
-
-This package would not have been written without me being introduced to regulatory
-fate modelling of pesticides by Adrian Gurney during my time at Harlan Laboratories Ltd
-(formerly RCC Ltd). Parts of the package were written during my employment at Harlan.
-
-\bibliographystyle{plainnat}
-\bibliography{references}
-
-\end{document}
-% vim: set foldmethod=syntax:
+%\VignetteIndexEntry{Routines for fitting kinetic models with one or more state variables to chemical degradation data}
+%\VignetteEngine{knitr::knitr}
+\documentclass[12pt,a4paper]{article}
+\usepackage{a4wide}
+\input{header}
+\hypersetup{
+ pdftitle = {mkin - Routines for fitting kinetic models with one or more state variables to chemical degradation data},
+ pdfsubject = {Manuscript},
+ pdfauthor = {Johannes Ranke},
+ colorlinks = {true},
+ linkcolor = {blue},
+ citecolor = {blue},
+ urlcolor = {red},
+ linktocpage = {true},
+}
+
+\begin{document}
+
+<<include=FALSE>>=
+require(knitr)
+opts_chunk$set(engine='R', tidy=FALSE)
+@
+
+\title{mkin -\\
+Routines for fitting kinetic models with one or more state variables to
+chemical degradation data}
+\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}
+In the regulatory evaluation of chemical substances like plant protection
+products (pesticides), biocides and other chemicals, degradation data play an
+important role. For the evaluation of pesticide degradation experiments,
+detailed guidance has been developed, based on nonlinear optimisation.
+The \RR{} add-on package \Rpackage{mkin} implements fitting some of the models
+recommended in this guidance from within R and calculates some statistical
+measures for data series within one or more compartments, for parent and
+metabolites.
+\end{abstract}
+
+
+\thispagestyle{empty} \setcounter{page}{0}
+
+\clearpage
+
+\tableofcontents
+
+\textbf{Key words}: Kinetics, FOCUS, nonlinear optimisation
+
+\section{Introduction}
+\label{intro}
+
+Many approaches are possible regarding the evaluation of chemical degradation
+data. The \Rpackage{kinfit} package \citep{pkg:kinfit} in \RR{}
+\citep{rcore2013} implements the approach recommended in the kinetics report
+provided by the FOrum for Co-ordination of pesticide fate models and their
+USe \citep{FOCUS2006, FOCUSkinetics2011} for simple data series for one parent
+compound in one compartment.
+
+The \Rpackage{mkin} package \citep{pkg:mkin} extends this approach to data series
+with metabolites and more than one compartment and includes the possibility
+for back reactions.
+
+\bibliographystyle{plainnat}
+\bibliography{references}
+
+\end{document}
+% vim: set foldmethod=syntax:
diff --git a/vignettes/mkin.pdf b/vignettes/mkin.pdf
new file mode 100644
index 0000000..6849fb4
--- /dev/null
+++ b/vignettes/mkin.pdf
Binary files differ
diff --git a/vignettes/references.bib b/vignettes/references.bib
index 7796000..e069daf 100644
--- a/vignettes/references.bib
+++ b/vignettes/references.bib
@@ -1,4 +1,4 @@
-% This file was created with JabRef 2.7b.
+% This file was originally created with JabRef 2.7b.
% Encoding: ISO8859_1
@BOOK{bates88,
@@ -16,8 +16,6 @@
month = {November},
year = {2011},
file = {FOCUS kinetics 2011 Generic guidance:/home/ranke/dok/orgs/focus/FOCUSkineticsvc_1_0_Nov23.pdf:PDF},
- owner = {ranke},
- timestamp = {2012.09.20},
url = {http://focus.jrc.ec.europa.eu/dk}
}
@@ -46,7 +44,7 @@
degradation data},
author = {Johannes Ranke},
year = {2013},
- url = {http://CRAN.R-project.org}
+ url = {http://CRAN.R-project.org/package=kinfit}
}
@MANUAL{pkg:mkin,
@@ -54,7 +52,7 @@
variables to chemical degradation data},
author = {Johannes Ranke},
year = {2013},
- url = {http://CRAN.R-project.org}
+ url = {http://CRAN.R-project.org/package/kinfit}
}
@INPROCEEDINGS{schaefer2007,
@@ -79,4 +77,3 @@
number = {3},
url = {http://www.jstatsoft.org/v33/i03/}
}
-

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