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.

-