From f52fffd9eab13b7902bf767dd9cd7f0e7abf8069 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 17 Nov 2016 17:47:17 +0100 Subject: Improve yaml header, remove trailing whitespace Now the year is showing in the reference, and the TOC is not collapsed. --- vignettes/FOCUS_L.Rmd | 38 +++++++++--------- vignettes/FOCUS_L.html | 106 +++++++++++++++++++++++++++---------------------- 2 files changed, 78 insertions(+), 66 deletions(-) diff --git a/vignettes/FOCUS_L.Rmd b/vignettes/FOCUS_L.Rmd index b500243b..fa6155d2 100644 --- a/vignettes/FOCUS_L.Rmd +++ b/vignettes/FOCUS_L.Rmd @@ -5,7 +5,8 @@ date: "`r Sys.Date()`" output: html_document: toc: true - toc_float: true + toc_float: + collapsed: false mathjax: null fig_retina: null references: @@ -16,7 +17,8 @@ references: - family: Ranke given: Johannes type: report - year: 2014 + issued: + year: 2014 number: "Umweltbundesamt Projektnummer 27452" vignette: > %\VignetteIndexEntry{Example evaluation of FOCUS Laboratory Data L1 to L3} @@ -38,7 +40,7 @@ report, p. 284: 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, + 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) @@ -52,7 +54,7 @@ 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. +given in the FOCUS report. ```{r} m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE) @@ -81,7 +83,7 @@ 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 +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 @@ -92,7 +94,7 @@ 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. +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 @@ -102,7 +104,7 @@ 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 +$\chi^2$ error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt [@ranke2014]. # Laboratory Data L2 @@ -127,19 +129,19 @@ 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, +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 +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 +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 @@ -163,7 +165,7 @@ 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. ```{r fig.width = 7, fig.height = 6} m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE) @@ -172,7 +174,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE, summary(m.L2.DFOP, data = FALSE) ``` -Here, the DFOP model is clearly the best-fit model for dataset L2 based on the +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. @@ -191,7 +193,7 @@ 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 +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. @@ -211,7 +213,7 @@ considerably. ## Accessing mmkin objects -The objects returned by mmkin are arranged like a matrix, with +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, @@ -223,14 +225,14 @@ 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 +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 +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 @@ -250,7 +252,7 @@ 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), + list("FOCUS L4" = FOCUS_2006_L4_mkin), quiet = TRUE) plot(mm.L4) ``` diff --git a/vignettes/FOCUS_L.html b/vignettes/FOCUS_L.html index ab25f2f1..bcdee8df 100644 --- a/vignettes/FOCUS_L.html +++ b/vignettes/FOCUS_L.html @@ -11,7 +11,7 @@ - + Example evaluation of FOCUS Laboratory Data L1 to L3 @@ -24,10 +24,11 @@ + + + - - @@ -216,7 +223,7 @@ div.tocify {

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

2016-10-22

+

2016-11-17

@@ -227,7 +234,7 @@ div.tocify { 
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, 
+  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)
@@ -235,17 +242,17 @@ 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 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:39 2016 
-## Date of summary: Sat Oct 22 17:54:39 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:04 2016 
+## Date of summary: Thu Nov 17 17:46:04 2016 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 37 model solutions performed in 0.09 s
+## Fitted with method Port using 37 model solutions performed in 0.093 s
 ## 
 ## Weighting: none
 ## 
@@ -328,10 +335,10 @@ summary(m.L1.SFO)

 
plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

 

 
summary(m.L1.FOMC, data = FALSE)

-
## mkin version:    0.9.44 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:40 2016 
-## Date of summary: Sat Oct 22 17:54:40 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:05 2016 
+## Date of summary: Thu Nov 17 17:46:05 2016 
 ## 
 ## 
 ## Warning: Optimisation by method Port did not converge.
@@ -343,7 +350,7 @@ summary(m.L1.SFO)

 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 188 model solutions performed in 0.417 s
+## Fitted with method Port using 188 model solutions performed in 0.456 s
 ## 
 ## Weighting: none
 ## 
@@ -395,7 +402,7 @@ 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, n.d.).

+

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 2014).

Laboratory Data L2

@@ -410,7 +417,7 @@ 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.

m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = 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.

@@ -425,17 +432,17 @@ plot(m.L2.FOMC, show_residuals = TRUE, main = "FOCUS L2 - FOMC") 

summary(m.L2.FOMC, data = FALSE)
-
## mkin version:    0.9.44 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:40 2016 
-## Date of summary: Sat Oct 22 17:54:40 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:06 2016 
+## Date of summary: Thu Nov 17 17:46:06 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 0.179 s
+## Fitted with method Port using 81 model solutions performed in 0.227 s
 ## 
 ## Weighting: none
 ## 
@@ -495,10 +502,10 @@ 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 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:41 2016 
-## Date of summary: Sat Oct 22 17:54:41 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:07 2016 
+## Date of summary: Thu Nov 17 17:46:07 2016 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -507,7 +514,7 @@ 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 0.759 s
+## Fitted with method Port using 336 model solutions performed in 0.935 s
 ## 
 ## Weighting: none
 ## 
@@ -584,10 +591,10 @@ plot(mm.L3)

 
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 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:42 2016 
-## Date of summary: Sat Oct 22 17:54:42 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:08 2016 
+## Date of summary: Thu Nov 17 17:46:08 2016 
 ## 
 ## Equations:
 ## d_parent = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -596,7 +603,7 @@ plot(mm.L3)

 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 137 model solutions performed in 0.309 s
+## Fitted with method Port using 137 model solutions performed in 0.332 s
 ## 
 ## Weighting: none
 ## 
@@ -678,23 +685,23 @@ 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), 
+               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 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:42 2016 
-## Date of summary: Sat Oct 22 17:54:43 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:08 2016 
+## Date of summary: Thu Nov 17 17:46:08 2016 
 ## 
 ## Equations:
 ## d_parent = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 46 model solutions performed in 0.101 s
+## Fitted with method Port using 46 model solutions performed in 0.131 s
 ## 
 ## Weighting: none
 ## 
@@ -744,17 +751,17 @@ plot(mm.L4)

 ##        DT50 DT90
 ## parent  106  352

 
summary(mm.L4[["FOMC", 1]], data = FALSE)

-
## mkin version:    0.9.44 
-## R version:       3.3.1 
-## Date of fit:     Sat Oct 22 17:54:43 2016 
-## Date of summary: Sat Oct 22 17:54:43 2016 
+
## mkin version:    0.9.44.9000 
+## R version:       3.3.2 
+## Date of fit:     Thu Nov 17 17:46:08 2016 
+## Date of summary: Thu Nov 17 17:46:08 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 0.144 s
+## Fitted with method Port using 66 model solutions performed in 0.167 s
 ## 
 ## Weighting: none
 ## 
@@ -809,7 +816,7 @@ plot(mm.L4)

 
References

 

 

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

+
Ranke, Johannes. 2014. “Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0.” Umweltbundesamt Projektnummer 27452.
@@ -824,8 +831,11 @@ plot(mm.L4)