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docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png create mode 100644 docs/reference/Rplot001.png create mode 100644 docs/reference/Rplot002.png create mode 100644 docs/reference/Rplot003.png create mode 100644 docs/reference/Rplot004.png create mode 100644 docs/reference/Rplot005.png create mode 100644 docs/reference/Rplot006.png create mode 100644 docs/reference/Rplot007.png (limited to 'docs') diff --git a/docs/404.html b/docs/404.html index 29b71104..55b92696 100644 --- a/docs/404.html +++ b/docs/404.html @@ -71,7 +71,7 @@ mkin - 0.9.50.2 + 0.9.50.3 @@ -108,6 +108,9 @@
  • Example evaluation of NAFTA SOP Attachment examples
    • +
  • + Some benchmark timings +
  • @@ -116,7 +119,7 @@
  • @@ -76,7 +79,7 @@
  • @@ -76,7 +79,7 @@
    • - + @@ -97,10 +100,10 @@

      Example evaluation of FOCUS Laboratory Data L1 to L3

      Johannes Ranke

      -

      2020-05-27

      +

      2020-10-15

      - Source: vignettes/FOCUS_L.Rmd - + Source: vignettes/FOCUS_L.rmd + @@ -110,42 +113,44 @@

      Laboratory Data L1

      The following code defines example dataset L1 from the FOCUS kinetics report, p. 284:

      -
      library("mkin", quietly = TRUE)
-FOCUS_2006_L1 = data.frame(
-  t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
-  parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
+
      +library("mkin", quietly = TRUE)
+FOCUS_2006_L1 = data.frame(
+  t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
+  parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
              72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
-             27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
-FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
      
+             27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
+FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

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

      Since mkin version 0.9-32 (July 2014), we can use shorthand notation like "SFO" for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.

      -
      m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
-summary(m.L1.SFO)
      -
      ## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:36 2020 
-## Date of summary: Wed May 27 07:05:36 2020 
+
      +m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
+summary(m.L1.SFO)
      
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:03 2020 
+## Date of summary: Thu Oct 15 12:42:03 2020 
 ## 
 ## Equations:
-## d_parent/dt = - k_parent_sink * parent
+## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.031 s
+## Fitted using 133 model solutions performed in 0.032 s
 ## 
 ## Error model: Constant variance 
 ## 
 ## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##               value   type
-## parent_0      89.85  state
-## k_parent_sink  0.10 deparm
+##          value   type
+## parent_0 89.85  state
+## k_parent  0.10 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
-##                       value lower upper
-## parent_0          89.850000  -Inf   Inf
-## log_k_parent_sink -2.302585  -Inf   Inf
+##                  value lower upper
+## parent_0     89.850000  -Inf   Inf
+## log_k_parent -2.302585  -Inf   Inf
 ## 
 ## Fixed parameter values:
 ## None
@@ -156,25 +161,25 @@
 ##   93.88778 96.5589 -43.94389
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##                   Estimate Std. Error  Lower  Upper
-## parent_0            92.470    1.28200 89.740 95.200
-## log_k_parent_sink   -2.347    0.03763 -2.428 -2.267
-## sigma                2.780    0.46330  1.792  3.767
+##              Estimate Std. Error  Lower  Upper
+## parent_0       92.470    1.28200 89.740 95.200
+## log_k_parent   -2.347    0.03763 -2.428 -2.267
+## sigma           2.780    0.46330  1.792  3.767
 ## 
 ## Parameter correlation:
-##                     parent_0 log_k_parent_sink      sigma
-## parent_0           1.000e+00         6.186e-01 -1.712e-09
-## log_k_parent_sink  6.186e-01         1.000e+00 -3.237e-09
-## sigma             -1.712e-09        -3.237e-09  1.000e+00
+##                parent_0 log_k_parent      sigma
+## 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.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##               Estimate t value    Pr(>t)    Lower   Upper
-## parent_0      92.47000   72.13 8.824e-21 89.74000 95.2000
-## k_parent_sink  0.09561   26.57 2.487e-14  0.08824  0.1036
-## sigma          2.78000    6.00 1.216e-05  1.79200  3.7670
+##          Estimate t value    Pr(>t)    Lower   Upper
+## parent_0 92.47000   72.13 8.824e-21 89.74000 95.2000
+## k_parent  0.09561   26.57 2.487e-14  0.08824  0.1036
+## sigma     2.78000    6.00 1.216e-05  1.79200  3.7670
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -206,38 +211,38 @@
 ##    30   parent      2.9     5.251  -2.3513
 ##    30   parent      4.0     5.251  -1.2513
      
 
      A plot of the fit is obtained with the plot function for mkinfit objects.
      
-
      plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")
      
+
      +plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")
      
 
      
 
      The residual plot can be easily obtained by
      
-
      mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
      
+
      +mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
      
 
      
 
      For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level is checked.
      
-
      m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
      
+
      +m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
      
 
      ## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
 ## false convergence (8)
      
-
      plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
      
+
      +plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
      
 
      
-
      summary(m.L1.FOMC, data = FALSE)
      
+
      +summary(m.L1.FOMC, data = FALSE)
      
 
      ## Warning in sqrt(diag(covar)): NaNs 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:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:36 2020 
-## Date of summary: Wed May 27 07:05:36 2020 
-## 
-## 
-## Warning: Optimisation did not converge:
-## false convergence (8) 
-## 
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:03 2020 
+## Date of summary: Thu Oct 15 12:42:03 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 899 model solutions performed in 0.204 s
+## Fitted using 380 model solutions performed in 0.086 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -258,34 +263,39 @@
 ## Fixed parameter values:
 ## None
 ## 
+## 
+## Warning(s): 
+## Optimisation did not converge:
+## false convergence (8)
+## 
 ## Results:
 ## 
 ##        AIC      BIC    logLik
-##   95.88835 99.44984 -43.94418
+##   95.88778 99.44927 -43.94389
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
-## parent_0     92.47     1.2800 89.730 95.220
-## log_alpha    10.58        NaN    NaN    NaN
-## log_beta     12.93        NaN    NaN    NaN
-## sigma         2.78     0.4507  1.813  3.747
+## parent_0     92.47     1.2820 89.720 95.220
+## log_alpha    16.92        NaN    NaN    NaN
+## log_beta     19.26        NaN    NaN    NaN
+## sigma         2.78     0.4501  1.814  3.745
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta   sigma
-## parent_0   1.00000       NaN      NaN 0.01452
-## log_alpha      NaN         1      NaN     NaN
-## log_beta       NaN       NaN        1     NaN
-## sigma      0.01452       NaN      NaN 1.00000
+##           parent_0 log_alpha log_beta    sigma
+## parent_0  1.000000       NaN      NaN 0.002218
+## log_alpha      NaN         1      NaN      NaN
+## log_beta       NaN       NaN        1      NaN
+## sigma     0.002218       NaN      NaN 1.000000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##           Estimate  t value    Pr(>t)  Lower  Upper
-## parent_0     92.47 72.13000 1.052e-19 89.730 95.220
-## alpha     39440.00  0.02397 4.906e-01     NA     NA
-## beta     412500.00  0.02397 4.906e-01     NA     NA
-## sigma         2.78  6.00000 1.628e-05  1.813  3.747
+##           Estimate t value Pr(>t)  Lower  Upper
+## parent_0 9.247e+01      NA     NA 89.720 95.220
+## alpha    2.223e+07      NA     NA     NA     NA
+## beta     2.325e+08      NA     NA     NA     NA
+## sigma    2.780e+00      NA     NA  1.814  3.745
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -293,8 +303,8 @@
 ## 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).
      
@@ -303,19 +313,21 @@
 
      
 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,
+
      +FOCUS_2006_L2 = data.frame(
+  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
+  parent = c(96.1, 91.8, 41.4, 38.7,
              19.3, 22.3, 4.6, 4.6,
-             2.6, 1.2, 0.3, 0.6))
-FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
      
+             2.6, 1.2, 0.3, 0.6))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
      
 
      
 
      
 SFO fit for L2
      
 
      Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument show_residuals to the plot command.
      
-
      m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - SFO")
      
+
      +m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - SFO")
      
 
      
 
      The \(\chi^2\) error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.
      
 
      In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.
      
@@ -325,22 +337,24 @@
 
      
 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,
-     main = "FOCUS L2 - FOMC")
      
+
      +m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.FOMC, show_residuals = TRUE,
+     main = "FOCUS L2 - FOMC")
      
 
      
-
      summary(m.L2.FOMC, data = FALSE)
      
-
      ## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:37 2020 
-## Date of summary: Wed May 27 07:05:37 2020 
+
      +summary(m.L2.FOMC, data = FALSE)
      
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:04 2020 
+## Date of summary: Thu Oct 15 12:42:04 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.047 s
+## Fitted using 239 model solutions performed in 0.049 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -375,10 +389,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.436e-09
 ## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
-## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.386e-07
+## sigma     -7.436e-09 -1.617e-07 -1.386e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -404,15 +418,17 @@
 
      
 DFOP fit for L2
      
 
      Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level.
      
-
      m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - DFOP")
      
+
      +m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - DFOP")
      
 
      
-
      summary(m.L2.DFOP, data = FALSE)
      
-
      ## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:37 2020 
-## Date of summary: Wed May 27 07:05:37 2020 
+
      +summary(m.L2.DFOP, data = FALSE)
      
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:04 2020 
+## Date of summary: Thu Oct 15 12:42:04 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -421,7 +437,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 572 model solutions performed in 0.132 s
+## Fitted using 572 model solutions performed in 0.139 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -452,18 +468,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0  93.9500  9.998e-01    91.5900   96.3100
-## log_k1     3.1370  2.376e+03 -5616.0000 5622.0000
+## log_k1     3.1370  2.376e+03 -5615.0000 5622.0000
 ## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
 ## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
 ## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  5.155e-07  2.371e-09  2.665e-01 -6.849e-09
-## log_k1    5.155e-07  1.000e+00  8.434e-05 -1.659e-04 -7.791e-06
-## log_k2    2.371e-09  8.434e-05  1.000e+00 -7.903e-01 -1.262e-08
-## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.241e-08
-## sigma    -6.849e-09 -7.791e-06 -1.262e-08  3.241e-08  1.000e+00
+## parent_0  1.000e+00  5.157e-07  2.376e-09  2.665e-01 -6.837e-09
+## log_k1    5.157e-07  1.000e+00  8.434e-05 -1.659e-04 -7.786e-06
+## log_k2    2.376e-09  8.434e-05  1.000e+00 -7.903e-01 -1.263e-08
+## g_ilr     2.665e-01 -1.659e-04 -7.903e-01  1.000e+00  3.248e-08
+## sigma    -6.837e-09 -7.786e-06 -1.263e-08  3.248e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -482,8 +498,8 @@
 ## parent      2.53       4  2
 ## 
 ## Estimated disappearance times:
-##          DT50  DT90 DT50_k1 DT50_k2
-## parent 0.5335 5.311 0.03009   2.058
      
+##          DT50  DT90 DT50back DT50_k1 DT50_k2
+## parent 0.5335 5.311    1.599 0.03009   2.058
      
 
      Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.
      
 
      
 
@@ -491,18 +507,20 @@
 
      
 Laboratory Data L3
      
 
      The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.
      
-
      FOCUS_2006_L3 = data.frame(
-  t = c(0, 3, 7, 14, 30, 60, 91, 120),
-  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
-FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
      
+
      +FOCUS_2006_L3 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
+FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
      
 
      
 
      
 Fit multiple models
      
 
      As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function mmkin. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.
      
-
      # Only use one core here, not to offend the CRAN checks
-mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
-               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
-plot(mm.L3)
      
+
      +# Only use one core here, not to offend the CRAN checks
+mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
+               list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
+plot(mm.L3)
      
 
      
 
      The \(\chi^2\) error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the \(\chi^2\) test passes of 7%. Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level considerably.
      
 
      
@@ -511,11 +529,12 @@
 Accessing mmkin objects
 
      The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.
      
 
      We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.
      
-
      summary(mm.L3[["DFOP", 1]])
      
-
      ## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:38 2020 
-## Date of summary: Wed May 27 07:05:38 2020 
+
      +summary(mm.L3[["DFOP", 1]])
      
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:05 2020 
+## Date of summary: Thu Oct 15 12:42:05 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -524,7 +543,7 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 373 model solutions performed in 0.083 s
+## Fitted using 373 model solutions performed in 0.084 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -562,11 +581,11 @@
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.872e-07
-## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.200e-07
-## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.673e-07
-## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.731e-07
-## sigma    -6.872e-07  3.200e-07  7.673e-07 -8.731e-07  1.000e+00
+## parent_0  1.000e+00  1.732e-01  2.282e-02  4.009e-01 -6.868e-07
+## log_k1    1.732e-01  1.000e+00  4.945e-01 -5.809e-01  3.175e-07
+## log_k2    2.282e-02  4.945e-01  1.000e+00 -6.812e-01  7.631e-07
+## g_ilr     4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -8.694e-07
+## sigma    -6.868e-07  3.175e-07  7.631e-07 -8.694e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -585,8 +604,8 @@
 ## parent     2.225       4  4
 ## 
 ## Estimated disappearance times:
-##         DT50 DT90 DT50_k1 DT50_k2
-## parent 7.464  123   1.343   50.37
+##         DT50 DT90 DT50back DT50_k1 DT50_k2
+## parent 7.464  123    37.03   1.343   50.37
 ## 
 ## Data:
 ##  time variable observed predicted residual
@@ -598,7 +617,8 @@
 ##    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.
      
@@ -608,44 +628,47 @@
 
      
 Laboratory Data L4
      
 
      The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:
      
-
      FOCUS_2006_L4 = data.frame(
-  t = c(0, 3, 7, 14, 30, 60, 91, 120),
-  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
-FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
      
+
      +FOCUS_2006_L4 = data.frame(
+  t = c(0, 3, 7, 14, 30, 60, 91, 120),
+  parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
+FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
      
 
      Fits of the SFO and FOMC models, plots and summaries are produced below:
      
-
      # Only use one core here, not to offend the CRAN checks
-mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
-               list("FOCUS L4" = FOCUS_2006_L4_mkin),
-               quiet = TRUE)
-plot(mm.L4)
      
+
      +# Only use one core here, not to offend the CRAN checks
+mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
+               list("FOCUS L4" = FOCUS_2006_L4_mkin),
+               quiet = TRUE)
+plot(mm.L4)
      
 
      
 
      The \(\chi^2\) error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the \(\chi^2\) test passes is slightly lower for the FOMC model. However, the difference appears negligible.
      
-
      summary(mm.L4[["SFO", 1]], data = FALSE)
      
-
      ## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:38 2020 
-## Date of summary: Wed May 27 07:05:38 2020 
+
      +summary(mm.L4[["SFO", 1]], data = FALSE)
      
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:05 2020 
+## Date of summary: Thu Oct 15 12:42:06 2020 
 ## 
 ## Equations:
-## d_parent/dt = - k_parent_sink * parent
+## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.029 s
+## Fitted using 142 model solutions performed in 0.03 s
 ## 
 ## Error model: Constant variance 
 ## 
 ## Error model algorithm: OLS 
 ## 
 ## Starting values for parameters to be optimised:
-##               value   type
-## parent_0       96.6  state
-## k_parent_sink   0.1 deparm
+##          value   type
+## parent_0  96.6  state
+## k_parent   0.1 deparm
 ## 
 ## Starting values for the transformed parameters actually optimised:
-##                       value lower upper
-## parent_0          96.600000  -Inf   Inf
-## log_k_parent_sink -2.302585  -Inf   Inf
+##                  value lower upper
+## parent_0     96.600000  -Inf   Inf
+## log_k_parent -2.302585  -Inf   Inf
 ## 
 ## Fixed parameter values:
 ## None
@@ -656,25 +679,25 @@
 ##   47.12133 47.35966 -20.56067
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##                   Estimate Std. Error  Lower   Upper
-## parent_0            96.440    1.69900 92.070 100.800
-## log_k_parent_sink   -5.030    0.07059 -5.211  -4.848
-## sigma                3.162    0.79050  1.130   5.194
+##              Estimate Std. Error  Lower   Upper
+## parent_0       96.440    1.69900 92.070 100.800
+## log_k_parent   -5.030    0.07059 -5.211  -4.848
+## sigma           3.162    0.79050  1.130   5.194
 ## 
 ## Parameter correlation:
-##                    parent_0 log_k_parent_sink     sigma
-## parent_0          1.000e+00         5.938e-01 3.440e-07
-## log_k_parent_sink 5.938e-01         1.000e+00 5.885e-07
-## sigma             3.440e-07         5.885e-07 1.000e+00
+##               parent_0 log_k_parent     sigma
+## 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.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##                Estimate t value    Pr(>t)     Lower     Upper
-## parent_0      96.440000   56.77 1.604e-08 92.070000 1.008e+02
-## k_parent_sink  0.006541   14.17 1.578e-05  0.005455 7.842e-03
-## sigma          3.162000    4.00 5.162e-03  1.130000 5.194e+00
+##           Estimate t value    Pr(>t)     Lower     Upper
+## parent_0 96.440000   56.77 1.604e-08 92.070000 1.008e+02
+## k_parent  0.006541   14.17 1.578e-05  0.005455 7.842e-03
+## sigma     3.162000    4.00 5.162e-03  1.130000 5.194e+00
 ## 
 ## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -684,18 +707,19 @@
 ## Estimated disappearance times:
 ##        DT50 DT90
 ## parent  106  352
      
-
      summary(mm.L4[["FOMC", 1]], data = FALSE)
      
-
      ## mkin version used for fitting:    0.9.50.2 
-## R version used for fitting:       4.0.0 
-## Date of fit:     Wed May 27 07:05:38 2020 
-## Date of summary: Wed May 27 07:05:38 2020 
+
      +summary(mm.L4[["FOMC", 1]], data = FALSE)
      
+
      ## mkin version used for fitting:    0.9.50.3 
+## R version used for fitting:       4.0.3 
+## Date of fit:     Thu Oct 15 12:42:05 2020 
+## Date of summary: Thu Oct 15 12:42:06 2020 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.043 s
+## Fitted using 224 model solutions performed in 0.046 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -730,10 +754,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.456e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.169e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  4.910e-08
+## sigma     -2.456e-07  2.169e-08  4.910e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -780,7 +804,7 @@
 
 
 
      
-  
      Site built with pkgdown 1.5.1.
      
+  
      Site built with pkgdown 1.6.1.
      
 
      
 
       
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diff --git a/docs/articles/index.html b/docs/articles/index.html
index 6f97722c..0ff8d97f 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -71,7 +71,7 @@
       
       
         mkin
-        0.9.50.2
+        0.9.50.3
       
     
 
@@ -108,6 +108,9 @@
     
    • 
       Example evaluation of NAFTA SOP Attachment examples
     
      • 
+    
    • 
+      Some benchmark timings
+    
      •
  • @@ -116,7 +119,7 @@
  • @@ -76,7 +79,7 @@
    • - + @@ -97,49 +100,50 @@

      Introduction to mkin

      Johannes Ranke

      -

      2020-05-27

      +

      2020-10-15

      - Source: vignettes/mkin.Rmd - + Source: vignettes/mkin.rmd + -

      Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
      Privatdozent at the University of Bremen

      +

      Wissenschaftlicher Berater, Kronacher Str. 12, 79639 Grenzach-Wyhlen, Germany
      Privatdozent at the University of Bremen

      Abstract

      In the regulatory evaluation of chemical substances like plant protection products (pesticides), biocides and other chemicals, degradation data play an important role. For the evaluation of pesticide degradation experiments, detailed guidance has been developed, based on nonlinear optimisation. The R add-on package mkin 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)
+
      +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)
+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)
+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 )
+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)
+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"))
      
-
      
+plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
      +

      @@ -147,7 +151,7 @@

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

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

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

      -

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

      +

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

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

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

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

      @@ -157,7 +161,7 @@

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

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

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

      -

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

      +

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

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

      @@ -223,7 +227,7 @@

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

      -

      Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” Journal of Statistical Software 33 (3): 1–28. http://www.jstatsoft.org/v33/i03/.

      +

      Soetaert, Karline, and Thomas Petzoldt. 2010. “Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME.” Journal of Statistical Software 33 (3): 1–28. https://www.jstatsoft.org/v33/i03/.

      @@ -244,7 +248,7 @@
      -

      Site built with pkgdown 1.5.1.

      +

      Site built with pkgdown 1.6.1.

      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 new file mode 100644 index 00000000..2f3d7a46 Binary files /dev/null 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 e70205f2..3f7820b4 100644 --- a/docs/articles/twa.html +++ b/docs/articles/twa.html @@ -31,7 +31,7 @@ mkin - 0.9.50.2 + 0.9.50.3 @@ -68,6 +68,9 @@
    • Example evaluation of NAFTA SOP Attachment examples
      • +
    • + Some benchmark timings +
  • @@ -76,7 +79,7 @@
    • - + @@ -97,10 +100,10 @@

      Calculation of time weighted average concentrations with mkin

      Johannes Ranke

      -

      2020-05-27

      +

      2020-10-15

      - Source: vignettes/twa.Rmd - + Source: vignettes/twa.rmd + @@ -137,7 +140,7 @@

      \[f_\textrm{twa} = \frac{1}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right) \]

      -

      Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the max_twa_parent() function. If the same is needed for metabolites, the function pfm::max_twa() from the ‘pfm’ package can be used.

      +

      Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the max_twa_parent() function. If the same is needed for metabolites, the function pfm::max_twa() from the ‘pfm’ package can be used.

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

      @@ -158,7 +161,7 @@
      -

      Site built with pkgdown 1.5.1.

      +

      Site built with pkgdown 1.6.1.

      diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html index ccbfcc86..b740b5ed 100644 --- a/docs/articles/web_only/FOCUS_Z.html +++ b/docs/articles/web_only/FOCUS_Z.html @@ -31,7 +31,7 @@ mkin - 0.9.50.2 + 0.9.50.3
      @@ -68,6 +68,9 @@
    • Example evaluation of NAFTA SOP Attachment examples
      • +
    • + Some benchmark timings +
  • @@ -76,7 +79,7 @@
    • - + @@ -97,10 +100,10 @@

      Example evaluation of FOCUS dataset Z

      Johannes Ranke

      -

      2020-05-27

      +

      2020-10-15

      - Source: vignettes/web_only/FOCUS_Z.Rmd - + Source: vignettes/web_only/FOCUS_Z.rmd + @@ -111,35 +114,40 @@

      The data

      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))
+
      +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)
      
+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"))
      +
      +Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
+                Z1 = mkinsub("SFO"))
      ## Successfully compiled differential equation model from auto-generated C code.
      -
      m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE)
      +
      +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)$bpar
      +
      +summary(m.Z.2a, data = FALSE)$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
@@ -148,16 +156,20 @@
 ## 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")
      +
      +Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"),
+                   Z1 = mkinsub("SFO"),
+                   use_of_ff = "max")
      ## Successfully compiled differential equation model from auto-generated C code.
      -
      m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE)
      +
      +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)$bpar
      +
      +summary(m.Z.2a.ff, data = FALSE)$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
@@ -167,15 +179,19 @@
 
      Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised.
      
 
      A simplified model is obtained by removing the pathway to the sink. 
      
 
      In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite.
      
-
      Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-               Z1 = mkinsub("SFO"), use_of_ff = "max")
      
+
      +Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO"), use_of_ff = "max")
      
 
      ## Successfully compiled differential equation model from auto-generated C code.
      
-
      m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE)
      
+
      +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
      
+
      +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
@@ -187,51 +203,59 @@
 
      
 Metabolites Z2 and Z3
      
 
      As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2.
      
-
      Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-               Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-               Z2 = mkinsub("SFO"), use_of_ff = "max")
      
+
      +Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+               Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+               Z2 = mkinsub("SFO"), use_of_ff = "max")
      
 
      ## Successfully compiled differential equation model from auto-generated C code.
      
-
      m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE)
      
+
      +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")
      
+
      +Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                   Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                   Z2 = mkinsub("SFO", "Z3"),
+                   Z3 = mkinsub("SFO"),
+                   use_of_ff = "max")
      
 
      ## Successfully compiled differential equation model from auto-generated C code.
      
-
      m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin,
-                     parms.ini = m.Z.5$bparms.ode,
-                     quiet = TRUE)
      
+
      +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)
      
-
      plot_sep(m.Z.FOCUS)
      
+
      +plot_sep(m.Z.FOCUS)
      
 
      
-
      summary(m.Z.FOCUS, data = FALSE)$bpar
      
-
      ##             Estimate se_notrans t value     Pr(>t)     Lower     Upper
-## Z0_0       96.840695   1.994285 48.5591 4.0254e-42 92.828744 100.85265
-## k_Z0        2.215467   0.118463 18.7018 1.0417e-23  1.989524   2.46707
-## k_Z1        0.478325   0.028259 16.9265 6.2441e-22  0.424725   0.53869
-## k_Z2        0.451638   0.042139 10.7177 1.6309e-14  0.374346   0.54489
-## k_Z3        0.058692   0.015245  3.8498 1.7807e-04  0.034806   0.09897
-## f_Z2_to_Z3  0.471484   0.058348  8.0805 9.6599e-11  0.357736   0.58827
-## sigma       3.984431   0.383402 10.3923 4.5576e-14  3.213126   4.75574
      
-
      endpoints(m.Z.FOCUS)
      
+
      +summary(m.Z.FOCUS, data = FALSE)$bpar
      
+
      ##             Estimate se_notrans t value     Pr(>t)     Lower      Upper
+## Z0_0       96.838721   1.994275 48.5584 4.0283e-42 92.826878 100.850563
+## k_Z0        2.215400   0.118459 18.7019 1.0414e-23  1.989462   2.466998
+## k_Z1        0.478301   0.028257 16.9267 6.2411e-22  0.424705   0.538662
+## k_Z2        0.451623   0.042138 10.7176 1.6313e-14  0.374336   0.544867
+## k_Z3        0.058694   0.015246  3.8499 1.7804e-04  0.034809   0.098967
+## f_Z2_to_Z3  0.471510   0.058352  8.0804 9.6640e-11  0.357775   0.588283
+## sigma       3.984431   0.383402 10.3923 4.5575e-14  3.213126   4.755736
      
+
      +endpoints(m.Z.FOCUS)
      
 
      ## $ff
 ##   Z2_Z3 Z2_sink 
-## 0.47148 0.52852 
+## 0.47151 0.52849 
 ## 
 ## $distimes
 ##        DT50    DT90
-## Z0  0.31287  1.0393
-## Z1  1.44911  4.8138
-## Z2  1.53474  5.0983
-## Z3 11.80989 39.2316
      
+## Z0  0.31288  1.0394
+## Z1  1.44919  4.8141
+## Z2  1.53479  5.0985
+## Z3 11.80955 39.2305
      
 
      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.
      @@ -239,85 +263,108 @@ Using the SFORB model

      As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain.

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

      -
      Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))
      +
      +Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))
      ## Successfully compiled differential equation model from auto-generated C code.
      -
      m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE)
      +
      +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)
      +
      +plot_sep(m.Z.mkin.1)

      -
      summary(m.Z.mkin.1, data = FALSE)$cov.unscaled
      +
      +summary(m.Z.mkin.1, data = FALSE)$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"))
      +
      +Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO"))
      ## Successfully compiled differential equation model from auto-generated C code.
      -
      m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE)
      +
      +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"))
      +
      +Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFO"))
      ## Successfully compiled differential equation model from auto-generated C code.
      -
      m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
-                      parms.ini = m.Z.mkin.3$bparms.ode,
-                      quiet = TRUE)
      +
      +m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin,
+                      parms.ini = m.Z.mkin.3$bparms.ode,
+                      quiet = TRUE)
      ## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
 ## 3$bparms.ode, : Observations with value of zero were removed from the data
      -
      plot_sep(m.Z.mkin.4)
      +
      ## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 3$bparms.ode, : Shapiro-Wilk test for standardized residuals: p = 0.0449
      +
      +plot_sep(m.Z.mkin.4)

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

      -
      Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
-                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
-                    Z2 = mkinsub("SFO", "Z3"),
-                    Z3 = mkinsub("SFORB"))
      +
      +Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE),
+                    Z1 = mkinsub("SFO", "Z2", sink = FALSE),
+                    Z2 = mkinsub("SFO", "Z3"),
+                    Z3 = mkinsub("SFORB"))
      ## Successfully compiled differential equation model from auto-generated C code.
      -
      m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
-                      parms.ini = m.Z.mkin.4$bparms.ode[1:4],
-                      quiet = TRUE)
      +
      +m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+                      parms.ini = m.Z.mkin.4$bparms.ode[1:4],
+                      quiet = TRUE)
      ## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
 ## 4$bparms.ode[1:4], : Observations with value of zero were removed from the data
      -
      plot_sep(m.Z.mkin.5)
      +
      ## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin.
+## 4$bparms.ode[1:4], : Shapiro-Wilk test for standardized residuals: p = 0.00785
      +
      +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$bparms.ode[1:7],
-                                     k_Z3_bound_free = 0),
-                       fixed_parms = "k_Z3_bound_free",
-                       quiet = TRUE)
      +
      +m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin,
+                       parms.ini = c(m.Z.mkin.5$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$bparms.ode[1:7], : Observations with value of zero were removed from the data
      -
      plot_sep(m.Z.mkin.5a)
      +
      ## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin.
+## 5$bparms.ode[1:7], : Shapiro-Wilk test for standardized residuals: p = 0.00785
      +
      +plot_sep(m.Z.mkin.5a)

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

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

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

      The endpoints obtained with this model are

      -
      endpoints(m.Z.mkin.5a)
      +
      +endpoints(m.Z.mkin.5a)
      ## $ff
 ## Z0_free   Z2_Z3 Z2_sink Z3_free 
 ## 1.00000 0.53656 0.46344 1.00000 
 ## 
 ## $SFORB
 ##     Z0_b1     Z0_b2     Z3_b1     Z3_b2 
-## 2.4471337 0.0075125 0.0800071 0.0000000 
+## 2.4471358 0.0075126 0.0800073 0.0000000 
 ## 
 ## $distimes
-##      DT50   DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2
-## Z0 0.3043 1.1848    0.28325     92.266         NA         NA
-## Z1 1.5148 5.0320         NA         NA         NA         NA
-## Z2 1.6414 5.4526         NA         NA         NA         NA
-## Z3     NA     NA         NA         NA     8.6636        Inf
      +## DT50 DT90 DT50back DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2 +## Z0 0.3043 1.1848 0.35666 0.28325 92.265 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.

      @@ -347,7 +394,7 @@
      -

      Site built with pkgdown 1.5.1.

      +

      Site built with pkgdown 1.6.1.

      diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png index 23d051ce..575def46 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_1-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png index 96738dd0..abdded73 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_10-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png index 4f3c2554..599f3226 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png index b8c3ed26..ce993d09 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11a-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png index 132a7317..4b71d7b8 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_11b-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png index 23d051ce..575def46 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_2-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png index 6e9f4efa..98ce34a7 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_3-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png index 146acea9..d04a411e 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_5-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png index b25bf26a..0a9265f5 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_6-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png index 7db8b07d..0acfa2a4 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_7-1.png differ diff --git a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png index dd5d89cd..ca191b00 100644 Binary files a/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png and b/docs/articles/web_only/FOCUS_Z_files/figure-html/FOCUS_2006_Z_fits_9-1.png differ diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html index b91e7ee7..411d4bb8 100644 --- a/docs/articles/web_only/NAFTA_examples.html +++ b/docs/articles/web_only/NAFTA_examples.html @@ -31,7 +31,7 @@ mkin - 0.9.50.2 + 0.9.50.3 @@ -68,6 +68,9 @@
    • Example evaluation of NAFTA SOP Attachment examples
      • +
    • + Some benchmark timings +
  • @@ -76,7 +79,7 @@
    • - + @@ -97,10 +100,10 @@

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

      Johannes Ranke

      -

      2020-05-27

      +

      2020-10-15

      - Source: vignettes/web_only/NAFTA_examples.Rmd - + Source: vignettes/web_only/NAFTA_examples.rmd + @@ -119,12 +122,15 @@

      Example on page 5, upper panel

      -
      p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])
      +
      +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)
      +
      +print(p5a)
      ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 465.21753  56.27506  32.06401 
@@ -134,23 +140,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       95.8401 4.67e-21 92.245 99.4357
-## k_parent_sink   0.0102 3.92e-12  0.009  0.0117
-## sigma           4.8230 3.81e-06  3.214  6.4318
+##          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_sink 1.54e-05     NA 4.08e-06 5.84e-05
-## N_parent            2.57e+00     NA 2.25e+00 2.89e+00
-## sigma               1.68e+00     NA 1.12e+00 2.24e+00
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       1.01e+02     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       2.86e-12 5.00e-01  0.0000      Inf
+## k2       2.17e-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
 ## 
@@ -159,7 +165,7 @@
 ##      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 4.42e+11 2.42e+11
+## DFOP 55.5 5.83e+11 3.20e+11
 ## 
 ## Representative half-life:
 ## [1] 321.51
      @@ -167,12 +173,15 @@

      Example on page 5, lower panel

      -
      p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]])
      +
      +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)
      +
      +print(p5b)
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 94.81123 10.10936  7.55871 
@@ -182,23 +191,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0        96.497 2.32e-24 94.85271 98.14155
-## k_parent_sink    0.008 3.42e-14  0.00737  0.00869
-## sigma            2.295 1.22e-05  1.47976  3.11036
+##          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_sink 1.53e-04 6.50e-03 7.21e-05 3.26e-04
-## N_parent            1.94e+00 5.88e-13 1.76e+00 2.12e+00
-## sigma               7.49e-01 1.63e-05 4.82e-01 1.02e+00
+##                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       1.16e-11 5.00e-01  0.0000     Inf
+## k2       1.04e-11 5.00e-01  0.0000     Inf
 ## g        6.89e-01 2.92e-03  0.6626  0.7142
 ## sigma    6.48e-01 2.38e-05  0.4147  0.8813
 ## 
@@ -207,7 +216,7 @@
 ##      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 9.80e+10 5.98e+10
+## DFOP 83.6 1.09e+11 6.67e+10
 ## 
 ## Representative half-life:
 ## [1] 215.87
      @@ -215,12 +224,15 @@

      Example on page 6

      -
      p6 <- nafta(NAFTA_SOP_Attachment[["p6"]])
      +
      +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)
      +
      +print(p6)
      ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 188.45361  51.00699  42.46931 
@@ -230,23 +242,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)   Lower   Upper
-## parent_0       94.7759 7.29e-24 92.3478 97.2039
-## k_parent_sink   0.0179 8.02e-16  0.0166  0.0194
-## sigma           3.0696 3.81e-06  2.0456  4.0936
+##          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_sink  0.00252 1.95e-03  0.00134  0.00472
-## N_parent             1.49587 4.07e-13  1.33896  1.65279
-## sigma                1.59698 5.05e-06  1.06169  2.13227
+##                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       4.90e-11 5.00e-01  0.0000     Inf
+## k2       3.88e-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
 ## 
@@ -255,7 +267,7 @@
 ##      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 6.66e+09 1.41e+10
+## DFOP 34.1 8.42e+09 1.79e+10
 ## 
 ## Representative half-life:
 ## [1] 53.17
      @@ -263,12 +275,15 @@

      Example on page 7

      -
      p7 <- nafta(NAFTA_SOP_Attachment[["p7"]])
      +
      +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)
      +
      +print(p7)
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3661.661 3195.030 3174.145 
@@ -278,23 +293,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      96.41796 4.80e-53 93.32245 99.51347
-## k_parent_sink  0.00735 7.64e-21  0.00641  0.00843
-## sigma          7.94557 1.83e-15  6.46713  9.42401
+##          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_sink 1.60e-05     NA 1.45e-07 1.77e-03
-## N_parent            2.45e+00     NA 1.35e+00 3.54e+00
-## sigma               7.42e+00     NA 6.04e+00 8.80e+00
+##                Estimate Pr(>t)    Lower    Upper
+## parent_0       9.92e+01     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       1.97e-10 5.00e-01  0.0000      Inf
+## k2       2.30e-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
 ## 
@@ -303,7 +318,7 @@
 ##      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 6.97e+09 3.52e+09
+## DFOP 96.4 5.95e+09 3.01e+09
 ## 
 ## Representative half-life:
 ## [1] 454.55
      @@ -316,12 +331,15 @@

      Example on page 8

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

      -
      p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3))
      +
      +p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent = 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)
      +
      +print(p8)
      ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 1996.9408  444.9237  547.5616 
@@ -331,17 +349,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      88.16549 6.53e-29 83.37344 92.95754
-## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
-## sigma          7.44786 4.17e-10  5.66209  9.23363
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 88.16549 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_sink 6.14e-05 3.20e-02 2.12e-05 1.78e-04
-## N_parent            2.27e+00 4.23e-18 2.00e+00 2.54e+00
-## sigma               3.52e+00 5.36e-10 2.67e+00 4.36e+00
+##                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
@@ -368,12 +386,15 @@
 
      
 
      
 Example on page 9, upper panel
      
-
      p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]])
      
+
      +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)
      
+
      +print(p9a)
      
 
      ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 839.35238  88.57064   9.93363 
@@ -383,23 +404,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)   Lower   Upper
-## parent_0       88.1933 3.06e-12 79.9447 96.4419
-## k_parent_sink   0.0409 2.07e-07  0.0324  0.0516
-## sigma           7.2429 3.92e-05  4.4768 10.0090
+##          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_sink 1.93e-05 1.13e-01 3.49e-06 1.06e-04
-## N_parent            2.91e+00 1.45e-09 2.50e+00 3.32e+00
-## sigma               2.35e+00 5.31e-05 1.45e+00 3.26e+00
+##                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       6.02e-13 5.00e-01  0.000    Inf
+## k2       6.69e-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
 ## 
@@ -408,7 +429,7 @@
 ##      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 2.07e+12 1.15e+12
+## DFOP 10.5 1.86e+12 1.04e+12
 ## 
 ## Representative half-life:
 ## [1] 101.43
      
@@ -417,17 +438,15 @@
 
      
 
      
 Example on page 9, lower panel
      
-
      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
      
+
      +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)
      
+
      +plot(p9b)
      
 
      
-
      print(p9b)
      
+
      +print(p9b)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 35.64867 23.22334 35.64867 
@@ -437,24 +456,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       94.7123 2.15e-19 93.178 96.2464
-## k_parent_sink   0.0389 4.47e-14  0.037  0.0408
-## sigma           1.5957 1.28e-04  0.932  2.2595
+##          Estimate   Pr(>t)  Lower   Upper
+## parent_0  94.7123 2.15e-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_sink    0.127 1.85e-02  0.0504  0.321
-## N_parent               0.711 1.88e-05  0.4843  0.937
-## sigma                  1.288 1.76e-04  0.7456  1.830
+##                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 1.43e-06  0.0312  0.0485
 ## k2         0.0389 6.67e-03  0.0186  0.0812
-## g          0.7742      NaN      NA      NA
+## g          0.7742 5.00e-01  0.0000  1.0000
 ## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
@@ -471,12 +490,15 @@
 
      
 
      
 Example on page 10
      
-
      p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
      
+
      +p10 <- nafta(NAFTA_SOP_Attachment[["p10"]])
      
 
      ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
      
 
      ## The half-life obtained from the IORE model may be used
      
-
      plot(p10)
      
+
      +plot(p10)
      
 
      
-
      print(p10)
      
+
      +print(p10)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 899.4089 336.4348 899.4089 
@@ -486,25 +508,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)   Lower    Upper
-## parent_0      101.7315 6.42e-11 91.9259 111.5371
-## k_parent_sink   0.0495 1.70e-07  0.0404   0.0607
-## sigma           8.0152 1.28e-04  4.6813  11.3491
+##          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_sink     2.96 7.91e-02  0.687  12.761
-## N_parent                0.00 5.00e-01 -0.372   0.372
-## sigma                   4.90 1.77e-04  2.837   6.968
+##                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 6.42e-04  0.0301   0.0814
-## k2         0.0495 1.66e-02  0.0200   0.1225
-## g          0.6634 5.00e-01  0.0000   1.0000
-## sigma      8.0152 2.50e-04  4.5886  11.4418
+##          Estimate   Pr(>t)   Lower   Upper
+## parent_0 101.7315 1.41e-09 91.6534 111.810
+## k1         0.0495 6.48e-04  0.0303   0.081
+## k2         0.0495 1.67e-02  0.0201   0.122
+## g          0.6634 5.00e-01  0.0000   1.000
+## sigma      8.0152 2.50e-04  4.5886  11.442
 ## 
 ## 
 ## DTx values:
@@ -524,12 +546,15 @@
 
      
 
      
 Example on page 11
      
-
      p11 <- nafta(NAFTA_SOP_Attachment[["p11"]])
      
+
      +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)
      
+
      +plot(p11)
      
 
      
-
      print(p11)
      
+
      +print(p11)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 579.6805 204.7932 144.7783 
@@ -539,17 +564,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      96.15820 4.83e-13 90.24934 1.02e+02
-## k_parent_sink  0.00321 4.71e-05  0.00222 4.64e-03
-## sigma          6.43473 1.28e-04  3.75822 9.11e+00
+##          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_sink 3.11e-17     NA 1.35e-20 7.18e-14
-## N_parent            8.36e+00     NA 6.62e+00 1.01e+01
-## sigma               3.82e+00     NA 2.21e+00 5.44e+00
+##                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
@@ -567,7 +592,7 @@
 ## DFOP 4.21e+11 2.64e+12 9.56e+11
 ## 
 ## Representative half-life:
-## [1] 41148169
      
+## [1] 41148171
      
 
      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.
      
 
      
 
      
@@ -578,14 +603,17 @@
 
      
 
      
 Example on page 12, upper panel
      
-
      p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
      
+
      +p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])
      
 
      ## 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)
      
+
      +plot(p12a)
      
 
      
-
      print(p12a)
      
+
      +print(p12a)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -595,23 +623,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower   Upper
-## parent_0       100.521 8.75e-12 92.461 108.581
-## k_parent_sink    0.124 3.61e-08  0.104   0.148
-## sigma            7.048 1.28e-04  4.116   9.980
+##          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_sink    2.436     NA    NA    NA
-## N_parent               0.263     NA    NA    NA
-## sigma                  3.965     NA    NA    NA
+##                Estimate Pr(>t) Lower Upper
+## parent_0         96.823     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 5.74e-06  0.0958   0.161
-## k2          0.124 6.61e-02  0.0319   0.484
+## k1          0.124 5.75e-06  0.0958   0.161
+## k2          0.124 6.72e-02  0.0319   0.484
 ## g           0.877 5.00e-01  0.0000   1.000
 ## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
@@ -628,7 +656,8 @@
 
      
 
      
 Example on page 12, lower panel
      
-
      p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
      
+
      +p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
      
 
      ## Warning in sqrt(diag(covar)): NaNs produced
      
 
      ## Warning in qt(alpha/2, rdf): NaNs produced
      
 
      ## Warning in qt(1 - alpha/2, rdf): NaNs produced
      
@@ -639,9 +668,11 @@
 ## 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(p12b)
      
+
      +plot(p12b)
      
 
      
-
      print(p12b)
      
+
      +print(p12b)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 58.90242 19.06353 58.90242 
@@ -651,17 +682,17 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate  Pr(>t)   Lower    Upper
-## parent_0       97.6840 0.00039 85.9388 109.4292
-## k_parent_sink   0.0589 0.00261  0.0431   0.0805
-## sigma           3.4323 0.04356 -1.2377   8.1023
+##          Estimate  Pr(>t)   Lower    Upper
+## parent_0  97.6840 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_sink    0.333 0.1433  0.000717 154.57
-## N_parent               0.568 0.0677 -0.989464   2.13
-## sigma                  1.953 0.0975 -5.893100   9.80
+##                Estimate Pr(>t)     Lower  Upper
+## parent_0         95.523 0.0055 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
@@ -684,16 +715,15 @@
 
      
 
      
 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
      
+
      +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)
      
+
      +plot(p13)
      
 
      
-
      print(p13)
      
+
      +print(p13)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -703,24 +733,24 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      92.73500 5.99e-17 89.61936 95.85065
-## k_parent_sink  0.00258 2.42e-09  0.00223  0.00299
-## sigma          3.41172 7.07e-05  2.05455  4.76888
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 92.73500 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_sink   0.0396 2.36e-01  0.00207  0.759
-## N_parent              0.3541 1.46e-01 -0.35153  1.060
-## sigma                 3.0811 9.64e-05  1.84296  4.319
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0        91.6016 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 9.25e-15 8.95e+01 9.59e+01
-## k1        0.00258 4.28e-01 1.70e-08 3.92e+02
+## k1        0.00258 4.28e-01 1.45e-08 4.61e+02
 ## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
-## g         0.00442 5.00e-01       NA       NA
+## g         0.00442 5.00e-01 0.00e+00 1.00e+00
 ## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
 ## 
 ## 
@@ -737,16 +767,19 @@
 
      
 
      
 DT50 not observed in the study and DFOP problems in PestDF
      
-
      p14 <- nafta(NAFTA_SOP_Attachment[["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)
      
+
      +plot(p14)
      
 
      
-
      print(p14)
      
+
      +print(p14)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 48.43249 28.67746 27.26248 
@@ -756,23 +789,23 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      99.47124 2.06e-30 98.42254 1.01e+02
-## k_parent_sink  0.00279 3.75e-15  0.00256 3.04e-03
-## sigma          1.55616 3.81e-06  1.03704 2.08e+00
+##          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_sink 9.44e-08     NA   NaN   NaN
-## N_parent            3.31e+00     NA   NaN   NaN
-## sigma               1.20e+00     NA 0.796   1.6
+##                Estimate Pr(>t) Lower Upper
+## parent_0       1.00e+02     NA   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       7.29e-12 5.00e-01  0.00000      Inf
+## k2       7.70e-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
 ## 
@@ -781,7 +814,7 @@
 ##          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 2.54e+10 2.46e+11 9.51e+10
+## DFOP 2.41e+10 2.33e+11 9.00e+10
 ## 
 ## Representative half-life:
 ## [1] 6697.44
      
@@ -790,17 +823,19 @@
 
      
 
      
 N is less than 1 and DFOP fraction parameter is below zero
      
-
      p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
      
+
      +p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]])
      
 
      ## 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(p15a)
      
+
      +plot(p15a)
      
 
      
-
      print(p15a)
      
+
      +print(p15a)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 245.5248 135.0132 245.5248 
@@ -810,25 +845,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower   Upper
-## parent_0      97.96751 2.00e-15 94.32049 101.615
-## k_parent_sink  0.00952 4.93e-09  0.00824   0.011
-## sigma          4.18778 1.28e-04  2.44588   5.930
+##          Estimate   Pr(>t)    Lower   Upper
+## parent_0 97.96751 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_sink    0.629 2.11e-01  0.044  8.982
-## N_parent               0.000 5.00e-01 -0.642  0.642
-## sigma                  3.105 1.78e-04  1.795  4.416
+##                Estimate   Pr(>t)  Lower  Upper
+## parent_0         95.874 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 97.96752 2.85e-13 94.21914 101.7159
-## k1        0.00952 6.80e-02  0.00277   0.0327
-## k2        0.00952 3.82e-06  0.00902   0.0100
-## g         0.17247      NaN       NA       NA
-## sigma     4.18778 2.50e-04  2.39747   5.9781
+##          Estimate Pr(>t)    Lower    Upper
+## parent_0 97.96752     NA 94.21914 101.7159
+## k1        0.00952     NA  0.00241   0.0377
+## k2        0.00952     NA  0.00747   0.0121
+## g         0.17247     NA       NA       NA
+## sigma     4.18778     NA  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -839,16 +874,19 @@
 ## 
 ## Representative half-life:
 ## [1] 41.33
      
-
      p15b <- nafta(NAFTA_SOP_Attachment[["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)
      
+
      +plot(p15b)
      
 
      
-
      print(p15b)
      
+
      +print(p15b)
      
 
      ## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -858,25 +896,25 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)    Lower    Upper
-## parent_0      1.01e+02 3.06e-17 98.31594 1.03e+02
-## k_parent_sink 4.86e-03 2.48e-10  0.00435 5.42e-03
-## sigma         2.76e+00 1.28e-04  1.61402 3.91e+00
+##          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_sink     0.38 3.22e-01  0.00352  41.05
-## N_parent                0.00 5.00e-01 -1.07695   1.08
-## sigma                   2.21 2.57e-04  1.23245   3.19
+##                Estimate   Pr(>t)    Lower  Upper
+## parent_0          99.83 1.81e-16 97.51348 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 6.75e-04 3.49e-02
-## k2       4.86e-03     NA 3.37e-03 6.99e-03
+## parent_0 1.01e+02     NA 98.24464 1.04e+02
+## k1       4.86e-03     NA  0.00068 3.47e-02
+## k2       4.86e-03     NA  0.00338 6.99e-03
 ## g        1.50e-01     NA       NA       NA
-## sigma    2.76e+00     NA 1.58e+00 3.94e+00
+## sigma    2.76e+00     NA  1.58208 3.94e+00
 ## 
 ## 
 ## DTx values:
@@ -892,14 +930,17 @@
 
      
 
      
 The DFOP fraction parameter is greater than 1
      
-
      p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
      
+
      +p16 <- nafta(NAFTA_SOP_Attachment[["p16"]])
      
 
      ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c
      
 
      ## The representative half-life of the IORE model is longer than the one corresponding
      
 
      ## to the terminal degradation rate found with the DFOP model.
      
 
      ## The representative half-life obtained from the DFOP model may be used
      
-
      plot(p16)
      
+
      +plot(p16)
      
 
      
-
      print(p16)
      
+
      +print(p16)
      
 
      ## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 3831.804 2062.008 1550.980 
@@ -909,22 +950,22 @@
 ## 
 ## Parameters:
 ## $SFO
-##               Estimate   Pr(>t)  Lower Upper
-## parent_0        71.953 2.33e-13 60.509 83.40
-## k_parent_sink    0.159 4.86e-05  0.102  0.25
-## sigma           11.302 1.25e-08  8.308 14.30
+##          Estimate   Pr(>t)  Lower Upper
+## parent_0   71.953 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_sink 4.55e-04 2.16e-01 3.48e-05  0.00595
-## N_parent            2.70e+00 1.21e-08 1.99e+00  3.40046
-## sigma               8.29e+00 1.61e-08 6.09e+00 10.49062
+##                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        18.5561 5.00e-01  0.0000    Inf
+## k1        18.5560 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
@@ -972,7 +1013,7 @@
 
      
 
 
      
-  
      Site built with pkgdown 1.5.1.
      
+  
      Site built with pkgdown 1.6.1.
      
 
      
 
       
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diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html
index 0698baf6..28a3b68a 100644
--- a/docs/articles/web_only/benchmarks.html
+++ b/docs/articles/web_only/benchmarks.html
@@ -5,13 +5,13 @@
 
 
 
-Benchmark timings for mkin on various systems • mkin
+Benchmark timings for mkin • mkin
 
 
 
 
 
-
+