@@ -37,13 +38,14 @@

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

2016-10-06

2016-10-26

Laboratory Data L1

The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:

library("mkin", quietly = TRUE)
 FOCUS_2006_L1 = data.frame(
@@ -58,15 +60,15 @@ FOCUS_2006_L1_mkin <- summary(m.L1.SFO)

## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:05 2016 
-## Date of summary: Thu Oct  6 08:54:05 2016 
+## Date of fit:     Wed Oct 26 23:18:11 2016 
+## Date of summary: Wed Oct 26 23:18:11 2016 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.087 s
+## Fitted with method Port using 37 model solutions performed in 0.089 s
 ## 
 ## Weighting: none
 ## 
@@ -138,21 +140,21 @@ FOCUS_2006_L1_mkin <- plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")


-
+
 The residual plot can be easily obtained by
 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.
 m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
 ## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation by method Port did not converge.
 ## Convergence code is 1
 plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
-
+
 summary(m.L1.FOMC, data = FALSE)
 ## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:06 2016 
-## Date of summary: Thu Oct  6 08:54:06 2016 
+## Date of fit:     Wed Oct 26 23:18:12 2016 
+## Date of summary: Wed Oct 26 23:18:12 2016 
 ## 
 ## 
 ## Warning: Optimisation by method Port did not converge.
@@ -164,7 +166,7 @@ FOCUS_2006_L1_mkin <-  \(\chi^2\) 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 (Ranke, n.d.).


 
-Laboratory Data L2
+ Laboratory Data L2
 The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:
 FOCUS_2006_L2 = data.frame(
   t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
@@ -228,35 +230,35 @@ FOCUS_2006_L1_mkin <- 2.6, 1.2, 0.3, 0.6))
 FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
 
-SFO fit for 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.
 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
+ FOMC fit for L2
 For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.
 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)
 ## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:07 2016 
-## Date of summary: Thu Oct  6 08:54:07 2016 
+## Date of fit:     Wed Oct 26 23:18:12 2016 
+## Date of summary: Wed Oct 26 23:18:12 2016 
 ## 
 ## Equations:
 ## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 81 model solutions performed in 0.19 s
+## Fitted with method Port using 81 model solutions performed in 0.191 s
 ## 
 ## Weighting: none
 ## 
@@ -309,17 +311,17 @@ FOCUS_2006_L2_mkin <- \(\chi^2\) 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
+ DFOP fit for L2
 Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level.
 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)
 ## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:08 2016 
-## Date of summary: Thu Oct  6 08:54:08 2016 
+## Date of fit:     Wed Oct 26 23:18:13 2016 
+## Date of summary: Wed Oct 26 23:18:14 2016 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -328,7 +330,7 @@ FOCUS_2006_L2_mkin <-  
-Laboratory Data L3
+ Laboratory Data L3
 The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.
 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)
 
-Use mmkin to fit multiple models
+ Use mmkin to 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.
 # 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 elements of mmkin objects
+ Accessing elements of 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.
 summary(mm.L3[["DFOP", 1]])
 ## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:09 2016 
-## Date of summary: Thu Oct  6 08:54:09 2016 
+## Date of fit:     Wed Oct 26 23:18:15 2016 
+## Date of summary: Wed Oct 26 23:18:15 2016 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -417,7 +419,7 @@ mm.L3 <-  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
+ Laboratory Data L4
 The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:
 FOCUS_2006_L4 = data.frame(
   t = c(0, 3, 7, 14, 30, 60, 91, 120),
@@ -502,20 +504,20 @@ mm.L4 <- 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.
 summary(mm.L4[["SFO", 1]], data = FALSE)
 ## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:10 2016 
-## Date of summary: Thu Oct  6 08:54:10 2016 
+## Date of fit:     Wed Oct 26 23:18:15 2016 
+## Date of summary: Wed Oct 26 23:18:16 2016 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.158 s
+## Fitted with method Port using 46 model solutions performed in 0.108 s
 ## 
 ## Weighting: none
 ## 
@@ -567,8 +569,8 @@ mm.L4 <- summary(mm.L4[["FOMC", 1]], data = FALSE)

 ## mkin version:    0.9.44.9000 
 ## R version:       3.3.1 
-## Date of fit:     Thu Oct  6 08:54:10 2016 
-## Date of summary: Thu Oct  6 08:54:10 2016 
+## Date of fit:     Wed Oct 26 23:18:16 2016 
+## Date of summary: Wed Oct 26 23:18:16 2016 
 ## 
 ## Equations:
 ## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -627,16 +629,17 @@ mm.L4 <- 
-References
+ References
 
 
 Ranke, Johannes. n.d. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.
 
 
+


 
-  
+  
         
       Contents
       Laboratory Data L1
@@ -655,7 +658,14 @@ mm.L4 <- pkgdown. Styled with Bootstrap 3.
+      
+  Developed by Johannes Ranke, Eurofins Regulatory AG.
+
+
+
+  Site built with pkgdown.
+
+
       
 
   
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