- - -

Introduction -

+ + +

Testing hierarchical parent degradation +kinetics with residue data on dimethenamid and dimethenamid-P

Johannes Ranke

Last change on 5 January 2023, last compiled on 13 +Februar 2025

+ +

+true +

+ +

Introduction

The purpose of this document is to demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS can be fitted with the mkin package.

@@ -116,7 +398,7 @@ FOMC, DFOP and HS can be fitted with the mkin package.

173340 (Application of nonlinear hierarchical models to the kinetic evaluation of chemical degradation data) of the German Environment Agency carried out in 2022 and 2023.

The mkin package is used in version 1.2.6. It contains the test data +

The mkin package is used in version 1.2.9. It contains the test data and the functions used in the evaluations. The saemix package is used as a backend for fitting the NLHM, but is also loaded to make the convergence plot function available.

@@ -124,21 +406,19 @@ make the convergence plot function available.

also provides the kable function that is used to improve the display of tabular data in R markdown documents. For parallel processing, the parallel package is used.

-library(mkin)
-library(knitr)
-library(saemix)
-library(parallel)
-n_cores <- detectCores()
-if (Sys.info()["sysname"] == "Windows") {
-  cl <- makePSOCKcluster(n_cores)
-} else {
-  cl <- makeForkCluster(n_cores)
-}

library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+n_cores <- detectCores()
+if (Sys.info()["sysname"] == "Windows") {
+  cl <- makePSOCKcluster(n_cores)
+} else {
+  cl <- makeForkCluster(n_cores)
+}

Data -

Data

The test data are available in the mkin package as an object of class mkindsg (mkin dataset group) under the identifier dimethenamid_2018. The following preprocessing steps are @@ -160,37 +440,37 @@ and Elliot 2) are combined, resulting in dimethenamid (DMTA) data from six soils.

The following commented R code performs this preprocessing.

-# Apply a function to each of the seven datasets in the mkindsg object to create a list
-dmta_ds <- lapply(1:7, function(i) {
-  ds_i <- dimethenamid_2018$ds[[i]]$data                     # Get a dataset
-  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"              # Rename DMTAP to DMTA
-  ds_i <- subset(ds_i, name == "DMTA", c("name", "time", "value")) # Select data
-  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]  # Normalise time
-  ds_i                                                       # Return the dataset
-})
-
-# Use dataset titles as names for the list elements
-names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
-
-# Combine data for Elliot soil to obtain a named list with six elements
-dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]]) #
-dmta_ds[["Elliot 1"]] <- NULL
-dmta_ds[["Elliot 2"]] <- NULL

# Apply a function to each of the seven datasets in the mkindsg object to create a list
+dmta_ds <- lapply(1:7, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data                     # Get a dataset
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"              # Rename DMTAP to DMTA
+  ds_i <- subset(ds_i, name == "DMTA", c("name", "time", "value")) # Select data
+  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]  # Normalise time
+  ds_i                                                       # Return the dataset
+})
+
+# Use dataset titles as names for the list elements
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+
+# Combine data for Elliot soil to obtain a named list with six elements
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]]) #
+dmta_ds[["Elliot 1"]] <- NULL
+dmta_ds[["Elliot 2"]] <- NULL

The following tables show the 6 datasets.

-for (ds_name in names(dmta_ds)) {
-    print(kable(mkin_long_to_wide(dmta_ds[[ds_name]]),
-      caption = paste("Dataset", ds_name),
-      label = paste0("tab:", ds_name), booktabs = TRUE))
-    cat("\n\\clearpage\n")
-}

- +

for (ds_name in names(dmta_ds)) {
+    print(kable(mkin_long_to_wide(dmta_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      label = paste0("tab:", ds_name), booktabs = TRUE))
+    cat("\n\\clearpage\n")
+}

- + + - + + @@ -222,12 +502,14 @@ and Elliot 2) are combined, resulting in dimethenamid

Dataset Calke
time	DMTA
0

- +

- + + - + + @@ -295,12 +577,14 @@ and Elliot 2) are combined, resulting in dimethenamid

Dataset Borstel
time	DMTA
0.000000

- +

- + + - + + @@ -448,12 +732,14 @@ and Elliot 2) are combined, resulting in dimethenamid

Dataset Flaach
time	DMTA
0.0000000

- +

- + + - + + @@ -553,12 +839,14 @@ and Elliot 2) are combined, resulting in dimethenamid

Dataset BBA 2.2
time	DMTA
0.0000000

- +

- + + - + + @@ -658,12 +946,14 @@ and Elliot 2) are combined, resulting in dimethenamid

Dataset BBA 2.3
time	DMTA
0.0000000

- +

- + + - + + @@ -860,25 +1150,24 @@ and Elliot 2) are combined, resulting in dimethenamid

Dataset Elliot
time	DMTA
0.000000

Separate evaluations -

Separate evaluations

In order to obtain suitable starting parameters for the NLHM fits, separate fits of the four models to the data for each soil are generated using the mmkin function from the mkin package. In a first step, constant variance is assumed. Convergence is checked with the status function.

-deg_mods <- c("SFO", "FOMC", "DFOP", "HS")
-f_sep_const <- mmkin(
-  deg_mods,
-  dmta_ds,
-  error_model = "const",
-  quiet = TRUE)
-
-status(f_sep_const) |> kable()

- - +

deg_mods <- c("SFO", "FOMC", "DFOP", "HS")
+f_sep_const <- mmkin(
+  deg_mods,
+  dmta_ds,
+  error_model = "const",
+  quiet = TRUE)
+
+status(f_sep_const) |> kable()

+ + @@ -886,7 +1175,8 @@ checked with the status function.

- + + @@ -931,11 +1221,11 @@ to converge. All separate fits with constant variance converged, with the sole exception of the HS fit to the BBA 2.2 data. To prepare for fitting NLHM using the two-component error model, the separate fits are updated assuming two-component error.

-f_sep_tc <- update(f_sep_const, error_model = "tc")
-status(f_sep_tc) |> kable()

	Calke	Borstel	BBA 2.2	BBA 2.3	Elliot
SFO

- +

f_sep_tc <- update(f_sep_const, error_model = "tc")
+status(f_sep_tc) |> kable()

+ + @@ -943,7 +1233,8 @@ updated assuming two-component error.

- + + @@ -987,9 +1278,8 @@ updated assuming two-component error.

converge with constant variance did converge, but other non-SFO fits failed to converge.

Hierarchichal model fits -

Hierarchichal model fits

The following code fits eight versions of hierarchical models to the data, using SFO, FOMC, DFOP and HS for the parent compound, and using either constant variance or two-component error for the error model. The @@ -1001,18 +1291,18 @@ all eight versions in parallel (given a sufficient number of computing cores being available) to save execution time.

Convergence plots and summaries for these fits are shown in the appendix.

-f_saem <- mhmkin(list(f_sep_const, f_sep_tc), transformations = "saemix")

f_saem <- mhmkin(list(f_sep_const, f_sep_tc), transformations = "saemix")

The output of the status function shows that all fits terminated successfully.

-status(f_saem) |> kable()

	Calke	Borstel	BBA 2.2	BBA 2.3	Elliot
SFO

- +

status(f_saem) |> kable()

+ + - + + @@ -1038,16 +1328,17 @@ terminated successfully.

	const	tc
SFO

The AIC and BIC values show that the biphasic models DFOP and HS give the best fits.

-anova(f_saem) |> kable(digits = 1)

- - +

anova(f_saem) |> kable(digits = 1)

+ + - + + @@ -1113,22 +1404,22 @@ it shows the lowest AIC and BIC values in the first set of fits when combined with the two-component error model. Therefore, the DFOP model was selected for further refinements of the fits with the aim to make the model fully identifiable.

Parameter identifiability based on the Fisher Information -Matrix -

Parameter identifiability based on the Fisher Information +Matrix

Using the illparms function, ill-defined statistical model parameters such as standard deviations of the degradation parameters in the population and error model parameters can be found.

-illparms(f_saem) |> kable()

	npar	AIC	BIC	Lik
SFO const

- +

illparms(f_saem) |> kable()

+ + - + + @@ -1159,34 +1450,32 @@ be obtained for this standard deviation when using different starting values.

The thus identified overparameterisation is addressed by removing the random effect for k2 from the parameter model.

-f_saem_dfop_tc_no_ranef_k2 <- update(f_saem[["DFOP", "tc"]],
-  no_random_effect = "k2")

f_saem_dfop_tc_no_ranef_k2 <- update(f_saem[["DFOP", "tc"]],
+  no_random_effect = "k2")

For the resulting fit, it is checked whether there are still ill-defined parameters,

-illparms(f_saem_dfop_tc_no_ranef_k2)

illparms(f_saem_dfop_tc_no_ranef_k2)

which is not the case. Below, the refined model is compared with the previous best model. The model without random effect for k2 is a reduced version of the previous model. Therefore, the models are nested and can be compared using the likelihood ratio test. This is achieved with the argument test = TRUE to the anova function.

-anova(f_saem[["DFOP", "tc"]], f_saem_dfop_tc_no_ranef_k2, test = TRUE) |>
-  kable(format.args = list(digits = 4))

	const	tc
SFO

anova(f_saem[["DFOP", "tc"]], f_saem_dfop_tc_no_ranef_k2, test = TRUE) |>
+  kable(format.args = list(digits = 4))

--------++++++++ - + + @@ -1195,7 +1484,8 @@ achieved with the argument test = TRUE to the - + + @@ -1223,35 +1513,35 @@ achieved with the argument test = TRUE to the random effect for k2. The p value of the likelihood ratio test is much greater than 0.05, indicating that the model with the higher likelihood (here the model with random effects for all -degradation parameters f_saem[["DFOP", "tc"]]) does not fit +degradation parameters f_saem[["DFOP", "tc"]]) does not fit significantly better than the model with the lower likelihood (the reduced model f_saem_dfop_tc_no_ranef_k2).

Therefore, AIC, BIC and likelihood ratio test suggest the use of the reduced model.

The convergence of the fit is checked visually.

+ Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on 'k2' +

Convergence plot for the NLHM DFOP fit with two-component error and without a random effect on ‘k2’

All parameters appear to have converged to a satisfactory degree. The final fit is plotted using the plot method from the mkin package.

-plot(f_saem_dfop_tc_no_ranef_k2)

plot(f_saem_dfop_tc_no_ranef_k2)

+ Plot of the final NLHM DFOP fit +

Plot of the final NLHM DFOP fit

Finally, a summary report of the fit is produced.

-summary(f_saem_dfop_tc_no_ranef_k2)

saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:35 2023 
-Date of summary: Thu Nov 16 04:59:35 2023 
+summary(f_saem_dfop_tc_no_ranef_k2)
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:33 2025 
+Date of summary: Thu Feb 13 16:33:34 2025 
 
 Equations:
 d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1263,7 +1553,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 4.4 s
+Fitted in 3.778 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -1298,11 +1588,11 @@ DMTA_0    98.256267 96.286112 100.22642
 k1         0.064037  0.033281   0.09479
 k2         0.008469  0.006002   0.01094
 g          0.954167  0.914460   0.99387
-a.1        1.061795  0.863943   1.25965
-b.1        0.029550  0.022529   0.03657
-SD.DMTA_0  2.068581  0.427706   3.70946
+a.1        1.061795  0.878608   1.24498
+b.1        0.029550  0.022593   0.03651
+SD.DMTA_0  2.068581  0.427178   3.70998
 SD.k1      0.598285  0.258235   0.93833
-SD.g       1.016689  0.360057   1.67332
+SD.g       1.016689  0.360061   1.67332
 
 Correlation: 
    DMTA_0  k1      k2     
@@ -1312,22 +1602,21 @@ g  -0.0521 -0.0286 -0.2744
 
 Random effects:
             est.  lower  upper
-SD.DMTA_0 2.0686 0.4277 3.7095
+SD.DMTA_0 2.0686 0.4272 3.7100
 SD.k1     0.5983 0.2582 0.9383
 SD.g      1.0167 0.3601 1.6733
 
 Variance model:
        est.   lower   upper
-a.1 1.06180 0.86394 1.25965
-b.1 0.02955 0.02253 0.03657
+a.1 1.06180 0.87861 1.24498
+b.1 0.02955 0.02259 0.03651
 
 Estimated disappearance times:
       DT50  DT90 DT50back DT50_k1 DT50_k2
 DMTA 11.45 41.32    12.44   10.82   81.85
 
-
-Alternative check of parameter identifiability
-
+
+Alternative check of parameter identifiability
 The parameter check used in the illparms function is
 based on a quadratic approximation of the likelihood surface near its
 optimum, which is calculated using the Fisher Information Matrix (FIM).
@@ -1337,13 +1626,12 @@ approach has recently been implemented in mkin.
 of the saem algorithm with different parameter combinations, sampled
 from the range of the parameters obtained for the individual datasets
 fitted separately using nonlinear regression.
--f_saem_dfop_tc_multi <- multistart(f_saem[["DFOP", "tc"]], n = 50, cores = 15)
--par(mar = c(6.1, 4.1, 2.1, 2.1))
-parplot(f_saem_dfop_tc_multi, lpos = "bottomright", ylim = c(0.3, 10), las = 2)
+f_saem_dfop_tc_multi <- multistart(f_saem[["DFOP", "tc"]], n = 50, cores = 15)
+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_multi, lpos = "bottomright", ylim = c(0.3, 10), las = 2)
 
-
+
+

 Scaled parameters from the multistart runs, full model
 
 
@@ -1354,36 +1642,34 @@ parameter g.
 The parameter boxplots of the multistart runs with the reduced model
 shown below indicate that all runs give similar results, regardless of
 the starting parameters.
--f_saem_dfop_tc_no_ranef_k2_multi <- multistart(f_saem_dfop_tc_no_ranef_k2,
-  n = 50, cores = 15)
--par(mar = c(6.1, 4.1, 2.1, 2.1))
-parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2,
-  lpos = "bottomright")
+f_saem_dfop_tc_no_ranef_k2_multi <- multistart(f_saem_dfop_tc_no_ranef_k2,
+  n = 50, cores = 15)
+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2,
+  lpos = "bottomright")
 
-
+
+

 Scaled parameters from the multistart runs, reduced model
 
 
 When only the parameters of the top 25% of the fits are shown (based
 on a feature introduced in mkin 1.2.2 currently under development), the
 scatter is even less as shown below.
--par(mar = c(6.1, 4.1, 2.1, 2.1))
-parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2, llquant = 0.25,
-  lpos = "bottomright")
+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2, llquant = 0.25,
+  lpos = "bottomright")
 
-
+
+

 Scaled parameters from the multistart runs, reduced model, fits with the
 top 25% likelihood values
 
 
 
 
-
-Conclusions
-
+
+Conclusions
 Fitting the four parent degradation models SFO, FOMC, DFOP and HS as
 part of hierarchical model fits with two different error models and
 normal distributions of the transformed degradation parameters works
@@ -1395,39 +1681,35 @@ was fully identifiable and showed the lowest values for the model
 selection criteria AIC and BIC. The reliability of the identification of
 all model parameters was confirmed using multiple starting values.
 
-
-Acknowledgements
-
+
+Acknowledgements
 The helpful comments by Janina Wöltjen of the German Environment
 Agency are gratefully acknowledged.
 
-
-References
-
+
+References
 
 
 Duchesne, Ronan, Anissa Guillemin, Olivier Gandrillon, and Fabien
 Crauste. 2021. “Practical Identifiability in the Frame of
 Nonlinear Mixed Effects Models: The Example of the in Vitro
-Erythropoiesis.” BMC Bioinformatics 22 (478). https://doi.org/10.1186/s12859-021-04373-4.
+Erythropoiesis.” BMC Bioinformatics 22 (478). https://doi.org/10.1186/s12859-021-04373-4.
 
 
 
-
-Appendix
-
-
-Hierarchical model fit listings
-
+
+Appendix
+
+Hierarchical model fit listings


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:26 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:26 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - k_DMTA * DMTA
@@ -1437,7 +1719,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 0.788 s
+Fitted in 0.792 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -1489,17 +1771,17 @@ Estimated disappearance times:
       DT50  DT90
 DMTA 12.24 40.65
 
-


-
+
+


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:28 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - k_DMTA * DMTA
@@ -1509,7 +1791,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.428 s
+Fitted in 2.245 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -1537,13 +1819,13 @@ Likelihood computed by importance sampling
   798.3 797.1 -393.2
 
 Optimised parameters:
-               est.     lower    upper
-DMTA_0    97.271822 95.703157 98.84049
-k_DMTA     0.056638  0.029110  0.08417
-a.1        2.660081  2.230398  3.08976
-b.1        0.001665 -0.006911  0.01024
-SD.DMTA_0  1.545520  0.145035  2.94601
-SD.k_DMTA  0.606422  0.262274  0.95057
+               est.    lower    upper
+DMTA_0    97.271822 95.70316 98.84049
+k_DMTA     0.056638  0.02911  0.08417
+a.1        2.660081  2.27492  3.04525
+b.1        0.001665 -0.14451  0.14784
+SD.DMTA_0  1.545520  0.14301  2.94803
+SD.k_DMTA  0.606422  0.26227  0.95057
 
 Correlation: 
        DMTA_0
@@ -1551,29 +1833,29 @@ k_DMTA 0.0169
 
 Random effects:
             est.  lower  upper
-SD.DMTA_0 1.5455 0.1450 2.9460
+SD.DMTA_0 1.5455 0.1430 2.9480
 SD.k_DMTA 0.6064 0.2623 0.9506
 
 Variance model:
-        est.     lower   upper
-a.1 2.660081  2.230398 3.08976
-b.1 0.001665 -0.006911 0.01024
+        est.   lower  upper
+a.1 2.660081  2.2749 3.0452
+b.1 0.001665 -0.1445 0.1478
 
 Estimated disappearance times:
       DT50  DT90
 DMTA 12.24 40.65
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:27 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:27 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
@@ -1583,7 +1865,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.28 s
+Fitted in 1.409 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -1640,17 +1922,17 @@ Estimated disappearance times:
       DT50  DT90 DT50back
 DMTA 11.41 42.53     12.8
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:28 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
@@ -1660,7 +1942,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.793 s
+Fitted in 2.811 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -1693,11 +1975,11 @@ Optimised parameters:
 DMTA_0    99.10577 97.33296 100.87859
 alpha      5.46260  2.52199   8.40321
 beta      81.66080 30.46664 132.85497
-a.1        1.50219  1.23601   1.76836
-b.1        0.02893  0.02099   0.03687
-SD.DMTA_0  1.61887 -0.03636   3.27411
+a.1        1.50219  1.25801   1.74636
+b.1        0.02893  0.02048   0.03739
+SD.DMTA_0  1.61887 -0.03843   3.27618
 SD.alpha   0.58145  0.17364   0.98925
-SD.beta    0.68205  0.21108   1.15303
+SD.beta    0.68205  0.21108   1.15302
 
 Correlation: 
       DMTA_0  alpha  
@@ -1706,30 +1988,30 @@ beta  -0.1430  0.2467
 
 Random effects:
             est.    lower  upper
-SD.DMTA_0 1.6189 -0.03636 3.2741
+SD.DMTA_0 1.6189 -0.03843 3.2762
 SD.alpha  0.5814  0.17364 0.9892
 SD.beta   0.6821  0.21108 1.1530
 
 Variance model:
        est.   lower   upper
-a.1 1.50219 1.23601 1.76836
-b.1 0.02893 0.02099 0.03687
+a.1 1.50219 1.25801 1.74636
+b.1 0.02893 0.02048 0.03739
 
 Estimated disappearance times:
       DT50  DT90 DT50back
 DMTA 11.05 42.81    12.89
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:27 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:27 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1741,7 +2023,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.752 s
+Fitted in 1.638 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -1803,17 +2085,17 @@ Estimated disappearance times:
       DT50 DT90 DT50back DT50_k1 DT50_k2
 DMTA 11.79 42.8    12.88   11.09   76.46
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:29 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1825,7 +2107,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.186 s
+Fitted in 3.024 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -1860,12 +2142,12 @@ DMTA_0    98.347470 96.380815 100.31413
 k1         0.064524  0.034279   0.09477
 k2         0.008304  0.005843   0.01076
 g          0.952128  0.909578   0.99468
-a.1        1.068907  0.868694   1.26912
-b.1        0.029265  0.022262   0.03627
-SD.DMTA_0  2.065796  0.428485   3.70311
+a.1        1.068907  0.883665   1.25415
+b.1        0.029265  0.022318   0.03621
+SD.DMTA_0  2.065796  0.427951   3.70364
 SD.k1      0.583703  0.251796   0.91561
-SD.k2      0.004167 -7.832168   7.84050
-SD.g       1.064450  0.397476   1.73142
+SD.k2      0.004167 -7.831228   7.83956
+SD.g       1.064450  0.397479   1.73142
 
 Correlation: 
    DMTA_0  k1      k2     
@@ -1875,31 +2157,31 @@ g  -0.0464 -0.0269 -0.2713
 
 Random effects:
               est.   lower  upper
-SD.DMTA_0 2.065796  0.4285 3.7031
+SD.DMTA_0 2.065796  0.4280 3.7036
 SD.k1     0.583703  0.2518 0.9156
-SD.k2     0.004167 -7.8322 7.8405
+SD.k2     0.004167 -7.8312 7.8396
 SD.g      1.064450  0.3975 1.7314
 
 Variance model:
        est.   lower   upper
-a.1 1.06891 0.86869 1.26912
-b.1 0.02927 0.02226 0.03627
+a.1 1.06891 0.88367 1.25415
+b.1 0.02927 0.02232 0.03621
 
 Estimated disappearance times:
       DT50  DT90 DT50back DT50_k1 DT50_k2
 DMTA 11.39 41.36    12.45   10.74   83.48
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:28 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
@@ -1909,7 +2191,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.28 s
+Fitted in 2.301 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -1971,17 +2253,17 @@ Estimated disappearance times:
       DT50  DT90 DT50back DT50_k1 DT50_k2
 DMTA 8.801 67.91    20.44   8.801   31.13
 
-

+ +


-saemix version used for fitting:      3.2 
-mkin version used for pre-fitting:  1.2.6 
-R version used for fitting:         4.3.2 
-Date of fit:     Thu Nov 16 04:59:29 2023 
-Date of summary: Thu Nov 16 05:00:43 2023 
+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:29 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
 
 Equations:
 d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
@@ -1991,7 +2273,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.658 s
+Fitted in 3.264 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -2026,12 +2308,12 @@ DMTA_0    97.76571 95.81350 99.71791
 k1         0.05855  0.03080  0.08630
 k2         0.02337  0.01664  0.03010
 tb        31.09638 29.38289 32.80987
-a.1        1.08835  0.88590  1.29080
-b.1        0.02964  0.02257  0.03671
-SD.DMTA_0  2.04877  0.42607  3.67147
+a.1        1.08835  0.90059  1.27611
+b.1        0.02964  0.02261  0.03667
+SD.DMTA_0  2.04877  0.42553  3.67200
 SD.k1      0.59166  0.25621  0.92711
 SD.k2      0.30698  0.09561  0.51835
-SD.tb      0.01274 -0.10914  0.13462
+SD.tb      0.01274 -0.10915  0.13464
 
 Correlation: 
    DMTA_0  k1      k2     
@@ -2041,72 +2323,78 @@ tb -0.0668 -0.0103 -0.2013
 
 Random effects:
              est.    lower  upper
-SD.DMTA_0 2.04877  0.42607 3.6715
+SD.DMTA_0 2.04877  0.42553 3.6720
 SD.k1     0.59166  0.25621 0.9271
 SD.k2     0.30698  0.09561 0.5183
-SD.tb     0.01274 -0.10914 0.1346
+SD.tb     0.01274 -0.10915 0.1346
 
 Variance model:
        est.   lower   upper
-a.1 1.08835 0.88590 1.29080
-b.1 0.02964 0.02257 0.03671
+a.1 1.08835 0.90059 1.27611
+b.1 0.02964 0.02261 0.03667
 
 Estimated disappearance times:
       DT50  DT90 DT50back DT50_k1 DT50_k2
 DMTA 11.84 51.71    15.57   11.84   29.66
 
-

+ +

Hierarchical model convergence plots -

Hierarchical model convergence plots

+ Convergence plot for the NLHM SFO fit with constant variance +

Convergence plot for the NLHM SFO fit with constant variance

+ Convergence plot for the NLHM SFO fit with two-component error +

Convergence plot for the NLHM SFO fit with two-component error

+ Convergence plot for the NLHM FOMC fit with constant variance +

Convergence plot for the NLHM FOMC fit with constant variance

+ Convergence plot for the NLHM FOMC fit with two-component error +

Convergence plot for the NLHM FOMC fit with two-component error

+ Convergence plot for the NLHM DFOP fit with constant variance +

Convergence plot for the NLHM DFOP fit with constant variance

+ Convergence plot for the NLHM DFOP fit with two-component error +

Convergence plot for the NLHM DFOP fit with two-component error

+ Convergence plot for the NLHM HS fit with constant variance +

Convergence plot for the NLHM HS fit with constant variance

+ Convergence plot for the NLHM HS fit with two-component error +

Convergence plot for the NLHM HS fit with two-component error

Session info -

R version 4.3.2 (2023-10-31)
-Platform: x86_64-pc-linux-gnu (64-bit)
+
+Session info
+R version 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
@@ -2129,53 +2417,73 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.2 npde_3.3   knitr_1.42 mkin_1.2.6
+[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
+[5] rmarkdown_2.29  nvimcom_0.9-167
 
 loaded via a namespace (and not attached):
- [1] sass_0.4.6        utf8_1.2.3        generics_0.1.3    stringi_1.7.12   
- [5] lattice_0.21-8    digest_0.6.31     magrittr_2.0.3    evaluate_0.21    
- [9] grid_4.3.2        fastmap_1.1.1     rprojroot_2.0.3   jsonlite_1.8.4   
-[13] DBI_1.1.3         mclust_6.0.0      gridExtra_2.3     purrr_1.0.1      
-[17] fansi_1.0.4       scales_1.2.1      codetools_0.2-19  textshaping_0.3.6
-[21] jquerylib_0.1.4   cli_3.6.1         rlang_1.1.1       munsell_0.5.0    
-[25] cachem_1.0.8      yaml_2.3.7        tools_4.3.2       memoise_2.0.1    
-[29] dplyr_1.1.2       colorspace_2.1-0  ggplot2_3.4.2     vctrs_0.6.2      
-[33] R6_2.5.1          zoo_1.8-12        lifecycle_1.0.3   stringr_1.5.0    
-[37] fs_1.6.2          MASS_7.3-60       ragg_1.2.5        pkgconfig_2.0.3  
-[41] desc_1.4.2        pkgdown_2.0.7     bslib_0.4.2       pillar_1.9.0     
-[45] gtable_0.3.3      glue_1.6.2        systemfonts_1.0.4 highr_0.10       
-[49] xfun_0.39         tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.0 
-[53] htmltools_0.5.5   nlme_3.1-163      rmarkdown_2.21    compiler_4.3.2   
+ [1] jsonlite_1.8.9    gtable_0.3.6      dplyr_1.1.4       compiler_4.4.2   
+ [5] tidyselect_1.2.1  colorout_1.3-2    tinytex_0.54      gridExtra_2.3    
+ [9] jquerylib_0.1.4   scales_1.3.0      yaml_2.3.10       fastmap_1.2.0    
+[13] lattice_0.22-6    ggplot2_3.5.1     R6_2.5.1          generics_0.1.3   
+[17] lmtest_0.9-40     MASS_7.3-61       tibble_3.2.1      munsell_0.5.1    
+[21] bslib_0.8.0       pillar_1.9.0      rlang_1.1.4       utf8_1.2.4       
+[25] cachem_1.1.0      xfun_0.49         sass_0.4.9        cli_3.6.3        
+[29] magrittr_2.0.3    digest_0.6.37     grid_4.4.2        mclust_6.1.1     
+[33] lifecycle_1.0.4   nlme_3.1-166      vctrs_0.6.5       evaluate_1.0.1   
+[37] glue_1.8.0        codetools_0.2-20  zoo_1.8-12        fansi_1.0.6      
+[41] colorspace_2.1-1  tools_4.4.2       pkgconfig_2.0.3   htmltools_0.5.8.1

Hardware info -

Hardware info

CPU model: AMD Ryzen 9 7950X 16-Core Processor

MemTotal:       64927712 kB

MemTotal:       64927788 kB

- -

- - + + + + + + + - - + + - + -- cgit v1.2.3

Hierarchical mkin fit of the SFO model with error model const
	npar	AIC	Chisq	Df	Pr(>Chisq)
f_saem_dfop_tc_no_ranef_k2

Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P

Johannes -Ranke

Last change on 5 January -2023, last compiled on 16 November 2023

Introduction -

Testing hierarchical parent degradation +kinetics with residue data on dimethenamid and dimethenamid-P

Johannes Ranke

Last change on 5 January 2023, last compiled on 13 +Februar 2025

Introduction

Data -

Data

Separate evaluations -

Separate evaluations

Hierarchichal model fits -

Hierarchichal model fits

Parameter identifiability based on the Fisher Information -Matrix -

Parameter identifiability based on the Fisher Information +Matrix

Alternative check of parameter identifiability -

Alternative check of parameter identifiability

Conclusions -

Conclusions

Acknowledgements -

Acknowledgements

References -

References

Appendix -

Hierarchical model fit listings -

Appendix

Hierarchical model fit listings

Hierarchical model convergence plots -

Hierarchical model convergence plots

Session info -

Session info

Hardware info -

Hardware info