t7	t8
Ryzen 7 1700	Linux	1.2.0	3.2	5.645	7.415	7.848	7.967
5.678	7.441	8.000	7.980
Ryzen 7 1700	Linux	1.2.2	3.2	5.352	7.201	8.174	8.401

+ + + + +

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.

The mkin package is used in version 1.2.2. 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.

This document is processed with the knitr package, which +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)
+}

Preprocessing of test 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 +still necessary:

The data available for the enantiomer dimethenamid-P (DMTAP) are +renamed to have the same substance name as the data for the racemic +mixture dimethenamid (DMTA). The reason for this is that no difference +between their degradation behaviour was identified in the EU risk +assessment.
The data for transformation products and unnecessary columns are +discarded
The observation times of each dataset are multiplied with the +corresponding normalisation factor also available in the dataset, in +order to make it possible to describe all datasets with a single set of +parameters that are independent of temperature
Finally, datasets observed in the same soil (Elliot 1 +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

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")
+}

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

Dataset Calke
time	DMTA
0	95.8
0	98.7
14	60.5
30	39.1
59	15.2
120	4.8
120	4.6

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

Dataset Borstel
time	DMTA
0.000000	100.5
0.000000	99.6
1.941295	91.9
1.941295	91.3
6.794534	81.8
6.794534	82.1
13.589067	69.1
13.589067	68.0
27.178135	51.4
27.178135	51.4
56.297565	27.6
56.297565	26.8
86.387643	15.7
86.387643	15.3
115.507073	7.9
115.507073	8.1

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

Dataset Flaach
time	DMTA
0.0000000	96.5
0.0000000	96.8
0.0000000	97.0
0.6233856	82.9
0.6233856	86.7
0.6233856	87.4
1.8701567	72.8
1.8701567	69.9
1.8701567	71.9
4.3636989	51.4
4.3636989	52.9
4.3636989	48.6
8.7273979	28.5
8.7273979	27.3
8.7273979	27.5
13.0910968	14.8
13.0910968	13.4
13.0910968	14.4
17.4547957	7.7
17.4547957	7.3
17.4547957	8.1
26.1821936	2.0
26.1821936	1.5
26.1821936	1.9
34.9095915	1.3
34.9095915	1.0
34.9095915	1.1
43.6369893	0.9
43.6369893	0.7
43.6369893	0.7
52.3643872	0.6
52.3643872	0.4
52.3643872	0.5
74.8062674	0.4
74.8062674	0.3
74.8062674	0.3

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

Dataset BBA 2.2
time	DMTA
0.0000000	98.09
0.0000000	98.77
0.7678922	93.52
0.7678922	92.03
2.3036765	88.39
2.3036765	87.18
5.3752452	69.38
5.3752452	71.06
10.7504904	45.21
10.7504904	46.81
16.1257355	30.54
16.1257355	30.07
21.5009807	21.60
21.5009807	20.41
32.2514711	9.10
32.2514711	9.70
43.0019614	6.58
43.0019614	6.31
53.7524518	3.47
53.7524518	3.52
64.5029421	3.40
64.5029421	3.67
91.3791680	1.62
91.3791680	1.62

Dataset BBA 2.3
time	DMTA
0.0000000	99.33
0.0000000	97.44
0.6733938	93.73
0.6733938	93.77
2.0201814	87.84
2.0201814	89.82
4.7137565	71.61
4.7137565	71.42
9.4275131	45.60
9.4275131	45.42
14.1412696	31.12
14.1412696	31.68
18.8550262	23.20
18.8550262	24.13
28.2825393	9.43
28.2825393	9.82
37.7100523	7.08
37.7100523	8.64
47.1375654	4.41
47.1375654	4.78
56.5650785	4.92
56.5650785	5.08
80.1338612	2.13
80.1338612	2.23

Dataset Elliot
time	DMTA
0.000000	97.5
0.000000	100.7
1.228478	86.4
1.228478	88.5
3.685435	69.8
3.685435	77.1
8.599349	59.0
8.599349	54.2
17.198697	31.3
17.198697	33.5
25.798046	19.6
25.798046	20.9
34.397395	13.3
34.397395	15.8
51.596092	6.7
51.596092	8.7
68.794789	8.8
68.794789	8.7
103.192184	6.0
103.192184	4.4
146.188928	3.3
146.188928	2.8
223.583066	1.4
223.583066	1.8
0.000000	93.4
0.000000	103.2
1.228478	89.2
1.228478	86.6
3.685435	78.2
3.685435	78.1
8.599349	55.6
8.599349	53.0
17.198697	33.7
17.198697	33.2
25.798046	20.9
25.798046	19.9
34.397395	18.2
34.397395	12.7
51.596092	7.8
51.596092	9.0
68.794789	11.4
68.794789	9.0
103.192184	3.9
103.192184	4.4
146.188928	2.6
146.188928	3.4
223.583066	2.0
223.583066	1.7

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()

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

	Calke	Borstel	Flaach	BBA 2.2	BBA 2.3	Elliot
SFO	OK	OK	OK	OK	OK	OK
FOMC	OK	OK	OK	OK	OK	OK
DFOP	OK	OK	OK	OK	OK	OK
HS	OK	OK	OK	C	OK	OK

In the table above, OK indicates convergence, and C indicates failure +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	Flaach	BBA 2.2	BBA 2.3	Elliot
SFO	OK	OK	OK	OK	OK	OK
FOMC	OK	OK	OK	OK	C	OK
DFOP	OK	OK	C	OK	C	OK
HS	OK	C	OK	OK	OK	OK

Using the two-component error model, the one fit that did not +converge with constant variance did converge, but other non-SFO fits +failed to converge.

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 +default parameter distribution model in mkin allows for variation of all +degradation parameters across the assumed population of soils. In other +words, each degradation parameter is associated with a random effect as +a first step. The mhmkin function makes it possible to fit +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")

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

+status(f_saem) |> kable()

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

	const	tc
SFO	OK	OK
FOMC	OK	OK
DFOP	OK	OK
HS	OK	OK

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

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

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

	npar	AIC	BIC	Lik
SFO const	5	796.3	795.3	-393.2
SFO tc	6	798.3	797.1	-393.2
FOMC const	7	734.2	732.7	-360.1
FOMC tc	8	720.4	718.8	-352.2
DFOP const	9	711.8	710.0	-346.9
HS const	9	714.0	712.1	-348.0
DFOP tc	10	665.5	663.4	-322.8
HS tc	10	667.1	665.0	-323.6

The DFOP model is preferred here, as it has a better mechanistic +basis for batch experiments with constant incubation conditions. Also, +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 +

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()

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

	const	tc
SFO		b.1
FOMC		sd(DMTA_0)
DFOP	sd(k2)	sd(k2)
HS		sd(tb)

According to the illparms function, the fitted standard +deviation of the second kinetic rate constant k2 is +ill-defined in both DFOP fits. This suggests that different values would +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")

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

+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))

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

	npar	AIC	BIC	Lik	Chisq	Df	Pr(>Chisq)
f_saem_dfop_tc_no_ranef_k2	9	663.8	661.9	-322.9	NA	NA	NA
f_saem[[“DFOP”, “tc”]]	10	665.5	663.4	-322.8	0.2809	1	0.5961

The AIC and BIC criteria are lower after removal of the ill-defined +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 +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’ +

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 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:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:13 2023 
+Date of summary: Thu Jan  5 08:19:13 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 4.075 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  663.8 661.9 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.228939 96.285869 100.17201
+k1         0.064063  0.033477   0.09465
+k2         0.008297  0.005824   0.01077
+g          0.953821  0.914328   0.99331
+a.1        1.068479  0.869538   1.26742
+b.1        0.029424  0.022406   0.03644
+SD.DMTA_0  2.030437  0.404824   3.65605
+SD.k1      0.594692  0.256660   0.93272
+SD.g       1.006754  0.361327   1.65218
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0218                
+k2  0.0556  0.0355        
+g  -0.0516 -0.0284 -0.2800
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 2.0304 0.4048 3.6560
+SD.k1     0.5947 0.2567 0.9327
+SD.g      1.0068 0.3613 1.6522
+
+Variance model:
+       est.   lower   upper
+a.1 1.06848 0.86954 1.26742
+b.1 0.02942 0.02241 0.03644
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.4    12.46   10.82   83.54

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). +An alternative way to check parameter identifiability based on a +multistart approach has recently been implemented in mkin.

The graph below shows boxplots of the parameters obtained in 50 runs +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)

+Scaled parameters from the multistart runs, full model +

The graph clearly confirms the lack of identifiability of the +variance of k2 in the full model. The overparameterisation +of the model also indicates a lack of identifiability of the variance of +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")

+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")

+ $Scaled parameters from the multistart runs, reduced model, fits with the top 25\% likelihood values$

+Scaled parameters from the multistart runs, reduced model, fits with the +top 25% likelihood values +

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 +without technical problems. The biphasic models DFOP and HS gave the +best fit to the data, but the default parameter distribution model was +not fully identifiable. Removing the random effect for the second +kinetic rate constant of the DFOP model resulted in a reduced model that +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.

Appendix +

Hierarchical model fit listings +

+ +Hierarchical mkin fit of the SFO model with error model const + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:06 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 1.09 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+ DMTA_0  k_DMTA 
+97.2953  0.0566 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0   97.3      0
+k_DMTA    0.0      1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  796.3 795.3 -393.2
+
+Optimised parameters:
+              est.    lower   upper
+DMTA_0    97.28130 95.71113 98.8515
+k_DMTA     0.05665  0.02909  0.0842
+a.1        2.66442  2.35579  2.9731
+SD.DMTA_0  1.54776  0.15447  2.9411
+SD.k_DMTA  0.60690  0.26248  0.9513
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0168
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5478 0.1545 2.9411
+SD.k_DMTA 0.6069 0.2625 0.9513
+
+Variance model:
+     est. lower upper
+a.1 2.664 2.356 2.973
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+

+ +Hierarchical mkin fit of the SFO model with error model tc + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:07 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.441 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0   k_DMTA 
+96.99175  0.05603 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0  96.99      0
+k_DMTA   0.00      1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  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
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5455 0.1450 2.9460
+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
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+

+ +Hierarchical mkin fit of the FOMC model with error model const + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:06 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 1.156 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+ DMTA_0   alpha    beta 
+ 98.292   9.909 156.341 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 alpha beta
+DMTA_0  98.29     0    0
+alpha    0.00     1    0
+beta     0.00     0    1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  734.2 732.7 -360.1
+
+Optimised parameters:
+              est.   lower   upper
+DMTA_0     98.3435 96.9033  99.784
+alpha       7.2007  2.5889  11.812
+beta      112.8746 34.8816 190.868
+a.1         2.0459  1.8054   2.286
+SD.DMTA_0   1.4795  0.2717   2.687
+SD.alpha    0.6396  0.1509   1.128
+SD.beta     0.6874  0.1587   1.216
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1125        
+beta  -0.1227  0.3632
+
+Random effects:
+            est.  lower upper
+SD.DMTA_0 1.4795 0.2717 2.687
+SD.alpha  0.6396 0.1509 1.128
+SD.beta   0.6874 0.1587 1.216
+
+Variance model:
+     est. lower upper
+a.1 2.046 1.805 2.286
+
+Estimated disappearance times:
+      DT50  DT90 DT50back
+DMTA 11.41 42.53     12.8
+
+

+ +Hierarchical mkin fit of the FOMC model with error model tc + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:07 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.729 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+DMTA_0  alpha   beta 
+98.772  4.663 92.597 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 alpha beta
+DMTA_0  98.77     0    0
+alpha    0.00     1    0
+beta     0.00     0    1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  720.4 718.8 -352.2
+
+Optimised parameters:
+              est.    lower     upper
+DMTA_0    98.99136 97.26011 100.72261
+alpha      5.86312  2.57485   9.15138
+beta      88.55571 29.20889 147.90254
+a.1        1.51063  1.24384   1.77741
+b.1        0.02824  0.02040   0.03609
+SD.DMTA_0  1.57436 -0.04867   3.19739
+SD.alpha   0.59871  0.17132   1.02611
+SD.beta    0.72994  0.22849   1.23139
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1363        
+beta  -0.1414  0.2542
+
+Random effects:
+            est.    lower upper
+SD.DMTA_0 1.5744 -0.04867 3.197
+SD.alpha  0.5987  0.17132 1.026
+SD.beta   0.7299  0.22849 1.231
+
+Variance model:
+       est.  lower   upper
+a.1 1.51063 1.2438 1.77741
+b.1 0.02824 0.0204 0.03609
+
+Estimated disappearance times:
+      DT50 DT90 DT50back
+DMTA 11.11 42.6    12.82
+
+

+ +Hierarchical mkin fit of the DFOP model with error model const + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:07 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.007 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.64383  0.09211  0.02999  0.76814 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.64  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  711.8 710 -346.9
+
+Optimised parameters:
+               est.     lower    upper
+DMTA_0    98.092481 96.573898 99.61106
+k1         0.062499  0.030336  0.09466
+k2         0.009065 -0.005133  0.02326
+g          0.948967  0.862079  1.03586
+a.1        1.821671  1.604774  2.03857
+SD.DMTA_0  1.677785  0.472066  2.88350
+SD.k1      0.634962  0.270788  0.99914
+SD.k2      1.033498 -0.205994  2.27299
+SD.g       1.710046  0.428642  2.99145
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0246                
+k2  0.0491  0.0953        
+g  -0.0552 -0.0889 -0.4795
+
+Random effects:
+           est.   lower  upper
+SD.DMTA_0 1.678  0.4721 2.8835
+SD.k1     0.635  0.2708 0.9991
+SD.k2     1.033 -0.2060 2.2730
+SD.g      1.710  0.4286 2.9914
+
+Variance model:
+     est. lower upper
+a.1 1.822 1.605 2.039
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.79 42.8    12.88   11.09   76.46
+
+

+ +Hierarchical mkin fit of the DFOP model with error model tc + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:08 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.033 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  665.5 663.4 -322.8
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.377019 96.447952 100.30609
+k1         0.064843  0.034607   0.09508
+k2         0.008895  0.006368   0.01142
+g          0.949696  0.903815   0.99558
+a.1        1.065241  0.865754   1.26473
+b.1        0.029340  0.022336   0.03634
+SD.DMTA_0  2.007754  0.387982   3.62753
+SD.k1      0.580473  0.250286   0.91066
+SD.k2      0.006105 -4.920337   4.93255
+SD.g       1.097149  0.412779   1.78152
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0235                
+k2  0.0595  0.0424        
+g  -0.0470 -0.0278 -0.2731
+
+Random effects:
+              est.   lower  upper
+SD.DMTA_0 2.007754  0.3880 3.6275
+SD.k1     0.580473  0.2503 0.9107
+SD.k2     0.006105 -4.9203 4.9325
+SD.g      1.097149  0.4128 1.7815
+
+Variance model:
+       est.   lower   upper
+a.1 1.06524 0.86575 1.26473
+b.1 0.02934 0.02234 0.03634
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.36 41.32    12.44   10.69   77.92
+
+

+ +Hierarchical mkin fit of the HS model with error model const + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:07 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.004 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+97.82176  0.06931  0.02997 11.13945 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  97.82  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+  AIC   BIC logLik
+  714 712.1   -348
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    98.16102 96.47747 99.84456
+k1         0.07876  0.05261  0.10491
+k2         0.02227  0.01706  0.02747
+tb        13.99089 -7.40049 35.38228
+a.1        1.82305  1.60700  2.03910
+SD.DMTA_0  1.88413  0.56204  3.20622
+SD.k1      0.34292  0.10482  0.58102
+SD.k2      0.19851  0.01718  0.37985
+SD.tb      1.68168  0.58064  2.78272
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0142                
+k2  0.0001 -0.0025        
+tb  0.0165 -0.1256 -0.0301
+
+Random effects:
+            est.   lower  upper
+SD.DMTA_0 1.8841 0.56204 3.2062
+SD.k1     0.3429 0.10482 0.5810
+SD.k2     0.1985 0.01718 0.3798
+SD.tb     1.6817 0.58064 2.7827
+
+Variance model:
+     est. lower upper
+a.1 1.823 1.607 2.039
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 8.801 67.91    20.44   8.801   31.13
+
+

+ +Hierarchical mkin fit of the HS model with error model tc + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:08 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.287 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+98.45190  0.07525  0.02576 19.19375 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  98.45  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  667.1 665 -323.6
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    97.76570 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
+SD.k1      0.59166  0.25621  0.92711
+SD.k2      0.30698  0.09561  0.51835
+SD.tb      0.01274 -0.10914  0.13462
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0160                
+k2 -0.0070 -0.0024        
+tb -0.0668 -0.0103 -0.2013
+
+Random effects:
+             est.    lower  upper
+SD.DMTA_0 2.04877  0.42607 3.6715
+SD.k1     0.59166  0.25621 0.9271
+SD.k2     0.30698  0.09561 0.5183
+SD.tb     0.01274 -0.10914 0.1346
+
+Variance model:
+       est.   lower   upper
+a.1 1.08835 0.88590 1.29080
+b.1 0.02964 0.02257 0.03671
+
+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 +

+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 FOMC fit with constant variance +

+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 two-component error +

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

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

Session info +

R version 4.2.2 Patched (2022-11-10 r83330)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux bookworm/sid
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so
+
+locale:
+ [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
+ [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=de_DE.UTF-8    
+ [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=de_DE.UTF-8   
+ [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
+ [9] LC_ADDRESS=C               LC_TELEPHONE=C            
+[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.2 npde_3.3   knitr_1.41 mkin_1.2.2
+
+loaded via a namespace (and not attached):
+ [1] deSolve_1.34      zoo_1.8-11        tidyselect_1.2.0  xfun_0.35        
+ [5] bslib_0.4.2       purrr_1.0.0       lattice_0.20-45   colorspace_2.0-3 
+ [9] vctrs_0.5.1       generics_0.1.3    htmltools_0.5.4   yaml_2.3.6       
+[13] utf8_1.2.2        rlang_1.0.6       pkgdown_2.0.7     jquerylib_0.1.4  
+[17] pillar_1.8.1      glue_1.6.2        DBI_1.1.3         lifecycle_1.0.3  
+[21] stringr_1.5.0     munsell_0.5.0     gtable_0.3.1      ragg_1.2.4       
+[25] codetools_0.2-18  memoise_2.0.1     evaluate_0.19     fastmap_1.1.0    
+[29] lmtest_0.9-40     fansi_1.0.3       highr_0.9         scales_1.2.1     
+[33] cachem_1.0.6      desc_1.4.2        jsonlite_1.8.4    systemfonts_1.0.4
+[37] fs_1.5.2          textshaping_0.3.6 gridExtra_2.3     ggplot2_3.4.0    
+[41] digest_0.6.31     stringi_1.7.8     dplyr_1.0.10      grid_4.2.2       
+[45] rprojroot_2.0.3   cli_3.5.0         tools_4.2.2       magrittr_2.0.3   
+[49] sass_0.4.4        tibble_3.1.8      pkgconfig_2.0.3   assertthat_0.2.1 
+[53] rmarkdown_2.19    R6_2.5.1          mclust_6.0.0      nlme_3.1-161     
+[57] compiler_4.2.2

+ + + +

- Functions and data + Reference
@@ -34,6 +34,8 @@
- Introduction to mkin
- +
- Example evaluations with (generalised) nonlinear least squares
- Example evaluation of FOCUS Example Dataset D
- - Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models + Example evaluation of FOCUS Example Dataset Z
- +
- Example evaluations with hierarchical models (nonlinear mixed-effects models)
- - Short demo of the multistart method + Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P
- - Performance benefit by using compiled model definitions in mkin + Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P
- - Example evaluation of FOCUS Example Dataset Z + Testing hierarchical pathway kinetics with residue data on cyantraniliprole
- - Calculation of time weighted average concentrations with mkin + Comparison of saemix and nlme evaluations of dimethenamid data from 2018
- - Example evaluation of NAFTA SOP Attachment examples + Short demo of the multistart method +
- +
- Performance
- + Performance benefit by using compiled model definitions in mkin
- Benchmark timings for mkin @@ -64,6 +73,14 @@
- Benchmark timings for saem.mmkin
- +
- Miscellaneous
- + Calculation of time weighted average concentrations with mkin +
- + Example evaluation of NAFTA SOP Attachment examples +

News @@ -90,14 +107,18 @@

All vignettes

Work package 1.1: Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P: -
Example evaluation of FOCUS Example Dataset D

Covariate data
	pH
Nambsheim	7.90
Tama	6.20
Gross-Umstadt	7.04
Sassafras	4.62
Lleida	8.05

Dataset Nambsheim
time	cyan	JCZ38	J9C38	JSE76	J9Z38
0.000000	105.79	NA	NA	NA	NA
3.210424	77.26	7.92	11.94	5.58	9.12
7.490988	57.13	15.46	16.58	12.59	11.74
17.122259	37.74	15.98	13.36	26.05	10.77
23.543105	31.47	6.05	14.49	34.71	4.96
43.875788	16.74	6.07	7.57	40.38	6.52
67.418893	8.85	10.34	6.39	30.71	8.90
107.014116	5.19	9.61	1.95	20.41	12.93
129.487080	3.45	6.18	1.36	21.78	6.99
195.835832	2.15	9.13	0.95	16.29	7.69
254.693596	1.92	6.92	0.20	13.57	7.16
321.042348	2.26	7.02	NA	11.12	8.66
383.110535	NA	5.05	NA	10.64	5.56
0.000000	105.57	NA	NA	NA	NA
3.210424	78.88	12.77	11.94	5.47	9.12
7.490988	59.94	15.27	16.58	13.60	11.74
17.122259	39.67	14.26	13.36	29.44	10.77
23.543105	30.21	16.07	14.49	35.90	4.96
43.875788	18.06	9.44	7.57	42.30	6.52
67.418893	8.54	5.78	6.39	34.70	8.90
107.014116	7.26	4.54	1.95	23.33	12.93
129.487080	3.60	4.22	1.36	23.56	6.99
195.835832	2.84	3.05	0.95	16.21	7.69
254.693596	2.00	2.90	0.20	15.53	7.16
321.042348	1.79	0.94	NA	9.80	8.66
383.110535	NA	1.82	NA	9.49	5.56

Dataset Tama
time	cyan	JCZ38	J9Z38	JSE76
0.000000	106.14	NA	NA	NA
2.400833	93.47	6.46	2.85	NA
5.601943	88.39	10.86	4.65	3.85
12.804442	72.29	11.97	4.91	11.24
17.606108	65.79	13.11	6.63	13.79
32.811382	53.16	11.24	8.90	23.40
50.417490	44.01	11.34	9.98	29.56
80.027761	33.23	8.82	11.31	35.63
96.833591	40.68	5.94	8.32	29.09
146.450803	20.65	4.49	8.72	36.88
190.466072	17.71	4.66	11.10	40.97
240.083284	14.86	2.27	11.62	40.11
286.499386	12.02	NA	10.73	42.58
0.000000	109.11	NA	NA	NA
2.400833	96.84	5.52	2.04	2.02
5.601943	85.29	9.65	2.99	4.39
12.804442	73.68	12.48	5.05	11.47
17.606108	64.89	12.44	6.29	15.00
32.811382	52.27	10.86	7.65	23.30
50.417490	42.61	10.54	9.37	31.06
80.027761	34.29	10.02	9.04	37.87
96.833591	30.50	6.34	8.14	33.97
146.450803	19.21	6.29	8.52	26.15
190.466072	17.55	5.81	9.89	32.08
240.083284	13.22	5.99	10.79	40.66
286.499386	11.09	6.05	8.82	42.90

Dataset Gross-Umstadt
time	cyan	JCZ38	J9Z38	JSE76
0.0000000	103.03	NA	NA	NA
2.1014681	87.85	4.79	3.26	0.62
4.9034255	77.35	8.05	9.89	1.32
10.5073404	69.33	9.74	12.32	4.74
21.0146807	55.65	14.57	13.59	9.84
31.5220211	49.03	14.66	16.71	12.32
42.0293615	41.86	15.97	13.64	15.53
63.0440422	34.88	18.20	14.12	22.02
84.0587230	28.26	15.64	14.06	25.60
0.0000000	104.05	NA	NA	NA
2.1014681	85.25	2.68	7.32	0.69
4.9034255	77.22	7.28	8.37	1.45
10.5073404	65.23	10.73	10.93	4.74
21.0146807	57.78	12.29	14.80	9.05
31.5220211	54.83	14.05	12.01	11.05
42.0293615	45.17	12.12	17.89	15.71
63.0440422	34.83	12.90	15.86	22.52
84.0587230	26.59	14.28	14.91	28.48
0.0000000	104.62	NA	NA	NA
0.8145225	97.21	NA	4.00	NA
1.9005525	89.64	3.59	5.24	NA
4.0726125	87.90	4.10	9.58	NA
8.1452251	86.90	5.96	9.45	NA
12.2178376	74.74	7.83	15.03	5.33
16.2904502	74.13	8.84	14.41	5.10
24.4356753	65.26	11.84	18.33	6.71
32.5809004	57.70	12.74	19.93	9.74
0.0000000	101.94	NA	NA	NA
0.8145225	99.94	NA	NA	NA
1.9005525	94.87	NA	4.56	NA
4.0726125	86.96	6.75	6.90	NA
8.1452251	80.51	10.68	7.43	2.58
12.2178376	78.38	10.35	9.46	3.69
16.2904502	70.05	13.73	9.27	7.18
24.4356753	61.28	12.57	13.28	13.19
32.5809004	52.85	12.67	12.95	13.69

Dataset Sassafras
time	cyan	JCZ38	J9Z38	JSE76
0.000000	102.17	NA	NA	NA
2.216719	95.49	1.11	0.10	0.83
5.172343	83.35	6.43	2.89	3.30
11.083593	78.18	10.00	5.59	0.81
22.167186	70.44	17.21	4.23	1.09
33.250779	68.00	20.45	5.86	1.17
44.334371	59.64	24.64	3.17	2.72
66.501557	50.73	27.50	6.19	1.27
88.668742	45.65	32.77	5.69	4.54
0.000000	100.43	NA	NA	NA
2.216719	95.34	3.21	0.14	0.46
5.172343	84.38	5.73	4.75	0.62
11.083593	78.50	11.89	3.99	0.73
22.167186	71.17	17.28	4.39	0.66
33.250779	59.41	18.73	11.85	2.65
44.334371	64.57	22.93	5.13	2.01
66.501557	49.08	33.39	5.67	3.63
88.668742	40.41	39.60	5.93	6.17

Dataset Lleida
time	cyan	JCZ38	J9Z38	JSE76
0.000000	102.71	NA	NA	NA
2.821051	79.11	5.70	8.07	0.97
6.582451	70.03	7.17	11.31	4.72
14.105253	50.93	10.25	14.84	9.95
28.210505	33.43	10.40	14.82	24.06
42.315758	24.69	9.75	16.38	29.38
56.421010	22.99	10.06	15.51	29.25
84.631516	14.63	5.63	14.74	31.04
112.842021	12.43	4.17	13.53	33.28
0.000000	99.31	NA	NA	NA
2.821051	82.07	6.55	5.60	1.12
6.582451	70.65	7.61	8.01	3.21
14.105253	53.52	11.48	10.82	12.24
28.210505	35.60	11.19	15.43	23.53
42.315758	34.26	11.09	13.26	27.42
56.421010	21.79	4.80	18.30	30.20
84.631516	14.06	6.30	16.35	32.32
112.842021	11.51	5.57	12.64	32.51

	const	tc
SFO	sd(cyan_0)	sd(cyan_0)
FOMC	sd(log_beta)	sd(cyan_0)
DFOP	sd(cyan_0)	sd(cyan_0), sd(log_k1)
SFORB	sd(cyan_free_0)	sd(cyan_free_0), sd(log_k_cyan_free_bound)
HS	sd(cyan_0)	sd(cyan_0)

	npar	AIC	BIC	Lik
SFO const	5	833.9	832.0	-412.0
SFO tc	6	831.6	829.3	-409.8
FOMC const	7	709.1	706.4	-347.6
FOMC tc	8	689.2	686.1	-336.6
DFOP const	9	703.0	699.5	-342.5
SFORB const	9	701.3	697.8	-341.7
HS const	9	718.6	715.1	-350.3
DFOP tc	10	703.1	699.2	-341.6
SFORB tc	10	700.1	696.2	-340.1
HS tc	10	716.7	712.8	-348.3

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1	OK	OK	OK	OK	OK
fomc_path_1	OK	OK	OK	OK	OK
dfop_path_1	OK	OK	OK	OK	OK
sforb_path_1	OK	OK	OK	OK	OK
hs_path_1	C	C	C	C	C

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
sfo_path_1	OK	OK	OK	OK	OK
fomc_path_1	OK	OK	OK	OK	C
dfop_path_1	OK	OK	OK	OK	OK
sforb_path_1	OK	C	OK	OK	OK
hs_path_1	C	OK	C	OK	OK

	const	tc
sfo_path_1	Fth, FO	Fth, FO
fomc_path_1	OK	Fth, FO
dfop_path_1	Fth, FO	Fth, FO
sforb_path_1	Fth, FO	Fth, FO
hs_path_1	Fth, FO	Fth, FO

	const	tc
sfo_path_1	NA	NA
fomc_path_1	sd(log_k_J9Z38), sd(f_cyan_ilr_2), +sd(f_JCZ38_qlogis)	NA
dfop_path_1	NA	NA
sforb_path_1	NA	NA
hs_path_1	NA	NA

	npar	AIC	BIC	Lik
sfo_path_1 const	16	2692.8	2686.6	-1330.4
sfo_path_1 tc	17	2657.7	2651.1	-1311.9
fomc_path_1 const	18	2427.8	2420.8	-1195.9
fomc_path_1 tc	19	2423.4	2416.0	-1192.7
dfop_path_1 const	20	2403.2	2395.4	-1181.6
sforb_path_1 const	20	2401.4	2393.6	-1180.7
hs_path_1 const	20	2427.3	2419.5	-1193.7
dfop_path_1 tc	20	2398.0	2390.2	-1179.0
sforb_path_1 tc	20	2399.8	2392.0	-1179.9
hs_path_1 tc	21	2422.3	2414.1	-1190.2

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2	OK	OK	OK	C	OK
dfop_path_2	OK	OK	OK	C	OK
sforb_path_2	OK	OK	OK	C	OK

	Nambsheim	Tama	Gross-Umstadt	Sassafras	Lleida
fomc_path_2	OK	C	OK	C	OK
dfop_path_2	OK	OK	OK	C	OK
sforb_path_2	OK	OK	OK	OK	OK

	const	tc
fomc_path_2	OK	FO
dfop_path_2	OK	OK
sforb_path_2	OK	OK

	const	tc
fomc_path_2	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)	NA
dfop_path_2	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)
sforb_path_2	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)	sd(f_JCZ38_qlogis), sd(f_JSE76_qlogis)

	npar	AIC	BIC	Lik
fomc_path_2 const	20	2308.3	2300.5	-1134.2
fomc_path_2 tc	21	2248.3	2240.1	-1103.2
dfop_path_2 const	22	2289.6	2281.0	-1122.8
sforb_path_2 const	22	2284.1	2275.5	-1120.0
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2240.4	2231.8	-1098.2

	const	tc
fomc_path_2	E	Fth
dfop_path_2	Fth	Fth
sforb_path_2	Fth	Fth

	npar	AIC	BIC	Lik
fomc_path_2 tc	19	2250.9	2243.5	-1106.5
dfop_path_2 const	20	2281.7	2273.9	-1120.8
sforb_path_2 const	20	2279.5	2271.7	-1119.7
dfop_path_2 tc	20	2231.5	2223.7	-1095.8
sforb_path_2 tc	20	2235.7	2227.9	-1097.9

Dataset Calke
time	DMTA	M23	M27	M31
0	95.8	NA	NA	NA
0	98.7	NA	NA	NA
14	60.5	4.1	1.5	2.0
30	39.1	5.3	2.4	2.1
59	15.2	6.0	3.2	2.2
120	4.8	4.3	3.8	1.8
120	4.6	4.1	3.7	2.1

Dataset Borstel
time	DMTA	M23	M27	M31
0.000000	100.5	NA	NA	NA
0.000000	99.6	NA	NA	NA
1.941295	91.9	0.4	NA	NA
1.941295	91.3	0.5	0.3	0.1
6.794534	81.8	1.2	0.8	1.0
6.794534	82.1	1.3	0.9	0.9
13.589067	69.1	2.8	1.4	2.0
13.589067	68.0	2.0	1.4	2.5
27.178135	51.4	2.9	2.7	4.3
27.178135	51.4	4.9	2.6	3.2
56.297565	27.6	12.2	4.4	4.3
56.297565	26.8	12.2	4.7	4.8
86.387643	15.7	12.2	5.4	5.0
86.387643	15.3	12.0	5.2	5.1
115.507073	7.9	10.4	5.4	4.3
115.507073	8.1	11.6	5.4	4.4

Dataset Flaach
time	DMTA	M23	M27	M31
0.0000000	96.5	NA	NA	NA
0.0000000	96.8	NA	NA	NA
0.0000000	97.0	NA	NA	NA
0.6233856	82.9	0.7	1.1	0.3
0.6233856	86.7	0.7	1.1	0.3
0.6233856	87.4	0.2	0.3	0.1
1.8701567	72.8	2.2	2.6	0.7
1.8701567	69.9	1.8	2.4	0.6
1.8701567	71.9	1.6	2.3	0.7
4.3636989	51.4	4.1	5.0	1.3
4.3636989	52.9	4.2	5.9	1.2
4.3636989	48.6	4.2	4.8	1.4
8.7273979	28.5	7.5	8.5	2.4
8.7273979	27.3	7.1	8.5	2.1
8.7273979	27.5	7.5	8.3	2.3
13.0910968	14.8	8.4	9.3	3.3
13.0910968	13.4	6.8	8.7	2.4
13.0910968	14.4	8.0	9.1	2.6
17.4547957	7.7	7.2	8.6	4.0
17.4547957	7.3	7.2	8.5	3.6
17.4547957	8.1	6.9	8.9	3.3
26.1821936	2.0	4.9	8.1	2.1
26.1821936	1.5	4.3	7.7	1.7
26.1821936	1.9	4.5	7.4	1.8
34.9095915	1.3	3.8	5.9	1.6
34.9095915	1.0	3.1	6.0	1.6
34.9095915	1.1	3.1	5.9	1.4
43.6369893	0.9	2.7	5.6	1.8
43.6369893	0.7	2.3	5.2	1.5
43.6369893	0.7	2.1	5.6	1.3
52.3643872	0.6	1.6	4.3	1.2
52.3643872	0.4	1.1	3.7	0.9
52.3643872	0.5	1.3	3.9	1.1
74.8062674	0.4	0.4	2.5	0.5
74.8062674	0.3	0.4	2.4	0.5
74.8062674	0.3	0.3	2.2	0.3

@@ -106,13 +127,15 @@ -

Benchmark timings for saem.mmkin

Johannes Ranke

Johannes +Ranke

Last change 14 November 2022 (rebuilt 2022-11-24)

Last change 14 November 2022 +(rebuilt 2023-01-28)

Source: vignettes/web_only/saem_benchmarks.rmd

saem_benchmarks.rmd

@@ -121,15 +144,19 @@ -

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

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

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

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

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

 n_cores <- parallel::detectCores()

Test data

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

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

 dmta_ds <- lapply(1:7, function(i) {
   ds_i <- dimethenamid_2018$ds[[i]]$data
@@ -232,19 +259,24 @@
 
 
 
-The above model comparison suggests to use the SFORB model with two-component error. For comparison, we keep the DFOP model with two-component error, as it competes with SFORB for biphasic curves.
+The above model comparison suggests to use the SFORB model with
+two-component error. For comparison, we keep the DFOP model with
+two-component error, as it competes with SFORB for biphasic curves.
  illparms(dfop_tc)
 ## [1] "sd(log_k2)"
  illparms(sforb_tc)
 ## [1] "sd(log_k_DMTA_bound_free)"
-For these two models, random effects for the transformed parameters k2 and k_DMTA_bound_free could not be quantified.
+For these two models, random effects for the transformed parameters
+k2 and k_DMTA_bound_free could not be
+quantified.


 
 One metabolite
 
-We remove parameters that were found to be ill-defined in the parent only fits.
+We remove parameters that were found to be ill-defined in the parent
+only fits.
  one_met_mods <- list(
   DFOP_SFO = mkinmod(
@@ -267,7 +299,11 @@
 
 Three metabolites
 
-For the case of three metabolites, we only keep the SFORB model in order to limit the time for compiling this vignette, and as fitting in parallel may disturb the benchmark. Again, we do not include random effects that were ill-defined in previous fits of subsets of the degradation model.
+For the case of three metabolites, we only keep the SFORB model in
+order to limit the time for compiling this vignette, and as fitting in
+parallel may disturb the benchmark. Again, we do not include random
+effects that were ill-defined in previous fits of subsets of the
+degradation model.
  illparms(sforb_sfo_tc)
 @@ -288,12 +324,24 @@
 
 Results
 
-Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.
+Benchmarks for all available error models are shown. They are
+intended for improving mkin, not for comparing CPUs or operating
+systems. All trademarks belong to their respective owners.
 
 Parent only
 
 Constant variance for SFO, DFOP, SFORB and HS.
-
+
++++++++++
@@ -325,10 +373,30 @@
 
+
+
+
+
+
+
+
+
+
+









 
 CPU
 OS 4.217
 4.851
 
Ryzen 9 7950X 16-Core Processor Linux 1.2.2 3.2 1.470 2.263 1.840 2.299
 
 
 Two-component error fits for SFO, DFOP, SFORB and HS.
-
+
++++++++++
@@ -360,6 +428,16 @@
 
+
+
+
+
+
+
+
+
+
+









 
 CPU
 OS 8.174
 8.401
 
Ryzen 9 7950X 16-Core Processor Linux 1.2.2 3.2 2.118 3.528 3.295 3.157
 
 
 
@@ -368,6 +446,14 @@
 
 Two-component error for DFOP-SFO and SFORB-SFO.
 
++++++++
@@ -393,6 +479,14 @@
 
+
+
+
+
+
+
+
+







 
 CPU
 OS 25.193
 798.580
 
Ryzen 9 7950X 16-Core Processor Linux 1.2.2 3.2 12.336 277.666
 
 
 
@@ -423,6 +517,13 @@
 3.2
 1312.445
 
+
+Ryzen 9 7950X 16-Core Processor
+Linux
+1.2.2
+3.2
+459.051
+
 
 
 
@@ -446,7 +547,7 @@
 
 
   
-Site built with pkgdown 2.0.6.
+Site built with pkgdown 2.0.7.
 
 
       
-- 
cgit v1.2.1

Introduction to mkin

Johannes Ranke

Last change 15 February 2021 (rebuilt 2022-02-28)

Last change 15 February 2021 (rebuilt 2022-11-16)

Benchmark timings for saem.mmkin

Johannes Ranke

Last change 14 November 2022 (rebuilt 2022-11-15)

Last change 14 November 2022 (rebuilt 2022-11-16)

Example evaluation of FOCUS Example Dataset D

Johannes Ranke

Johannes Ranke

Last change 31 January 2019 (rebuilt 2021-02-15)

Last change 31 January 2019 (rebuilt 2022-11-24)

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

Last change 18 May 2022 (rebuilt 2022-09-16)

Last change 18 May 2022 (rebuilt 2022-11-24)

Introduction to mkin

Johannes Ranke

Last change 15 February 2021 (rebuilt 2022-11-16)

Last change 15 February 2021 (rebuilt 2022-11-24)

Calculation of time weighted average concentrations with mkin

Johannes Ranke

Johannes Ranke

Last change 18 September 2019 (rebuilt 2021-02-15)

Last change 18 September 2019 (rebuilt 2022-11-24)

Example evaluation of FOCUS dataset Z

Johannes Ranke

Johannes Ranke

Last change 16 January 2018 (rebuilt 2021-02-15)

Last change 16 January 2018 (rebuilt 2022-11-24)

-The data

The data +

-Parent and one metabolite

Parent and one metabolite +

-Metabolites Z2 and Z3

Metabolites Z2 and Z3 +

-Using the SFORB model

Using the SFORB model +

-References

References +

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

Johannes Ranke

Johannes Ranke

26 February 2019 (rebuilt 2021-02-15)

26 February 2019 (rebuilt 2022-11-24)

-Introduction

Introduction +

-Examples where DFOP did not converge with PestDF 0.8.4

Examples where DFOP did not converge with PestDF 0.8.4 +

-Example on page 5, upper panel

Example on page 5, upper panel +

-Example on page 5, lower panel

Example on page 5, lower panel +

-Example on page 6

Example on page 6 +

-Example on page 7

Example on page 7 +

-Examples where the representative half-life deviates from the observed DT50

-Example on page 8

Examples where the representative half-life deviates from the observed DT50 +

Example on page 8 +

-Examples where SFO was not selected for an abiotic study

-Example on page 9, upper panel

Examples where SFO was not selected for an abiotic study +

Example on page 9, upper panel +

-Example on page 9, lower panel

Example on page 9, lower panel +

-Example on page 10

Example on page 10 +

-The DT50 was not observed during the study

-Example on page 11

The DT50 was not observed during the study +

Example on page 11 +

-N is less than 1 and the DFOP rate constants are like the SFO rate constant

N is less than 1 and the DFOP rate constants are like the SFO rate constant +

-Example on page 12, upper panel

Example on page 12, upper panel +

-Example on page 12, lower panel

Example on page 12, lower panel +