From 4596667b19f032232ceb8f3f762aaad5d69c15be Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 5 Jul 2019 15:57:24 +0200 Subject: Static documentation rebuilt by pkgdown --- docs/articles/FOCUS_D.html | 81 ++- docs/articles/FOCUS_D_files/figure-html/plot-1.png | Bin 97716 -> 98242 bytes .../FOCUS_D_files/figure-html/plot_2-1.png | Bin 14220 -> 14232 bytes docs/articles/FOCUS_L.html | 444 +++++++--------- .../figure-html/unnamed-chunk-12-1.png | Bin 54890 -> 54888 bytes docs/articles/index.html | 2 +- docs/articles/mkin.html | 26 +- docs/articles/twa.html | 4 +- docs/articles/web_only/FOCUS_Z.html | 251 ++++----- .../figure-html/FOCUS_2006_Z_fits_1-1.png | Bin 84962 -> 85687 bytes .../figure-html/FOCUS_2006_Z_fits_10-1.png | Bin 127841 -> 129144 bytes .../figure-html/FOCUS_2006_Z_fits_11-1.png | Bin 127069 -> 128685 bytes .../figure-html/FOCUS_2006_Z_fits_11a-1.png | Bin 95832 -> 96948 bytes .../figure-html/FOCUS_2006_Z_fits_11b-1.png | Bin 22086 -> 22115 bytes .../figure-html/FOCUS_2006_Z_fits_2-1.png | Bin 85657 -> 86379 bytes .../figure-html/FOCUS_2006_Z_fits_3-1.png | Bin 85239 -> 85961 bytes .../figure-html/FOCUS_2006_Z_fits_5-1.png | Bin 101416 -> 102300 bytes .../figure-html/FOCUS_2006_Z_fits_6-1.png | Bin 128185 -> 129356 bytes .../figure-html/FOCUS_2006_Z_fits_7-1.png | Bin 127782 -> 129340 bytes .../figure-html/FOCUS_2006_Z_fits_9-1.png | Bin 107730 -> 108583 bytes docs/articles/web_only/NAFTA_examples.html | 589 ++++++++++----------- .../NAFTA_examples_files/figure-html/p13-1.png | Bin 51343 -> 51344 bytes .../NAFTA_examples_files/figure-html/p5a-1.png | Bin 55286 -> 55292 bytes .../NAFTA_examples_files/figure-html/p8-1.png | Bin 61400 -> 61447 bytes .../NAFTA_examples_files/figure-html/p9a-1.png | Bin 53005 -> 53005 bytes .../NAFTA_examples_files/figure-html/p9b-1.png | Bin 49914 -> 49912 bytes docs/articles/web_only/benchmarks.html | 144 +++-- docs/articles/web_only/compiled_models.html | 106 +--- 28 files changed, 719 insertions(+), 928 deletions(-) (limited to 'docs/articles') diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html index ed41e555..341c7e7d 100644 --- a/docs/articles/FOCUS_D.html +++ b/docs/articles/FOCUS_D.html @@ -30,7 +30,7 @@ mkin - 0.9.49.5 + 0.9.49.6 @@ -88,7 +88,7 @@

Example evaluation of FOCUS Example Dataset D

Johannes Ranke

-

2019-07-04

+

2019-07-05

@@ -156,20 +156,18 @@ ## "d_m1 = + k_parent_m1 * parent - k_m1_sink * m1"

We do the fitting without progress report (quiet = TRUE).

fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
-## value of zero were removed from the data

A plot of the fit including a residual plot for both observed variables is obtained using the plot_sep method for mkinfit objects, which shows separate graphs for all compounds and their residuals.

-
plot_sep(fit, lpos = c("topright", "bottomright"))
+
plot_sep(fit, lpos = c("topright", "bottomright"))

Confidence intervals for the parameter estimates are obtained using the mkinparplot function.

-
mkinparplot(fit)
+
mkinparplot(fit)

A comprehensive report of the results is obtained using the summary method for mkinfit objects.

-
summary(fit)
-
## mkin version used for fitting:    0.9.49.5 
+
summary(fit)

+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:23 2019 
-## Date of summary: Thu Jul  4 08:04:24 2019 
+## Date of fit:     Fri Jul  5 15:52:50 2019 
+## Date of summary: Fri Jul  5 15:52:50 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent - k_parent_m1 * parent
@@ -177,19 +175,16 @@
 ## 
 ## Model predictions using solution type deSolve 
 ## 
-## Fitted using 389 model solutions performed in 0.982 s
+## Fitted with method Port using 153 model solutions performed in 0.63 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##                    value   type
-## parent_0      100.750000  state
-## k_parent_sink   0.100000 deparm
-## k_parent_m1     0.100100 deparm
-## k_m1_sink       0.100200 deparm
-## sigma           3.125504  error
+##                  value   type
+## parent_0      100.7500  state
+## k_parent_sink   0.1000 deparm
+## k_parent_m1     0.1001 deparm
+## k_m1_sink       0.1002 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##                        value lower upper
@@ -197,7 +192,6 @@
 ## log_k_parent_sink  -2.302585  -Inf   Inf
 ## log_k_parent_m1    -2.301586  -Inf   Inf
 ## log_k_m1_sink      -2.300587  -Inf   Inf
-## sigma               3.125504     0   Inf
 ## 
 ## Fixed parameter values:
 ##      value  type
@@ -205,38 +199,31 @@
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower   Upper
-## parent_0            99.600    1.57000 96.400 102.800
-## log_k_parent_sink   -3.038    0.07626 -3.193  -2.883
-## log_k_parent_m1     -2.980    0.04033 -3.062  -2.898
-## log_k_m1_sink       -5.248    0.13320 -5.518  -4.977
-## sigma                3.126    0.35850  2.396   3.855
+## parent_0            99.600    1.61400 96.330 102.900
+## log_k_parent_sink   -3.038    0.07826 -3.197  -2.879
+## log_k_parent_m1     -2.980    0.04124 -3.064  -2.897
+## log_k_m1_sink       -5.248    0.13610 -5.523  -4.972
 ## 
 ## Parameter correlation:
-##                     parent_0 log_k_parent_sink log_k_parent_m1
-## parent_0           1.000e+00         6.067e-01      -6.372e-02
-## log_k_parent_sink  6.067e-01         1.000e+00      -8.550e-02
-## log_k_parent_m1   -6.372e-02        -8.550e-02       1.000e+00
-## log_k_m1_sink     -1.688e-01        -6.252e-01       4.731e-01
-## sigma              1.164e-09        -8.908e-10       1.652e-08
-##                   log_k_m1_sink      sigma
-## parent_0             -1.688e-01  1.164e-09
-## log_k_parent_sink    -6.252e-01 -8.908e-10
-## log_k_parent_m1       4.731e-01  1.652e-08
-## log_k_m1_sink         1.000e+00 -1.340e-10
-## sigma                -1.340e-10  1.000e+00
+##                   parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink
+## parent_0           1.00000            0.6075        -0.06625       -0.1701
+## log_k_parent_sink  0.60752            1.0000        -0.08740       -0.6253
+## log_k_parent_m1   -0.06625           -0.0874         1.00000        0.4716
+## log_k_m1_sink     -0.17006           -0.6253         0.47164        1.0000
+## 
+## Residual standard error: 3.211 on 36 degrees of freedom
 ## 
 ## 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      99.600000  63.430 2.298e-36 96.400000 1.028e+02
-## k_parent_sink  0.047920  13.110 6.126e-15  0.041030 5.596e-02
-## k_parent_m1    0.050780  24.800 3.269e-23  0.046780 5.512e-02
-## k_m1_sink      0.005261   7.510 6.165e-09  0.004012 6.898e-03
-## sigma          3.126000   8.718 2.235e-10  2.396000 3.855e+00
+## parent_0      99.600000  61.720 2.024e-38 96.330000 1.029e+02
+## k_parent_sink  0.047920  12.780 3.050e-15  0.040890 5.616e-02
+## k_parent_m1    0.050780  24.250 3.407e-24  0.046700 5.521e-02
+## k_m1_sink      0.005261   7.349 5.758e-09  0.003992 6.933e-03
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   6.398       4 15
 ## parent     6.827       3  6
@@ -273,6 +260,8 @@
 ##    50   parent     0.63   0.71624 -8.624e-02
 ##    75   parent     0.05   0.06074 -1.074e-02
 ##    75   parent     0.06   0.06074 -7.382e-04
+##     0       m1     0.00   0.00000  0.000e+00
+##     0       m1     0.00   0.00000  0.000e+00
 ##     1       m1     4.84   4.80296  3.704e-02
 ##     1       m1     5.64   4.80296  8.370e-01
 ##     3       m1    12.91  13.02400 -1.140e-01
@@ -287,8 +276,8 @@
 ##    35       m1    37.95  43.31312 -5.363e+00
 ##    50       m1    41.19  41.21831 -2.831e-02
 ##    50       m1    40.01  41.21831 -1.208e+00
-##    75       m1    40.09  36.44703  3.643e+00
-##    75       m1    33.85  36.44703 -2.597e+00
+##    75       m1    40.09  36.44704  3.643e+00
+##    75       m1    33.85  36.44704 -2.597e+00
 ##   100       m1    31.04  31.98163 -9.416e-01
 ##   100       m1    33.13  31.98163  1.148e+00
 ##   120       m1    25.15  28.78984 -3.640e+00
diff --git a/docs/articles/FOCUS_D_files/figure-html/plot-1.png b/docs/articles/FOCUS_D_files/figure-html/plot-1.png
index fc1142ab..c0c6e567 100644
Binary files a/docs/articles/FOCUS_D_files/figure-html/plot-1.png and b/docs/articles/FOCUS_D_files/figure-html/plot-1.png differ
diff --git a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png
index 97c61a16..9caac2b9 100644
Binary files a/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png and b/docs/articles/FOCUS_D_files/figure-html/plot_2-1.png differ
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index 0060bd69..73ea645a 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -30,7 +30,7 @@
       
       
         mkin
-        0.9.49.5
+        0.9.49.6
       
     
 
@@ -88,7 +88,7 @@
       
Example evaluation of FOCUS Laboratory Data L1 to L3

                         
Johannes Ranke

             
-            
2019-07-04

+            
2019-07-05

       
       
       
@@ -112,59 +112,54 @@
 
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:    0.9.49.5 
+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:26 2019 
-## Date of summary: Thu Jul  4 08:04:26 2019 
+## Date of fit:     Fri Jul  5 15:52:52 2019 
+## Date of summary: Fri Jul  5 15:52:52 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.278 s
+## Fitted with method Port using 37 model solutions performed in 0.084 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##                   value   type
-## parent_0      89.850000  state
-## k_parent_sink  0.100000 deparm
-## sigma          2.779827  error
+##               value   type
+## parent_0      89.85  state
+## k_parent_sink  0.10 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##                       value lower upper
 ## parent_0          89.850000  -Inf   Inf
 ## log_k_parent_sink -2.302585  -Inf   Inf
-## sigma              2.779827     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower  Upper
-## parent_0            92.470    1.28200 89.740 95.200
-## log_k_parent_sink   -2.347    0.03763 -2.428 -2.267
-## sigma                2.780    0.46330  1.792  3.767
+## parent_0            92.470    1.36800 89.570 95.370
+## log_k_parent_sink   -2.347    0.04057 -2.433 -2.261
 ## 
 ## 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 log_k_parent_sink
+## parent_0            1.0000            0.6248
+## log_k_parent_sink   0.6248            1.0000
+## 
+## Residual standard error: 2.948 on 16 degrees of freedom
 ## 
 ## 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      92.47000   72.13 8.824e-21 89.74000 95.2000
-## k_parent_sink  0.09561   26.57 2.487e-14  0.08824  0.1036
-## sigma          2.78000    6.00 1.216e-05  1.79200  3.7670
+## parent_0      92.47000   67.58 2.170e-21 89.57000 95.3700
+## k_parent_sink  0.09561   24.65 1.867e-14  0.08773  0.1042
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.424       2  7
 ## parent     3.424       2  7
@@ -205,22 +200,18 @@
 

 
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:
+
## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation by method Port did not converge:
 ## false convergence (8)

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

 

 
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$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful

-
## mkin version used for fitting:    0.9.49.5 
+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:28 2019 
-## Date of summary: Thu Jul  4 08:04:28 2019 
+## Date of fit:     Fri Jul  5 15:52:54 2019 
+## Date of summary: Fri Jul  5 15:52:54 2019 
 ## 
 ## 
-## Warning: Optimisation did not converge:
+## Warning: Optimisation by method Port did not converge:
 ## false convergence (8) 
 ## 
 ## 
@@ -229,54 +220,49 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 899 model solutions performed in 1.876 s
+## Fitted with method Port using 741 model solutions performed in 1.637 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##              value   type
-## parent_0 89.850000  state
-## alpha     1.000000 deparm
-## beta     10.000000 deparm
-## sigma     2.779871  error
+##          value   type
+## parent_0 89.85  state
+## alpha     1.00 deparm
+## beta     10.00 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  89.850000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
-## sigma      2.779871     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## 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
+##           Estimate Std. Error    Lower   Upper
+## parent_0     92.47      1.454    89.37   95.57
+## log_alpha    10.58   1164.000 -2471.00 2492.00
+## log_beta     12.93   1164.000 -2469.00 2495.00
 ## 
 ## 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
+## parent_0    1.0000    0.2361   0.2361
+## log_alpha   0.2361    1.0000   1.0000
+## log_beta    0.2361    1.0000   1.0000
+## 
+## Residual standard error: 3.045 on 15 degrees of freedom
 ## 
 ## 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     92.47 65.32000 3.886e-20 89.37 95.57
+## alpha     39440.00  0.01639 4.936e-01  0.00   Inf
+## beta     412500.00  0.01639 4.936e-01  0.00   Inf
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.619       3  6
 ## parent     3.619       3  6
@@ -292,19 +278,19 @@
 

 Laboratory Data L2

 
The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:

-
+
 

 

 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.

@@ -314,69 +300,64 @@
 

 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:    0.9.49.5 
+
summary(m.L2.FOMC, data = FALSE)

+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:29 2019 
-## Date of summary: Thu Jul  4 08:04:29 2019 
+## Date of fit:     Fri Jul  5 15:52:55 2019 
+## Date of summary: Fri Jul  5 15:52:55 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.486 s
-## 
-## Error model: Constant variance 
+## Fitted with method Port using 81 model solutions performed in 0.178 s
 ## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##              value   type
-## parent_0 93.950000  state
-## alpha     1.000000 deparm
-## beta     10.000000 deparm
-## sigma     2.275722  error
+##          value   type
+## parent_0 93.95  state
+## alpha     1.00 deparm
+## beta     10.00 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  93.950000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
-## sigma      2.275722     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error    Lower   Upper
-## parent_0   93.7700     1.6130 90.05000 97.4900
-## log_alpha   0.3180     0.1559 -0.04149  0.6776
-## log_beta    0.2102     0.2493 -0.36460  0.7850
-## sigma       2.2760     0.4645  1.20500  3.3470
+##           Estimate Std. Error   Lower   Upper
+## parent_0   93.7700     1.8560 89.5700 97.9700
+## log_alpha   0.3180     0.1867 -0.1044  0.7405
+## log_beta    0.2102     0.2943 -0.4555  0.8759
 ## 
 ## Parameter correlation:
-##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-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
+##           parent_0 log_alpha log_beta
+## parent_0   1.00000  -0.09553  -0.1863
+## log_alpha -0.09553   1.00000   0.9757
+## log_beta  -0.18628   0.97567   1.0000
+## 
+## Residual standard error: 2.628 on 9 degrees of freedom
 ## 
 ## 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   93.770  58.120 4.267e-12 90.0500 97.490
-## alpha       1.374   6.414 1.030e-04  0.9594  1.969
-## beta        1.234   4.012 1.942e-03  0.6945  2.192
-## sigma       2.276   4.899 5.977e-04  1.2050  3.347
+## parent_0   93.770  50.510 1.173e-12 89.5700 97.970
+## alpha       1.374   5.355 2.296e-04  0.9009  2.097
+## beta        1.234   3.398 3.949e-03  0.6341  2.401
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   6.205       3  3
 ## parent     6.205       3  3
@@ -390,15 +371,17 @@
 

 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:    0.9.49.5 
+
summary(m.L2.DFOP, data = FALSE)

+
## Warning in summary.mkinfit(m.L2.DFOP, data = FALSE): Could not estimate
+## covariance matrix; singular system.

+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:30 2019 
-## Date of summary: Thu Jul  4 08:04:30 2019 
+## Date of fit:     Fri Jul  5 15:52:56 2019 
+## Date of summary: Fri Jul  5 15:52:56 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -407,19 +390,16 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 572 model solutions performed in 1.19 s
+## Fitted with method Port using 336 model solutions performed in 0.752 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##              value   type
-## parent_0 93.950000  state
-## k1        0.100000 deparm
-## k2        0.010000 deparm
-## g         0.500000 deparm
-## sigma     1.413899  error
+##          value   type
+## parent_0 93.95  state
+## k1        0.10 deparm
+## k2        0.01 deparm
+## g         0.50 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##              value lower upper
@@ -427,39 +407,32 @@
 ## log_k1   -2.302585  -Inf   Inf
 ## log_k2   -4.605170  -Inf   Inf
 ## g_ilr     0.000000  -Inf   Inf
-## sigma     1.413899     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## 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_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
+##          Estimate Std. Error Lower Upper
+## parent_0  93.9500         NA    NA    NA
+## log_k1     3.1370         NA    NA    NA
+## log_k2    -1.0880         NA    NA    NA
+## g_ilr     -0.2821         NA    NA    NA
 ## 
 ## 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
+## Could not estimate covariance matrix; singular system.
+## Residual standard error: 1.732 on 8 degrees of freedom
 ## 
 ## 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  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        23.0400 4.303e-04 4.998e-01  0.0000     Inf
-## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
-## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
-## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
-## 
-## FOCUS Chi2 error levels in percent:
+##          Estimate t value Pr(>t) Lower Upper
+## parent_0  93.9500      NA     NA    NA    NA
+## k1        23.0400      NA     NA    NA    NA
+## k2         0.3369      NA     NA    NA    NA
+## g          0.4016      NA     NA    NA    NA
+## 
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data    2.53       4  2
 ## parent      2.53       4  2
@@ -474,18 +447,18 @@
 

 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.

 

@@ -494,11 +467,11 @@
 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:    0.9.49.5 
+
summary(mm.L3[["DFOP", 1]])

+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:32 2019 
-## Date of summary: Thu Jul  4 08:04:32 2019 
+## Date of fit:     Fri Jul  5 15:52:56 2019 
+## Date of summary: Fri Jul  5 15:52:57 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -507,19 +480,16 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 373 model solutions performed in 0.773 s
+## Fitted with method Port using 137 model solutions performed in 0.305 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##              value   type
-## parent_0 97.800000  state
-## k1        0.100000 deparm
-## k2        0.010000 deparm
-## g         0.500000 deparm
-## sigma     1.017292  error
+##          value   type
+## parent_0 97.80  state
+## k1        0.10 deparm
+## k2        0.01 deparm
+## g         0.50 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##              value lower upper
@@ -527,39 +497,37 @@
 ## log_k1   -2.302585  -Inf   Inf
 ## log_k2   -4.605170  -Inf   Inf
 ## g_ilr     0.000000  -Inf   Inf
-## sigma     1.017292     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error   Lower      Upper
-## parent_0  97.7500    1.01900 94.5000 101.000000
-## log_k1    -0.6612    0.10050 -0.9812  -0.341300
-## log_k2    -4.2860    0.04322 -4.4230  -4.148000
-## g_ilr     -0.1229    0.03727 -0.2415  -0.004343
-## sigma      1.0170    0.25430  0.2079   1.827000
+##          Estimate Std. Error   Lower     Upper
+## parent_0  97.7500    1.43800 93.7500 101.70000
+## log_k1    -0.6612    0.13340 -1.0310  -0.29100
+## log_k2    -4.2860    0.05902 -4.4500  -4.12200
+## g_ilr     -0.1229    0.05121 -0.2651   0.01925
 ## 
 ## 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  log_k1   log_k2   g_ilr
+## parent_0  1.00000  0.1640  0.01315  0.4253
+## log_k1    0.16400  1.0000  0.46478 -0.5526
+## log_k2    0.01315  0.4648  1.00000 -0.6631
+## g_ilr     0.42526 -0.5526 -0.66310  1.0000
+## 
+## Residual standard error: 1.439 on 4 degrees of freedom
 ## 
 ## 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 97.75000  95.960 1.248e-06 94.50000 101.00000
-## k1        0.51620   9.947 1.081e-03  0.37490   0.71090
-## k2        0.01376  23.140 8.840e-05  0.01199   0.01579
-## g         0.45660  34.920 2.581e-05  0.41540   0.49850
-## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
+## parent_0 97.75000  67.970 1.404e-07 93.75000 101.70000
+## k1        0.51620   7.499 8.460e-04  0.35650   0.74750
+## k2        0.01376  16.940 3.557e-05  0.01168   0.01621
+## g         0.45660  25.410 7.121e-06  0.40730   0.50680
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   2.225       4  4
 ## parent     2.225       4  4
@@ -578,7 +546,7 @@
 ##    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.

@@ -588,72 +556,67 @@
 

 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:    0.9.49.5 
+
summary(mm.L4[["SFO", 1]], data = FALSE)

+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:33 2019 
-## Date of summary: Thu Jul  4 08:04:33 2019 
+## Date of fit:     Fri Jul  5 15:52:57 2019 
+## Date of summary: Fri Jul  5 15:52:57 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.29 s
+## Fitted with method Port using 46 model solutions performed in 0.1 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##                  value   type
-## parent_0      96.60000  state
-## k_parent_sink  0.10000 deparm
-## sigma          3.16181  error
+##               value   type
+## parent_0       96.6  state
+## k_parent_sink   0.1 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##                       value lower upper
 ## parent_0          96.600000  -Inf   Inf
 ## log_k_parent_sink -2.302585  -Inf   Inf
-## sigma              3.161810     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##                   Estimate Std. Error  Lower   Upper
-## parent_0            96.440    1.69900 92.070 100.800
-## log_k_parent_sink   -5.030    0.07059 -5.211  -4.848
-## sigma                3.162    0.79050  1.130   5.194
+## parent_0             96.44    1.94900 91.670 101.200
+## log_k_parent_sink    -5.03    0.07999 -5.225  -4.834
 ## 
 ## 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 log_k_parent_sink
+## parent_0            1.0000            0.5865
+## log_k_parent_sink   0.5865            1.0000
+## 
+## Residual standard error: 3.651 on 6 degrees of freedom
 ## 
 ## 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      96.440000   56.77 1.604e-08 92.070000 1.008e+02
-## k_parent_sink  0.006541   14.17 1.578e-05  0.005455 7.842e-03
-## sigma          3.162000    4.00 5.162e-03  1.130000 5.194e+00
+## parent_0      96.440000   49.49 2.283e-09 91.670000 1.012e+02
+## k_parent_sink  0.006541   12.50 8.008e-06  0.005378 7.955e-03
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.287       2  6
 ## parent     3.287       2  6
@@ -665,65 +628,60 @@
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352

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

-
## mkin version used for fitting:    0.9.49.5 
+
summary(mm.L4[["FOMC", 1]], data = FALSE)

+
## mkin version used for fitting:    0.9.48.1 
 ## R version used for fitting:       3.6.0 
-## Date of fit:     Thu Jul  4 08:04:33 2019 
-## Date of summary: Thu Jul  4 08:04:33 2019 
+## Date of fit:     Fri Jul  5 15:52:57 2019 
+## Date of summary: Fri Jul  5 15:52:57 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.453 s
+## Fitted with method Port using 66 model solutions performed in 0.145 s
 ## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: d_3 
+## Weighting: none
 ## 
 ## Starting values for parameters to be optimised:
-##              value   type
-## parent_0 96.600000  state
-## alpha     1.000000 deparm
-## beta     10.000000 deparm
-## sigma     1.830055  error
+##          value   type
+## parent_0  96.6  state
+## alpha      1.0 deparm
+## beta      10.0 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  96.600000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
-## sigma      1.830055     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error   Lower    Upper
-## parent_0   99.1400     1.2670 95.6300 102.7000
-## log_alpha  -0.3506     0.2616 -1.0770   0.3756
-## log_beta    4.1740     0.3938  3.0810   5.2670
-## sigma       1.8300     0.4575  0.5598   3.1000
+##           Estimate Std. Error  Lower    Upper
+## parent_0   99.1400     1.6800 94.820 103.5000
+## log_alpha  -0.3506     0.3725 -1.308   0.6068
+## log_beta    4.1740     0.5635  2.726   5.6230
 ## 
 ## 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 log_alpha log_beta
+## parent_0    1.0000   -0.5365  -0.6083
+## log_alpha  -0.5365    1.0000   0.9913
+## log_beta   -0.6083    0.9913   1.0000
+## 
+## Residual standard error: 2.315 on 5 degrees of freedom
 ## 
 ## 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  99.1400  78.250 7.993e-08 95.6300 102.700
-## alpha      0.7042   3.823 9.365e-03  0.3407   1.456
-## beta      64.9800   2.540 3.201e-02 21.7800 193.900
-## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
+## parent_0  99.1400  59.020 1.322e-08 94.8200 103.500
+## alpha      0.7042   2.685 2.178e-02  0.2703   1.835
+## beta      64.9800   1.775 6.807e-02 15.2600 276.600
 ## 
-## FOCUS Chi2 error levels in percent:
+## Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   2.029       3  5
 ## parent     2.029       3  5
diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png
index f23a4c97..7e231d84 100644
Binary files a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png and b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png differ
diff --git a/docs/articles/index.html b/docs/articles/index.html
index c2982f4b..95828a82 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -60,7 +60,7 @@
       
       
         mkin
-        0.9.49.5
+        0.9.49.6
       
     

 
diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index 8ad4a8e9..b2df33b7 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -30,7 +30,7 @@
       
       
         mkin
-        0.9.49.5
+        0.9.49.6
       
     
 
@@ -88,7 +88,7 @@
       
Introduction to mkin

                         
Johannes Ranke

             
-            
2019-07-04

+            
2019-07-05

       
       
       
@@ -101,7 +101,7 @@
 

 

 Abstract

-
In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The R add-on package mkin (Ranke 2016) implements fitting some of the models recommended in this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.

+
In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The R add-on package mkin implements fitting some of the models recommended in this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.

 
library("mkin", quietly = TRUE)
 # Define the kinetic model
 m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
@@ -136,24 +136,26 @@
 

 Background

 
Many approaches are possible regarding the evaluation of chemical degradation data.

-
The mkin package (Ranke 2016) implements the approach recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe (FOCUS Work Group on Degradation Kinetics 2006, 2014) implements this approach for simple decline data series, data series with transformation products, commonly termed metabolites, data series for more than one compartment. It is also possible to include back reactions, so equilibrium reactions and equilibrium partitioning can be specified, although this oftentimes leads to an overparameterisation of the model.

+
The mkin package (Ranke 2019) implements the approach recommended in the kinetics report provided by the FOrum for Co-ordination of pesticide fate models and their USe (FOCUS Work Group on Degradation Kinetics 2006, 2014) for simple decline data series, data series with transformation products, commonly termed metabolites, and for data series for more than one compartment. It is also possible to include back reactions, so equilibrium reactions and equilibrium partitioning can be specified, although this oftentimes leads to an overparameterisation of the model.

 
When the first mkin code was published in 2010, the most commonly used tools for fitting more complex kinetic degradation models to experimental data were KinGUI (Schäfer et al. 2007), a MATLAB based tool with a graphical user interface that was specifically tailored to the task and included some output as proposed by the FOCUS Kinetics Workgroup, and ModelMaker, a general purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.

 
The code was first uploaded to the BerliOS platform. When this was taken down, the version control history was imported into the R-Forge site (see e.g. the initial commit on 11 May 2010), where the code is still occasionally updated.

-
At that time, the R package FME (Flexible Modelling Environment) (Soetaert and Petzoldt 2010) was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the relative standard deviation that has to be assumed for the residuals, such that the \(\chi^2\) goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass using an significance level \(\alpha\) of 0.05.

-
Also, mkin introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to mkin for the case of linear differential equations (i.e. where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases.

+
At that time, the R package FME (Flexible Modelling Environment) (Soetaert and Petzoldt 2010) was already available, and provided a good basis for developing a package specifically tailored to the task. The remaining challenge was to make it as easy as possible for the users (including the author of this vignette) to specify the system of differential equations and to include the output requested by the FOCUS guidance, such as the relative standard deviation that has to be assumed for the residuals, such that the \(\chi^2\) goodness-of-fit test as defined by the FOCUS kinetics workgroup would pass using an significance level \(\alpha\) of 0.05. This relative error, expressed as a percentage, is often termed \(\chi^2\) error level or similar.

+
Also, mkin introduced using analytical solutions for parent only kinetics for improved optimization speed. Later, Eigenvalue based solutions were introduced to mkin for the case of linear differential equations (i.e. where the FOMC or DFOP models were not used for the parent compound), greatly improving the optimization speed for these cases. This, however, has become somehow obsolete, as the use of compiled code described below gives even smaller execution times.

 
The possibility to specify back-reactions and a biphasic model (SFORB) for metabolites were present in mkin from the very beginning.

 

 

 Derived software tools

 
Soon after the publication of mkin, two derived tools were published, namely KinGUII (available from Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical user interface (GUI), and added fitting by iteratively reweighted least squares (IRLS) and characterisation of likely parameter distributions by Markov Chain Monte Carlo (MCMC) sampling.

-
CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.2 of CAKE release in March 2016 uses a basic scheme for up to six metabolites in a flexible arrangement, but does not support back-reactions (non-instantaneous equilibria) or biphasic kinetics for metabolites.

+
CAKE focuses on a smooth use experience, sacrificing some flexibility in the model definition, originally allowing only two primary metabolites in parallel. The current version 3.3 of CAKE release in March 2016 uses a basic scheme for up to six metabolites in a flexible arrangement, but does not support back-reactions (non-instantaneous equilibria) or biphasic kinetics for metabolites.

 
KinGUI offers an even more flexible widget for specifying complex kinetic models. Back-reactions (non-instanteneous equilibria) were supported early on, but until 2014, only simple first-order models could be specified for transformation products. Starting with KinGUII version 2.1, biphasic modelling of metabolites was also available in KinGUII.

 
A further graphical user interface (GUI) that has recently been brought to a decent degree of maturity is the browser based GUI named gmkin. Please see its documentation page and manual for further information.

+
A comparison of scope, usability and numerical results obtained with these tools has been recently been published by Ranke, Wöltjen, and Meinecke (2018).

 

 

 

 Recent developments

-
Currently (June 2016), the main features available in mkin which are not present in KinGUII or CAKE, are the speed increase by using compiled code when a compiler is present, parallel model fitting on multicore machines using the mmkin function, and the estimation of parameter confidence intervals based on transformed parameters. These are explained in more detail below.

+
Currently (July 2019), the main features available in mkin which are not present in KinGUII or CAKE, are the speed increase by using compiled code when a compiler is present, parallel model fitting on multicore machines using the mmkin function, and the estimation of parameter confidence intervals based on transformed parameters.

+
In addition, the possibility to use two alternative error models to constant variance have been integrated. The variance by variable error model introduced by Gao et al. (2011) has been available via an iteratively reweighted least squares (IRLS) procedure since mkin version 0.9-22. With release 0.9.49.5, the IRLS algorithm has been replaced by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a two-component error model inspired by error models developed in analytical chemistry.

 

 

 

@@ -193,8 +195,11 @@
 

 
———. 2014. Generic Guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in Eu Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.

 

+

+
Gao, Z., J.W. Green, J. Vanderborght, and W. Schmitt. 2011. “Improving Uncertainty Analysis in Kinetic Evaluations Using Iteratively Reweighted Least Squares.” Journal. Environmental Science and Technology 45: 4429–37.

+

 

-
Ranke, J. 2016. ‘Mkin‘: Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.

+
Ranke, J. 2019. ‘mkin‘: Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.

 

 

 
Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In SETAC World 20-24 May. Berlin.

@@ -202,6 +207,9 @@
 

 
———. 2015. “To T-Test or Not to T-Test, That Is the Question.” In XV Symposium on Pesticide Chemistry 2-4 September 2015. Piacenza. http://chem.uft.uni-bremen.de/ranke/posters/piacenza_2015.pdf.

 

+

+
Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” Environmental Sciences Europe 30 (1): 17. https://doi.org/10.1186/s12302-018-0145-1.

+

 

 
Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. “KinGUI: A New Kinetic Software Tool for Evaluations According to FOCUS Degradation Kinetics.” In Proceedings of the Xiii Symposium Pesticide Chemistry, edited by Del Re A. A. M., Capri E., Fragoulis G., and Trevisan M., 916–23. Piacenza.

 

diff --git a/docs/articles/twa.html b/docs/articles/twa.html
index 98e5efdf..fabae1bc 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -30,7 +30,7 @@
       
       
         mkin
-        0.9.49.5
+        0.9.49.6
       
     

 
@@ -88,7 +88,7 @@
       
Calculation of time weighted average concentrations with mkin

                         
Johannes Ranke

             
-            
2019-07-04

+            
2019-07-05

       
       
       
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index 4a856b71..2a59b69d 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -30,7 +30,7 @@
       
       
         mkin
-        0.9.49.5
+        0.9.49.6
       
     

 
@@ -88,7 +88,7 @@
       
Example evaluation of FOCUS dataset Z

                         
Johannes Ranke

             
-            
2019-07-04

+            
2019-07-05

       
       
       
@@ -125,92 +125,82 @@
 
Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
                 Z1 = mkinsub("SFO"))

 
## Successfully compiled differential equation model from auto-generated C code.

-
m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)

-
## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
-## with value of zero were removed from the data

-
plot_sep(m.Z.2a)

+
m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot_sep(m.Z.2a)

 

-
summary(m.Z.2a, data = FALSE)$bpar

-
##             Estimate se_notrans    t value     Pr(>t)    Lower    Upper
-## Z0_0      9.7015e+01   3.393176 2.8591e+01 6.4352e-21 91.66556 102.3642
-## k_Z0_sink 7.2231e-10   0.225254 3.2067e-09 5.0000e-01  0.00000      Inf
-## k_Z0_Z1   2.2360e+00   0.159134 1.4051e+01 1.1369e-13  1.95303   2.5600
-## k_Z1_sink 4.8212e-01   0.065454 7.3658e+00 5.1186e-08  0.40341   0.5762
-## sigma     4.8041e+00   0.637618 7.5345e+00 3.4431e-08  3.52677   6.0815

+
summary(m.Z.2a, data = FALSE)$bpar

+
##             Estimate se_notrans    t value     Pr(>t)   Lower     Upper
+## Z0_0      9.7015e+01   3.553140 2.7304e+01 1.6792e-21 91.4112 102.61853
+## k_Z0_sink 7.2008e-10   0.226895 3.1736e-09 5.0000e-01  0.0000       Inf
+## k_Z0_Z1   2.2360e+00   0.165074 1.3545e+01 7.3943e-14  1.8393   2.71827
+## k_Z1_sink 4.8212e-01   0.065854 7.3212e+00 3.5520e-08  0.4006   0.58023

 
As obvious from the parameter summary (the  component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink.

 
A similar result can be obtained when formation fractions are used in the model formulation:

-
+
 
## Successfully compiled differential equation model from auto-generated C code.

-
m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)

-
## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
-## with value of zero were removed from the data

-
plot_sep(m.Z.2a.ff)

+
m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot_sep(m.Z.2a.ff)

 

-
summary(m.Z.2a.ff, data = FALSE)$bpar

-
##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
-## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
-## k_Z1        0.48212   0.063265  7.6207 2.8155e-08  0.40341   0.5762
-## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
-## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815

+
summary(m.Z.2a.ff, data = FALSE)$bpar

+
## Warning in summary.mkinfit(m.Z.2a.ff, data = FALSE): Could not estimate
+## covariance matrix; singular system.

+
##            Estimate se_notrans t value     Pr(>t) Lower Upper
+## Z0_0       97.01488   3.553145 27.3040 1.6793e-21    NA    NA
+## k_Z0        2.23601   0.216848 10.3114 3.6620e-11    NA    NA
+## k_Z1        0.48212   0.065854  7.3211 3.5520e-08    NA    NA
+## f_Z0_to_Z1  1.00000   0.101473  9.8548 9.7068e-11    NA    NA

 
Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.

 
A simplified model is obtained by removing the pathway to the sink. 

 
In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.

-
Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-               Z1 = mkinsub("SFO"), use_of_ff = "max")

+
Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO"), use_of_ff = "max")

 
## Successfully compiled differential equation model from auto-generated C code.

-
m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE)

-
## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data

-
plot_sep(m.Z.3)

+
m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot_sep(m.Z.3)

 

-
summary(m.Z.3, data = FALSE)$bpar

-
##       Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0  97.01488   2.597342  37.352 2.0106e-24 91.67597 102.3538
-## k_Z0   2.23601   0.146904  15.221 9.1477e-15  1.95354   2.5593
-## k_Z1   0.48212   0.041727  11.554 4.8268e-12  0.40355   0.5760
-## sigma  4.80411   0.620208   7.746 1.6110e-08  3.52925   6.0790

+
summary(m.Z.3, data = FALSE)$bpar

+
##      Estimate se_notrans t value     Pr(>t)    Lower   Upper
+## Z0_0 97.01488   2.681770  36.176 2.3636e-25 91.52153 102.508
+## k_Z0  2.23601   0.146862  15.225 2.2469e-15  1.95453   2.558
+## k_Z1  0.48212   0.042687  11.294 3.0685e-12  0.40216   0.578

 
As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.

 

 

 

 Metabolites Z2 and Z3

 
As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.

-
Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-               Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-               Z2 = mkinsub("SFO"), use_of_ff = "max")

+
Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+               Z2 = mkinsub("SFO"), use_of_ff = "max")

 
## Successfully compiled differential equation model from auto-generated C code.

-
m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)

-
## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with
-## value of zero were removed from the data

-
plot_sep(m.Z.5)

+
m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot_sep(m.Z.5)

 

 
Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization.

-
Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-                   Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                   Z2 = mkinsub("SFO", "Z3"),
-                   Z3 = mkinsub("SFO"),
-                   use_of_ff = "max")

+
Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                   Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                   Z2 = mkinsub("SFO", "Z3"),
+                   Z3 = mkinsub("SFO"),
+                   use_of_ff = "max")

 
## Successfully compiled differential equation model from auto-generated C code.

-
-
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.
-## 5$bparms.ode, : Observations with value of zero were removed from the data

-
plot_sep(m.Z.FOCUS)

+
+
## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation by method Port did not converge:
+## false convergence (8)

+
plot_sep(m.Z.FOCUS)

 

-
summary(m.Z.FOCUS, data = FALSE)$bpar

-
##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
-## Z0_0       96.838607   1.994273 48.5584 4.0283e-42 92.826626 100.850589
-## k_Z0        2.215405   0.118459 18.7018 1.0415e-23  1.989465   2.467003
-## k_Z1        0.478300   0.028257 16.9267 6.2408e-22  0.424701   0.538662
-## k_Z2        0.451618   0.042138 10.7177 1.6308e-14  0.374328   0.544867
-## k_Z3        0.058693   0.015246  3.8498 1.7806e-04  0.034805   0.098978
-## f_Z2_to_Z3  0.471508   0.058352  8.0804 9.6648e-11  0.357735   0.588320
-## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736

-
endpoints(m.Z.FOCUS)

+
summary(m.Z.FOCUS, data = FALSE)$bpar

+
##             Estimate se_notrans t value     Pr(>t)     Lower     Upper
+## Z0_0       96.838695   2.058856 47.0352 5.5825e-44 92.705465 100.97192
+## k_Z0        2.215407   0.118130 18.7540 7.7427e-25  1.990629   2.46557
+## k_Z1        0.478300   0.029289 16.3305 3.3382e-22  0.422974   0.54086
+## k_Z2        0.451619   0.044213 10.2146 3.1113e-14  0.371037   0.54970
+## k_Z3        0.058693   0.014295  4.1058 7.2882e-05  0.035996   0.09570
+## f_Z2_to_Z3  0.471507   0.057053  8.2643 2.8118e-11  0.360388   0.58552

+
endpoints(m.Z.FOCUS)

 
## $ff
 ##   Z2_Z3 Z2_sink 
 ## 0.47151 0.52849 
@@ -222,8 +212,8 @@
 ##        DT50    DT90
 ## Z0  0.31288  1.0394
 ## Z1  1.44919  4.8141
-## Z2  1.53481  5.0985
-## Z3 11.80965 39.2308

+## Z2  1.53480  5.0985
+## Z3 11.80969 39.2310

 
This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however.

 
 

@@ -231,116 +221,77 @@
 Using the SFORB model
 
As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.

 
Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the \(\chi^2\) error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned.

-
Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))

+
Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))

 
## Successfully compiled differential equation model from auto-generated C code.

-
m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE)

-
## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
-## with value of zero were removed from the data

-
plot_sep(m.Z.mkin.1)

+
m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot_sep(m.Z.mkin.1)

 

-
summary(m.Z.mkin.1, data = FALSE)$cov.unscaled

-
##                            Z0_0 log_k_Z0_Z1 log_k_Z1_Z2 log_k_Z2_sink
-## Z0_0                 3.8375e+00  5.4918e-03  3.0584e-02    1.2969e-01
-## log_k_Z0_Z1          5.4918e-03  2.7613e-03 -1.8820e-04    2.6634e-04
-## log_k_Z1_Z2          3.0584e-02 -1.8820e-04  3.3807e-03    3.2177e-03
-## log_k_Z2_sink        1.2969e-01  2.6634e-04  3.2177e-03    3.4256e-02
-## log_k_Z2_Z3_free    -2.4223e-02 -2.6169e-04 -1.1845e-03   -8.1134e-03
-## log_k_Z3_free_sink  -6.5467e-02 -4.0815e-04 -3.2978e-03   -3.6010e-02
-## log_k_Z3_free_bound -6.0659e-02 -4.4768e-04 -3.0588e-03   -3.9074e-02
-## log_k_Z3_bound_free  5.2844e-01  4.5458e-03  7.9800e-03    4.6274e-02
-## sigma                2.0366e-10 -3.4658e-10  8.9910e-11   -2.5946e-10
-##                     log_k_Z2_Z3_free log_k_Z3_free_sink
-## Z0_0                     -2.4223e-02        -6.5467e-02
-## log_k_Z0_Z1              -2.6169e-04        -4.0815e-04
-## log_k_Z1_Z2              -1.1845e-03        -3.2978e-03
-## log_k_Z2_sink            -8.1134e-03        -3.6010e-02
-## log_k_Z2_Z3_free          1.5500e-02         2.1583e-02
-## log_k_Z3_free_sink        2.1583e-02         7.5705e-02
-## log_k_Z3_free_bound       2.5836e-02         1.1964e-01
-## log_k_Z3_bound_free       5.2534e-02         2.9441e-01
-## sigma                     1.3063e-10         3.4170e-10
-##                     log_k_Z3_free_bound log_k_Z3_bound_free       sigma
-## Z0_0                        -6.0659e-02          5.2844e-01  2.0366e-10
-## log_k_Z0_Z1                 -4.4768e-04          4.5458e-03 -3.4658e-10
-## log_k_Z1_Z2                 -3.0588e-03          7.9800e-03  8.9910e-11
-## log_k_Z2_sink               -3.9074e-02          4.6274e-02 -2.5946e-10
-## log_k_Z2_Z3_free             2.5836e-02          5.2534e-02  1.3063e-10
-## log_k_Z3_free_sink           1.1964e-01          2.9441e-01  3.4170e-10
-## log_k_Z3_free_bound          6.5902e-01          5.4737e+00 -6.7704e-10
-## log_k_Z3_bound_free          5.4737e+00          2.8722e+08  7.2421e-02
-## sigma                       -6.7704e-10          7.2421e-02  1.4170e-01

+
summary(m.Z.mkin.1, data = FALSE)$cov.unscaled

+
## Warning in summary.mkinfit(m.Z.mkin.1, data = FALSE): Could not estimate
+## covariance matrix; singular system.

+
## NULL

 
Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model.

-
Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO"))

+
Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO"))

 
## Successfully compiled differential equation model from auto-generated C code.

-
m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)

-
## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations
-## with value of zero were removed from the data

-
plot_sep(m.Z.mkin.3)

+
m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
+plot_sep(m.Z.mkin.3)

 

 
This results in a much better representation of the behaviour of the parent compound Z0.

 
Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models.

-
Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFO"))

+
Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFO"))

 
## Successfully compiled differential equation model from auto-generated C code.

-
-
## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
-## 3$bparms.ode, : Observations with value of zero were removed from the data

-
plot_sep(m.Z.mkin.4)

+
 

 
The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase.

-
Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))

+
Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))

 
## Successfully compiled differential equation model from auto-generated C code.

-
-
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
-## 4$bparms.ode[1:4], : Observations with value of zero were removed from the
-## data

-
plot_sep(m.Z.mkin.5)

+
 

 
The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized  is excessively small, it seems reasonable to fix it to zero.

-
-
## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
-## 5$bparms.ode[1:7], : Observations with value of zero were removed from the
-## data

-
plot_sep(m.Z.mkin.5a)

+
m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+                       parms.ini = c(m.Z.mkin.5$bparms.ode[1:7],
+                                     k_Z3_bound_free = 0),
+                       fixed_parms = "k_Z3_bound_free",
+                       quiet = TRUE)
+plot_sep(m.Z.mkin.5a)

 

 
As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model  is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report.

 
A graphical representation of the confidence intervals can finally be obtained.

-
mkinparplot(m.Z.mkin.5a)

+
mkinparplot(m.Z.mkin.5a)

 

 
The endpoints obtained with this model are

-
endpoints(m.Z.mkin.5a)

+
endpoints(m.Z.mkin.5a)

 
## $ff
 ##   Z0_free_Z1        Z1_Z2      Z2_sink   Z2_Z3_free Z3_free_sink 
 ##      1.00000      1.00000      0.46344      0.53656      1.00000 
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471381 0.0075124 0.0800075 0.0000000 
+## 2.4471359 0.0075125 0.0800071 0.0000000 
 ## 
 ## $distimes
 ##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848    0.28325     92.267         NA         NA
+## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
 ## Z1 1.5148 5.0320         NA         NA         NA         NA
 ## Z2 1.6414 5.4526         NA         NA         NA         NA
-## Z3     NA     NA         NA         NA     8.6635        Inf

+## Z3     NA     NA         NA         NA     8.6636        Inf

 
It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. However, this appears to be a feature of the data.

 
 

diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png
index 471db177..2df6eb44 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png
index 3c983f21..7090c421 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png
index 0e0a78a9..7b98d13d 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png
index d7dd85a5..bce36d10 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png
index 7764f4e2..415f29f0 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png
index d24b8a40..3f49dfa6 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png
index dd8c1e0a..41c863dc 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png
index 45a32027..d898f299 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png
index 18832ed2..3e58f8b6 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png
index 0d3b4d1a..f7e57fb3 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png differ
diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png
index 898e6190..c61388ab 100644
Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png differ
diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html
index 3f6ff8b9..c614166d 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -30,7 +30,7 @@
       
       
         mkin
-        0.9.49.5
+        0.9.49.6
       
     

 
@@ -88,7 +88,7 @@
       
Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance

                         
Johannes Ranke

             
-            
2019-07-04

+            
2019-07-05

       
       
       
@@ -111,11 +111,13 @@
 

 Example on page 5, upper panel

 
p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])

+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p5a)

+
plot(p5a)

 

-
print(p5a)

+
print(p5a)

 
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 465.21753  56.27506  32.06401 
@@ -126,24 +128,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       95.8401 4.67e-21 92.245 99.4357
-## k_parent_sink   0.0102 3.92e-12  0.009  0.0117
-## sigma           4.8230 3.81e-06  3.214  6.4318
+## parent_0       95.8401 1.10e-21 92.121 99.5597
+## k_parent_sink   0.0102 1.71e-12  0.009  0.0117
 ## 
 ## $IORE
-##                     Estimate Pr(>t)    Lower    Upper
-## parent_0            1.01e+02     NA 9.91e+01 1.02e+02
-## k__iore_parent_sink 1.54e-05     NA 4.08e-06 5.84e-05
-## N_parent            2.57e+00     NA 2.25e+00 2.89e+00
-## sigma               1.68e+00     NA 1.12e+00 2.24e+00
+##                     Estimate   Pr(>t)    Lower    Upper
+## parent_0            1.01e+02 2.37e-26 9.89e+01 1.03e+02
+## k__iore_parent_sink 1.54e-05 8.73e-02 3.48e-06 6.85e-05
+## N_parent            2.57e+00 1.14e-11 2.22e+00 2.92e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 9.99e+01 1.41e-26 98.8116 101.0810
-## k1       2.67e-02 5.05e-06  0.0243   0.0295
-## k2       2.86e-12 5.00e-01  0.0000      Inf
-## g        6.47e-01 3.67e-06  0.6248   0.6677
-## sigma    1.27e+00 8.91e-06  0.8395   1.6929
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 9.99e+01 4.33e-27    NA    NA
+## k1       2.67e-02 3.17e-05    NA    NA
+## k2       2.86e-12 5.00e-01    NA    NA
+## g        6.47e-01 2.13e-05    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -153,17 +152,19 @@
 ## DFOP 55.5 4.42e+11 2.42e+11
 ## 
 ## Representative half-life:
-## [1] 321.51

+## [1] 321.5119

 
 

 

 Example on page 5, lower panel

-
p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])

+
p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])

+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p5b)

+
plot(p5b)

 

-
print(p5b)

+
print(p5b)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 94.81123 10.10936  7.55871 
@@ -174,24 +175,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)    Lower    Upper
-## parent_0        96.497 2.32e-24 94.85271 98.14155
-## k_parent_sink    0.008 3.42e-14  0.00737  0.00869
-## sigma            2.295 1.22e-05  1.47976  3.11036
+## parent_0        96.497 2.62e-25 94.77653 98.21774
+## k_parent_sink    0.008 1.35e-14  0.00736  0.00871
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)    Lower    Upper
-## parent_0            9.85e+01 1.17e-28 9.79e+01 9.92e+01
-## k__iore_parent_sink 1.53e-04 6.50e-03 7.21e-05 3.26e-04
-## N_parent            1.94e+00 5.88e-13 1.76e+00 2.12e+00
-## sigma               7.49e-01 1.63e-05 4.82e-01 1.02e+00
+## parent_0            9.85e+01 1.02e-29 9.78e+01 9.93e+01
+## k__iore_parent_sink 1.53e-04 1.15e-02 6.60e-05 3.56e-04
+## N_parent            1.94e+00 8.18e-13 1.74e+00 2.14e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0 9.84e+01 1.24e-27 97.8078 98.9187
-## k1       1.55e-02 4.10e-04  0.0143  0.0167
-## k2       1.16e-11 5.00e-01  0.0000     Inf
-## g        6.89e-01 2.92e-03  0.6626  0.7142
-## sigma    6.48e-01 2.38e-05  0.4147  0.8813
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 9.84e+01 1.90e-28    NA    NA
+## k1       1.55e-02 2.83e-03    NA    NA
+## k2       1.16e-11 5.00e-01    NA    NA
+## g        6.89e-01 1.31e-02    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -201,17 +199,19 @@
 ## DFOP 83.6 9.80e+10 5.98e+10
 ## 
 ## Representative half-life:
-## [1] 215.87

+## [1] 215.8655

 
 

 

 Example on page 6

-
p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])

+
p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])

+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p6)

+
plot(p6)

 

-
print(p6)

+
print(p6)

 
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 188.45361  51.00699  42.46931 
@@ -222,24 +222,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)   Lower   Upper
-## parent_0       94.7759 7.29e-24 92.3478 97.2039
-## k_parent_sink   0.0179 8.02e-16  0.0166  0.0194
-## sigma           3.0696 3.81e-06  2.0456  4.0936
+## parent_0       94.7759 1.25e-24 92.2558 97.2960
+## k_parent_sink   0.0179 2.35e-16  0.0166  0.0194
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)    Lower    Upper
-## parent_0            97.12446 2.63e-26 95.62461 98.62431
-## k__iore_parent_sink  0.00252 1.95e-03  0.00134  0.00472
-## N_parent             1.49587 4.07e-13  1.33896  1.65279
-## sigma                1.59698 5.05e-06  1.06169  2.13227
+## parent_0            97.12446 5.62e-27 95.49343 98.75549
+## k__iore_parent_sink  0.00252 3.54e-03  0.00126  0.00502
+## N_parent             1.49587 6.13e-13  1.32380  1.66794
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0 9.66e+01 1.57e-25 95.3476 97.8979
-## k1       2.55e-02 7.33e-06  0.0233  0.0278
-## k2       4.90e-11 5.00e-01  0.0000     Inf
-## g        8.61e-01 7.55e-06  0.8314  0.8867
-## sigma    1.46e+00 6.93e-06  0.9661  1.9483
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 9.66e+01 4.17e-26    NA    NA
+## k1       2.55e-02 2.12e-05    NA    NA
+## k2       4.90e-11 5.00e-01    NA    NA
+## g        8.61e-01 2.10e-05    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -249,17 +246,19 @@
 ## DFOP 34.1 6.66e+09 1.41e+10
 ## 
 ## Representative half-life:
-## [1] 53.17

+## [1] 53.16582

 
 

 

 Example on page 7

-
p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])

+
p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])

+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p7)

+
plot(p7)

 

-
print(p7)

+
print(p7)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3661.661 3195.030 3174.145 
@@ -270,24 +269,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      96.41796 4.80e-53 93.32245 99.51347
-## k_parent_sink  0.00735 7.64e-21  0.00641  0.00843
-## sigma          7.94557 1.83e-15  6.46713  9.42401
+## parent_0      96.41796 1.52e-53 93.29554 99.54038
+## k_parent_sink  0.00735 3.59e-21  0.00641  0.00842
 ## 
 ## $IORE
-##                     Estimate Pr(>t)    Lower    Upper
-## parent_0            9.92e+01     NA 9.55e+01 1.03e+02
-## k__iore_parent_sink 1.60e-05     NA 1.45e-07 1.77e-03
-## N_parent            2.45e+00     NA 1.35e+00 3.54e+00
-## sigma               7.42e+00     NA 6.04e+00 8.80e+00
+##                     Estimate   Pr(>t)    Lower    Upper
+## parent_0            9.92e+01 7.33e-49 9.53e+01 1.03e+02
+## k__iore_parent_sink 1.60e-05 3.47e-01 9.98e-08 2.57e-03
+## N_parent            2.45e+00 6.14e-05 1.26e+00 3.63e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 9.89e+01 9.44e-49 95.4640 102.2573
-## k1       1.81e-02 1.75e-01  0.0116   0.0281
-## k2       1.97e-10 5.00e-01  0.0000      Inf
-## g        6.06e-01 2.19e-01  0.4826   0.7178
-## sigma    7.40e+00 2.97e-15  6.0201   8.7754
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 9.89e+01 8.13e-48    NA    NA
+## k1       1.81e-02 2.20e-01    NA    NA
+## k2       1.97e-10 5.00e-01    NA    NA
+## g        6.06e-01 2.60e-01    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -297,7 +293,7 @@
 ## DFOP 96.4 6.97e+09 3.52e+09
 ## 
 ## Representative half-life:
-## [1] 454.55

+## [1] 454.5528

 
 
 

@@ -307,12 +303,17 @@
 

 Example on page 8

 
For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here.

-
p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3))

+
p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3))

+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
+
+## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p8)

+
plot(p8)

 

-
print(p8)

+
print(p8)

 
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 1996.9408  444.9237  547.5616 
@@ -322,25 +323,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      88.16549 6.53e-29 83.37344 92.95754
-## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
-## sigma          7.44786 4.17e-10  5.66209  9.23363
+##                     Estimate Pr(>t) Lower Upper
+## parent_0            88.16549     NA    NA    NA
+## k__iore_parent_sink  0.00100     NA    NA    NA
+## k_parent_sink        0.00803     NA    NA    NA
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)    Lower    Upper
-## parent_0            9.77e+01 7.03e-35 9.44e+01 1.01e+02
-## k__iore_parent_sink 6.14e-05 3.20e-02 2.12e-05 1.78e-04
-## N_parent            2.27e+00 4.23e-18 2.00e+00 2.54e+00
-## sigma               3.52e+00 5.36e-10 2.67e+00 4.36e+00
+## parent_0            9.77e+01 1.05e-35 9.44e+01 1.01e+02
+## k__iore_parent_sink 6.14e-05 2.76e-02 2.21e-05 1.71e-04
+## N_parent            2.27e+00 6.00e-19 2.02e+00 2.53e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 95.70619 8.99e-32 91.87941 99.53298
-## k1        0.02500 5.25e-04  0.01422  0.04394
-## k2        0.00273 6.84e-03  0.00125  0.00597
-## g         0.58835 2.84e-06  0.36595  0.77970
-## sigma     3.90001 6.94e-10  2.96260  4.83741
+##                     Estimate Pr(>t) Lower Upper
+## parent_0            95.70619     NA    NA    NA
+## k__iore_parent_sink  0.00100     NA    NA    NA
+## k1                   0.02500     NA    NA    NA
+## k2                   0.00273     NA    NA    NA
+## g                    0.58835     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -350,7 +350,7 @@
 ## DFOP 55.6  517    253.0
 ## 
 ## Representative half-life:
-## [1] 201.03

+## [1] 201.0316
@@ -359,12 +359,14 @@

Example on page 9, upper panel

-
p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
+
p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p9a)
+
plot(p9a)

-
print(p9a)
+
print(p9a)
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 839.35238  88.57064   9.93363 
@@ -375,24 +377,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)   Lower   Upper
-## parent_0       88.1933 3.06e-12 79.9447 96.4419
-## k_parent_sink   0.0409 2.07e-07  0.0324  0.0516
-## sigma           7.2429 3.92e-05  4.4768 10.0090
+## parent_0       88.1933 1.12e-12 79.7671 96.6195
+## k_parent_sink   0.0409 9.50e-08  0.0326  0.0513
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)    Lower    Upper
-## parent_0            9.89e+01 1.12e-16 9.54e+01 1.02e+02
-## k__iore_parent_sink 1.93e-05 1.13e-01 3.49e-06 1.06e-04
-## N_parent            2.91e+00 1.45e-09 2.50e+00 3.32e+00
-## sigma               2.35e+00 5.31e-05 1.45e+00 3.26e+00
+## parent_0            9.89e+01 5.16e-17 9.50e+01 1.03e+02
+## k__iore_parent_sink 1.93e-05 1.48e-01 2.65e-06 1.40e-04
+## N_parent            2.91e+00 3.74e-09 2.43e+00 3.39e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)  Lower  Upper
-## parent_0 9.85e+01 2.54e-20 97.390 99.672
-## k1       1.38e-01 3.52e-05  0.131  0.146
-## k2       6.02e-13 5.00e-01  0.000    Inf
-## g        6.52e-01 8.13e-06  0.642  0.661
-## sigma    7.88e-01 6.13e-02  0.481  1.095
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 9.85e+01 1.31e-21    NA    NA
+## k1       1.38e-01 3.63e-09    NA    NA
+## k2       6.02e-13 5.00e-01    NA    NA
+## g        6.52e-01 1.50e-10    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -402,23 +401,20 @@
 ## DFOP 10.5 2.07e+12 1.15e+12
 ## 
 ## Representative half-life:
-## [1] 101.43
+## [1] 101.4264

In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.

Example on page 9, lower panel

-
p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
-
## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt
-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful
+
p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p9b)
+
plot(p9b)

-
print(p9b)
+
print(p9b)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -428,25 +424,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       94.7123 2.15e-19 93.178 96.2464
-## k_parent_sink   0.0389 4.47e-14  0.037  0.0408
-## sigma           1.5957 1.28e-04  0.932  2.2595
+##               Estimate   Pr(>t)   Lower  Upper
+## parent_0       94.7123 2.21e-20 93.0673 96.357
+## k_parent_sink   0.0389 1.48e-14  0.0369  0.041
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)   Lower  Upper
-## parent_0              93.863 2.32e-18 92.4565 95.269
-## k__iore_parent_sink    0.127 1.85e-02  0.0504  0.321
-## N_parent               0.711 1.88e-05  0.4843  0.937
-## sigma                  1.288 1.76e-04  0.7456  1.830
+## parent_0              93.863 2.91e-19 92.2996 95.426
+## k__iore_parent_sink    0.127 2.73e-02  0.0457  0.354
+## N_parent               0.711 3.13e-05  0.4605  0.961
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  94.7123 1.61e-16 93.1355 96.2891
-## k1         0.0389 1.43e-06  0.0312  0.0485
-## k2         0.0389 6.67e-03  0.0186  0.0812
-## g          0.7742      NaN      NA      NA
-## sigma      1.5957 2.50e-04  0.9135  2.2779
+##          Estimate Pr(>t) Lower Upper
+## parent_0  94.7123     NA    NA    NA
+## k1         0.0389     NA    NA    NA
+## k2         0.0389     NA    NA    NA
+## g          0.7742     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -456,18 +449,20 @@
 ## DFOP 17.8 59.2     17.8
 ## 
 ## Representative half-life:
-## [1] 14.8
+## [1] 14.80012

Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.

Example on page 10

-
p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
+
p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p10)
+
plot(p10)

-
print(p10)
+
print(p10)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -478,24 +473,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)   Lower    Upper
-## parent_0      101.7315 6.42e-11 91.9259 111.5371
-## k_parent_sink   0.0495 1.70e-07  0.0404   0.0607
-## sigma           8.0152 1.28e-04  4.6813  11.3491
+## parent_0      101.7315 4.95e-11 90.9683 112.4947
+## k_parent_sink   0.0495 3.40e-07  0.0393   0.0624
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)  Lower   Upper
-## parent_0               96.86 3.32e-12 90.848 102.863
-## k__iore_parent_sink     2.96 7.91e-02  0.687  12.761
-## N_parent                0.00 5.00e-01 -0.372   0.372
-## sigma                   4.90 1.77e-04  2.837   6.968
+## parent_0               96.86 2.71e-12 89.884 103.826
+## k__iore_parent_sink     2.96 1.31e-01  0.461  19.020
+## N_parent                0.00 5.00e-01 -0.473   0.473
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 101.7315 1.41e-09 91.6534 111.8097
-## k1         0.0495 6.42e-04  0.0301   0.0814
-## k2         0.0495 1.66e-02  0.0200   0.1225
-## g          0.6634 5.00e-01  0.0000   1.0000
-## sigma      8.0152 2.50e-04  4.5886  11.4418
+##          Estimate Pr(>t) Lower Upper
+## parent_0 101.7315     NA    NA    NA
+## k1         0.0495     NA    NA    NA
+## k2         0.0495     NA    NA    NA
+## g          0.6634     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -505,7 +497,7 @@
 ## DFOP 14.0 46.5    14.00
 ## 
 ## Representative half-life:
-## [1] 8.86
+## [1] 8.862193

Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.

@@ -515,12 +507,14 @@

Example on page 11

-
p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
+
p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p11)
+
plot(p11)

-
print(p11)
+
print(p11)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -531,24 +525,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      96.15820 4.83e-13 90.24934 1.02e+02
-## k_parent_sink  0.00321 4.71e-05  0.00222 4.64e-03
-## sigma          6.43473 1.28e-04  3.75822 9.11e+00
+## parent_0      96.15820 1.56e-13 89.91373 1.02e+02
+## k_parent_sink  0.00321 5.27e-05  0.00218 4.71e-03
 ## 
 ## $IORE
 ##                     Estimate Pr(>t)    Lower    Upper
-## parent_0            1.05e+02     NA 9.90e+01 1.10e+02
-## k__iore_parent_sink 3.11e-17     NA 1.35e-20 7.18e-14
-## N_parent            8.36e+00     NA 6.62e+00 1.01e+01
-## sigma               3.82e+00     NA 2.21e+00 5.44e+00
+## parent_0            1.05e+02     NA 9.80e+01 1.11e+02
+## k__iore_parent_sink 3.11e-17     NA 6.88e-25 1.41e-09
+## N_parent            8.36e+00     NA 4.40e+00 1.23e+01
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 1.05e+02 9.47e-13  99.9990 109.1224
-## k1       4.41e-02 5.95e-03   0.0296   0.0658
-## k2       7.25e-13 5.00e-01   0.0000      Inf
-## g        3.22e-01 1.45e-03   0.2814   0.3650
-## sigma    3.22e+00 3.52e-04   1.8410   4.5906
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 1.05e+02 7.50e-13    NA    NA
+## k1       4.41e-02 3.34e-02    NA    NA
+## k2       7.25e-13 5.00e-01    NA    NA
+## g        3.22e-01 7.87e-03    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -569,14 +560,14 @@
 

 

 Example on page 12, upper panel

-
p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

-
## Warning in summary.mkinfit(x): Could not calculate correlation; no
-## covariance matrix

+
p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.

 
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c

 
## The half-life obtained from the IORE model may be used

-
plot(p12a)

+
plot(p12a)

 

-
print(p12a)

+
print(p12a)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -587,24 +578,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       100.521 8.75e-12 92.461 108.581
-## k_parent_sink    0.124 3.61e-08  0.104   0.148
-## sigma            7.048 1.28e-04  4.116   9.980
+## parent_0       100.521 5.61e-12 91.687 109.355
+## k_parent_sink    0.124 7.24e-08  0.102   0.152
 ## 
 ## $IORE
-##                     Estimate Pr(>t) Lower Upper
-## parent_0              96.823     NA    NA    NA
-## k__iore_parent_sink    2.436     NA    NA    NA
-## N_parent               0.263     NA    NA    NA
-## sigma                  3.965     NA    NA    NA
+##                     Estimate   Pr(>t)   Lower   Upper
+## parent_0              96.823 1.24e-13 91.5691 102.078
+## k__iore_parent_sink    2.436 3.89e-02  0.7854   7.556
+## N_parent               0.263 3.64e-02 -0.0288   0.554
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  100.521 2.74e-10 92.2366 108.805
-## k1          0.124 5.74e-06  0.0958   0.161
-## k2          0.124 6.61e-02  0.0319   0.484
-## g           0.877 5.00e-01  0.0000   1.000
-## sigma       7.048 2.50e-04  4.0349  10.061
+##          Estimate Pr(>t) Lower Upper
+## parent_0  100.521     NA    NA    NA
+## k1          0.124     NA    NA    NA
+## k2          0.124     NA    NA    NA
+## g           0.877     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -614,25 +602,19 @@
 ## DFOP 5.58 18.5     5.58
 ## 
 ## Representative half-life:
-## [1] 3.99

+## [1] 3.987308

Example on page 12, lower panel

-
p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
-
## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt
-
## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt
-
## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt
-
## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs wurden erzeugt
-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful
+
p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p12b)
+
plot(p12b)

-
print(p12b)
+
print(p12b)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -642,25 +624,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate  Pr(>t)   Lower    Upper
-## parent_0       97.6840 0.00039 85.9388 109.4292
-## k_parent_sink   0.0589 0.00261  0.0431   0.0805
-## sigma           3.4323 0.04356 -1.2377   8.1023
+##               Estimate   Pr(>t)   Lower    Upper
+## parent_0       97.6840 5.36e-05 86.3205 109.0475
+## k_parent_sink   0.0589 9.87e-04  0.0432   0.0803
 ## 
 ## $IORE
-##                     Estimate Pr(>t)     Lower  Upper
-## parent_0              95.523 0.0055 74.539157 116.51
-## k__iore_parent_sink    0.333 0.1433  0.000717 154.57
-## N_parent               0.568 0.0677 -0.989464   2.13
-## sigma                  1.953 0.0975 -5.893100   9.80
+##                     Estimate   Pr(>t)   Lower  Upper
+## parent_0              95.523 0.000386 84.0963 106.95
+## k__iore_parent_sink    0.333 0.170886  0.0103  10.80
+## N_parent               0.568 0.054881 -0.3161   1.45
 ## 
 ## $DFOP
 ##          Estimate Pr(>t) Lower Upper
-## parent_0  97.6840    NaN   NaN   NaN
-## k1         0.0589    NaN    NA    NA
-## k2         0.0589    NaN    NA    NA
-## g          0.6902    NaN    NA    NA
-## sigma      3.4323    NaN   NaN   NaN
+## parent_0  97.6840     NA    NA    NA
+## k1         0.0589     NA    NA    NA
+## k2         0.0589     NA    NA    NA
+## g          0.6902     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -670,21 +649,19 @@
 ## DFOP 11.8 39.1    11.80
 ## 
 ## Representative half-life:
-## [1] 9.46
+## [1] 9.461912

Example on page 13

-
p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful
+
p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p13)
+
plot(p13)

-
print(p13)
+
print(p13)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -694,25 +671,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      92.73500 5.99e-17 89.61936 95.85065
-## k_parent_sink  0.00258 2.42e-09  0.00223  0.00299
-## sigma          3.41172 7.07e-05  2.05455  4.76888
+##               Estimate   Pr(>t)   Lower    Upper
+## parent_0      92.73500 1.45e-17 89.3891 96.08094
+## k_parent_sink  0.00258 2.63e-09  0.0022  0.00303
 ## 
 ## $IORE
-##                     Estimate   Pr(>t)    Lower  Upper
-## parent_0             91.6016 6.34e-16 88.53086 94.672
-## k__iore_parent_sink   0.0396 2.36e-01  0.00207  0.759
-## N_parent              0.3541 1.46e-01 -0.35153  1.060
-## sigma                 3.0811 9.64e-05  1.84296  4.319
+##                     Estimate   Pr(>t)    Lower Upper
+## parent_0             91.6016 2.93e-16 88.08711 95.12
+## k__iore_parent_sink   0.0396 2.81e-01  0.00102  1.53
+## N_parent              0.3541 1.97e-01 -0.51943  1.23
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01
-## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
-## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
-## g         0.00442 5.00e-01       NA       NA
-## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
+##          Estimate Pr(>t) Lower Upper
+## parent_0 92.73500     NA    NA    NA
+## k1        0.00258     NA    NA    NA
+## k2        0.00258     NA    NA    NA
+## g         0.00442     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -722,22 +696,20 @@
 ## DFOP  269  892      269
 ## 
 ## Representative half-life:
-## [1] 168.51
+## [1] 168.5123

DT50 not observed in the study and DFOP problems in PestDF

-
p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful
+
p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p14)
+
plot(p14)

-
print(p14)
+
print(p14)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -748,24 +720,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      99.47124 2.06e-30 98.42254 1.01e+02
-## k_parent_sink  0.00279 3.75e-15  0.00256 3.04e-03
-## sigma          1.55616 3.81e-06  1.03704 2.08e+00
+## parent_0      99.47124 1.71e-31 98.37313 1.01e+02
+## k_parent_sink  0.00279 2.22e-15  0.00255 3.05e-03
 ## 
 ## $IORE
-##                     Estimate Pr(>t) Lower Upper
-## parent_0            1.00e+02     NA   NaN   NaN
-## k__iore_parent_sink 9.44e-08     NA   NaN   NaN
-## N_parent            3.31e+00     NA   NaN   NaN
-## sigma               1.20e+00     NA 0.796   1.6
+##                     Estimate Pr(>t)    Lower    Upper
+## parent_0            1.00e+02     NA 9.93e+01 1.01e+02
+## k__iore_parent_sink 9.44e-08     NA 6.81e-11 1.31e-04
+## N_parent            3.31e+00     NA 1.69e+00 4.93e+00
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 1.00e+02 2.96e-28 99.40280 101.2768
-## k1       9.53e-03 1.20e-01  0.00638   0.0143
-## k2       7.29e-12 5.00e-01  0.00000      Inf
-## g        3.98e-01 2.19e-01  0.30481   0.4998
-## sigma    1.17e+00 7.68e-06  0.77406   1.5610
+##          Estimate   Pr(>t) Lower Upper
+## parent_0 1.00e+02 2.70e-28    NA    NA
+## k1       9.53e-03 3.39e-01    NA    NA
+## k2       7.29e-12 5.00e-01    NA    NA
+## g        3.98e-01 3.92e-01    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -775,23 +744,20 @@
 ## DFOP 2.54e+10 2.46e+11 9.51e+10
 ## 
 ## Representative half-life:
-## [1] 6697.44
+## [1] 6697.437

The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.

N is less than 1 and DFOP fraction parameter is below zero

-
p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
-
## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt
-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful
+
p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p15a)
+
plot(p15a)

-
print(p15a)
+
print(p15a)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -801,25 +767,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower   Upper
-## parent_0      97.96751 2.00e-15 94.32049 101.615
-## k_parent_sink  0.00952 4.93e-09  0.00824   0.011
-## sigma          4.18778 1.28e-04  2.44588   5.930
+##               Estimate   Pr(>t)    Lower    Upper
+## parent_0      97.96751 4.98e-16 94.03829 101.8967
+## k_parent_sink  0.00952 5.24e-09  0.00813   0.0112
 ## 
 ## $IORE
-##                     Estimate   Pr(>t)  Lower  Upper
-## parent_0              95.874 2.94e-15 92.937 98.811
-## k__iore_parent_sink    0.629 2.11e-01  0.044  8.982
-## N_parent               0.000 5.00e-01 -0.642  0.642
-## sigma                  3.105 1.78e-04  1.795  4.416
+##                     Estimate   Pr(>t)   Lower  Upper
+## parent_0              95.874 8.30e-16 92.5802 99.167
+## k__iore_parent_sink    0.629 2.39e-01  0.0316 12.519
+## N_parent               0.000 5.00e-01 -0.7219  0.722
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 97.96752 2.85e-13 94.21914 101.7159
-## k1        0.00952 6.80e-02  0.00277   0.0327
-## k2        0.00952 3.82e-06  0.00902   0.0100
-## g         0.17247      NaN       NA       NA
-## sigma     4.18778 2.50e-04  2.39747   5.9781
+##          Estimate Pr(>t) Lower Upper
+## parent_0 97.96752     NA    NA    NA
+## k1        0.00952     NA    NA    NA
+## k2        0.00952     NA    NA    NA
+## g         0.17247     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -829,17 +792,15 @@
 ## DFOP 72.8  242     72.8
 ## 
 ## Representative half-life:
-## [1] 41.33
-
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
-
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
-
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
-
## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
-## finite result is doubtful
+## [1] 41.32749 +
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
+
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
+## singular system.
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The half-life obtained from the IORE model may be used
-
plot(p15b)
+
plot(p15b)

-
print(p15b)
+
print(p15b)
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -850,24 +811,21 @@
 ## Parameters:
 ## $SFO
 ##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      1.01e+02 3.06e-17 98.31594 1.03e+02
-## k_parent_sink 4.86e-03 2.48e-10  0.00435 5.42e-03
-## sigma         2.76e+00 1.28e-04  1.61402 3.91e+00
+## parent_0      1.01e+02 4.99e-18 98.12761 1.04e+02
+## k_parent_sink 4.86e-03 1.76e-10  0.00432 5.46e-03
 ## 
 ## $IORE
-##                     Estimate   Pr(>t)    Lower  Upper
-## parent_0               99.83 1.81e-16 97.51349 102.14
-## k__iore_parent_sink     0.38 3.22e-01  0.00352  41.05
-## N_parent                0.00 5.00e-01 -1.07695   1.08
-## sigma                   2.21 2.57e-04  1.23245   3.19
+##                     Estimate   Pr(>t)    Lower Upper
+## parent_0               99.83 4.49e-17 97.19753 102.5
+## k__iore_parent_sink     0.38 3.41e-01  0.00206  70.0
+## N_parent                0.00 5.00e-01 -1.20105   1.2
 ## 
 ## $DFOP
-##          Estimate Pr(>t)    Lower    Upper
-## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
-## k1       4.86e-03     NA 6.75e-04 3.49e-02
-## k2       4.86e-03     NA 3.37e-03 6.99e-03
-## g        1.50e-01     NA       NA       NA
-## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+##          Estimate Pr(>t) Lower Upper
+## parent_0 1.01e+02     NA    NA    NA
+## k1       4.86e-03     NA    NA    NA
+## k2       4.86e-03     NA    NA    NA
+## g        1.50e-01     NA    NA    NA
 ## 
 ## 
 ## DTx values:
@@ -877,20 +835,20 @@
 ## DFOP  143  474    143.0
 ## 
 ## Representative half-life:
-## [1] 71.18
+## [1] 71.18014

In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.

The DFOP fraction parameter is greater than 1

-
p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
+
p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
## The representative half-life of the IORE model is longer than the one corresponding
## to the terminal degradation rate found with the DFOP model.
## The representative half-life obtained from the DFOP model may be used
-
plot(p16)
+
plot(p16)

-
print(p16)
+
print(p16)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -900,25 +858,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower Upper
-## parent_0        71.953 2.33e-13 60.509 83.40
-## k_parent_sink    0.159 4.86e-05  0.102  0.25
-## sigma           11.302 1.25e-08  8.308 14.30
+##               Estimate   Pr(>t)  Lower  Upper
+## parent_0        71.953 3.92e-14 61.087 82.819
+## k_parent_sink    0.159 2.27e-06  0.111  0.229
 ## 
 ## $IORE
 ##                     Estimate   Pr(>t)    Lower    Upper
-## parent_0            8.74e+01 2.48e-16 7.72e+01 97.52972
-## k__iore_parent_sink 4.55e-04 2.16e-01 3.48e-05  0.00595
-## N_parent            2.70e+00 1.21e-08 1.99e+00  3.40046
-## sigma               8.29e+00 1.61e-08 6.09e+00 10.49062
+## parent_0            8.74e+01 1.74e-16 7.71e+01 97.70701
+## k__iore_parent_sink 4.55e-04 2.28e-01 3.01e-05  0.00688
+## N_parent            2.70e+00 1.87e-08 1.97e+00  3.42611
 ## 
 ## $DFOP
-##          Estimate   Pr(>t)   Lower  Upper
-## parent_0  88.5333 7.40e-18 79.9836 97.083
-## k1        18.5561 5.00e-01  0.0000    Inf
-## k2         0.0776 1.41e-05  0.0518  0.116
-## g          0.4733 1.41e-09  0.3674  0.582
-## sigma      7.1902 2.11e-08  5.2785  9.102
+##          Estimate Pr(>t)   Lower  Upper
+## parent_0  88.5333     NA 79.3673 97.699
+## k1        18.5561     NA  0.0000    Inf
+## k2         0.0776     NA  0.0471  0.128
+## g          0.4733     NA  0.3138  0.639
 ## 
 ## 
 ## DTx values:
@@ -928,7 +883,7 @@
 ## DFOP 0.67 21.4     8.93
 ## 
 ## Representative half-life:
-## [1] 8.93
+## [1] 8.932679

In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower \(\chi^2\) error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.

diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png index d0f89858..4cf9c8ea 100644 Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p13-1.png differ diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png index 596a33b2..c1f61bab 100644 Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5a-1.png differ diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png index fa8621e7..2747b2d6 100644 Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p8-1.png differ diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png index aac3600b..32b3bf29 100644 Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9a-1.png differ diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png index cb52aecd..8b8ea5aa 100644 Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p9b-1.png differ diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html index 005834cc..eacecc2f 100644 --- a/docs/articles/web_only/benchmarks.html +++ b/docs/articles/web_only/benchmarks.html @@ -30,7 +30,7 @@ mkin - 0.9.49.5 + 0.9.49.6
@@ -88,7 +88,7 @@

Benchmark timings for mkin on various systems

Johannes Ranke

-

2019-07-04

+

2019-07-05

@@ -116,8 +116,17 @@ 
# Parent only
 t1 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D)))[["elapsed"]]
 t2 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D), error_model = "tc"))[["elapsed"]]
-
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation did not converge:
-## iteration limit reached without convergence (10)
+
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
+## false convergence (8)
+
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
+## false convergence (8)
+
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
+## false convergence (8)
+
+## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
+## false convergence (8)
# One metabolite
 SFO_SFO <- mkinmod(
   parent = mkinsub("SFO", "m1"),
@@ -131,149 +140,124 @@
   parent = mkinsub("FOMC", "m1"),
   m1 = mkinsub("SFO"))
## Successfully compiled differential equation model from auto-generated C code.
-
t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D)))[["elapsed"]]
-
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data
-
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data
-
t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(subset(FOCUS_2006_D, value != 0)), error_model = "tc"))[["elapsed"]]
-t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D), error_model = "obs"))[["elapsed"]]
-
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data
-
-## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...):
-## Observations with value of zero were removed from the data
-
# Two metabolites, synthetic data
-m_synth_SFO_lin <- mkinmod(parent = mkinsub("SFO", "M1"),
-                           M1 = mkinsub("SFO", "M2"),
-                           M2 = mkinsub("SFO"),
-                           use_of_ff = "max", quiet = TRUE)
-
-m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
-                           M1 = mkinsub("SFO"),
-                           M2 = mkinsub("SFO"),
-                           use_of_ff = "max", quiet = TRUE)
-
-SFO_lin_a <- synthetic_data_for_UBA_2014[[1]]$data
-
-DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
-
-t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))["elapsed"]
-t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))["elapsed"]
-
-t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "tc"))["elapsed"]
-t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "tc"))["elapsed"]
-
-t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "obs"))["elapsed"]
-t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "obs"))["elapsed"]
-
-mkin_benchmarks[system_string, paste0("t", 1:11)] <- c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)
-mkin_benchmarks
+
t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D)))[["elapsed"]]
+t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(subset(FOCUS_2006_D, value != 0)), error_model = "tc"))[["elapsed"]]
+t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D), error_model = "obs"))[["elapsed"]]
+
+# Two metabolites, synthetic data
+m_synth_SFO_lin <- mkinmod(parent = mkinsub("SFO", "M1"),
+                           M1 = mkinsub("SFO", "M2"),
+                           M2 = mkinsub("SFO"),
+                           use_of_ff = "max", quiet = TRUE)
+
+m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
+                           M1 = mkinsub("SFO"),
+                           M2 = mkinsub("SFO"),
+                           use_of_ff = "max", quiet = TRUE)
+
+SFO_lin_a <- synthetic_data_for_UBA_2014[[1]]$data
+
+DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
+
+t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))["elapsed"]
+t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))["elapsed"]
+
+t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "tc"))["elapsed"]
+
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
+## false convergence (8)
+
t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "tc"))["elapsed"]
+
+t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "obs"))["elapsed"]
+t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "obs"))["elapsed"]
+
## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): Optimisation by method Port did not converge:
+## false convergence (8)
+
mkin_benchmarks[system_string, paste0("t", 1:11)] <- c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11)
+mkin_benchmarks
##                                                                                                       CPU
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 AMD Ryzen 7 1700 Eight-Core Processor
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 AMD Ryzen 7 1700 Eight-Core Processor
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 AMD Ryzen 7 1700 Eight-Core Processor
 ##                                                                        OS
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 Linux
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 Linux
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 Linux
 ##                                                                         mkin
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 0.9.48.1
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 0.9.49.1
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 0.9.49.2
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 0.9.49.3
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 0.9.49.4
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 0.9.49.5
 ##                                                                        t1
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.610
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.107
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 8.184
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 7.064
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.296
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.936
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 5.843
 ##                                                                         t2
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 11.019
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 10.105
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 22.889
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 12.558
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 21.239
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 20.545
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 35.863
 ##                                                                        t3
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.764
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.415
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.649
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.786
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.510
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.446
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 4.417
 ##                                                                         t4
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 14.347
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 13.228
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 13.789
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  8.461
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 13.805
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 15.335
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 30.484
-##                                                                         t5
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1  9.495
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  6.395
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  5.675
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.386
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  6.002
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 10.307
+##                                                                        t5
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.511
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 6.395
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.675
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.386
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.002
 ##                                                                        t6
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 2.623
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 2.368
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 2.542
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 2.723
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 2.643
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 2.635
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 2.538
 ##                                                                        t7
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 4.587
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1  4.12
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.128
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.478
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.374
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.259
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 4.196
 ##                                                                        t8
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 7.525
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 6.357
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.632
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.862
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.02
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.737
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 7.853
 ##                                                                         t9
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 16.621
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1  15.42
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  8.171
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  7.618
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 11.124
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  7.763
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 15.643
 ##                                                                       t10
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.576
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 7.868
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 3.676
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 3.579
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 5.388
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 3.427
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 7.733
 ##                                                                        t11
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 31.267
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 28.858
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1  5.636
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2  5.574
 ## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3  7.365
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4  5.626
-## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.5 10.511
-
save(mkin_benchmarks, file = "~/git/mkin/vignettes/mkin_benchmarks.rda")
+## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.626 +
save(mkin_benchmarks, file = "~/git/mkin/vignettes/mkin_benchmarks.rda")
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html index 3fc54cfa..ca883f17 100644 --- a/docs/articles/web_only/compiled_models.html +++ b/docs/articles/web_only/compiled_models.html @@ -30,7 +30,7 @@ mkin - 0.9.49.5 + 0.9.49.6 @@ -88,7 +88,7 @@

Performance benefit by using compiled model definitions in mkin

Johannes Ranke

-

2019-07-04

+

2019-07-05

@@ -128,99 +128,45 @@ print("R package rbenchmark is not available") } 
## Lade nötiges Paket: rbenchmark
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
-## use_compiled = FALSE, : Observations with value of zero were removed from
-## the data
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
-## TRUE): Observations with value of zero were removed from the data
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
-## = TRUE): Observations with value of zero were removed from the data
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
-## use_compiled = FALSE, : Observations with value of zero were removed from
-## the data
-
-## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
-## use_compiled = FALSE, : Observations with value of zero were removed from
-## the data
-
-## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve",
-## use_compiled = FALSE, : Observations with value of zero were removed from
-## the data
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
-## TRUE): Observations with value of zero were removed from the data
-
-## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
-## TRUE): Observations with value of zero were removed from the data
-
-## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet =
-## TRUE): Observations with value of zero were removed from the data
-
## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
-## = TRUE): Observations with value of zero were removed from the data
-
-## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
-## = TRUE): Observations with value of zero were removed from the data
-
-## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet
-## = TRUE): Observations with value of zero were removed from the data
##                    test replications elapsed relative user.self sys.self
-## 3     deSolve, compiled            3   3.061    1.000     3.059        0
-## 1 deSolve, not compiled            3  28.502    9.311    28.487        0
-## 2      Eigenvalue based            3   4.321    1.412     4.318        0
+## 3     deSolve, compiled            3   2.147    1.000     2.145        0
+## 1 deSolve, not compiled            3  12.653    5.893    12.646        0
+## 2      Eigenvalue based            3   2.690    1.253     2.688        0
 ##   user.child sys.child
 ## 3          0         0
 ## 1          0         0
 ## 2          0         0
-

We see that using the compiled model is by a factor of around 9 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs.

+

We see that using the compiled model is by a factor of around 6 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs.

Model that can not be solved with Eigenvalues

This evaluation is also taken from the example section of mkinfit.

-
if (require(rbenchmark)) {
-  FOMC_SFO <- mkinmod(
-    parent = mkinsub("FOMC", "m1"),
-    m1 = mkinsub( "SFO"))
-
-  b.2 <- benchmark(
-    "deSolve, not compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D,
-                                      use_compiled = FALSE, quiet = TRUE),
-    "deSolve, compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE),
-    replications = 3)
-  print(b.2)
-  factor_FOMC_SFO <- round(b.2["1", "relative"])
-} else {
-  factor_FOMC_SFO <- NA
-  print("R package benchmark is not available")
-}
+
if (require(rbenchmark)) {
+  FOMC_SFO <- mkinmod(
+    parent = mkinsub("FOMC", "m1"),
+    m1 = mkinsub( "SFO"))
+
+  b.2 <- benchmark(
+    "deSolve, not compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D,
+                                      use_compiled = FALSE, quiet = TRUE),
+    "deSolve, compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE),
+    replications = 3)
+  print(b.2)
+  factor_FOMC_SFO <- round(b.2["1", "relative"])
+} else {
+  factor_FOMC_SFO <- NA
+  print("R package benchmark is not available")
+}
## Successfully compiled differential equation model from auto-generated C code.
-
## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
-## TRUE): Observations with value of zero were removed from the data
-
## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
-## value of zero were removed from the data
-
## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
-## TRUE): Observations with value of zero were removed from the data
-
-## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
-## TRUE): Observations with value of zero were removed from the data
-
-## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet =
-## TRUE): Observations with value of zero were removed from the data
-
## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
-## value of zero were removed from the data
-
-## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
-## value of zero were removed from the data
-
-## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
-## value of zero were removed from the data
##                    test replications elapsed relative user.self sys.self
-## 2     deSolve, compiled            3   4.818    1.000     4.814        0
-## 1 deSolve, not compiled            3  53.275   11.057    53.249        0
+## 2     deSolve, compiled            3   3.773    1.000     3.770        0
+## 1 deSolve, not compiled            3  27.812    7.371    27.798        0
 ##   user.child sys.child
 ## 2          0         0
 ## 1          0         0
-

Here we get a performance benefit of a factor of 11 using the version of the differential equation model compiled from C code!

-

This vignette was built with mkin 0.9.49.5 on

+

Here we get a performance benefit of a factor of 7 using the version of the differential equation model compiled from C code!

+

This vignette was built with mkin 0.9.48.1 on

## R version 3.6.0 (2019-04-26)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
 ## Running under: Debian GNU/Linux 10 (buster)
-- cgit v1.2.1