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diff --git a/docs/articles/FOCUS_L.Rmd b/docs/articles/FOCUS_L.Rmd deleted file mode 100644 index e017b674..00000000 --- a/docs/articles/FOCUS_L.Rmd +++ /dev/null @@ -1,271 +0,0 @@ ---- -title: "Example evaluation of FOCUS Laboratory Data L1 to L3" -author: "Johannes Ranke" -date: "`r Sys.Date()`" -output: - html_document: - toc: true - toc_float: - collapsed: false - mathjax: null - fig_retina: null -references: -- id: ranke2014 - title: <span class="nocase">Prüfung und Validierung von Modellierungssoftware als Alternative zu - ModelMaker 4.0</span> - author: - - family: Ranke - given: Johannes - type: report - issued: - year: 2014 - number: "Umweltbundesamt Projektnummer 27452" -vignette: > - %\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3} - %\VignetteEngine{knitr::rmarkdown} - %\VignetteEncoding{UTF-8} ---- - -```{r, include = FALSE} -library(knitr) -opts_chunk$set(tidy = FALSE, cache = FALSE) -``` - -# Laboratory Data L1 - -The following code defines example dataset L1 from the FOCUS kinetics -report, p. 284: - -```{r} -library("mkin", quietly = TRUE) -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) -``` - -Here we use the assumptions 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. - -Since mkin version 0.9-32 (July 2014), we can use shorthand notation like `"SFO"` -for parent only degradation models. 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 = 6, fig.height = 5} -plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO") -``` - -The residual plot can be easily obtained by - -```{r fig.width = 6, 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 fig.width = 6, fig.height = 5} -m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE) -plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC") -summary(m.L1.FOMC, data = FALSE) -``` - -We get a warning that the default optimisation algorithm `Port` did not converge, which -is an indication that the model is overparameterised, *i.e.* contains too many -parameters that are ill-defined as a consequence. - -And in fact, 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 -parameters `log_alpha` and `log_beta` internally fitted in the model have -excessive confidence intervals, that span more than 25 orders of magnitude (!) -when backtransformed to the scale of `alpha` and `beta`. Also, the t-test -for significant difference from zero does not indicate such a significant difference, -with p-values greater than 0.1, and finally, the parameter correlation of `log_alpha` -and `log_beta` is 1.000, clearly indicating that the model is overparameterised. - -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 and 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 was the first -widely used standard package in this field. Also, the calculation of -$\chi^2$ error levels was compared with KinGUII, CAKE and DegKin manager in -a project sponsored by the German Umweltbundesamt [@ranke2014]. - -# 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) -``` - -## SFO fit for L2 - -Again, the SFO model is fitted and the result is plotted. The residual plot -can be obtained simply by adding the argument `show_residuals` to the plot -command. - -```{r fig.width = 7, fig.height = 6} -m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE) -plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE, - main = "FOCUS 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, in which we have included -the residual plot. - -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. - -## FOMC fit for L2 - -For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level -is checked. - -```{r fig.width = 7, fig.height = 6} -m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE) -plot(m.L2.FOMC, show_residuals = TRUE, - main = "FOCUS 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. - -## DFOP fit for L2 - -Fitting the four parameter DFOP model further reduces the $\chi^2$ error level. - -```{r fig.width = 7, fig.height = 6} -m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE) -plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE, - main = "FOCUS 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) -``` - -## Fit multiple models - -As of mkin version 0.9-39 (June 2015), we can fit several models to -one or more datasets in one call to the function `mmkin`. The datasets -have to be passed in a list, in this case a named list holding only -the L3 dataset prepared above. - -```{r fig.height = 8} -# Only use one core here, not to offend the CRAN checks -mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1, - list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE) -plot(mm.L3) -``` - -The $\chi^2$ error level of 21% as well as the plot suggest that the SFO model -does not fit very well. The FOMC model performs better, with an -error level at which the $\chi^2$ test passes of 7%. Fitting the four -parameter DFOP model further reduces the $\chi^2$ error level -considerably. - -## Accessing mmkin objects - -The objects returned by mmkin are arranged like a matrix, with -models as a row index and datasets as a column index. - -We can extract the summary and plot for *e.g.* the DFOP fit, -using square brackets for indexing which will result in the use of -the summary and plot functions working on mkinfit objects. - -```{r fig.height = 5} -summary(mm.L3[["DFOP", 1]]) -plot(mm.L3[["DFOP", 1]], show_errmin = TRUE) -``` - -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. - -This is also an example where the standard t-test for the parameter `g_ilr` is -misleading, as it tests for a significant difference from zero. In this case, -zero appears to be the correct value for this parameter, and the confidence -interval for the backtransformed parameter `g` is quite narrow. - -# 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) -``` - -Fits of the SFO and FOMC models, plots and summaries are produced below: - -```{r fig.height = 6} -# Only use one core here, not to offend the CRAN checks -mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1, - list("FOCUS L4" = FOCUS_2006_L4_mkin), - quiet = TRUE) -plot(mm.L4) -``` - -The $\chi^2$ error level of 3.3% as well as the plot suggest that the SFO model -fits very well. The error level at which the $\chi^2$ test passes is slightly -lower for the FOMC model. However, the difference appears negligible. - - -```{r fig.height = 8} -summary(mm.L4[["SFO", 1]], data = FALSE) -summary(mm.L4[["FOMC", 1]], data = FALSE) -``` - - -# References |