From e959fde98f95f3595e01490b67892678bbcd1b27 Mon Sep 17 00:00:00 2001
From: Johannes Ranke <jranke@uni-bremen.de>
Date: Wed, 7 May 2014 14:47:28 +0200
Subject: Fork the gmkin GUI from mkin. See ChangeLog for details

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-<!--
-%\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.
-
-- 
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