From e5d1df9a9b1f0951d7dfbaf24eee4294470b73e2 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 17 Nov 2022 14:54:20 +0100 Subject: Complete update of online docs for v1.2.0 --- docs/articles/FOCUS_D.html | 390 ++--- docs/articles/FOCUS_L.html | 236 +-- .../figure-html/unnamed-chunk-6-1.png | Bin 36120 -> 36101 bytes docs/articles/index.html | 16 +- docs/articles/mkin.html | 72 +- .../mkin_files/figure-html/unnamed-chunk-2-1.png | Bin 90169 -> 90167 bytes docs/articles/twa.html | 16 +- docs/articles/web_only/FOCUS_Z.html | 368 ++--- .../figure-html/FOCUS_2006_Z_fits_10-1.png | Bin 105896 -> 105896 bytes .../figure-html/FOCUS_2006_Z_fits_11-1.png | Bin 104797 -> 104793 bytes .../figure-html/FOCUS_2006_Z_fits_11a-1.png | Bin 75232 -> 75230 bytes .../figure-html/FOCUS_2006_Z_fits_11b-1.png | Bin 36302 -> 36314 bytes .../figure-html/FOCUS_2006_Z_fits_5-1.png | Bin 80380 -> 80373 bytes .../figure-html/FOCUS_2006_Z_fits_6-1.png | Bin 105229 -> 105210 bytes .../figure-html/FOCUS_2006_Z_fits_9-1.png | Bin 88797 -> 88801 bytes docs/articles/web_only/NAFTA_examples.html | 1498 ++++++++++---------- .../NAFTA_examples_files/figure-html/p10-1.png | Bin 79762 -> 79758 bytes .../NAFTA_examples_files/figure-html/p15a-1.png | Bin 76938 -> 76925 bytes .../NAFTA_examples_files/figure-html/p15b-1.png | Bin 78977 -> 78968 bytes .../NAFTA_examples_files/figure-html/p5b-1.png | Bin 80721 -> 80721 bytes .../NAFTA_examples_files/figure-html/p6-1.png | Bin 83052 -> 83052 bytes .../NAFTA_examples_files/figure-html/p7-1.png | Bin 102570 -> 102568 bytes docs/articles/web_only/benchmarks.html | 67 +- docs/articles/web_only/compiled_models.html | 32 +- docs/articles/web_only/dimethenamid_2018.html | 158 +-- docs/articles/web_only/multistart.html | 200 +++ .../accessible-code-block-0.0.1/empty-anchor.js | 15 + .../figure-html/unnamed-chunk-3-1.png | Bin 0 -> 60747 bytes .../figure-html/unnamed-chunk-4-1.png | Bin 0 -> 58448 bytes .../figure-html/unnamed-chunk-5-1.png | Bin 0 -> 21847 bytes .../figure-html/unnamed-chunk-6-1.png | Bin 0 -> 50597 bytes docs/articles/web_only/saem_benchmarks.html | 417 ++++++ .../accessible-code-block-0.0.1/empty-anchor.js | 15 + 33 files changed, 2120 insertions(+), 1380 deletions(-) create mode 100644 docs/articles/web_only/multistart.html create mode 100644 docs/articles/web_only/multistart_files/accessible-code-block-0.0.1/empty-anchor.js create mode 100644 docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-3-1.png create mode 100644 docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-4-1.png create mode 100644 docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-5-1.png create mode 100644 docs/articles/web_only/multistart_files/figure-html/unnamed-chunk-6-1.png create mode 100644 docs/articles/web_only/saem_benchmarks.html create mode 100644 docs/articles/web_only/saem_benchmarks_files/accessible-code-block-0.0.1/empty-anchor.js (limited to 'docs/articles') diff --git a/docs/articles/FOCUS_D.html b/docs/articles/FOCUS_D.html index 39cf7e1a..3c8ad547 100644 --- a/docs/articles/FOCUS_D.html +++ b/docs/articles/FOCUS_D.html @@ -33,7 +33,7 @@ @@ -62,11 +62,14 @@ Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models

@@ -105,7 +111,7 @@

Example evaluation of FOCUS Example Dataset D

Johannes Ranke

Last change 31 January 2019 (rebuilt 2022-05-18)

Last change 31 January 2019 (rebuilt 2022-11-17)

Source: vignettes/FOCUS_D.rmd

FOCUS_D.rmd

@@ -116,207 +122,207 @@

This is just a very simple vignette showing how to fit a degradation model for a parent compound with one transformation product using mkin. After loading the library we look at the data. We have observed concentrations in the column named value at the times specified in column time for the two observed variables named parent and m1.

-library(mkin, quietly = TRUE)
-print(FOCUS_2006_D)

##      name time  value
-## 1  parent    0  99.46
-## 2  parent    0 102.04
-## 3  parent    1  93.50
-## 4  parent    1  92.50
-## 5  parent    3  63.23
-## 6  parent    3  68.99
-## 7  parent    7  52.32
-## 8  parent    7  55.13
-## 9  parent   14  27.27
-## 10 parent   14  26.64
-## 11 parent   21  11.50
-## 12 parent   21  11.64
-## 13 parent   35   2.85
-## 14 parent   35   2.91
-## 15 parent   50   0.69
-## 16 parent   50   0.63
-## 17 parent   75   0.05
-## 18 parent   75   0.06
-## 19 parent  100     NA
-## 20 parent  100     NA
-## 21 parent  120     NA
-## 22 parent  120     NA
-## 23     m1    0   0.00
-## 24     m1    0   0.00
-## 25     m1    1   4.84
-## 26     m1    1   5.64
-## 27     m1    3  12.91
-## 28     m1    3  12.96
-## 29     m1    7  22.97
-## 30     m1    7  24.47
-## 31     m1   14  41.69
-## 32     m1   14  33.21
-## 33     m1   21  44.37
-## 34     m1   21  46.44
-## 35     m1   35  41.22
-## 36     m1   35  37.95
-## 37     m1   50  41.19
-## 38     m1   50  40.01
-## 39     m1   75  40.09
-## 40     m1   75  33.85
-## 41     m1  100  31.04
-## 42     m1  100  33.13
-## 43     m1  120  25.15
-## 44     m1  120  33.31

library(mkin, quietly = TRUE)
+print(FOCUS_2006_D)

##      name time  value
+## 1  parent    0  99.46
+## 2  parent    0 102.04
+## 3  parent    1  93.50
+## 4  parent    1  92.50
+## 5  parent    3  63.23
+## 6  parent    3  68.99
+## 7  parent    7  52.32
+## 8  parent    7  55.13
+## 9  parent   14  27.27
+## 10 parent   14  26.64
+## 11 parent   21  11.50
+## 12 parent   21  11.64
+## 13 parent   35   2.85
+## 14 parent   35   2.91
+## 15 parent   50   0.69
+## 16 parent   50   0.63
+## 17 parent   75   0.05
+## 18 parent   75   0.06
+## 19 parent  100     NA
+## 20 parent  100     NA
+## 21 parent  120     NA
+## 22 parent  120     NA
+## 23     m1    0   0.00
+## 24     m1    0   0.00
+## 25     m1    1   4.84
+## 26     m1    1   5.64
+## 27     m1    3  12.91
+## 28     m1    3  12.96
+## 29     m1    7  22.97
+## 30     m1    7  24.47
+## 31     m1   14  41.69
+## 32     m1   14  33.21
+## 33     m1   21  44.37
+## 34     m1   21  46.44
+## 35     m1   35  41.22
+## 36     m1   35  37.95
+## 37     m1   50  41.19
+## 38     m1   50  40.01
+## 39     m1   75  40.09
+## 40     m1   75  33.85
+## 41     m1  100  31.04
+## 42     m1  100  33.13
+## 43     m1  120  25.15
+## 44     m1  120  33.31

Next we specify the degradation model: The parent compound degrades with simple first-order kinetics (SFO) to one metabolite named m1, which also degrades with SFO kinetics.

The call to mkinmod returns a degradation model. The differential equations represented in R code can be found in the character vector $diffs of the mkinmod object. If a C compiler (gcc) is installed and functional, the differential equation model will be compiled from auto-generated C code.

-SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))

## Temporary DLL for differentials generated and loaded

+SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO")) +

## Temporary DLL for differentials generated and loaded

-print(SFO_SFO$diffs)

##                                                    parent 
-##                          "d_parent = - k_parent * parent" 
-##                                                        m1 
-## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"

+print(SFO_SFO$diffs) +

##                                                    parent 
+##                          "d_parent = - k_parent * parent" 
+##                                                        m1 
+## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * 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

+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:    1.1.0 
-## R version used for fitting:       4.2.0 
-## Date of fit:     Wed May 18 20:42:29 2022 
-## Date of summary: Wed May 18 20:42:30 2022 
-## 
-## Equations:
-## d_parent/dt = - k_parent * parent
-## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
-## 
-## Model predictions using solution type analytical 
-## 
-## Fitted using 401 model solutions performed in 0.144 s
-## 
-## Error model: Constant variance 
-## 
-## Error model algorithm: OLS 
-## 
-## Starting values for parameters to be optimised:
-##                   value   type
-## parent_0       100.7500  state
-## k_parent         0.1000 deparm
-## k_m1             0.1001 deparm
-## f_parent_to_m1   0.5000 deparm
-## 
-## Starting values for the transformed parameters actually optimised:
-##                      value lower upper
-## parent_0        100.750000  -Inf   Inf
-## log_k_parent     -2.302585  -Inf   Inf
-## log_k_m1         -2.301586  -Inf   Inf
-## f_parent_qlogis   0.000000  -Inf   Inf
-## 
-## Fixed parameter values:
-##      value  type
-## m1_0     0 state
-## 
-## 
-## Warning(s): 
-## Observations with value of zero were removed from the data
-## 
-## Results:
-## 
-##        AIC      BIC    logLik
-##   204.4486 212.6365 -97.22429
-## 
-## Optimised, transformed parameters with symmetric confidence intervals:
-##                 Estimate Std. Error   Lower    Upper
-## parent_0        99.60000    1.57000 96.4000 102.8000
-## log_k_parent    -2.31600    0.04087 -2.3990  -2.2330
-## log_k_m1        -5.24700    0.13320 -5.5180  -4.9770
-## f_parent_qlogis  0.05792    0.08926 -0.1237   0.2395
-## sigma            3.12600    0.35850  2.3960   3.8550
-## 
-## Parameter correlation:
-##                   parent_0 log_k_parent   log_k_m1 f_parent_qlogis      sigma
-## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.174e-06
-## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.492e-07
-## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.220e-07
-## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.307e-06
-## sigma           -1.174e-06   -8.492e-07  8.220e-07       1.307e-06  1.000e+00
-## 
-## 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        0.098700  24.470 4.955e-23  0.090820 1.073e-01
-## k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
-## f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
-## sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
-## 
-## FOCUS Chi2 error levels in percent:
-##          err.min n.optim df
-## All data   6.398       4 15
-## parent     6.459       2  7
-## m1         4.690       2  8
-## 
-## Resulting formation fractions:
-##                 ff
-## parent_m1   0.5145
-## parent_sink 0.4855
-## 
-## Estimated disappearance times:
-##           DT50   DT90
-## parent   7.023  23.33
-## m1     131.761 437.70
-## 
-## Data:
-##  time variable observed predicted   residual
-##     0   parent    99.46  99.59848 -1.385e-01
-##     0   parent   102.04  99.59848  2.442e+00
-##     1   parent    93.50  90.23787  3.262e+00
-##     1   parent    92.50  90.23787  2.262e+00
-##     3   parent    63.23  74.07319 -1.084e+01
-##     3   parent    68.99  74.07319 -5.083e+00
-##     7   parent    52.32  49.91207  2.408e+00
-##     7   parent    55.13  49.91207  5.218e+00
-##    14   parent    27.27  25.01258  2.257e+00
-##    14   parent    26.64  25.01258  1.627e+00
-##    21   parent    11.50  12.53462 -1.035e+00
-##    21   parent    11.64  12.53462 -8.946e-01
-##    35   parent     2.85   3.14787 -2.979e-01
-##    35   parent     2.91   3.14787 -2.379e-01
-##    50   parent     0.69   0.71624 -2.624e-02
-##    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
-##     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
-##     3       m1    12.96  13.02400 -6.400e-02
-##     7       m1    22.97  25.04476 -2.075e+00
-##     7       m1    24.47  25.04476 -5.748e-01
-##    14       m1    41.69  36.69003  5.000e+00
-##    14       m1    33.21  36.69003 -3.480e+00
-##    21       m1    44.37  41.65310  2.717e+00
-##    21       m1    46.44  41.65310  4.787e+00
-##    35       m1    41.22  43.31313 -2.093e+00
-##    35       m1    37.95  43.31313 -5.363e+00
-##    50       m1    41.19  41.21832 -2.832e-02
-##    50       m1    40.01  41.21832 -1.208e+00
-##    75       m1    40.09  36.44704  3.643e+00
-##    75       m1    33.85  36.44704 -2.597e+00
-##   100       m1    31.04  31.98162 -9.416e-01
-##   100       m1    33.13  31.98162  1.148e+00
-##   120       m1    25.15  28.78984 -3.640e+00
-##   120       m1    33.31  28.78984  4.520e+00

+summary(fit) +

## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:21 2022 
+## Date of summary: Thu Nov 17 14:04:21 2022 
+## 
+## Equations:
+## d_parent/dt = - k_parent * parent
+## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 401 model solutions performed in 0.154 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##                   value   type
+## parent_0       100.7500  state
+## k_parent         0.1000 deparm
+## k_m1             0.1001 deparm
+## f_parent_to_m1   0.5000 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                      value lower upper
+## parent_0        100.750000  -Inf   Inf
+## log_k_parent     -2.302585  -Inf   Inf
+## log_k_m1         -2.301586  -Inf   Inf
+## f_parent_qlogis   0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+##      value  type
+## m1_0     0 state
+## 
+## 
+## Warning(s): 
+## Observations with value of zero were removed from the data
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   204.4486 212.6365 -97.22429
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                 Estimate Std. Error   Lower    Upper
+## parent_0        99.60000    1.57000 96.4000 102.8000
+## log_k_parent    -2.31600    0.04087 -2.3990  -2.2330
+## log_k_m1        -5.24700    0.13320 -5.5180  -4.9770
+## f_parent_qlogis  0.05792    0.08926 -0.1237   0.2395
+## sigma            3.12600    0.35850  2.3960   3.8550
+## 
+## Parameter correlation:
+##                   parent_0 log_k_parent   log_k_m1 f_parent_qlogis      sigma
+## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.172e-06
+## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.483e-07
+## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.205e-07
+## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.305e-06
+## sigma           -1.172e-06   -8.483e-07  8.205e-07       1.305e-06  1.000e+00
+## 
+## 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        0.098700  24.470 4.955e-23  0.090820 1.073e-01
+## k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
+## f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
+## sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   6.398       4 15
+## parent     6.459       2  7
+## m1         4.690       2  8
+## 
+## Resulting formation fractions:
+##                 ff
+## parent_m1   0.5145
+## parent_sink 0.4855
+## 
+## Estimated disappearance times:
+##           DT50   DT90
+## parent   7.023  23.33
+## m1     131.761 437.70
+## 
+## Data:
+##  time variable observed predicted   residual
+##     0   parent    99.46  99.59848 -1.385e-01
+##     0   parent   102.04  99.59848  2.442e+00
+##     1   parent    93.50  90.23787  3.262e+00
+##     1   parent    92.50  90.23787  2.262e+00
+##     3   parent    63.23  74.07319 -1.084e+01
+##     3   parent    68.99  74.07319 -5.083e+00
+##     7   parent    52.32  49.91207  2.408e+00
+##     7   parent    55.13  49.91207  5.218e+00
+##    14   parent    27.27  25.01258  2.257e+00
+##    14   parent    26.64  25.01258  1.627e+00
+##    21   parent    11.50  12.53462 -1.035e+00
+##    21   parent    11.64  12.53462 -8.946e-01
+##    35   parent     2.85   3.14787 -2.979e-01
+##    35   parent     2.91   3.14787 -2.379e-01
+##    50   parent     0.69   0.71624 -2.624e-02
+##    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
+##     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
+##     3       m1    12.96  13.02400 -6.400e-02
+##     7       m1    22.97  25.04476 -2.075e+00
+##     7       m1    24.47  25.04476 -5.748e-01
+##    14       m1    41.69  36.69003  5.000e+00
+##    14       m1    33.21  36.69003 -3.480e+00
+##    21       m1    44.37  41.65310  2.717e+00
+##    21       m1    46.44  41.65310  4.787e+00
+##    35       m1    41.22  43.31313 -2.093e+00
+##    35       m1    37.95  43.31313 -5.363e+00
+##    50       m1    41.19  41.21832 -2.832e-02
+##    50       m1    40.01  41.21832 -1.208e+00
+##    75       m1    40.09  36.44704  3.643e+00
+##    75       m1    33.85  36.44704 -2.597e+00
+##   100       m1    31.04  31.98162 -9.416e-01
+##   100       m1    33.13  31.98162  1.148e+00
+##   120       m1    25.15  28.78984 -3.640e+00
+##   120       m1    33.31  28.78984  4.520e+00

@@ -62,11 +62,14 @@ Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models

- Example evaluation of FOCUS Example Dataset Z + Short demo of the multistart method

Performance benefit by using compiled model definitions in mkin

+ Example evaluation of FOCUS Example Dataset Z +

Calculation of time weighted average concentrations with mkin

@@ -74,7 +77,10 @@ Example evaluation of NAFTA SOP Attachment examples

- Some benchmark timings + Benchmark timings for mkin +

+ Benchmark timings for saem.mmkin

@@ -105,7 +111,7 @@

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

Last change 18 May 2022 (rebuilt 2022-07-08)

Last change 18 May 2022 (rebuilt 2022-11-17)

Source: vignettes/FOCUS_L.rmd

FOCUS_L.rmd

@@ -130,18 +136,18 @@

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:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:00 2022 
-## Date of summary: Fri Jul  8 17:34:00 2022 
+summary(m.L1.SFO)

## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:25 2022 
+## Date of summary: Thu Nov 17 14:04:25 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.028 s
+## Fitted using 133 model solutions performed in 0.033 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -173,9 +179,9 @@
 ## 
 ## Parameter correlation:
 ##                parent_0 log_k_parent      sigma
-## parent_0      1.000e+00    6.186e-01 -1.712e-09
-## log_k_parent  6.186e-01    1.000e+00 -3.237e-09
-## sigma        -1.712e-09   -3.237e-09  1.000e+00
+## parent_0      1.000e+00    6.186e-01 -1.516e-09
+## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
+## sigma        -1.516e-09   -3.124e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -217,7 +223,7 @@
 ##    30   parent      4.0     5.251  -1.2513

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

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

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

The residual plot can be easily obtained by

@@ -225,26 +231,29 @@
 
 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)
-plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
+m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)

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

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

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

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

## Warning in sqrt(diag(covar)): NaNs produced

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

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

## mkin version used for fitting:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:00 2022 
-## Date of summary: Fri Jul  8 17:34:00 2022 
+## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:25 2022 
+## Date of summary: Thu Nov 17 14:04:25 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 357 model solutions performed in 0.07 s
+## Fitted using 369 model solutions performed in 0.08 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -265,34 +274,39 @@
 ## Fixed parameter values:
 ## None
 ## 
+## 
+## Warning(s): 
+## Optimisation did not converge:
+## false convergence (8)
+## 
 ## Results:
 ## 
-##        AIC      BIC    logLik
-##   95.88804 99.44953 -43.94402
+##        AIC      BIC   logLik
+##   95.88781 99.44929 -43.9439
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
 ## parent_0     92.47     1.2820 89.720 95.220
-## log_alpha    11.37        NaN    NaN    NaN
-## log_beta     13.72        NaN    NaN    NaN
-## sigma         2.78     0.4621  1.789  3.771
+## log_alpha    13.78        NaN    NaN    NaN
+## log_beta     16.13        NaN    NaN    NaN
+## sigma         2.78     0.4598  1.794  3.766
 ## 
 ## Parameter correlation:
 ##            parent_0 log_alpha log_beta     sigma
-## parent_0  1.0000000       NaN      NaN 0.0005548
+## parent_0  1.0000000       NaN      NaN 0.0001671
 ## log_alpha       NaN         1      NaN       NaN
 ## log_beta        NaN       NaN        1       NaN
-## sigma     0.0005548       NaN      NaN 1.0000000
+## sigma     0.0001671       NaN      NaN 1.0000000
 ## 
 ## 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      NA     NA 89.720 95.220
-## alpha     87110.00      NA     NA     NA     NA
-## beta     911100.00      NA     NA     NA     NA
-## sigma         2.78      NA     NA  1.789  3.771
+## parent_0 9.247e+01      NA     NA 89.720 95.220
+## alpha    9.658e+05      NA     NA     NA     NA
+## beta     1.010e+07      NA     NA     NA     NA
+## sigma    2.780e+00      NA     NA  1.794  3.766
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -300,8 +314,8 @@
 ## parent     3.619       3  6
 ## 
 ## Estimated disappearance times:
-##         DT50  DT90 DT50back
-## parent 7.249 24.08    7.249
+##        DT50  DT90 DT50back
+## parent 7.25 24.08     7.25

We get a warning that the default optimisation algorithm Port did not converge, which is an indication that the model is overparameterised, i.e. contains too many parameters that are ill-defined as a consequence.

And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the $\chi^2$ error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters log_alpha and log_beta internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of alpha and beta. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of log_alpha and log_beta is 1.000, clearly indicating that the model is overparameterised.

The $\chi^2$ error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same $\chi^2$ error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of $\chi^2$ error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

@@ -310,7 +324,7 @@

Laboratory Data L2

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

+ FOCUS_2006_L2 = data.frame(
   t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
   parent = c(96.1, 91.8, 41.4, 38.7,
@@ -321,9 +335,9 @@
 SFO fit for L2
 
 Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument show_residuals to the plot command.
-+ m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
      main = "FOCUS L2 - SFO")
 
 The \(\chi^2\) 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.
@@ -334,24 +348,24 @@
 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,
+plot(m.L2.FOMC, show_residuals = TRUE,
      main = "FOCUS L2 - FOMC")
 
--summary(m.L2.FOMC, data = FALSE)
-## mkin version used for fitting:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:01 2022 
-## Date of summary: Fri Jul  8 17:34:01 2022 
++summary(m.L2.FOMC, data = FALSE)
+## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:26 2022 
+## Date of summary: Thu Nov 17 14:04:26 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.044 s
+## Fitted using 239 model solutions performed in 0.048 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -386,10 +400,10 @@
 ## 
 ## 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   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
+## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -415,17 +429,17 @@
 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,
+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:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:01 2022 
-## Date of summary: Fri Jul  8 17:34:01 2022 
++summary(m.L2.DFOP, data = FALSE)
+## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:27 2022 
+## Date of summary: Thu Nov 17 14:04:27 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -434,7 +448,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.119 s
+## Fitted using 581 model solutions performed in 0.128 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -465,18 +479,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.113  1.845e+03 -4360.0000 4367.0000
+## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
 ## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
 ## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
 ## sigma       1.414  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  6.784e-07 -5.188e-10  2.665e-01 -5.800e-10
-## log_k1    6.784e-07  1.000e+00  1.114e-04 -2.191e-04 -1.029e-05
-## log_k2   -5.188e-10  1.114e-04  1.000e+00 -7.903e-01  5.080e-09
-## g_qlogis  2.665e-01 -2.191e-04 -7.903e-01  1.000e+00 -7.991e-09
-## sigma    -5.800e-10 -1.029e-05  5.080e-09 -7.991e-09  1.000e+00
+## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
+## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
+## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
+## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
+## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -484,7 +498,7 @@
 ## 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        22.4800 5.544e-04 4.998e-01  0.0000     Inf
+## k1        22.4800 5.553e-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
@@ -496,7 +510,7 @@
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599 0.03083   2.058
+## parent 0.5335 5.311    1.599 0.03084   2.058
 Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.
 
 

@@ -504,7 +518,7 @@
 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))
@@ -513,11 +527,11 @@
 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)
+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.
 
@@ -526,12 +540,12 @@
 
 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:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:02 2022 
-## Date of summary: Fri Jul  8 17:34:02 2022 
++summary(mm.L3[["DFOP", 1]])
+## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:27 2022 
+## Date of summary: Thu Nov 17 14:04:28 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -540,7 +554,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 376 model solutions performed in 0.072 s
+## Fitted using 376 model solutions performed in 0.078 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -578,11 +592,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.632e-08
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.145e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.021e-06
-## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.925e-07
-## sigma    -9.632e-08  7.145e-07  1.021e-06 -7.925e-07  1.000e+00
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -9.664e-08
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  7.147e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  1.022e-06
+## g_qlogis  4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -7.926e-07
+## sigma    -9.664e-08  7.147e-07  1.022e-06 -7.926e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -614,8 +628,8 @@
 ##    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.
@@ -625,33 +639,33 @@
 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)
 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)
+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:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:02 2022 
-## Date of summary: Fri Jul  8 17:34:02 2022 
++summary(mm.L4[["SFO", 1]], data = FALSE)
+## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:28 2022 
+## Date of summary: Thu Nov 17 14:04:29 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.026 s
+## Fitted using 142 model solutions performed in 0.029 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -683,9 +697,9 @@
 ## 
 ## Parameter correlation:
 ##               parent_0 log_k_parent     sigma
-## parent_0     1.000e+00    5.938e-01 3.440e-07
-## log_k_parent 5.938e-01    1.000e+00 5.885e-07
-## sigma        3.440e-07    5.885e-07 1.000e+00
+## parent_0     1.000e+00    5.938e-01 3.387e-07
+## log_k_parent 5.938e-01    1.000e+00 5.830e-07
+## sigma        3.387e-07    5.830e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -704,19 +718,19 @@
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352
--summary(mm.L4[["FOMC", 1]], data = FALSE)
-## mkin version used for fitting:    1.1.1 
-## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 17:34:02 2022 
-## Date of summary: Fri Jul  8 17:34:02 2022 
++summary(mm.L4[["FOMC", 1]], data = FALSE)
+## mkin version used for fitting:    1.2.0 
+## R version used for fitting:       4.2.2 
+## Date of fit:     Thu Nov 17 14:04:28 2022 
+## Date of summary: Thu Nov 17 14:04:29 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.041 s
+## Fitted using 224 model solutions performed in 0.046 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -751,10 +765,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
+## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -803,7 +817,7 @@
 
 
   
-Site built with pkgdown 2.0.5.
+Site built with pkgdown 2.0.6.
 
 
       
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index c3a39708..292a72a4 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -17,7 +17,7 @@
       
       
         mkin
-        1.1.2
+        1.2.0
       
     

 
@@ -44,11 +44,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -56,7 +59,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -102,6 +108,10 @@
         
         
Example evaluations of the dimethenamid data from 2018
         
+        
Short demo of the multistart method
+        
+        
Benchmark timings for saem.mmkin
+        
       

   

 

diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html
index a32f4b41..da499501 100644
--- a/docs/articles/mkin.html
+++ b/docs/articles/mkin.html
@@ -33,7 +33,7 @@
       
       
         mkin
-        1.1.0
+        1.2.0


 
@@ -62,11 +62,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -74,7 +77,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -105,7 +111,7 @@
       Introduction to mkin
                         Johannes Ranke
             
-            Last change 15 February 2021 (rebuilt 2022-05-18)
+            Last change 15 February 2021 (rebuilt 2022-11-17)
       
       Source: vignettes/mkin.rmd
       mkin.rmd
@@ -120,34 +126,34 @@
 
 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"),
-                         M1 = mkinsub("SFO", "M2"),
-                         M2 = mkinsub("SFO"),
-                         use_of_ff = "max", quiet = TRUE)
-
-
-# Produce model predictions using some arbitrary parameters
-sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
-  c(k_parent = 0.03,
-    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
-    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
-  c(parent = 100, M1 = 0, M2 = 0),
-  sampling_times)
-
-# Generate a dataset by adding normally distributed errors with
-# standard deviation 3, for two replicates at each sampling time
-d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
-                             sdfunc = function(x) 3,
-                             n = 1, seed = 123456789 )
-
-# Fit the model to the dataset
-f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
-
-# Plot the results separately for parent and metabolites
-plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
+library("mkin", quietly = TRUE)
+# Define the kinetic model
+m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
+                         M1 = mkinsub("SFO", "M2"),
+                         M2 = mkinsub("SFO"),
+                         use_of_ff = "max", quiet = TRUE)
+
+
+# Produce model predictions using some arbitrary parameters
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
+  c(k_parent = 0.03,
+    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
+    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
+  c(parent = 100, M1 = 0, M2 = 0),
+  sampling_times)
+
+# Generate a dataset by adding normally distributed errors with
+# standard deviation 3, for two replicates at each sampling time
+d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
+                             sdfunc = function(x) 3,
+                             n = 1, seed = 123456789 )
+
+# Fit the model to the dataset
+f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
+
+# Plot the results separately for parent and metabolites
+plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
 
 
 
@@ -264,7 +270,7 @@
 
 
   
-Site built with pkgdown 2.0.3.
+Site built with pkgdown 2.0.6.
 
 
       
diff --git a/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png b/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png
index d1e7048d..63246387 100644
Binary files a/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png and b/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png differ
diff --git a/docs/articles/twa.html b/docs/articles/twa.html
index dad8ee44..41340e88 100644
--- a/docs/articles/twa.html
+++ b/docs/articles/twa.html
@@ -33,7 +33,7 @@
       
       
         mkin
-        1.1.0
+        1.2.0
       
     
 
@@ -62,11 +62,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -74,7 +77,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -105,7 +111,7 @@
       Calculation of time weighted average concentrations with mkin
                         Johannes Ranke
             
-            Last change 18 September 2019 (rebuilt 2022-05-18)
+            Last change 18 September 2019 (rebuilt 2022-11-17)
       
       Source: vignettes/twa.rmd
       twa.rmd
@@ -168,7 +174,7 @@
 
 
   
-Site built with pkgdown 2.0.3.
+Site built with pkgdown 2.0.6.
 
 
       
diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html
index 0dafb98a..ea20ecd9 100644
--- a/docs/articles/web_only/FOCUS_Z.html
+++ b/docs/articles/web_only/FOCUS_Z.html
@@ -33,7 +33,7 @@
       
       
         mkin
-        1.1.0
+        1.2.0
       
     
 
@@ -62,11 +62,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -74,7 +77,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -105,7 +111,7 @@
       Example evaluation of FOCUS dataset Z
                         Johannes Ranke
             
-            Last change 16 January 2018 (rebuilt 2022-05-18)
+            Last change 16 January 2018 (rebuilt 2022-11-17)
       
       Source: vignettes/web_only/FOCUS_Z.rmd
       FOCUS_Z.rmd
@@ -120,88 +126,88 @@
 
 The following code defines the example dataset from Appendix 7 to the FOCUS kinetics report (FOCUS Work Group on Degradation Kinetics 2014, 354).
 -library(mkin, quietly = TRUE)
-LOD = 0.5
-FOCUS_2006_Z = data.frame(
-  t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21,
-        42, 61, 96, 124),
-  Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8,
-         2.9, 3.5, 5.3, 4.4, 1.2, 0.7),
-  Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1,
-         1.6, 0.6, 0.5 * LOD, NA, NA, NA),
-  Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5,
-         0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA),
-  Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5,
-         25.2, 17.2, 4.8, 4.5, 2.8, 4.4))
-
-FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)
+library(mkin, quietly = TRUE)
+LOD = 0.5
+FOCUS_2006_Z = data.frame(
+  t = c(0, 0.04, 0.125, 0.29, 0.54, 1, 2, 3, 4, 7, 10, 14, 21,
+        42, 61, 96, 124),
+  Z0 = c(100, 81.7, 70.4, 51.1, 41.2, 6.6, 4.6, 3.9, 4.6, 4.3, 6.8,
+         2.9, 3.5, 5.3, 4.4, 1.2, 0.7),
+  Z1 = c(0, 18.3, 29.6, 46.3, 55.1, 65.7, 39.1, 36, 15.3, 5.6, 1.1,
+         1.6, 0.6, 0.5 * LOD, NA, NA, NA),
+  Z2 = c(0, NA, 0.5 * LOD, 2.6, 3.8, 15.3, 37.2, 31.7, 35.6, 14.5,
+         0.8, 2.1, 1.9, 0.5 * LOD, NA, NA, NA),
+  Z3 = c(0, NA, NA, NA, NA, 0.5 * LOD, 9.2, 13.1, 22.3, 28.4, 32.5,
+         25.2, 17.2, 4.8, 4.5, 2.8, 4.4))
+
+FOCUS_2006_Z_mkin <- mkin_wide_to_long(FOCUS_2006_Z)
 
 
 Parent and one metabolite
 
 The next step is to set up the models used for the kinetic analysis. As the simultaneous fit of parent and the first metabolite is usually straightforward, Step 1 (SFO for parent only) is skipped here. We start with the model 2a, with formation and decline of metabolite Z1 and the pathway from parent directly to sink included (default in mkin).
 -Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
-                Z1 = mkinsub("SFO"))
-## Temporary DLL for differentials generated and loaded
+Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
+                Z1 = mkinsub("SFO"))
+## Temporary DLL for differentials generated and loaded
 -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
+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)
+plot_sep(m.Z.2a)
 
 -summary(m.Z.2a, data = FALSE)$bpar
-##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
-## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
-## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
-## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
-## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815
+summary(m.Z.2a, data = FALSE)$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 2.8154e-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
 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:
 -Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
-                   Z1 = mkinsub("SFO"),
-                   use_of_ff = "max")
-## Temporary DLL for differentials generated and loaded
+Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
+                   Z1 = mkinsub("SFO"),
+                   use_of_ff = "max")
+## Temporary DLL for differentials generated and loaded
 -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
+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)
+plot_sep(m.Z.2a.ff)
 
 -summary(m.Z.2a.ff, data = FALSE)$bpar
-##            Estimate se_notrans t value     Pr(>t)    Lower    Upper
-## Z0_0       97.01488   3.301084 29.3888 3.2971e-21 91.66556 102.3642
-## k_Z0        2.23601   0.207078 10.7979 3.3309e-11  1.95303   2.5600
-## k_Z1        0.48212   0.063265  7.6207 2.8154e-08  0.40341   0.5762
-## f_Z0_to_Z1  1.00000   0.094764 10.5525 5.3560e-11  0.00000   1.0000
-## sigma       4.80411   0.635638  7.5579 3.2592e-08  3.52677   6.0815
+summary(m.Z.2a.ff, data = FALSE)$bpar
+##            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 2.8154e-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
 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")
-## Temporary DLL for differentials generated and loaded
+Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO"), use_of_ff = "max")
+## Temporary DLL for differentials generated and loaded
 -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
+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)
+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   2.597342  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
 As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity.
 
 
@@ -209,56 +215,58 @@
 
 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")
-## Temporary DLL for differentials generated and loaded
+Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+               Z2 = mkinsub("SFO"), use_of_ff = "max")
+## Temporary DLL for differentials generated and loaded
 -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
+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)
+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")
-## Temporary DLL for differentials generated and loaded
+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")
+## Temporary DLL for differentials generated and loaded
 -m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
-                     parms.ini = m.Z.5$bparms.ode,
-                     quiet = TRUE)
-## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
-## Observations with value of zero were removed from the data
--plot_sep(m.Z.FOCUS)
-
+m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
+                     parms.ini = m.Z.5$bparms.ode,
+                     quiet = TRUE)
+## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, :
+## Observations with value of zero were removed from the data
+## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge:
+## false convergence (8)
 -summary(m.Z.FOCUS, data = FALSE)$bpar
-##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
-## Z0_0       96.838397   1.994270 48.5583 4.0284e-42 92.826435 100.850359
-## k_Z0        2.215406   0.118459 18.7018 1.0416e-23  1.989466   2.467005
-## k_Z1        0.478300   0.028257 16.9267 6.2409e-22  0.424702   0.538662
-## k_Z2        0.451616   0.042137 10.7178 1.6305e-14  0.374328   0.544863
-## k_Z3        0.058693   0.015245  3.8499 1.7803e-04  0.034805   0.098976
-## f_Z2_to_Z3  0.471509   0.058352  8.0804 9.6622e-11  0.357739   0.588317
-## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
--endpoints(m.Z.FOCUS)
-## $ff
-##   Z2_Z3 Z2_sink 
-## 0.47151 0.52849 
-## 
-## $distimes
-##        DT50    DT90
-## Z0  0.31288  1.0394
-## Z1  1.44919  4.8141
-## Z2  1.53481  5.0985
-## Z3 11.80971 39.2310
+plot_sep(m.Z.FOCUS)
+
++summary(m.Z.FOCUS, data = FALSE)$bpar
+##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.838822   1.994274 48.5584 4.0280e-42 92.826981 100.850664
+## k_Z0        2.215393   0.118458 18.7019 1.0413e-23  1.989456   2.466989
+## k_Z1        0.478305   0.028258 16.9266 6.2418e-22  0.424708   0.538666
+## k_Z2        0.451627   0.042139 10.7176 1.6314e-14  0.374339   0.544872
+## k_Z3        0.058692   0.015245  3.8499 1.7803e-04  0.034808   0.098965
+## f_Z2_to_Z3  0.471502   0.058351  8.0805 9.6608e-11  0.357769   0.588274
+## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
++endpoints(m.Z.FOCUS)
+## $ff
+##   Z2_Z3 Z2_sink 
+##  0.4715  0.5285 
+## 
+## $distimes
+##        DT50    DT90
+## Z0  0.31288  1.0394
+## Z1  1.44917  4.8141
+## Z2  1.53478  5.0984
+## Z3 11.80986 39.2315
 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.
 
 
@@ -266,107 +274,105 @@
 
 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"))
-## Temporary DLL for differentials generated and loaded
--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)
-
++Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))
+## Temporary DLL for differentials generated and loaded
++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
 -summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
-## NULL
+plot_sep(m.Z.mkin.1)
+
++summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
+## 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"))
-## Temporary DLL for differentials generated and loaded
--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
-## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Optimisation did not converge:
-## false convergence (8)
++Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO"))
+## Temporary DLL for differentials generated and loaded
++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)
+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"))
-## Temporary DLL for differentials generated and loaded
+Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFO"))
+## Temporary DLL for differentials generated and loaded
 -m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
-                      parms.ini = m.Z.mkin.3$bparms.ode,
-                      quiet = TRUE)
-## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =
-## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the
-## data
+m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
+                      parms.ini = m.Z.mkin.3$bparms.ode,
+                      quiet = TRUE)
+## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini =
+## m.Z.mkin.3$bparms.ode, : Observations with value of zero were removed from the
+## data
 -plot_sep(m.Z.mkin.4)
+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"))
-## Temporary DLL for differentials generated and loaded
+Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))
+## Temporary DLL for differentials generated and loaded
 -m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
-                      parms.ini = m.Z.mkin.4$bparms.ode[1:4],
-                      quiet = TRUE)
-## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =
-## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from
-## the data
+m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+                      parms.ini = m.Z.mkin.4$bparms.ode[1:4],
+                      quiet = TRUE)
+## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =
+## m.Z.mkin.4$bparms.ode[1:4], : Observations with value of zero were removed from
+## the data
 -plot_sep(m.Z.mkin.5)
+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.
 -m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
-                       parms.ini = c(m.Z.mkin.5$bparms.ode[1:7],
-                                     k_Z3_bound_free = 0),
-                       fixed_parms = "k_Z3_bound_free",
-                       quiet = TRUE)
-## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =
-## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed
-## from the data
+m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+                       parms.ini = c(m.Z.mkin.5$bparms.ode[1:7],
+                                     k_Z3_bound_free = 0),
+                       fixed_parms = "k_Z3_bound_free",
+                       quiet = TRUE)
+## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini =
+## c(m.Z.mkin.5$bparms.ode[1:7], : Observations with value of zero were removed
+## from the data
 -plot_sep(m.Z.mkin.5a)
+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)
-## $ff
-## Z0_free   Z2_Z3 Z2_sink Z3_free 
-## 1.00000 0.53656 0.46344 1.00000 
-## 
-## $SFORB
-##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471376 0.0075126 0.0800073 0.0000000 
-## 
-## $distimes
-##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848  0.35666    0.28325     92.264         NA         NA
-## Z1 1.5148 5.0320       NA         NA         NA         NA         NA
-## Z2 1.6414 5.4526       NA         NA         NA         NA         NA
-## Z3     NA     NA       NA         NA         NA     8.6636        Inf
+endpoints(m.Z.mkin.5a)
+## $ff
+## Z0_free   Z2_Z3 Z2_sink Z3_free 
+## 1.00000 0.53656 0.46344 1.00000 
+## 
+## $SFORB
+##     Z0_b1     Z0_b2      Z0_g     Z3_b1     Z3_b2      Z3_g 
+## 2.4471322 0.0075125 0.9519862 0.0800069 0.0000000 0.9347820 
+## 
+## $distimes
+##      DT50   DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
+## Z0 0.3043 1.1848  0.35666    0.28325     92.266         NA         NA
+## Z1 1.5148 5.0320       NA         NA         NA         NA         NA
+## Z2 1.6414 5.4526       NA         NA         NA         NA         NA
+## Z3     NA     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.
 
 
@@ -398,7 +404,7 @@
 
 
   
-Site built with pkgdown 2.0.3.
+Site built with pkgdown 2.0.6.
 
 
       
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diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html
index df1e06db..b8ec5059 100644
--- a/docs/articles/web_only/NAFTA_examples.html
+++ b/docs/articles/web_only/NAFTA_examples.html
@@ -33,7 +33,7 @@
       
       
         mkin
-        1.1.0
+        1.2.0
       
     
 
@@ -62,11 +62,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -74,7 +77,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -105,7 +111,7 @@
       Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance
                         Johannes Ranke
             
-            26 February 2019 (rebuilt 2022-05-18)
+            26 February 2019 (rebuilt 2022-11-17)
       
       Source: vignettes/web_only/NAFTA_examples.rmd
       NAFTA_examples.rmd
@@ -128,205 +134,205 @@
 Example on page 5, upper panel
 
 -p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])
-## 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
+p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])
+## 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)
-## Sums of squares:
-##       SFO      IORE      DFOP 
-## 465.21753  56.27506  32.06401 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 64.4304
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower   Upper
-## parent_0  95.8401 4.67e-21 92.245 99.4357
-## k_parent   0.0102 3.92e-12  0.009  0.0117
-## sigma      4.8230 3.81e-06  3.214  6.4318
-## 
-## $IORE
-##                Estimate Pr(>t)    Lower    Upper
-## parent_0       1.01e+02     NA 9.91e+01 1.02e+02
-## k__iore_parent 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
-## 
-## $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       2.95e-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
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  67.7 2.25e+02 6.77e+01
-## IORE 58.2 1.07e+03 3.22e+02
-## DFOP 55.5 4.28e+11 2.35e+11
-## 
-## Representative half-life:
-## [1] 321.51
+print(p5a)
+## Sums of squares:
+##       SFO      IORE      DFOP 
+## 465.21753  56.27506  32.06401 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 64.4304
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  95.8401 4.67e-21 92.245 99.4357
+## k_parent   0.0102 3.92e-12  0.009  0.0117
+## sigma      4.8230 3.81e-06  3.214  6.4318
+## 
+## $IORE
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       1.01e+02     NA 9.91e+01 1.02e+02
+## k__iore_parent 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
+## 
+## $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       2.26e-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
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  67.7 2.25e+02 6.77e+01
+## IORE 58.2 1.07e+03 3.22e+02
+## DFOP 55.5 5.59e+11 3.07e+11
+## 
+## Representative half-life:
+## [1] 321.51
 
 
 Example on page 5, lower panel
 
 -p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])
-## 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
+p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])
+## 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)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 94.81123 10.10936  7.55871 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 11.77879
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0   96.497 2.32e-24 94.85271 98.14155
-## k_parent    0.008 3.42e-14  0.00737  0.00869
-## sigma       2.295 1.22e-05  1.47976  3.11036
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       9.85e+01 1.17e-28 9.79e+01 9.92e+01
-## k__iore_parent 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
-## 
-## $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       9.41e-12 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
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  86.6 2.88e+02 8.66e+01
-## IORE 85.5 7.17e+02 2.16e+02
-## DFOP 83.6 1.21e+11 7.36e+10
-## 
-## Representative half-life:
-## [1] 215.87
+print(p5b)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 94.81123 10.10936  7.55871 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 11.77879
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0   96.497 2.32e-24 94.85271 98.14155
+## k_parent    0.008 3.42e-14  0.00737  0.00869
+## sigma       2.295 1.22e-05  1.47976  3.11036
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       9.85e+01 1.17e-28 9.79e+01 9.92e+01
+## k__iore_parent 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
+## 
+## $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       8.63e-12 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
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  86.6 2.88e+02 8.66e+01
+## IORE 85.5 7.17e+02 2.16e+02
+## DFOP 83.6 1.32e+11 8.04e+10
+## 
+## Representative half-life:
+## [1] 215.87
 
 
 Example on page 6
 
 -p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])
-## 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
+p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])
+## 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)
-## Sums of squares:
-##       SFO      IORE      DFOP 
-## 188.45361  51.00699  42.46931 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 58.39888
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  94.7759 7.29e-24 92.3478 97.2039
-## k_parent   0.0179 8.02e-16  0.0166  0.0194
-## sigma      3.0696 3.81e-06  2.0456  4.0936
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       97.12446 2.63e-26 95.62461 98.62431
-## k__iore_parent  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
-## 
-## $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       4.40e-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
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  38.6 1.28e+02 3.86e+01
-## IORE 34.0 1.77e+02 5.32e+01
-## DFOP 34.1 7.43e+09 1.58e+10
-## 
-## Representative half-life:
-## [1] 53.17
+print(p6)
+## Sums of squares:
+##       SFO      IORE      DFOP 
+## 188.45361  51.00699  42.46931 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 58.39888
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  94.7759 7.29e-24 92.3478 97.2039
+## k_parent   0.0179 8.02e-16  0.0166  0.0194
+## sigma      3.0696 3.81e-06  2.0456  4.0936
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       97.12446 2.63e-26 95.62461 98.62431
+## k__iore_parent  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
+## 
+## $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       3.22e-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
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  38.6 1.28e+02 3.86e+01
+## IORE 34.0 1.77e+02 5.32e+01
+## DFOP 34.1 1.01e+10 2.15e+10
+## 
+## Representative half-life:
+## [1] 53.17
 
 
 Example on page 7
 
 -p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])
-## 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
+p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])
+## 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)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 3661.661 3195.030 3174.145 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 3334.194
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 96.41796 4.80e-53 93.32245 99.51347
-## k_parent  0.00735 7.64e-21  0.00641  0.00843
-## sigma     7.94557 1.83e-15  6.46713  9.42401
-## 
-## $IORE
-##                Estimate Pr(>t)    Lower    Upper
-## parent_0       9.92e+01     NA 9.55e+01 1.03e+02
-## k__iore_parent 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
-## 
-## $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       2.81e-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
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  94.3 3.13e+02 9.43e+01
-## IORE 96.7 1.51e+03 4.55e+02
-## DFOP 96.4 4.87e+09 2.46e+09
-## 
-## Representative half-life:
-## [1] 454.55
+print(p7)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 3661.661 3195.030 3174.145 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 3334.194
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 96.41796 4.80e-53 93.32245 99.51347
+## k_parent  0.00735 7.64e-21  0.00641  0.00843
+## sigma     7.94557 1.83e-15  6.46713  9.42401
+## 
+## $IORE
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       9.92e+01     NA 9.55e+01 1.03e+02
+## k__iore_parent 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
+## 
+## $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       3.63e-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
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  94.3 3.13e+02 9.43e+01
+## IORE 96.7 1.51e+03 4.55e+02
+## DFOP 96.4 3.77e+09 1.91e+09
+## 
+## Representative half-life:
+## [1] 454.55
 
 
 
@@ -337,52 +343,52 @@
 
 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 = 1e-3))
-## 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
+p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent = 1e-3))
+## 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)
-## Sums of squares:
-##       SFO      IORE      DFOP 
-## 1996.9408  444.9237  547.5616 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 477.4924
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 88.16549 6.53e-29 83.37344 92.95754
-## k_parent  0.00803 1.67e-13  0.00674  0.00957
-## sigma     7.44786 4.17e-10  5.66209  9.23363
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       9.77e+01 7.03e-35 9.44e+01 1.01e+02
-## k__iore_parent 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
-## 
-## $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
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  86.3  287     86.3
-## IORE 53.4  668    201.0
-## DFOP 55.6  517    253.0
-## 
-## Representative half-life:
-## [1] 201.03
+print(p8)
+## Sums of squares:
+##       SFO      IORE      DFOP 
+## 1996.9408  444.9237  547.5616 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 477.4924
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 88.16549 6.53e-29 83.37344 92.95754
+## k_parent  0.00803 1.67e-13  0.00674  0.00957
+## sigma     7.44786 4.17e-10  5.66209  9.23363
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       9.77e+01 7.03e-35 9.44e+01 1.01e+02
+## k__iore_parent 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
+## 
+## $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
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  86.3  287     86.3
+## IORE 53.4  668    201.0
+## DFOP 55.6  517    253.0
+## 
+## Representative half-life:
+## [1] 201.03
 
 
 
@@ -392,160 +398,165 @@
 Example on page 9, upper panel
 
 -p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
-## 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
+p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
+## 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)
-## Sums of squares:
-##       SFO      IORE      DFOP 
-## 839.35238  88.57064   9.93363 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 105.5678
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  88.1933 3.06e-12 79.9447 96.4419
-## k_parent   0.0409 2.07e-07  0.0324  0.0516
-## sigma      7.2429 3.92e-05  4.4768 10.0090
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       9.89e+01 1.12e-16 9.54e+01 1.02e+02
-## k__iore_parent 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
-## 
-## $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       9.02e-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
-## 
-## 
-## DTx values:
-##      DT50     DT90 DT50_rep
-## SFO  16.9 5.63e+01 1.69e+01
-## IORE 11.6 3.37e+02 1.01e+02
-## DFOP 10.5 1.38e+12 7.68e+11
-## 
-## Representative half-life:
-## [1] 101.43
+print(p9a)
+## Sums of squares:
+##       SFO      IORE      DFOP 
+## 839.35238  88.57064   9.93363 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 105.5678
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  88.1933 3.06e-12 79.9447 96.4419
+## k_parent   0.0409 2.07e-07  0.0324  0.0516
+## sigma      7.2429 3.92e-05  4.4768 10.0090
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       9.89e+01 1.12e-16 9.54e+01 1.02e+02
+## k__iore_parent 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
+## 
+## $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       9.02e-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
+## 
+## 
+## DTx values:
+##      DT50     DT90 DT50_rep
+## SFO  16.9 5.63e+01 1.69e+01
+## IORE 11.6 3.37e+02 1.01e+02
+## DFOP 10.5 1.38e+12 7.69e+11
+## 
+## Representative half-life:
+## [1] 101.43
 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"]])
-## 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)
+p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]])
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(diag(covar_notrans)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+## 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)
 
--print(p9b)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 35.64867 23.22334 35.64867 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 28.54188
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower   Upper
-## parent_0  94.7123 2.15e-19 93.178 96.2464
-## k_parent   0.0389 4.47e-14  0.037  0.0408
-## sigma      1.5957 1.28e-04  0.932  2.2595
-## 
-## $IORE
-##                Estimate   Pr(>t)   Lower  Upper
-## parent_0         93.863 2.32e-18 92.4565 95.269
-## k__iore_parent    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
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower   Upper
-## parent_0  94.7123 1.61e-16 93.1355 96.2891
-## k1         0.0389 1.08e-04  0.0266  0.0569
-## k2         0.0389 2.24e-04  0.0255  0.0592
-## g          0.5256 5.00e-01  0.0000  1.0000
-## sigma      1.5957 2.50e-04  0.9135  2.2779
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  17.8 59.2     17.8
-## IORE 18.4 49.2     14.8
-## DFOP 17.8 59.2     17.8
-## 
-## Representative half-life:
-## [1] 14.8
++print(p9b)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 35.64867 23.22334 35.64867 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 28.54188
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  94.7123 2.15e-19 93.178 96.2464
+## k_parent   0.0389 4.47e-14  0.037  0.0408
+## sigma      1.5957 1.28e-04  0.932  2.2595
+## 
+## $IORE
+##                Estimate   Pr(>t)   Lower  Upper
+## parent_0         93.863 2.32e-18 92.4565 95.269
+## k__iore_parent    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
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  94.7123 1.61e-16 93.1355 96.2891
+## k1         0.0389 1.08e-04  0.0266  0.0569
+## k2         0.0389 2.23e-04  0.0255  0.0592
+## g          0.5256      NaN      NA      NA
+## sigma      1.5957 2.50e-04  0.9135  2.2779
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  17.8 59.2     17.8
+## IORE 18.4 49.2     14.8
+## DFOP 17.8 59.2     17.8
+## 
+## Representative half-life:
+## [1] 14.8
 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"]])
-## Warning in sqrt(diag(covar)): NaNs produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-## The half-life obtained from the IORE model may be used
--plot(p10)
++p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+## 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)
 
--print(p10)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 899.4089 336.4348 899.4089 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 413.4841
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 101.7315 6.42e-11 91.9259 111.5371
-## k_parent   0.0495 1.70e-07  0.0404   0.0607
-## sigma      8.0152 1.28e-04  4.6813  11.3491
-## 
-## $IORE
-##                Estimate   Pr(>t)  Lower   Upper
-## parent_0          96.86 3.32e-12 90.848 102.863
-## k__iore_parent     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
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower    Upper
-## parent_0 101.7315 1.41e-09 91.6534 111.8097
-## k1         0.0495 6.32e-03  0.0241   0.1018
-## k2         0.0495 2.41e-03  0.0272   0.0901
-## g          0.4487 5.00e-01      NA       NA
-## sigma      8.0152 2.50e-04  4.5886  11.4418
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  14.0 46.5    14.00
-## IORE 16.4 29.4     8.86
-## DFOP 14.0 46.5    14.00
-## 
-## Representative half-life:
-## [1] 8.86
++print(p10)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 899.4089 336.4348 899.4089 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 413.4841
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)   Lower    Upper
+## parent_0 101.7315 6.42e-11 91.9259 111.5371
+## k_parent   0.0495 1.70e-07  0.0404   0.0607
+## sigma      8.0152 1.28e-04  4.6813  11.3491
+## 
+## $IORE
+##                Estimate   Pr(>t)  Lower   Upper
+## parent_0          96.86 3.32e-12 90.848 102.863
+## k__iore_parent     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
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower    Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.8097
+## k1         0.0495 6.58e-03  0.0303   0.0809
+## k2         0.0495 2.60e-03  0.0410   0.0598
+## g          0.4487 5.00e-01      NA       NA
+## sigma      8.0152 2.50e-04  4.5886  11.4418
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  14.0 46.5    14.00
+## IORE 16.4 29.4     8.86
+## DFOP 14.0 46.5    14.00
+## 
+## Representative half-life:
+## [1] 8.86
 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.
 
 
@@ -555,53 +566,53 @@
 
 Example on page 11
 
--p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
-## 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)
-
 -print(p11)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 579.6805 204.7932 144.7783 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 251.6944
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 96.15820 4.83e-13 90.24934 1.02e+02
-## k_parent  0.00321 4.71e-05  0.00222 4.64e-03
-## sigma     6.43473 1.28e-04  3.75822 9.11e+00
-## 
-## $IORE
-##                Estimate Pr(>t)    Lower    Upper
-## parent_0       1.05e+02     NA 9.90e+01 1.10e+02
-## k__iore_parent 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
-## 
-## $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       9.93e-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
-## 
-## 
-## DTx values:
-##          DT50     DT90 DT50_rep
-## SFO  2.16e+02 7.18e+02 2.16e+02
-## IORE 9.73e+02 1.37e+08 4.11e+07
-## DFOP 3.07e+11 1.93e+12 6.98e+11
-## 
-## Representative half-life:
-## [1] 41148171
+p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
+## 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)
+
++print(p11)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 579.6805 204.7932 144.7783 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 251.6944
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 96.15820 4.83e-13 90.24934 1.02e+02
+## k_parent  0.00321 4.71e-05  0.00222 4.64e-03
+## sigma     6.43473 1.28e-04  3.75822 9.11e+00
+## 
+## $IORE
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       1.05e+02     NA 9.90e+01 1.10e+02
+## k__iore_parent 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
+## 
+## $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       9.94e-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
+## 
+## 
+## DTx values:
+##          DT50     DT90 DT50_rep
+## SFO  2.16e+02 7.18e+02 2.16e+02
+## IORE 9.73e+02 1.37e+08 4.11e+07
+## DFOP 3.07e+11 1.93e+12 6.98e+11
+## 
+## Representative half-life:
+## [1] 41148170
 In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.
 
 
@@ -612,380 +623,379 @@
 
 Example on page 12, upper panel
 
--p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
-## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
-## matrix
-
-## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
-## matrix
-## 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)
+p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
+## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
+## matrix
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(diag(covar_notrans)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+## 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)
 
--print(p12a)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 695.4440 220.0685 695.4440 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 270.4679
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower   Upper
-## parent_0  100.521 8.75e-12 92.461 108.581
-## k_parent    0.124 3.61e-08  0.104   0.148
-## sigma       7.048 1.28e-04  4.116   9.980
-## 
-## $IORE
-##                Estimate Pr(>t) Lower Upper
-## parent_0         96.823     NA    NA    NA
-## k__iore_parent    2.436     NA    NA    NA
-## N_parent          0.263     NA    NA    NA
-## sigma             3.965     NA    NA    NA
-## 
-## $DFOP
-##          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           0.793     NA    NA    NA
-## sigma       7.048     NA    NA    NA
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  5.58 18.5     5.58
-## IORE 6.49 13.2     3.99
-## DFOP 5.58 18.5     5.58
-## 
-## Representative half-life:
-## [1] 3.99
++print(p12a)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 695.4440 220.0685 695.4440 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 270.4679
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  100.521 8.75e-12 92.461 108.581
+## k_parent    0.124 3.61e-08  0.104   0.148
+## sigma       7.048 1.28e-04  4.116   9.980
+## 
+## $IORE
+##                Estimate Pr(>t) Lower Upper
+## parent_0         96.823     NA    NA    NA
+## k__iore_parent    2.436     NA    NA    NA
+## N_parent          0.263     NA    NA    NA
+## sigma             3.965     NA    NA    NA
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0  100.521 2.74e-10 92.2366 108.805
+## k1          0.124 2.53e-05  0.0908   0.170
+## k2          0.124 2.52e-02  0.0456   0.339
+## g           0.793      NaN      NA      NA
+## sigma       7.048 2.50e-04  4.0349  10.061
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  5.58 18.5     5.58
+## IORE 6.49 13.2     3.99
+## DFOP 5.58 18.5     5.58
+## 
+## Representative half-life:
+## [1] 3.99
 
 
 Example on page 12, lower panel
 
--p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
-## Warning in qt(alpha/2, rdf): NaNs produced
-## Warning in qt(1 - alpha/2, rdf): NaNs produced
-## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced
-## 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)
++p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
+## Warning in qt(alpha/2, rdf): NaNs produced
+## Warning in qt(1 - alpha/2, rdf): NaNs produced
+## Warning in sqrt(diag(covar_notrans)): NaNs produced
+## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs produced
+## 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)
 
--print(p12b)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 58.90242 19.06353 58.90242 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 51.51756
-## 
-## Parameters:
-## $SFO
-##          Estimate  Pr(>t)   Lower    Upper
-## parent_0  97.6840 0.00039 85.9388 109.4292
-## k_parent   0.0589 0.00261  0.0431   0.0805
-## sigma      3.4323 0.04356 -1.2377   8.1023
-## 
-## $IORE
-##                Estimate Pr(>t)     Lower  Upper
-## parent_0         95.523 0.0055 74.539157 116.51
-## k__iore_parent    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
-## 
-## $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          0.6473    NaN    NA    NA
-## sigma      3.4323    NaN   NaN   NaN
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  11.8 39.1    11.80
-## IORE 12.9 31.4     9.46
-## DFOP 11.8 39.1    11.80
-## 
-## Representative half-life:
-## [1] 9.46
++print(p12b)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 58.90242 19.06353 58.90242 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 51.51756
+## 
+## Parameters:
+## $SFO
+##          Estimate  Pr(>t)   Lower    Upper
+## parent_0  97.6840 0.00039 85.9388 109.4292
+## k_parent   0.0589 0.00261  0.0431   0.0805
+## sigma      3.4323 0.04356 -1.2377   8.1023
+## 
+## $IORE
+##                Estimate Pr(>t)     Lower  Upper
+## parent_0         95.523 0.0055 74.539157 116.51
+## k__iore_parent    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
+## 
+## $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          0.6473    NaN    NA    NA
+## sigma      3.4323    NaN   NaN   NaN
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  11.8 39.1    11.80
+## IORE 12.9 31.4     9.46
+## DFOP 11.8 39.1    11.80
+## 
+## Representative half-life:
+## [1] 9.46
 
 
 Example on page 13
 
--p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
-## Warning in sqrt(diag(covar)): NaNs produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-## 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)
++p13 <- nafta(NAFTA_SOP_Attachment[["p13"]])
+## 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)
 
--print(p13)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 174.5971 142.3951 174.5971 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 172.131
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 92.73500 5.99e-17 89.61936 95.85065
-## k_parent  0.00258 2.42e-09  0.00223  0.00299
-## sigma     3.41172 7.07e-05  2.05455  4.76888
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower  Upper
-## parent_0        91.6016 6.34e-16 88.53086 94.672
-## k__iore_parent   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
-## 
-## $DFOP
-##          Estimate Pr(>t)    Lower    Upper
-## parent_0 92.73500     NA 8.95e+01 95.92118
-## k1        0.00258     NA 4.24e-04  0.01573
-## k2        0.00258     NA 1.76e-03  0.00379
-## g         0.16452     NA       NA       NA
-## sigma     3.41172     NA 2.02e+00  4.79960
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO   269  892      269
-## IORE  261  560      169
-## DFOP  269  892      269
-## 
-## Representative half-life:
-## [1] 168.51
++print(p13)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 174.5971 142.3951 174.5971 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 172.131
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 92.73500 5.99e-17 89.61936 95.85065
+## k_parent  0.00258 2.42e-09  0.00223  0.00299
+## sigma     3.41172 7.07e-05  2.05455  4.76888
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0        91.6016 6.34e-16 88.53086 94.672
+## k__iore_parent   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
+## 
+## $DFOP
+##          Estimate Pr(>t)    Lower    Upper
+## parent_0 92.73500     NA 8.95e+01 95.92118
+## k1        0.00258     NA 4.14e-04  0.01611
+## k2        0.00258     NA 1.74e-03  0.00383
+## g         0.16452     NA 0.00e+00  1.00000
+## sigma     3.41172     NA 2.02e+00  4.79960
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO   269  892      269
+## IORE  261  560      169
+## DFOP  269  892      269
+## 
+## Representative half-life:
+## [1] 168.51
 
 
 
 DT50 not observed in the study and DFOP problems in PestDF
 
--p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
-## Warning in sqrt(diag(covar)): NaNs produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
-## The half-life obtained from the IORE model may be used
 -plot(p14)
+p14 <- nafta(NAFTA_SOP_Attachment[["p14"]])
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+## 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)
 
--print(p14)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 48.43249 28.67746 27.26248 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 32.83337
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 99.47124 2.06e-30 98.42254 1.01e+02
-## k_parent  0.00279 3.75e-15  0.00256 3.04e-03
-## sigma     1.55616 3.81e-06  1.03704 2.08e+00
-## 
-## $IORE
-##                Estimate Pr(>t) Lower Upper
-## parent_0       1.00e+02     NA   NaN   NaN
-## k__iore_parent 9.44e-08     NA   NaN   NaN
-## N_parent       3.31e+00     NA   NaN   NaN
-## sigma          1.20e+00     NA 0.796   1.6
-## 
-## $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       5.03e-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
-## 
-## 
-## DTx values:
-##          DT50     DT90 DT50_rep
-## SFO  2.48e+02 8.25e+02 2.48e+02
-## IORE 4.34e+02 2.22e+04 6.70e+03
-## DFOP 3.69e+10 3.57e+11 1.38e+11
-## 
-## Representative half-life:
-## [1] 6697.44
++print(p14)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 48.43249 28.67746 27.26248 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 32.83337
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 99.47124 2.06e-30 98.42254 1.01e+02
+## k_parent  0.00279 3.75e-15  0.00256 3.04e-03
+## sigma     1.55616 3.81e-06  1.03704 2.08e+00
+## 
+## $IORE
+##                Estimate Pr(>t) Lower Upper
+## parent_0       1.00e+02     NA   NaN   NaN
+## k__iore_parent 9.44e-08     NA   NaN   NaN
+## N_parent       3.31e+00     NA   NaN   NaN
+## sigma          1.20e+00     NA 0.796   1.6
+## 
+## $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       6.08e-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
+## 
+## 
+## DTx values:
+##          DT50     DT90 DT50_rep
+## SFO  2.48e+02 8.25e+02 2.48e+02
+## IORE 4.34e+02 2.22e+04 6.70e+03
+## DFOP 3.05e+10 2.95e+11 1.14e+11
+## 
+## Representative half-life:
+## [1] 6697.44
 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 produced
-## Warning in sqrt(1/diag(V)): NaNs produced
-## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
-## doubtful
-## 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)
-
--print(p15a)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 245.5248 135.0132 245.5248 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 165.9335
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower   Upper
-## parent_0 97.96751 2.00e-15 94.32049 101.615
-## k_parent  0.00952 4.93e-09  0.00824   0.011
-## sigma     4.18778 1.28e-04  2.44588   5.930
-## 
-## $IORE
-##                Estimate   Pr(>t)  Lower  Upper
-## parent_0         95.874 2.94e-15 92.937 98.811
-## k__iore_parent    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
-## 
-## $DFOP
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 97.96751 2.85e-13 94.21913 101.7159
-## k1        0.00952 6.28e-02  0.00260   0.0349
-## k2        0.00952 1.27e-04  0.00652   0.0139
-## g         0.21241 5.00e-01       NA       NA
-## sigma     4.18778 2.50e-04  2.39747   5.9781
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  72.8  242     72.8
-## IORE 76.3  137     41.3
-## DFOP 72.8  242     72.8
-## 
-## Representative half-life:
-## [1] 41.33
+p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
+## 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
 -p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
-## 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)
+
++print(p15a)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 245.5248 135.0132 245.5248 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 165.9335
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower   Upper
+## parent_0 97.96751 2.00e-15 94.32049 101.615
+## k_parent  0.00952 4.93e-09  0.00824   0.011
+## sigma     4.18778 1.28e-04  2.44588   5.930
+## 
+## $IORE
+##                Estimate   Pr(>t)  Lower  Upper
+## parent_0         95.874 2.94e-15 92.937 98.811
+## k__iore_parent    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
+## 
+## $DFOP
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 97.96751 2.85e-13 94.21913 101.7159
+## k1        0.00952 6.28e-02  0.00250   0.0363
+## k2        0.00952 1.27e-04  0.00646   0.0140
+## g         0.21241 5.00e-01  0.00000   1.0000
+## sigma     4.18778 2.50e-04  2.39747   5.9781
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  72.8  242     72.8
+## IORE 76.3  137     41.3
+## DFOP 72.8  242     72.8
+## 
+## Representative half-life:
+## [1] 41.33
 -plot(p15b)
+p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
+## Warning in sqrt(diag(covar)): NaNs produced
+## Warning in sqrt(1/diag(V)): NaNs produced
+## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
+## doubtful
+## 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)
 
--print(p15b)
-## Sums of squares:
-##       SFO      IORE      DFOP 
-## 106.91629  68.55574 106.91629 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 84.25618
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)    Lower    Upper
-## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02
-## k_parent 4.86e-03 2.48e-10  0.00435 5.42e-03
-## sigma    2.76e+00 1.28e-04  1.61402 3.91e+00
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower  Upper
-## parent_0          99.83 1.81e-16 97.51349 102.14
-## k__iore_parent     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
-## 
-## $DFOP
-##          Estimate Pr(>t)    Lower    Upper
-## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
-## k1       4.86e-03     NA 8.62e-04 2.74e-02
-## k2       4.86e-03     NA 3.21e-03 7.35e-03
-## g        1.88e-01     NA 0.00e+00 1.00e+00
-## sigma    2.76e+00     NA 1.58e+00 3.94e+00
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO   143  474    143.0
-## IORE  131  236     71.2
-## DFOP  143  474    143.0
-## 
-## Representative half-life:
-## [1] 71.18
++print(p15b)
+## Sums of squares:
+##       SFO      IORE      DFOP 
+## 106.91629  68.55574 106.91629 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 84.25618
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02
+## k_parent 4.86e-03 2.48e-10  0.00435 5.42e-03
+## sigma    2.76e+00 1.28e-04  1.61402 3.91e+00
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0          99.83 1.81e-16 97.51349 102.14
+## k__iore_parent     0.38 3.22e-01  0.00352  41.05
+## N_parent           0.00 5.00e-01 -1.07696   1.08
+## sigma              2.21 2.57e-04  1.23245   3.19
+## 
+## $DFOP
+##          Estimate Pr(>t)    Lower    Upper
+## parent_0 1.01e+02     NA 9.82e+01 1.04e+02
+## k1       4.86e-03     NA 8.63e-04 2.73e-02
+## k2       4.86e-03     NA 3.21e-03 7.35e-03
+## g        1.88e-01     NA       NA       NA
+## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO   143  474    143.0
+## IORE  131  236     71.2
+## DFOP  143  474    143.0
+## 
+## Representative half-life:
+## [1] 71.18
 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"]])
-## 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)
-
 -print(p16)
-## Sums of squares:
-##      SFO     IORE     DFOP 
-## 3831.804 2062.008 1550.980 
-## 
-## Critical sum of squares for checking the SFO model:
-## [1] 2247.348
-## 
-## Parameters:
-## $SFO
-##          Estimate   Pr(>t)  Lower Upper
-## parent_0   71.953 2.33e-13 60.509 83.40
-## k_parent    0.159 4.86e-05  0.102  0.25
-## sigma      11.302 1.25e-08  8.308 14.30
-## 
-## $IORE
-##                Estimate   Pr(>t)    Lower    Upper
-## parent_0       8.74e+01 2.48e-16 7.72e+01 97.52972
-## k__iore_parent 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
-## 
-## $DFOP
-##          Estimate   Pr(>t)   Lower  Upper
-## parent_0  88.5333 7.40e-18 79.9836 97.083
-## k1        18.8461 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
-## 
-## 
-## DTx values:
-##      DT50 DT90 DT50_rep
-## SFO  4.35 14.4     4.35
-## IORE 1.48 32.1     9.67
-## DFOP 0.67 21.4     8.93
-## 
-## Representative half-life:
-## [1] 8.93
+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)
+
++print(p16)
+## Sums of squares:
+##      SFO     IORE     DFOP 
+## 3831.804 2062.008 1550.980 
+## 
+## Critical sum of squares for checking the SFO model:
+## [1] 2247.348
+## 
+## Parameters:
+## $SFO
+##          Estimate   Pr(>t)  Lower Upper
+## parent_0   71.953 2.33e-13 60.509 83.40
+## k_parent    0.159 4.86e-05  0.102  0.25
+## sigma      11.302 1.25e-08  8.308 14.30
+## 
+## $IORE
+##                Estimate   Pr(>t)    Lower    Upper
+## parent_0       8.74e+01 2.48e-16 7.72e+01 97.52972
+## k__iore_parent 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
+## 
+## $DFOP
+##          Estimate   Pr(>t)   Lower  Upper
+## parent_0  88.5333 7.40e-18 79.9836 97.083
+## k1        18.8461 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
+## 
+## 
+## DTx values:
+##      DT50 DT90 DT50_rep
+## SFO  4.35 14.4     4.35
+## IORE 1.48 32.1     9.67
+## DFOP 0.67 21.4     8.93
+## 
+## Representative half-life:
+## [1] 8.93
 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.
 
 
@@ -1022,7 +1032,7 @@
 
 
   
-Site built with pkgdown 2.0.3.
+Site built with pkgdown 2.0.6.
 
 
       
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p10-1.png
index a53c48b2..75611a70 100644
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index fb211a8e..b6faeff9 100644
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diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p15b-1.png
index 9aedbf16..6b9ba98c 100644
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diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p5b-1.png
index 034eed46..db90244b 100644
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diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png
index 86cd9755..a33372e8 100644
Binary files a/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png and b/docs/articles/web_only/NAFTA_examples_files/figure-html/p6-1.png differ
diff --git a/docs/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png b/docs/articles/web_only/NAFTA_examples_files/figure-html/p7-1.png
index 10225504..d64ea98d 100644
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diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html
index 0b14fea2..64c68ea0 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -33,7 +33,7 @@
       
       
         mkin
-        1.1.2
+        1.2.0
       
     
 
@@ -62,11 +62,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -74,7 +77,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -105,7 +111,7 @@
       Benchmark timings for mkin
                         Johannes Ranke
             
-            Last change 14 July 2022 (rebuilt 2022-07-22)
+            Last change 14 July 2022 (rebuilt 2022-11-17)
       
       Source: vignettes/web_only/benchmarks.rmd
       benchmarks.rmd
@@ -149,7 +155,7 @@
   parent = mkinsub("FOMC", "m1"),
   m1 = mkinsub("SFO"))
 DFOP_SFO <- mkinmod(
-  parent = mkinsub("FOMC", "m1"),
+  parent = mkinsub("FOMC", "m1"), # erroneously used FOMC twice, not fixed for consistency
   m1 = mkinsub("SFO"))
 t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D)))[["elapsed"]]
 t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_D),
@@ -336,8 +342,16 @@
 Ryzen 7 1700
 4.2.1
 1.1.2
-1.962
-3.606
+1.957
+3.633
+
+
+Linux
+Ryzen 7 1700
+4.2.2
+1.2.0
+2.140
+3.774
 
 
 
@@ -506,9 +520,18 @@
 Ryzen 7 1700
 4.2.1
 1.1.2
-1.465
-6.184
-2.752
+1.503
+6.147
+2.803
+
+
+Linux
+Ryzen 7 1700
+4.2.2
+1.2.0
+1.554
+6.193
+2.843
 
 
 
@@ -728,12 +751,24 @@
 Ryzen 7 1700
 4.2.1
 1.1.2
-0.857
-1.298
-1.504
+0.861
+1.295
+1.507
+3.102
+1.961
+2.852
+
+
+Linux
+Ryzen 7 1700
+4.2.2
+1.2.0
+0.913
+1.345
+1.539
 3.011
-1.888
-2.756
+1.987
+2.802
 
 
 
@@ -758,7 +793,7 @@
 
 
   
-Site built with pkgdown 2.0.5.
+Site built with pkgdown 2.0.6.
 
 
       
diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html
index 0b78bb2e..d17d7aeb 100644
--- a/docs/articles/web_only/compiled_models.html
+++ b/docs/articles/web_only/compiled_models.html
@@ -33,7 +33,7 @@
       
       
         mkin
-        1.1.1
+        1.2.0
       
     
 
@@ -62,11 +62,14 @@
       Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -74,7 +77,10 @@
       Example evaluation of NAFTA SOP Attachment examples
     
     
-      Some benchmark timings
+      Benchmark timings for mkin
+    
+    
+      Benchmark timings for saem.mmkin
     
   
 
@@ -105,7 +111,7 @@
       Performance benefit by using compiled model definitions in mkin
                         Johannes Ranke
             
-            2022-10-29
+            2022-11-17
       
       Source: vignettes/web_only/compiled_models.rmd
       compiled_models.rmd
@@ -163,10 +169,10 @@
   print("R package rbenchmark is not available")
 }
 ##                    test replications relative elapsed
-## 4            analytical            1    1.000   0.188
-## 3     deSolve, compiled            1    1.628   0.306
-## 2      Eigenvalue based            1    2.064   0.388
-## 1 deSolve, not compiled            1   38.894   7.312
+## 4            analytical            1    1.000   0.218
+## 3     deSolve, compiled            1    1.550   0.338
+## 2      Eigenvalue based            1    1.950   0.425
+## 1 deSolve, not compiled            1   33.041   7.203
 We see that using the compiled model is by more than a factor of 10 faster than using deSolve without compiled code.


@@ -193,11 +199,11 @@
 }

## Temporary DLL for differentials generated and loaded

##                    test replications relative elapsed
-## 2     deSolve, compiled            1     1.00   0.441
-## 1 deSolve, not compiled            1    30.68  13.530

Here we get a performance benefit of a factor of 31 using the version of the differential equation model compiled from C code!

This vignette was built with mkin 1.1.2 on

## R version 4.2.1 (2022-06-23)
+## 2     deSolve, compiled            1    1.000   0.510
+## 1 deSolve, not compiled            1   26.247  13.386

Here we get a performance benefit of a factor of 26 using the version of the differential equation model compiled from C code!

This vignette was built with mkin 1.2.0 on

## R version 4.2.2 (2022-10-31)
 ## Platform: x86_64-pc-linux-gnu (64-bit)
 ## Running under: Debian GNU/Linux 11 (bullseye)

## CPU model: AMD Ryzen 7 1700 Eight-Core Processor

diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html index b020a7b0..8c37edd6 100644 --- a/docs/articles/web_only/dimethenamid_2018.html +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -33,7 +33,7 @@ @@ -62,11 +62,14 @@ Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models

- Example evaluation of FOCUS Example Dataset Z + Short demo of the multistart method

Performance benefit by using compiled model definitions in mkin

+ Example evaluation of FOCUS Example Dataset Z +

Calculation of time weighted average concentrations with mkin

@@ -74,7 +77,10 @@ Example evaluation of NAFTA SOP Attachment examples

- Some benchmark timings + Benchmark timings for mkin +

+ Benchmark timings for saem.mmkin

@@ -105,7 +111,7 @@

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 1 July 2022, built on 08 Jul 2022

Last change 1 July 2022, built on 17 Nov 2022

Source: vignettes/web_only/dimethenamid_2018.rmd

dimethenamid_2018.rmd

@@ -155,20 +161,20 @@ error_model = "tc", quiet = TRUE)

The plot of the individual SFO fits shown below suggests that at least in some datasets the degradation slows down towards later time points, and that the scatter of the residuals error is smaller for smaller values (panel to the right):

-plot(mixed(f_parent_mkin_const["SFO", ]))

+plot(mixed(f_parent_mkin_const["SFO", ]))

Using biexponential decline (DFOP) results in a slightly more random scatter of the residuals:

-plot(mixed(f_parent_mkin_const["DFOP", ]))

+plot(mixed(f_parent_mkin_const["DFOP", ]))

The population curve (bold line) in the above plot results from taking the mean of the individual transformed parameters, i.e. of log k1 and log k2, as well as of the logit of the g parameter of the DFOP model). Here, this procedure does not result in parameters that represent the degradation well, because in some datasets the fitted value for k2 is extremely close to zero, leading to a log k2 value that dominates the average. This is alleviated if only rate constants that pass the t-test for significant difference from zero (on the untransformed scale) are considered in the averaging:

-plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)

+plot(mixed(f_parent_mkin_const["DFOP", ]), test_log_parms = TRUE)

While this is visually much more satisfactory, such an average procedure could introduce a bias, as not all results from the individual fits enter the population curve with the same weight. This is where nonlinear mixed-effects models can help out by treating all datasets with equally by fitting a parameter distribution model together with the degradation model and the error model (see below).

The remaining trend of the residuals to be higher for higher predicted residues is reduced by using the two-component error model:

-plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)

+plot(mixed(f_parent_mkin_tc["DFOP", ]), test_log_parms = TRUE)

However, note that in the case of using this error model, the fits to the Flaach and BBA 2.3 datasets appear to be ill-defined, indicated by the fact that they did not converge:

@@ -178,7 +184,7 @@ Status of individual fits:
 
       dataset
 model  Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot
-  DFOP OK    OK      OK     OK      C       OK    
+  DFOP OK    OK      C      OK      C       OK    
 
 OK: No warnings
 C: Optimisation did not converge:
@@ -222,7 +228,7 @@ f_parent_nlme_dfop_tc       3 10 671.91 702.34 -325.96 2 vs 3  134.69  <.0001
 While the SFO variants converge fast, the additional parameters introduced by this lead to convergence warnings for the DFOP model. The model comparison clearly show that adding correlations between random effects does not improve the fits.
 The selected model (DFOP with two-component error) fitted to the data assuming no correlations between random effects is shown below.
 -plot(f_parent_nlme_dfop_tc)
+plot(f_parent_nlme_dfop_tc)

@@ -231,41 +237,32 @@ f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001

The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.

The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. We define control settings that work well for all the parent data fits shown in this vignette.

-library(saemix)

Loading required package: npde

Package saemix, version 3.0
-  please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr


-Attaching package: 'saemix'

The following objects are masked from 'package:npde':
-
-    kurtosis, skewness

-saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
+library(saemix)
+saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)


 The convergence plot for the SFO model using constant variance is shown below.
-

+ f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")
 
 Obviously the selected number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.
-+ f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")
 
 When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.
-+ f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")
 
-+ print(f_parent_saemix_dfop_const)
 Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -286,23 +283,21 @@ DMTA_0    97.99583 96.50079 99.4909
 k1         0.06377  0.03432  0.0932
 k2         0.00848  0.00444  0.0125
 g          0.95701  0.91313  1.0009
-a.1        1.82141  1.60516  2.0377
-SD.DMTA_0  1.64787  0.45729  2.8384
+a.1        1.82141  1.65974  1.9831
+SD.DMTA_0  1.64787  0.45779  2.8379
 SD.k1      0.57439  0.24731  0.9015
-SD.k2      0.03296 -2.50524  2.5712
-SD.g       1.10266  0.32354  1.8818
+SD.k2      0.03296 -2.50143  2.5673
+SD.g       1.10266  0.32371  1.8816

 While the other parameters converge to credible values, the variance of k2 (omega2.k2) converges to a very small value. The printout of the saem.mmkin model shows that the estimated standard deviation of k2 across the population of soils (SD.k2) is ill-defined, indicating overparameterisation of this model.
 When the DFOP model is fitted with the two-component error model, we also observe that the estimated variance of k2 becomes very small, while being ill-defined, as illustrated by the excessive confidence interval of SD.k2.
-+ f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_moreiter, transformations = "saemix")
-Likelihood cannot be computed by Importance Sampling.
--plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
+  control = saemix_control_moreiter, transformations = "saemix")
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")
 
-+ print(f_parent_saemix_dfop_tc)
 Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -318,21 +313,21 @@ Likelihood computed by importance sampling
   666 664   -323
 
 Fitted parameters:
-          estimate     lower    upper
-DMTA_0    9.82e+01  96.27937 100.1783
-k1        6.41e-02   0.03333   0.0948
-k2        8.56e-03   0.00608   0.0110
-g         9.55e-01   0.91440   0.9947
-a.1       1.07e+00   0.86542   1.2647
-b.1       2.96e-02   0.02258   0.0367
-SD.DMTA_0 2.04e+00   0.40629   3.6678
-SD.k1     5.98e-01   0.25796   0.9373
-SD.k2     5.28e-04 -58.93251  58.9336
-SD.g      1.04e+00   0.36509   1.7083
+          estimate    lower    upper
+DMTA_0    98.27617  96.3088 100.2436
+k1         0.06437   0.0337   0.0950
+k2         0.00880   0.0063   0.0113
+g          0.95249   0.9100   0.9949
+a.1        1.06161   0.8625   1.2607
+b.1        0.02967   0.0226   0.0367
+SD.DMTA_0  2.06075   0.4187   3.7028
+SD.k1      0.59357   0.2561   0.9310
+SD.k2      0.00292 -10.2960  10.3019
+SD.g       1.05725   0.3808   1.7337
 Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero and has been submitted as a bug to the saemix package, as the algorithm does not converge in this case.
 An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.
 The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:
-+ AIC_parent_saemix <- saemix::compare.saemix(
   f_parent_saemix_sfo_const$so,
   f_parent_saemix_sfo_tc$so,
@@ -340,7 +335,7 @@ SD.g      1.04e+00   0.36509   1.7083
   f_parent_saemix_dfop_tc$so,
   f_parent_saemix_dfop_tc_moreiter$so)
 Likelihoods calculated by importance sampling
-+ rownames(AIC_parent_saemix) <- c(
   "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations")
 print(AIC_parent_saemix)
@@ -348,10 +343,10 @@ SD.g      1.04e+00   0.36509   1.7083
 SFO const               796.38 795.34
 SFO tc                  798.38 797.13
 DFOP const              705.75 703.88
-DFOP tc                 665.72 663.63
-DFOP tc more iterations    NaN    NaN
+DFOP tc                 665.65 663.57
+DFOP tc more iterations 665.88 663.80
 In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.
-+ f_parent_saemix_dfop_tc$so <-
   saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
 AIC_parent_saemix_methods <- c(
@@ -361,11 +356,11 @@ DFOP tc more iterations    NaN    NaN
 )
 print(AIC_parent_saemix_methods)
     is     gq    lin 
-665.72 665.88 665.15 
+665.65 665.68 665.11

The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value.

In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.

When using OpenBlas for linear algebra, there is a large difference in the values obtained with Gaussian quadrature, so the larger number of iterations makes a lot of difference. When using the LAPACK version coming with Debian Bullseye, the AIC based on Gaussian quadrature is almost the same as the one obtained with the other methods, also when using defaults for the fit.

+ f_parent_saemix_dfop_tc_defaults <- mkin::saem(f_parent_mkin_tc["DFOP", ])
 f_parent_saemix_dfop_tc_defaults$so <-
   saemix::llgq.saemix(f_parent_saemix_dfop_tc_defaults$so)
@@ -376,14 +371,14 @@ DFOP tc more iterations    NaN    NaN
 )
 print(AIC_parent_saemix_methods_defaults)

    is     gq    lin 
-668.91 663.61 667.40

+669.77 669.36 670.95

Comparison

The following table gives the AIC values obtained with both backend packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains).

+ AIC_all <- data.frame(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
@@ -408,7 +403,7 @@ DFOP tc more iterations    NaN    NaN
 SFO
 const
 796.60
-794.17
+796.60
 796.38
 
 
@@ -422,15 +417,15 @@ DFOP tc more iterations    NaN    NaN

DFOP const NA -704.95 +671.98 705.75 DFOP tc 671.91 -665.15 -665.72 +665.11 +665.65 @@ -445,15 +440,15 @@ DFOP tc more iterations NaN NaN

Session Info

+ sessionInfo()
-R version 4.2.1 (2022-06-23)
+R version 4.2.2 (2022-10-31)
 Platform: x86_64-pc-linux-gnu (64-bit)
 Running under: Debian GNU/Linux 11 (bullseye)
 
 Matrix products: default
-BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.13.so
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -464,28 +459,27 @@ locale:
 [11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
 
 attached base packages:
-[1] parallel  stats     graphics  grDevices utils     datasets  methods  
-[8] base     
+[1] stats     graphics  grDevices utils     datasets  methods   base     
 
 other attached packages:
-[1] nlme_3.1-158 mkin_1.1.1   knitr_1.39  
+[1] nlme_3.1-160 mkin_1.2.0   knitr_1.40  
 
 loaded via a namespace (and not attached):
- [1] deSolve_1.32      zoo_1.8-10        tidyselect_1.1.2  xfun_0.31        
- [5] bslib_0.3.1       purrr_0.3.4       lattice_0.20-45   colorspace_2.0-3 
- [9] vctrs_0.4.1       generics_0.1.3    htmltools_0.5.2   yaml_2.3.5       
-[13] utf8_1.2.2        rlang_1.0.3       pkgdown_2.0.5     saemix_3.0       
-[17] jquerylib_0.1.4   pillar_1.7.0      glue_1.6.2        lifecycle_1.0.1  
-[21] stringr_1.4.0     munsell_0.5.0     gtable_0.3.0      ragg_1.2.2       
-[25] memoise_2.0.1     evaluate_0.15     npde_3.2          fastmap_1.1.0    
-[29] lmtest_0.9-40     fansi_1.0.3       highr_0.9         scales_1.2.0     
-[33] cachem_1.0.6      desc_1.4.1        jsonlite_1.8.0    systemfonts_1.0.4
-[37] fs_1.5.2          textshaping_0.3.6 gridExtra_2.3     ggplot2_3.3.6    
-[41] digest_0.6.29     stringi_1.7.6     dplyr_1.0.9       grid_4.2.1       
-[45] rprojroot_2.0.3   cli_3.3.0         tools_4.2.1       magrittr_2.0.3   
-[49] sass_0.4.1        tibble_3.1.7      crayon_1.5.1      pkgconfig_2.0.3  
-[53] ellipsis_0.3.2    rmarkdown_2.14    R6_2.5.1          mclust_5.4.10    
-[57] compiler_4.2.1   
+ [1] deSolve_1.34      zoo_1.8-11        tidyselect_1.2.0  xfun_0.33        
+ [5] bslib_0.4.0       purrr_0.3.5       lattice_0.20-45   colorspace_2.0-3 
+ [9] vctrs_0.5.0       generics_0.1.3    htmltools_0.5.3   yaml_2.3.6       
+[13] utf8_1.2.2        rlang_1.0.6       pkgdown_2.0.6     saemix_3.2       
+[17] jquerylib_0.1.4   pillar_1.8.1      glue_1.6.2        DBI_1.1.3        
+[21] lifecycle_1.0.3   stringr_1.4.1     munsell_0.5.0     gtable_0.3.1     
+[25] ragg_1.2.2        memoise_2.0.1     evaluate_0.18     npde_3.2         
+[29] fastmap_1.1.0     lmtest_0.9-40     parallel_4.2.2    fansi_1.0.3      
+[33] highr_0.9         scales_1.2.1      cachem_1.0.6      desc_1.4.2       
+[37] jsonlite_1.8.3    systemfonts_1.0.4 fs_1.5.2          textshaping_0.3.6
+[41] gridExtra_2.3     ggplot2_3.4.0     digest_0.6.30     stringi_1.7.8    
+[45] dplyr_1.0.10      grid_4.2.2        rprojroot_2.0.3   cli_3.4.1        
+[49] tools_4.2.2       magrittr_2.0.3    sass_0.4.2        tibble_3.1.8     
+[53] pkgconfig_2.0.3   assertthat_0.2.1  rmarkdown_2.16    R6_2.5.1         
+[57] mclust_6.0.0      compiler_4.2.2

References @@ -522,7 +516,7 @@ loaded via a namespace (and not attached):

Site built with pkgdown 2.0.5.

Site built with pkgdown 2.0.6.

diff --git a/docs/articles/web_only/multistart.html b/docs/articles/web_only/multistart.html new file mode 100644 index 00000000..720c6742 --- /dev/null +++ b/docs/articles/web_only/multistart.html @@ -0,0 +1,200 @@ + + + + + + + +Short demo of the multistart method • mkin + + + + + + + + + + + + +

+ + + + +

The dimethenamid data from 2018 from seven soils is used as example data in this vignette.

+library(mkin)
+dmta_ds <- lapply(1:7, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
+  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
+  ds_i
+})
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+dmta_ds[["Elliot 1"]] <- dmta_ds[["Elliot 2"]] <- NULL

First, we check the DFOP model with the two-component error model and random effects for all degradation parameters.

+f_mmkin <- mmkin("DFOP", dmta_ds, error_model = "tc", cores = 7, quiet = TRUE)
+f_saem_full <- saem(f_mmkin)
+illparms(f_saem_full)

## [1] "sd(log_k2)"

We see that not all variability parameters are identifiable. The illparms function tells us that the confidence interval for the standard deviation of ‘log_k2’ includes zero. We check this assessment using multiple runs with different starting values.

+f_saem_full_multi <- multistart(f_saem_full, n = 16, cores = 16)
+parplot(f_saem_full_multi)

This confirms that the variance of k2 is the most problematic parameter, so we reduce the parameter distribution model by removing the intersoil variability for k2.

+f_saem_reduced <- update(f_saem_full, no_random_effect = "log_k2")
+illparms(f_saem_reduced)
+f_saem_reduced_multi <- multistart(f_saem_reduced, n = 16, cores = 16)
+parplot(f_saem_reduced_multi, lpos = "topright")

The results confirm that all remaining parameters can be determined with sufficient certainty.

We can also analyse the log-likelihoods obtained in the multiple runs:

+llhist(f_saem_reduced_multi)

The parameter histograms can be further improved by excluding the result with the low likelihood.

+parplot(f_saem_reduced_multi, lpos = "topright", llmin = -326, ylim = c(0.5, 2))

We can use the anova method to compare the models, including a likelihood ratio test if the models are nested.

+anova(f_saem_full, best(f_saem_reduced_multi), test = TRUE)

## Data: 155 observations of 1 variable(s) grouped in 6 datasets
+## 
+##                            npar    AIC    BIC     Lik Chisq Df Pr(>Chisq)
+## best(f_saem_reduced_multi)    9 663.69 661.82 -322.85                    
+## f_saem_full                  10 669.77 667.69 -324.89     0  1          1

While AIC and BIC are lower for the reduced model, the likelihood ratio test does not indicate a significant difference between the fits.

+ + + +

+ + + + +

+ + + + +

Each system is characterized by operating system type, CPU type, mkin version, saemix version and R version. A compiler was available, so if no analytical solution was available, compiled ODE models are used.

Every fit is only performed once, so the accuracy of the benchmarks is limited.

For the initial mmkin fits, we use all available cores.

+n_cores <- parallel::detectCores()

Test data +

Please refer to the vignette dimethenamid_2018 for an explanation of the following preprocessing.

+dmta_ds <- lapply(1:7, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
+  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
+  ds_i
+})
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+dmta_ds[["Elliot 1"]] <- NULL
+dmta_ds[["Elliot 2"]] <- NULL

Test cases +

Parent only +

+parent_mods <- c("SFO", "DFOP", "SFORB", "HS")
+parent_sep_const <- mmkin(parent_mods, dmta_ds, quiet = TRUE, cores = n_cores)
+parent_sep_tc <- update(parent_sep_const, error_model = "tc")
+
+t1 <- system.time(sfo_const <- saem(parent_sep_const["SFO", ]))[["elapsed"]]
+t2 <- system.time(dfop_const <- saem(parent_sep_const["DFOP", ]))[["elapsed"]]
+t3 <- system.time(sforb_const <- saem(parent_sep_const["SFORB", ]))[["elapsed"]]
+t4 <- system.time(hs_const <- saem(parent_sep_const["HS", ]))[["elapsed"]]
+t5 <- system.time(sfo_tc <- saem(parent_sep_tc["SFO", ]))[["elapsed"]]
+t6 <- system.time(dfop_tc <- saem(parent_sep_tc["DFOP", ]))[["elapsed"]]
+t7 <- system.time(sforb_tc <- saem(parent_sep_tc["SFORB", ]))[["elapsed"]]
+t8 <- system.time(hs_tc <- saem(parent_sep_tc["HS", ]))[["elapsed"]]

+anova(
+  sfo_const, dfop_const, sforb_const, hs_const,
+  sfo_tc, dfop_tc, sforb_tc, hs_tc) |> kable(, digits = 1)

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

	npar	AIC	BIC	Lik
sfo_const	5	796.3	795.3	-393.2
sfo_tc	6	798.3	797.1	-393.2
dfop_const	9	709.4	707.5	-345.7
sforb_const	9	710.0	708.1	-346.0
hs_const	9	713.7	711.8	-347.8
dfop_tc	10	669.8	667.7	-324.9
sforb_tc	10	662.8	660.7	-321.4
hs_tc	10	667.3	665.2	-323.6

The above model comparison suggests to use the SFORB model with two-component error. For comparison, we keep the DFOP model with two-component error, as it competes with SFORB for biphasic curves.

+illparms(dfop_tc)

## [1] "sd(log_k2)"

+illparms(sforb_tc)

## [1] "sd(log_k_DMTA_bound_free)"

For these two models, random effects for the transformed parameters k2 and k_DMTA_bound_free could not be quantified.

One metabolite +

We remove parameters that were found to be ill-defined in the parent only fits.

+one_met_mods <- list(
+  DFOP_SFO = mkinmod(
+    DMTA = mkinsub("DFOP", "M23"),
+    M23 = mkinsub("SFO")),
+  SFORB_SFO = mkinmod(
+    DMTA = mkinsub("SFORB", "M23"),
+    M23 = mkinsub("SFO")))
+
+one_met_sep_const <- mmkin(one_met_mods, dmta_ds, error_model = "const",
+  cores = n_cores, quiet = TRUE)
+one_met_sep_tc <- mmkin(one_met_mods, dmta_ds, error_model = "tc",
+  cores = n_cores, quiet = TRUE)
+
+t9 <- system.time(dfop_sfo_tc <- saem(one_met_sep_tc["DFOP_SFO", ],
+    no_random_effect = "log_k2"))[["elapsed"]]
+t10 <- system.time(sforb_sfo_tc <- saem(one_met_sep_tc["SFORB_SFO", ],
+    no_random_effect = "log_k_DMTA_bound_free"))[["elapsed"]]

Three metabolites +

For the case of three metabolites, we only keep the SFORB model in order to limit the time for compiling this vignette, and as fitting in parallel may disturb the benchmark. Again, we do not include random effects that were ill-defined in previous fits of subsets of the degradation model.

+illparms(sforb_sfo_tc)

+three_met_mods <- list(
+  SFORB_SFO3_plus = mkinmod(
+    DMTA = mkinsub("SFORB", c("M23", "M27", "M31")),
+    M23 = mkinsub("SFO"),
+    M27 = mkinsub("SFO"),
+    M31 = mkinsub("SFO", "M27", sink = FALSE)))
+
+three_met_sep_tc <- mmkin(three_met_mods, dmta_ds, error_model = "tc",
+  cores = n_cores, quiet = TRUE)
+
+t11 <- system.time(sforb_sfo3_plus_const <- saem(three_met_sep_tc["SFORB_SFO3_plus", ],
+    no_random_effect = "log_k_DMTA_bound_free"))[["elapsed"]]

Results +

Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.

Parent only +

Constant variance for SFO, DFOP, SFORB and HS.

+ + + + + + + + + + + + + + + + + + + + + +

CPU	OS	mkin	saemix	t1	t2	t3	t4
Ryzen 7 1700	Linux	1.2.0	3.2	2.14	4.626	4.328	4.998

Two-component error fits for SFO, DFOP, SFORB and HS.

+ + + + + + + + + + + + + + + + + + + + + +

CPU	OS	mkin	saemix	t5	t6	t7	t8
Ryzen 7 1700	Linux	1.2.0	3.2	5.678	7.441	8	7.98

One metabolite +

Two-component error for DFOP-SFO and SFORB-SFO.

+ + + + + + + + + + + + + + + + + +

CPU	OS	mkin	saemix	t9	t10
Ryzen 7 1700	Linux	1.2.0	3.2	24.465	800.266

Three metabolites +

Two-component error for SFORB-SFO3-plus

+ + + + + + + + + + + + + + + +

CPU	OS	mkin	saemix	t11
Ryzen 7 1700	Linux	1.2.0	3.2	1289.198

+ + + +

+ + + + +

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Example evaluation of FOCUS Example Dataset D

Johannes Ranke

Last change 31 January 2019 (rebuilt 2022-05-18)

Last change 31 January 2019 (rebuilt 2022-11-17)

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

Last change 18 May 2022 (rebuilt 2022-07-08)

Last change 18 May 2022 (rebuilt 2022-11-17)

Laboratory Data L2

SFO fit for L2

FOMC fit for L2

DFOP fit for L2

Laboratory Data L3

Fit multiple models

Laboratory Data L4

Introduction to mkin

Johannes Ranke

Last change 15 February 2021 (rebuilt 2022-05-18)

Last change 15 February 2021 (rebuilt 2022-11-17)

Calculation of time weighted average concentrations with mkin

Johannes Ranke

Last change 18 September 2019 (rebuilt 2022-05-18)

Last change 18 September 2019 (rebuilt 2022-11-17)

Example evaluation of FOCUS dataset Z

Johannes Ranke

Last change 16 January 2018 (rebuilt 2022-05-18)

Last change 16 January 2018 (rebuilt 2022-11-17)

Parent and one metabolite

Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance

Johannes Ranke

26 February 2019 (rebuilt 2022-05-18)

26 February 2019 (rebuilt 2022-11-17)

Example on page 5, upper panel

Example on page 5, lower panel

Example on page 6

Example on page 7

Example on page 9, upper panel

Example on page 9, lower panel

Example on page 10

Example on page 11

Example on page 12, upper panel

Example on page 12, lower panel

Example on page 13

DT50 not observed in the study and DFOP problems in PestDF

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

The DFOP fraction parameter is greater than 1

Benchmark timings for mkin

Johannes Ranke

Last change 14 July 2022 (rebuilt 2022-07-22)

Last change 14 July 2022 (rebuilt 2022-11-17)

Performance benefit by using compiled model definitions in mkin

Johannes Ranke

2022-10-29

2022-11-17

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

Last change 1 July 2022, built on 08 Jul 2022

Last change 1 July 2022, built on 17 Nov 2022

Comparison

Session Info

Short demo of the multistart method

Johannes Ranke

Last change 26 September 2022 (rebuilt 2022-11-17)

Benchmark timings for saem.mmkin

Johannes Ranke

Last change 14 November 2022 (rebuilt 2022-11-17)

Test data +

Test cases +

Parent only +

One metabolite +

Three metabolites +

Results +

Parent only +

One metabolite +

Three metabolites +