Example evaluation of FOCUS Laboratory Data L1 to L3

+ +

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

Last change 18 May 2023 -(rebuilt 2023-11-16)

+(rebuilt 2025-02-13) Source: vignettes/FOCUS_L.rmd

FOCUS_L.rmd

@@ -131,10 +117,10 @@ report.

 m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
 summary(m.L1.SFO)

## mkin version used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:13 2023 
-## Date of summary: Thu Nov 16 04:20:13 2023 
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:54 2025 
+## Date of summary: Thu Feb 13 15:49:54 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
@@ -224,7 +210,9 @@ objects.
  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.
+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 did not converge:
@@ -235,13 +223,12 @@ objects.
  summary(m.L1.FOMC, data = FALSE)
 ## Warning in sqrt(diag(covar)): NaNs produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result
-## is doubtful
-## mkin version used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:13 2023 
-## Date of summary: Thu Nov 16 04:20:13 2023 
+## Warning in cov2cor(ans$covar): diag(V) had non-positive or NA entries; the
+## non-finite result may be dubious
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:55 2025 
+## Date of summary: Thu Feb 13 15:49:55 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -316,36 +303,40 @@ objects.
 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 (Ranke
-2014).
+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 (Ranke 2014).


 
 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),
   parent = c(96.1, 91.8, 41.4, 38.7,
@@ -358,15 +349,16 @@ report, p. 287:
 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.
+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
@@ -381,25 +373,27 @@ kinetics.
 
 FOMC fit for L2
 
-For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.
-+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 used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:13 2023 
-## Date of summary: Thu Nov 16 04:20:14 2023 
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:55 2025 
+## Date of summary: Thu Feb 13 15:49:55 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.014 s
+## Fitted using 239 model solutions performed in 0.015 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -457,26 +451,29 @@ kinetics.
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back
 ## parent 0.8092 5.356    1.612
-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.
+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.
-+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 used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:14 2023 
-## Date of summary: Thu Nov 16 04:20:14 2023 
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:55 2025 
+## Date of summary: Thu Feb 13 15:49:55 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -485,7 +482,7 @@ the data.
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.041 s
+## Fitted using 581 model solutions performed in 0.043 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -557,7 +554,7 @@ based on the chi^2 error level criterion.
 
 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))
@@ -569,16 +566,22 @@ report, p. 290.
 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.
+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
@@ -588,12 +591,12 @@ 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 used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:14 2023 
-## Date of summary: Thu Nov 16 04:20:14 2023 
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:56 2025 
+## Date of summary: Thu Feb 13 15:49:56 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -676,14 +679,15 @@ summary and plot functions working on mkinfit objects.
 ##    60   parent     22.0     23.26 -1.25919
 ##    91   parent     15.0     15.18 -0.18181
 ##   120   parent     12.0     10.19  1.81395
-+ 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.
+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
@@ -696,38 +700,40 @@ parameter g is quite narrow.
 

 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),
   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:
-+ # 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.
-+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 used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:14 2023 
-## Date of summary: Thu Nov 16 04:20:15 2023 
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:56 2025 
+## Date of summary: Thu Feb 13 15:49:56 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.01 s
+## Fitted using 142 model solutions performed in 0.009 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -780,19 +786,19 @@ appears negligible.
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352
-+ summary(mm.L4[["FOMC", 1]], data = FALSE)
-## mkin version used for fitting:    1.2.6 
-## R version used for fitting:       4.3.2 
-## Date of fit:     Thu Nov 16 04:20:15 2023 
-## Date of summary: Thu Nov 16 04:20:15 2023 
+## mkin version used for fitting:    1.2.9 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Thu Feb 13 15:49:56 2025 
+## Date of summary: Thu Feb 13 15:49:56 2025 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.014 s
+## Fitted using 224 model solutions performed in 0.013 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -862,28 +868,26 @@ Validierung von Modellierungssoftware als Alternative zu ModelMaker
 

 

 

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