From 6211f3ef4995657798686d8d4ab43ed9406e8a08 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Tue, 12 May 2020 16:34:00 +0200 Subject: Update vignettes and docs --- docs/articles/FOCUS_L.html | 372 +++++++++++++++++++++++---------------------- 1 file changed, 193 insertions(+), 179 deletions(-) (limited to 'docs/articles/FOCUS_L.html') diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html index 4033beba..742718cb 100644 --- a/docs/articles/FOCUS_L.html +++ b/docs/articles/FOCUS_L.html @@ -6,19 +6,19 @@ Example evaluation of FOCUS Laboratory Data L1 to L3 • mkin - - - - + + + + + - - + - +
@@ -87,12 +94,12 @@
-

Example evaluation of FOCUS Laboratory Data L1 to L3

+

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

2019-11-01

- +

2020-05-12

+ Source: vignettes/FOCUS_L.Rmd
@@ -103,28 +110,28 @@

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(
-  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,
-             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)
+
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,
+             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)

Here we use the assumptions of simple first order (SFO), the case of declining rate constant over time (FOMC) and the case of two different phases of the kinetics (DFOP). For a more detailed discussion of the models, please see the 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.

-
m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
-summary(m.L1.SFO)
-
## mkin version used for fitting:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:46 2019 
-## Date of summary: Fri Nov  1 10:10:46 2019 
+
m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
+summary(m.L1.SFO)

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:38 2020 
+## Date of summary: Tue May 12 15:31:38 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.287 s
+## Fitted using 133 model solutions performed in 0.03 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -143,6 +150,11 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC     BIC    logLik
+##   93.88778 96.5589 -43.94389
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower  Upper
 ## parent_0            92.470    1.28200 89.740 95.200
@@ -151,9 +163,9 @@
 ## 
 ## Parameter correlation:
 ##                     parent_0 log_k_parent_sink      sigma
-## parent_0           1.000e+00         6.186e-01 -1.712e-09
-## log_k_parent_sink  6.186e-01         1.000e+00 -3.237e-09
-## sigma             -1.712e-09        -3.237e-09  1.000e+00
+## parent_0           1.000e+00         6.186e-01 -1.516e-09
+## log_k_parent_sink  6.186e-01         1.000e+00 -3.124e-09
+## sigma             -1.516e-09        -3.124e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -169,10 +181,6 @@
 ## All data   3.424       2  7
 ## parent     3.424       2  7
 ## 
-## Resulting formation fractions:
-##             ff
-## parent_sink  1
-## 
 ## Estimated disappearance times:
 ##         DT50  DT90
 ## parent 7.249 24.08
@@ -198,26 +206,26 @@
 ##    30   parent      2.9     5.251  -2.3513
 ##    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")

+
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")

+
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)

+
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:
 ## false convergence (8)

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

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

 

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

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

 
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt

 
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt

-
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite
-## result is doubtful

-
## mkin version used for fitting:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:48 2019 
-## Date of summary: Fri Nov  1 10:10:48 2019 
+
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:38 2020 
+## Date of summary: Tue May 12 15:31:38 2020 
 ## 
 ## 
 ## Warning: Optimisation did not converge:
@@ -229,7 +237,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 899 model solutions performed in 1.91 s
+## Fitted using 380 model solutions performed in 0.081 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -250,29 +258,34 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   95.88778 99.44927 -43.94389
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
-## parent_0     92.47     1.2800 89.730 95.220
-## log_alpha    10.58        NaN    NaN    NaN
-## log_beta     12.93        NaN    NaN    NaN
-## sigma         2.78     0.4507  1.813  3.747
+## parent_0     92.47     1.2820 89.720 95.220
+## log_alpha    16.92        NaN    NaN    NaN
+## log_beta     19.26        NaN    NaN    NaN
+## sigma         2.78     0.4501  1.814  3.745
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta   sigma
-## parent_0   1.00000       NaN      NaN 0.01452
-## log_alpha      NaN         1      NaN     NaN
-## log_beta       NaN       NaN        1     NaN
-## sigma      0.01452       NaN      NaN 1.00000
+##           parent_0 log_alpha log_beta    sigma
+## parent_0  1.000000       NaN      NaN 0.002218
+## log_alpha      NaN         1      NaN      NaN
+## log_beta       NaN       NaN        1      NaN
+## sigma     0.002218       NaN      NaN 1.000000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##           Estimate  t value    Pr(>t)  Lower  Upper
-## parent_0     92.47 72.13000 1.052e-19 89.730 95.220
-## alpha     39440.00  0.02397 4.906e-01     NA     NA
-## beta     412500.00  0.02397 4.906e-01     NA     NA
-## sigma         2.78  6.00000 1.628e-05  1.813  3.747
+##           Estimate t value Pr(>t)  Lower  Upper
+## parent_0 9.247e+01      NA     NA 89.720 95.220
+## alpha    2.223e+07      NA     NA     NA     NA
+## beta     2.325e+08      NA     NA     NA     NA
+## sigma    2.780e+00      NA     NA  1.814  3.745
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -280,8 +293,8 @@
 ## parent     3.619       3  6
 ## 
 ## Estimated disappearance times:
-##         DT50  DT90 DT50back
-## parent 7.249 24.08    7.249

+##        DT50  DT90 DT50back
+## 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 \(\chi^2\) 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).

@@ -290,19 +303,19 @@
 

 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,
+             19.3, 22.3, 4.6, 4.6,
+             2.6, 1.2, 0.3, 0.6))
+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,
-     main = "FOCUS L2 - SFO")

+
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.

@@ -312,22 +325,22 @@
 

 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")

+
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:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:49 2019 
-## Date of summary: Fri Nov  1 10:10:49 2019 
+
summary(m.L2.FOMC, data = FALSE)

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:39 2020 
+## Date of summary: Tue May 12 15:31:39 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.489 s
+## Fitted using 239 model solutions performed in 0.047 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -348,6 +361,11 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   61.78966 63.72928 -26.89483
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error    Lower   Upper
 ## parent_0   93.7700     1.6130 90.05000 97.4900
@@ -357,10 +375,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.436e-09
 ## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
-## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.386e-07
+## sigma     -7.436e-09 -1.617e-07 -1.386e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -386,24 +404,24 @@
 

 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")

+
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:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:51 2019 
-## Date of summary: Fri Nov  1 10:10:51 2019 
+
summary(m.L2.DFOP, data = FALSE)

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:39 2020 
+## Date of summary: Tue May 12 15:31:39 2020 
 ## 
 ## Equations:
-## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
-##            exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
-##            exp(-k2 * time))) * parent
+## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+##            * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 572 model solutions performed in 1.218 s
+## Fitted using 572 model solutions performed in 0.13 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -426,21 +444,26 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   52.36695 54.79148 -21.18347
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0  93.9500  9.998e-01    91.5900   96.3100
-## log_k1     3.1370  2.376e+03 -5616.0000 5622.0000
+## log_k1     3.1370  2.376e+03 -5615.0000 5622.0000
 ## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
 ## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
 ## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  5.155e-07  2.371e-09  2.665e-01 -6.849e-09
-## log_k1    5.155e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
-## log_k2    2.371e-09  8.434e-05  1.000e+00 -7.903e-01 -1.262e-08
-## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.241e-08
-## sigma    -6.849e-09 -7.791e-06 -1.262e-08  3.241e-08  1.000e+00
+## parent_0  1.000e+00  5.157e-07  2.376e-09  2.665e-01 -6.837e-09
+## log_k1    5.157e-07  1.000e+00  8.434e-05 -1.659e-04 -7.786e-06
+## log_k2    2.376e-09  8.434e-05  1.000e+00 -7.903e-01 -1.263e-08
+## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.248e-08
+## sigma    -6.837e-09 -7.786e-06 -1.263e-08  3.248e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -468,18 +491,18 @@
 

 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)

+
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)

 

 

 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)

+
# 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.

 

@@ -488,20 +511,20 @@
 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 used for fitting:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:53 2019 
-## Date of summary: Fri Nov  1 10:10:53 2019 
+
summary(mm.L3[["DFOP", 1]])

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:39 2020 
+## Date of summary: Tue May 12 15:31:40 2020 
 ## 
 ## Equations:
-## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
-##            exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
-##            exp(-k2 * time))) * parent
+## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+##            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+##            * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 373 model solutions performed in 0.784 s
+## Fitted using 373 model solutions performed in 0.083 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -524,6 +547,11 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   32.97732 33.37453 -11.48866
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error   Lower      Upper
 ## parent_0  97.7500    1.01900 94.5000 101.000000
@@ -534,11 +562,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.872e-07
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.200e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.673e-07
-## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.731e-07
-## sigma    -6.872e-07  3.200e-07  7.673e-07 -8.731e-07  1.000e+00
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.868e-07
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.175e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.631e-07
+## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.694e-07
+## sigma    -6.868e-07  3.175e-07  7.631e-07 -8.694e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -570,7 +598,7 @@
 ##    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)

+
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.

@@ -580,30 +608,30 @@
 

 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),
-  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)

+
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)

+
# 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.

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

-
## mkin version used for fitting:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:53 2019 
-## Date of summary: Fri Nov  1 10:10:54 2019 
+
summary(mm.L4[["SFO", 1]], data = FALSE)

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:40 2020 
+## Date of summary: Tue May 12 15:31:40 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.292 s
+## Fitted using 142 model solutions performed in 0.029 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -622,6 +650,11 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   47.12133 47.35966 -20.56067
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower   Upper
 ## parent_0            96.440    1.69900 92.070 100.800
@@ -630,9 +663,9 @@
 ## 
 ## Parameter correlation:
 ##                    parent_0 log_k_parent_sink     sigma
-## parent_0          1.000e+00         5.938e-01 3.440e-07
-## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
-## sigma             3.440e-07         5.885e-07 1.000e+00
+## parent_0          1.000e+00         5.938e-01 3.387e-07
+## log_k_parent_sink 5.938e-01         1.000e+00 5.830e-07
+## sigma             3.387e-07         5.830e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -648,25 +681,21 @@
 ## All data   3.287       2  6
 ## parent     3.287       2  6
 ## 
-## Resulting formation fractions:
-##             ff
-## parent_sink  1
-## 
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352

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

-
## mkin version used for fitting:    0.9.49.6 
-## R version used for fitting:       3.6.1 
-## Date of fit:     Fri Nov  1 10:10:54 2019 
-## Date of summary: Fri Nov  1 10:10:54 2019 
+
summary(mm.L4[["FOMC", 1]], data = FALSE)

+
## mkin version used for fitting:    0.9.50.2 
+## R version used for fitting:       4.0.0 
+## Date of fit:     Tue May 12 15:31:40 2020 
+## Date of summary: Tue May 12 15:31:40 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.455 s
+## Fitted using 224 model solutions performed in 0.044 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -687,6 +716,11 @@
 ## Fixed parameter values:
 ## None
 ## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   40.37255 40.69032 -16.18628
+## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error   Lower    Upper
 ## parent_0   99.1400     1.2670 95.6300 102.7000
@@ -696,10 +730,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.456e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.169e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  4.910e-08
+## sigma     -2.456e-07  2.169e-08  4.910e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -731,31 +765,11 @@
- @@ -766,7 +780,7 @@
-

Site built with pkgdown 1.4.1.

+

Site built with pkgdown 1.5.1.

-- cgit v1.2.1