From 5d5c5b0c102aa9dbd849277c3e3b831c7cdd91fe Mon Sep 17 00:00:00 2001 From: jranke Date: Sun, 17 Nov 2013 15:52:42 +0000 Subject: Conflicts: README.md TODO git-svn-id: svn+ssh://svn.r-forge.r-project.org/svnroot/kinfit/pkg/mkin@163 edb9625f-4e0d-4859-8d74-9fd3b1da38cb --- vignettes/FOCUS_L.Rmd | 243 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 243 insertions(+) create mode 100644 vignettes/FOCUS_L.Rmd (limited to 'vignettes/FOCUS_L.Rmd') diff --git a/vignettes/FOCUS_L.Rmd b/vignettes/FOCUS_L.Rmd new file mode 100644 index 00000000..957b34ab --- /dev/null +++ b/vignettes/FOCUS_L.Rmd @@ -0,0 +1,243 @@ + + +# 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. + -- cgit v1.2.1