From 1c81442284a25a9cf4979d9236ec0c1a1cf8a8dd Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Sat, 22 Oct 2016 17:55:12 +0200 Subject: Update way to specify encoding, improve FOCUS_L TOC --- vignettes/FOCUS_L.html | 106 ++++++++++++++++++++++++++----------------------- 1 file changed, 56 insertions(+), 50 deletions(-) (limited to 'vignettes/FOCUS_L.html') diff --git a/vignettes/FOCUS_L.html b/vignettes/FOCUS_L.html index 16fa2ac0..ab25f2f1 100644 --- a/vignettes/FOCUS_L.html +++ b/vignettes/FOCUS_L.html @@ -11,19 +11,19 @@ - + Example evaluation of FOCUS Laboratory Data L1 to L3 - - - - + + + + @@ -98,6 +98,7 @@ button.code-folding-btn:focus { +
@@ -215,7 +216,7 @@ div.tocify {

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

2016-09-28

+

2016-10-22

@@ -234,17 +235,17 @@ FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

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.

m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
 summary(m.L1.SFO)
-
## mkin version:    0.9.44.9000 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:49 2016 
-## Date of summary: Wed Sep 28 08:12:49 2016 
+## Date of fit:     Sat Oct 22 17:54:39 2016 
+## Date of summary: Sat Oct 22 17:54:39 2016 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.092 s
+## Fitted with method Port using 37 model solutions performed in 0.09 s
 ## 
 ## Weighting: none
 ## 
@@ -316,21 +317,21 @@ summary(m.L1.SFO)

 ##    30   parent      4.0     5.251  -1.2513

A plot of the fit is obtained with the plot function for mkinfit objects.

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 χ2 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 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:49 2016 
-## Date of summary: Wed Sep 28 08:12:49 2016 
+## Date of fit:     Sat Oct 22 17:54:40 2016 
+## Date of summary: Sat Oct 22 17:54:40 2016 
 ## 
 ## 
 ## Warning: Optimisation by method Port did not converge.
@@ -342,7 +343,7 @@ summary(m.L1.SFO)

 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 188 model solutions performed in 0.43 s
+## Fitted with method Port using 188 model solutions performed in 0.417 s
 ## 
 ## Weighting: none
 ## 
@@ -394,7 +395,7 @@ summary(m.L1.SFO)
## parent 7.25 24.08 7.25

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 χ2 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 χ2 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 χ2 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 χ2 error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke).

+

The χ2 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 χ2 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 χ2 error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke, n.d.).

Laboratory Data L2

@@ -411,7 +412,7 @@ FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2) 
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 χ2 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.

@@ -422,19 +423,19 @@ plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE, 
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 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:50 2016 
-## Date of summary: Wed Sep 28 08:12:50 2016 
+## Date of fit:     Sat Oct 22 17:54:40 2016 
+## Date of summary: Sat Oct 22 17:54:40 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 0.177 s
+## Fitted with method Port using 81 model solutions performed in 0.179 s
 ## 
 ## Weighting: none
 ## 
@@ -492,12 +493,12 @@ plot(m.L2.FOMC, show_residuals = TRUE,
 
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 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:51 2016 
-## Date of summary: Wed Sep 28 08:12:51 2016 
+## Date of fit:     Sat Oct 22 17:54:41 2016 
+## Date of summary: Sat Oct 22 17:54:41 2016 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -506,7 +507,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 336 model solutions performed in 0.79 s
+## Fitted with method Port using 336 model solutions performed in 0.759 s
 ## 
 ## Weighting: none
 ## 
@@ -568,25 +569,25 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
   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

+

+
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 χ2 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 χ2 test passes of 7%. Fitting the four parameter DFOP model further reduces the χ2 error level considerably.

 

-

-
Accessing elements of mmkin objects

+

+
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.

 
summary(mm.L3[["DFOP", 1]])

-
## mkin version:    0.9.44.9000 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:51 2016 
-## Date of summary: Wed Sep 28 08:12:51 2016 
+## Date of fit:     Sat Oct 22 17:54:42 2016 
+## Date of summary: Sat Oct 22 17:54:42 2016 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -595,7 +596,7 @@ plot(mm.L3)

 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 137 model solutions performed in 0.32 s
+## Fitted with method Port using 137 model solutions performed in 0.309 s
 ## 
 ## Weighting: none
 ## 
@@ -662,7 +663,7 @@ plot(mm.L3)

 ##    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 χ2 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.
@@ -680,20 +681,20 @@ mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1, list("FOCUS L4" = FOCUS_2006_L4_mkin), quiet = TRUE) plot(mm.L4) -

+

The χ2 error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the χ2 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 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:52 2016 
-## Date of summary: Wed Sep 28 08:12:52 2016 
+## Date of fit:     Sat Oct 22 17:54:42 2016 
+## Date of summary: Sat Oct 22 17:54:43 2016 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.104 s
+## Fitted with method Port using 46 model solutions performed in 0.101 s
 ## 
 ## Weighting: none
 ## 
@@ -743,17 +744,17 @@ plot(mm.L4)

 ##        DT50 DT90
 ## parent  106  352
summary(mm.L4[["FOMC", 1]], data = FALSE)
-
## mkin version:    0.9.44.9000 
+
## mkin version:    0.9.44 
 ## R version:       3.3.1 
-## Date of fit:     Wed Sep 28 08:12:52 2016 
-## Date of summary: Wed Sep 28 08:12:52 2016 
+## Date of fit:     Sat Oct 22 17:54:43 2016 
+## Date of summary: Sat Oct 22 17:54:43 2016 
 ## 
 ## Equations:
 ## d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 66 model solutions performed in 0.148 s
+## Fitted with method Port using 66 model solutions performed in 0.144 s
 ## 
 ## Weighting: none
 ## 
@@ -804,9 +805,13 @@ plot(mm.L4)

 ##         DT50 DT90 DT50back
 ## parent 108.9 1644    494.9
-
+

References

-

Ranke, Johannes. Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0. Umweltbundesamt Projektnummer 27452.

+
+
+

Ranke, Johannes. n.d. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.

+
+
@@ -823,6 +828,7 @@ $(document).ready(function () { $('tr.header').parent('thead').parent('table').addClass('table table-condensed'); }); + -- cgit v1.2.1