diff options
Diffstat (limited to 'vignettes/FOCUS_L.Rmd')
-rw-r--r-- | vignettes/FOCUS_L.Rmd | 38 |
1 files changed, 20 insertions, 18 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)
```
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