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1.2.10 + + @@ -64,7 +84,7 @@ Ranke

Last change 18 May 2023 -(rebuilt 2025-02-13)

+(rebuilt 2025-05-12) Source: vignettes/mkin.rmd
mkin.rmd
@@ -72,11 +92,12 @@ Ranke -

Wissenschaftlicher Berater, Kronacher -Str. 12, 79639 Grenzach-Wyhlen, Germany
Privatdozent at the +

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

-
-

Abstract

+
+

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 @@ -86,38 +107,40 @@ nonlinear optimisation. The R add-on package this guidance from within R and calculates some statistical measures for data series within one or more compartments, for parent and metabolites.

-
library("mkin", quietly = TRUE)
-# Define the kinetic model
-m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
-                         M1 = mkinsub("SFO", "M2"),
-                         M2 = mkinsub("SFO"),
-                         use_of_ff = "max", quiet = TRUE)
-
-
-# Produce model predictions using some arbitrary parameters
-sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
-  c(k_parent = 0.03,
-    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
-    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
-  c(parent = 100, M1 = 0, M2 = 0),
-  sampling_times)
-
-# Generate a dataset by adding normally distributed errors with
-# standard deviation 3, for two replicates at each sampling time
-d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
-                             sdfunc = function(x) 3,
-                             n = 1, seed = 123456789 )
-
-# Fit the model to the dataset
-f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
-
-# Plot the results separately for parent and metabolites
-plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
-

+
+library("mkin", quietly = TRUE)
+# Define the kinetic model
+m_SFO_SFO_SFO <- mkinmod(parent = mkinsub("SFO", "M1"),
+                         M1 = mkinsub("SFO", "M2"),
+                         M2 = mkinsub("SFO"),
+                         use_of_ff = "max", quiet = TRUE)
+
+
+# Produce model predictions using some arbitrary parameters
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+d_SFO_SFO_SFO <- mkinpredict(m_SFO_SFO_SFO,
+  c(k_parent = 0.03,
+    f_parent_to_M1 = 0.5, k_M1 = log(2)/100,
+    f_M1_to_M2 = 0.9, k_M2 = log(2)/50),
+  c(parent = 100, M1 = 0, M2 = 0),
+  sampling_times)
+
+# Generate a dataset by adding normally distributed errors with
+# standard deviation 3, for two replicates at each sampling time
+d_SFO_SFO_SFO_err <- add_err(d_SFO_SFO_SFO, reps = 2,
+                             sdfunc = function(x) 3,
+                             n = 1, seed = 123456789 )
+
+# Fit the model to the dataset
+f_SFO_SFO_SFO <- mkinfit(m_SFO_SFO_SFO, d_SFO_SFO_SFO_err[[1]], quiet = TRUE)
+
+# Plot the results separately for parent and metabolites
+plot_sep(f_SFO_SFO_SFO, lpos = c("topright", "bottomright", "bottomright"))
+

-
-

Background

+
+

Background +

The mkin package (J. Ranke 2021) implements the approach to degradation kinetics recommended in the kinetics report provided by the FOrum for Co-ordination of @@ -138,8 +161,7 @@ purpose compartment based tool providing infrastructure for fitting dynamic simulation models based on differential equations to data.

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

At that time, the R package FME (Flexible Modelling @@ -162,8 +184,9 @@ times.

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

-
-

Derived software tools

+
+

Derived software tools +

Soon after the publication of mkin, two derived tools were published, namely KinGUII (developed at Bayer Crop Science) and CAKE (commissioned to Tessella by Syngenta), which added a graphical @@ -184,50 +207,44 @@ be specified for transformation products. Starting with KinGUII version 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 +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 Johannes Ranke, Wöltjen, and Meinecke +these tools has been recently been published by Johannes Ranke, Wöltjen, and Meinecke (2018).

-
-

Unique features

+
+

Unique features +

Currently, the main unique features available in mkin are

The iteratively reweighted least squares fitting of different variances for each variable as introduced by Gao -et al. (2011) has been available in mkin since version -0.9-22. With release +et al. (2011) has been available in mkin since version +0.9-22. With release 0.9.49.5, the IRLS algorithm has been complemented by direct or step-wise maximisation of the likelihood function, which makes it possible not only to fit the variance by variable error model but also a -two-component +two-component error model inspired by error models developed in analytical chemistry (Johannes Ranke and Meinecke 2019).

-
-

Internal parameter transformations

+
+

Internal parameter transformations +

For rate constants, the log transformation is used, as proposed by Bates and Watts (1988, 77, 149). Approximate intervals are constructed for the transformed rate constants @@ -252,9 +269,9 @@ well as in the subsequent calculation of parameter confidence intervals. In the current version of mkin, a logit transformation is used for parameters that are bound between 0 and 1, such as the g parameter of the DFOP model.

-
-

Confidence intervals based on transformed parameters

+
+

Confidence intervals based on transformed parameters +

In the first attempt at providing improved parameter confidence intervals introduced to mkin in 2013, confidence intervals obtained from FME on the transformed parameters were simply all @@ -276,14 +293,13 @@ are considered by the author of this vignette to be more accurate than those obtained using a re-estimation of the Hessian matrix after backtransformation, as implemented in the FME package.

-
-

Parameter t-test based on untransformed parameters

+
+

Parameter t-test based on untransformed parameters +

The standard output of many nonlinear regression software packages includes the results from a test for significant difference from zero for all parameters. Such a test is also recommended to check the -validity of rate constants in the FOCUS guidance (FOCUS Work Group on Degradation Kinetics 2014, +validity of rate constants in the FOCUS guidance (FOCUS Work Group on Degradation Kinetics 2014, 96ff).

It has been argued that the precondition for this test, i.e. normal distribution of the estimator for the parameters, is not @@ -304,8 +320,9 @@ t-test is based on the unjustified assumption of normal distribution of the parameter estimators.

-
-

References

+
+

References +

@@ -316,14 +333,12 @@ Applications. Wiley-Interscience. FOCUS Work Group on Degradation Kinetics. 2006. Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration. Report of the FOCUS Work Group -on Degradation Kinetics. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics. +on Degradation Kinetics. http://esdac.jrc.ec.europa.eu/projects/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. +Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.
Gao, Z., J. W. Green, J. Vanderborght, and W. Schmitt. 2011. @@ -333,34 +348,29 @@ Science and Technology 45: 4429–37.
Ranke, J. 2021. ‘mkin‘: -Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin. +Kinetic Evaluation of Chemical Degradation Data. https://CRAN.R-project.org/package=mkin.
Ranke, J., and R. Lehmann. 2012. “Parameter Reliability in Kinetic Evaluation of Environmental Metabolism Data - Assessment and the Influence of Model Specification.” In SETAC World 20-24 -May. Berlin. https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf. +May. Berlin. https://jrwb.de/posters/Poster_SETAC_2012_Kinetic_parameter_uncertainty_model_parameterization_Lehmann_Ranke.pdf.
———. 2015. “To t-Test or Not to t-Test, That Is the Question.” In XV Symposium on Pesticide Chemistry 2-4 -September 2015. Piacenza. https://jrwb.de/posters/piacenza_2015.pdf. +September 2015. Piacenza. https://jrwb.de/posters/piacenza_2015.pdf.
Ranke, Johannes, and Stefan Meinecke. 2019. “Error Models for the Kinetic Evaluation of Chemical Degradation Data.” -Environments 6 (12). https://doi.org/10.3390/environments6120124. +Environments 6 (12). https://doi.org/10.3390/environments6120124.
Ranke, Johannes, Janina Wöltjen, and Stefan Meinecke. 2018. “Comparison of Software Tools for Kinetic Evaluation of Chemical Degradation Data.” Environmental Sciences Europe 30 (1): -17. https://doi.org/10.1186/s12302-018-0145-1. +17. https://doi.org/10.1186/s12302-018-0145-1.
Schäfer, D., B. Mikolasch, P. Rainbird, and B. Harvey. 2007. @@ -374,13 +384,13 @@ 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. https://doi.org/10.18637/jss.v033.i03. +(3): 1–28. https://doi.org/10.18637/jss.v033.i03.
+ +
@@ -392,10 +402,12 @@ href="https://doi.org/10.18637/jss.v033.i03">https://doi.org/10.18637/jss.v033.i

Site built with pkgdown 2.1.1.

-
+ +
- + + 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..65c1a613 Binary files /dev/null and b/docs/articles/mkin_files/figure-html/unnamed-chunk-2-1.png differ diff --git a/docs/articles/prebuilt/2022_cyan_pathway.html b/docs/articles/prebuilt/2022_cyan_pathway.html index ea4dd035..3dd83fee 100644 --- a/docs/articles/prebuilt/2022_cyan_pathway.html +++ b/docs/articles/prebuilt/2022_cyan_pathway.html @@ -1,374 +1,100 @@ - - - + - - - - - - - - - -Testing hierarchical pathway kinetics with residue data on cyantraniliprole - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + +Testing hierarchical pathway kinetics with residue data on cyantraniliprole • mkin + + + + + - + Skip to contents + + +
-

Testing hierarchical pathway kinetics with -residue data on cyantraniliprole

-

Johannes Ranke

-

Last change on 13 February 2023, last compiled on 13 -Februar 2025

-
+
+
-
-true -
+

Testing hierarchical pathway kinetics with residue data on cyantraniliprole

+

Johannes +Ranke

+ +

Last change on 13 February +2023, last compiled on 12 Mai 2025

+ + Source: vignettes/prebuilt/2022_cyan_pathway.rmd +
2022_cyan_pathway.rmd
+
-
-

Introduction

+ + +
+

Introduction +

The purpose of this document is to test demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS, with serial formation of two or more metabolites can @@ -377,7 +103,7 @@ 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 1.2.9 which is currently under +

The mkin package is used in version 1.2.10 which is currently under development. The newly introduced functionality that is used here is a simplification of excluding random effects for a set of fits based on a related set of fits with a reduced model, and the documentation of the @@ -389,47 +115,49 @@ but is also loaded to 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()
-
-# We need to start a new cluster after defining a compiled model that is
-# saved as a DLL to the user directory, therefore we define a function
-# This is used again after defining the pathway model
-start_cluster <- function(n_cores) {
-  if (Sys.info()["sysname"] == "Windows") {
-    ret <- makePSOCKcluster(n_cores)
-  } else {
-    ret <- makeForkCluster(n_cores)
-  }
-  return(ret)
-}
-cl <- start_cluster(n_cores)
-
-

Test data

+
+library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+n_cores <- detectCores()
+
+# We need to start a new cluster after defining a compiled model that is
+# saved as a DLL to the user directory, therefore we define a function
+# This is used again after defining the pathway model
+start_cluster <- function(n_cores) {
+  if (Sys.info()["sysname"] == "Windows") {
+    ret <- makePSOCKcluster(n_cores)
+  } else {
+    ret <- makeForkCluster(n_cores)
+  }
+  return(ret)
+}
+cl <- start_cluster(n_cores)
+
+

Test data +

The example data are taken from the final addendum to the DAR from 2014 and are distributed with the mkin package. Residue data and time step normalisation factors are read in using the function read_spreadsheet from the mkin package. This function also performs the time step normalisation.

-
data_file <- system.file(
-  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
-  package = "mkin")
-cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)
+
+data_file <- system.file(
+  "testdata", "cyantraniliprole_soil_efsa_2014.xlsx",
+  package = "mkin")
+cyan_ds <- read_spreadsheet(data_file, parent_only = FALSE)

The following tables show the covariate data and the 5 datasets that were read in from the spreadsheet file.

-
pH <- attr(cyan_ds, "covariates")
-kable(pH, caption = "Covariate data")
- +
+pH <- attr(cyan_ds, "covariates")
+kable(pH, caption = "Covariate data")
+
- - + - - + @@ -453,25 +181,24 @@ kable(pH, caption = "Covariate data")
Covariate data
pH
Nambsheim
-
for (ds_name in names(cyan_ds)) {
-  print(
-    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
-      caption = paste("Dataset", ds_name),
-      booktabs = TRUE, row.names = FALSE))
-    cat("\n\\clearpage\n")
-}
- +
+for (ds_name in names(cyan_ds)) {
+  print(
+    kable(mkin_long_to_wide(cyan_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+    cat("\n\\clearpage\n")
+}
+
- - + - - + @@ -683,17 +410,15 @@ kable(pH, caption = "Covariate data")
Dataset Nambsheim
time cyan JCZ38 J9C38 JSE76 J9Z38
0.000000
- +
- - + - - + @@ -879,17 +604,15 @@ kable(pH, caption = "Covariate data")
Dataset Tama
time cyan JCZ38 J9Z38 JSE76
0.000000
- +
- - + - - + @@ -1145,17 +868,15 @@ kable(pH, caption = "Covariate data")
Dataset Gross-Umstadt
time cyan JCZ38 J9Z38 JSE76
0.0000000
- +
- - + - - + @@ -1285,17 +1006,15 @@ kable(pH, caption = "Covariate data")
Dataset Sassafras
time cyan JCZ38 J9Z38 JSE76
0.000000
- +
- - + - - + @@ -1427,25 +1146,25 @@ kable(pH, caption = "Covariate data")
Dataset Lleida
time cyan JCZ38 J9Z38 JSE76
0.000000
-
-

Parent only evaluations

+
+

Parent only evaluations +

As the pathway fits have very long run times, evaluations of the parent data are performed first, in order to determine for each hierarchical parent degradation model which random effects on the degradation model parameters are ill-defined.

-
cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
-  cyan_ds, quiet = TRUE, cores = n_cores)
-cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
-cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
-status(cyan_saem_full) |> kable()
- - - +
+cyan_sep_const <- mmkin(c("SFO", "FOMC", "DFOP", "SFORB", "HS"),
+  cyan_ds, quiet = TRUE, cores = n_cores)
+cyan_sep_tc <- update(cyan_sep_const, error_model = "tc")
+cyan_saem_full <- mhmkin(list(cyan_sep_const, cyan_sep_tc))
+status(cyan_saem_full) |> kable()
+
+ - - + @@ -1475,15 +1194,14 @@ status(cyan_saem_full) |> kable()
const tc
SFO

All fits converged successfully.

-
illparms(cyan_saem_full) |> kable()
- - - +
+illparms(cyan_saem_full) |> kable()
+
+ - - + @@ -1516,17 +1234,16 @@ status(cyan_saem_full) |> kable() of the parent compound is ill-defined. For the biexponential models DFOP and SFORB, the random effect of one additional parameter is ill-defined when the two-component error model is used.

-
anova(cyan_saem_full) |> kable(digits = 1)
-
const tc
SFO
- - +
+anova(cyan_saem_full) |> kable(digits = 1)
+
+ - - + @@ -1604,71 +1321,74 @@ when the two-component error model is used.

two-component error model is preferable for all parent models with the exception of DFOP. The lowest AIC and BIC values are are obtained with the FOMC model, followed by SFORB and DFOP.

-
stopCluster(cl)
+ -
-

Pathway fits

-
-

Evaluations with pathway established previously

+
+

Pathway fits +

+
+

Evaluations with pathway established previously +

To test the technical feasibility of coupling the relevant parent degradation models with different transformation pathway models, a list of mkinmod models is set up below. As in the EU evaluation, parallel formation of metabolites JCZ38 and J9Z38 and secondary formation of metabolite JSE76 from JCZ38 is used.

-
if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
-cyan_path_1 <- list(
-  sfo_path_1 = mkinmod(
-    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  fomc_path_1 = mkinmod(
-    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  dfop_path_1 = mkinmod(
-    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  sforb_path_1 = mkinmod(
-    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
-  hs_path_1 = mkinmod(
-    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO"), quiet = TRUE,
-    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
-)
-cl_path_1 <- start_cluster(n_cores)
+
+if (!dir.exists("cyan_dlls")) dir.create("cyan_dlls")
+cyan_path_1 <- list(
+  sfo_path_1 = mkinmod(
+    cyan = mkinsub("SFO", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sfo_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  fomc_path_1 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "fomc_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  dfop_path_1 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "dfop_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  sforb_path_1 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "sforb_path_1", dll_dir = "cyan_dlls", overwrite = TRUE),
+  hs_path_1 = mkinmod(
+    cyan = mkinsub("HS", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO"), quiet = TRUE,
+    name = "hs_path_1", dll_dir = "cyan_dlls", overwrite = TRUE)
+)
+cl_path_1 <- start_cluster(n_cores)

To obtain suitable starting values for the NLHM fits, separate pathway fits are performed for all datasets.

-
f_sep_1_const <- mmkin(
-  cyan_path_1,
-  cyan_ds,
-  error_model = "const",
-  cluster = cl_path_1,
-  quiet = TRUE)
-status(f_sep_1_const) |> kable()
-
npar AIC BIC Lik
SFO const
- - +
+f_sep_1_const <- mmkin(
+  cyan_path_1,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_1,
+  quiet = TRUE)
+status(f_sep_1_const) |> kable()
+
+ - - + @@ -1712,19 +1432,18 @@ status(f_sep_1_const) |> kable()
Nambsheim Tama Gross-Umstadt Sassafras Lleida
sfo_path_1
-
f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
-status(f_sep_1_tc) |> kable()
- - - +
+f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
+status(f_sep_1_tc) |> kable()
+
+ - - + @@ -1778,18 +1497,18 @@ for the parent only fits is used as an argument no_random_effect to the mhmkin function. The possibility to do so was introduced in mkin version 1.2.2 which is currently under development.

-
f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
-  no_random_effect = illparms(cyan_saem_full),
-  cluster = cl_path_1)
-
status(f_saem_1) |> kable()
-
Nambsheim Tama Gross-Umstadt Sassafras Lleida
sfo_path_1
- - +
+f_saem_1 <- mhmkin(list(f_sep_1_const, f_sep_1_tc),
+  no_random_effect = illparms(cyan_saem_full),
+  cluster = cl_path_1)
+
+status(f_saem_1) |> kable()
+
+ - - + @@ -1825,20 +1544,19 @@ Fisher Information Matrix could not be inverted for the fixed effects fits, ill-defined parameters cannot be determined using the illparms function, because it relies on the Fisher Information Matrix.

-
illparms(f_saem_1) |> kable()
-
const tc
sfo_path_1
+
+illparms(f_saem_1) |> kable()
+
---+++ - - + - - + @@ -1870,17 +1588,16 @@ sd(f_JCZ38_qlogis)
const tc
sfo_path_1

The model comparisons below suggest that the pathway fits using DFOP or SFORB for the parent compound provide the best fit.

-
anova(f_saem_1[, "const"]) |> kable(digits = 1)
- - - +
+anova(f_saem_1[, "const"]) |> kable(digits = 1)
+
+ - - + @@ -1919,17 +1636,16 @@ or SFORB for the parent compound provide the best fit.

npar AIC BIC Lik
sfo_path_1 const
-
anova(f_saem_1[1:4, ]) |> kable(digits = 1)
- - - +
+anova(f_saem_1[1:4, ]) |> kable(digits = 1)
+
+ - - + @@ -1991,27 +1707,29 @@ or SFORB for the parent compound provide the best fit.

npar AIC BIC Lik
sfo_path_1 const

For these two parent model, successful fits are shown below. Plots of the fits with the other parent models are shown in the Appendix.

-
plot(f_saem_1[["dfop_path_1", "tc"]])
+
+plot(f_saem_1[["dfop_path_1", "tc"]])
-DFOP pathway fit with two-component error -

+DFOP pathway fit with two-component error

DFOP pathway fit with two-component error

-
plot(f_saem_1[["sforb_path_1", "tc"]])
+
+plot(f_saem_1[["sforb_path_1", "tc"]])
-SFORB pathway fit with two-component error -

+SFORB pathway fit with two-component error

SFORB pathway fit with two-component error

A closer graphical analysis of these Figures shows that the residues of transformation product JCZ38 in the soils Tama and Nambsheim observed at later time points are strongly and systematically underestimated.

-
stopCluster(cl_path_1)
+
+stopCluster(cl_path_1)
-
-

Alternative pathway fits

+
+

Alternative pathway fits +

To improve the fit for JCZ38, a back-reaction from JSE76 to JCZ38 was introduced in an alternative version of the transformation pathway, in analogy to the back-reaction from K5A78 to K5A77. Both pairs of @@ -2020,56 +1738,55 @@ corresponding amide (Addendum 2014, p. 109). As FOMC provided the best fit for the parent, and the biexponential models DFOP and SFORB provided the best initial pathway fits, these three parent models are used in the alternative pathway fits.

-
cyan_path_2 <- list(
-  fomc_path_2 = mkinmod(
-    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "fomc_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  ),
-  dfop_path_2 = mkinmod(
-    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "dfop_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  ),
-  sforb_path_2 = mkinmod(
-    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
-    JCZ38 = mkinsub("SFO", "JSE76"),
-    J9Z38 = mkinsub("SFO"),
-    JSE76 = mkinsub("SFO", "JCZ38"),
-    name = "sforb_path_2", quiet = TRUE,
-    dll_dir = "cyan_dlls",
-    overwrite = TRUE
-  )
-)
-
-cl_path_2 <- start_cluster(n_cores)
-f_sep_2_const <- mmkin(
-  cyan_path_2,
-  cyan_ds,
-  error_model = "const",
-  cluster = cl_path_2,
-  quiet = TRUE)
-
-status(f_sep_2_const) |> kable()
- - - +
+cyan_path_2 <- list(
+  fomc_path_2 = mkinmod(
+    cyan = mkinsub("FOMC", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "fomc_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  dfop_path_2 = mkinmod(
+    cyan = mkinsub("DFOP", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "dfop_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  ),
+  sforb_path_2 = mkinmod(
+    cyan = mkinsub("SFORB", c("JCZ38", "J9Z38")),
+    JCZ38 = mkinsub("SFO", "JSE76"),
+    J9Z38 = mkinsub("SFO"),
+    JSE76 = mkinsub("SFO", "JCZ38"),
+    name = "sforb_path_2", quiet = TRUE,
+    dll_dir = "cyan_dlls",
+    overwrite = TRUE
+  )
+)
+
+cl_path_2 <- start_cluster(n_cores)
+f_sep_2_const <- mmkin(
+  cyan_path_2,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_2,
+  quiet = TRUE)
+
+status(f_sep_2_const) |> kable()
+
+ - - + @@ -2099,19 +1816,18 @@ status(f_sep_2_const) |> kable()
Nambsheim Tama Gross-Umstadt Sassafras Lleida
fomc_path_2

Using constant variance, separate fits converge with the exception of the fits to the Sassafras soil data.

-
f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
-status(f_sep_2_tc) |> kable()
- - - +
+f_sep_2_tc <- update(f_sep_2_const, error_model = "tc")
+status(f_sep_2_tc) |> kable()
+
+ - - + @@ -2142,18 +1858,18 @@ status(f_sep_2_tc) |> kable()

Using the two-component error model, all separate fits converge with the exception of the alternative pathway fit with DFOP used for the parent and the Sassafras dataset.

-
f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
-  no_random_effect = illparms(cyan_saem_full[2:4, ]),
-  cluster = cl_path_2)
-
status(f_saem_2) |> kable()
-
Nambsheim Tama Gross-Umstadt Sassafras Lleida
fomc_path_2
- - +
+f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc),
+  no_random_effect = illparms(cyan_saem_full[2:4, ]),
+  cluster = cl_path_2)
+
+status(f_saem_2) |> kable()
+
+ - - + @@ -2175,20 +1891,19 @@ parent and the Sassafras dataset.

The hierarchical fits for the alternative pathway completed successfully, with the exception of the model using FOMC for the parent compound and constant variance as the error model.

-
illparms(f_saem_2) |> kable()
-
const tc
fomc_path_2
+
+illparms(f_saem_2) |> kable()
+
---+++ - - + - - + @@ -2211,17 +1926,16 @@ compound and constant variance as the error model.

random effects for the formation fractions for the pathways from JCZ38 to JSE76, and for the reverse pathway from JSE76 to JCZ38 are ill-defined.

-
anova(f_saem_2[, "tc"]) |> kable(digits = 1)
-
const tc
fomc_path_2
- - +
+anova(f_saem_2[, "tc"]) |> kable(digits = 1)
+
+ - - + @@ -2246,17 +1960,16 @@ ill-defined.

npar AIC BIC Lik
fomc_path_2 tc
-
anova(f_saem_2[2:3,]) |> kable(digits = 1)
- - - +
+anova(f_saem_2[2:3,]) |> kable(digits = 1)
+
+ - - + @@ -2294,30 +2007,31 @@ and BIC values and are plotted below. Compared with the original pathway, the AIC and BIC values indicate a large improvement. This is confirmed by the plots, which show that the metabolite JCZ38 is fitted much better with this model.

-
plot(f_saem_2[["fomc_path_2", "tc"]])
+
+plot(f_saem_2[["fomc_path_2", "tc"]])
-FOMC pathway fit with two-component error, alternative pathway -

+FOMC pathway fit with two-component error, alternative pathway

FOMC pathway fit with two-component error, alternative pathway

-
plot(f_saem_2[["dfop_path_2", "tc"]])
+
+plot(f_saem_2[["dfop_path_2", "tc"]])
-DFOP pathway fit with two-component error, alternative pathway -

+DFOP pathway fit with two-component error, alternative pathway

DFOP pathway fit with two-component error, alternative pathway

-
plot(f_saem_2[["sforb_path_2", "tc"]])
+
+plot(f_saem_2[["sforb_path_2", "tc"]])
-SFORB pathway fit with two-component error, alternative pathway -

+SFORB pathway fit with two-component error, alternative pathway

SFORB pathway fit with two-component error, alternative pathway

-
-

Refinement of alternative pathway fits

+
+

Refinement of alternative pathway fits +

All ill-defined random effects that were identified in the parent only fits and in the above pathway fits, are excluded for the final evaluations below. For this purpose, a list of character vectors is @@ -2325,29 +2039,29 @@ created below that can be indexed by row and column indices, and which contains the degradation parameter names for which random effects should be excluded for each of the hierarchical fits contained in f_saem_2.

-
no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
-no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
-  "f_JCZ38_qlogis", "f_JSE76_qlogis")
-no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
-  "f_JCZ38_qlogis", "f_JSE76_qlogis")
-clusterExport(cl_path_2, "no_ranef")
-
-f_saem_3 <- update(f_saem_2,
-  no_random_effect = no_ranef,
-  cluster = cl_path_2)
-
status(f_saem_3) |> kable()
-
npar AIC BIC Lik
dfop_path_2 const
- - +
+no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
+no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+clusterExport(cl_path_2, "no_ranef")
+
+f_saem_3 <- update(f_saem_2,
+  no_random_effect = no_ranef,
+  cluster = cl_path_2)
+
+status(f_saem_3) |> kable()
+
+ - - + @@ -2370,15 +2084,14 @@ f_saem_3 <- update(f_saem_2, all updated fits completed successfully. However, the Fisher Information Matrix for the fixed effects (Fth) could not be inverted, so no confidence intervals for the optimised parameters are available.

-
illparms(f_saem_3) |> kable()
-
const tc
fomc_path_2
- - +
+illparms(f_saem_3) |> kable()
+
+ - - + @@ -2397,17 +2110,16 @@ confidence intervals for the optimised parameters are available.

const tc
fomc_path_2
-
anova(f_saem_3[, "tc"]) |> kable(digits = 1)
- - - +
+anova(f_saem_3[, "tc"]) |> kable(digits = 1)
+
+ - - + @@ -2432,17 +2144,16 @@ confidence intervals for the optimised parameters are available.

npar AIC BIC Lik
fomc_path_2 tc
-
anova(f_saem_3[2:3,]) |> kable(digits = 1)
- - - +
+anova(f_saem_3[2:3,]) |> kable(digits = 1)
+
+ - - + @@ -2478,11 +2189,13 @@ confidence intervals for the optimised parameters are available.

two-component error) are lower than in the previous fits with the alternative pathway, the practical value of these refined evaluations is limited as no confidence intervals are obtained.

-
stopCluster(cl_path_2)
+
+stopCluster(cl_path_2)
-
-

Conclusion

+
+

Conclusion +

It was demonstrated that a relatively complex transformation pathway with parallel formation of two primary metabolites and one secondary metabolite can be fitted even if the data in the individual datasets are @@ -2492,50 +2205,55 @@ practical feasibility of iterative refinements based on ill-defined parameters and of alternative checks of parameter identifiability based on multistart runs.

-
-

Acknowledgements

+
+

Acknowledgements +

The helpful comments by Janina Wöltjen of the German Environment Agency are gratefully acknowledged.

-
-

Appendix

-
-

Plots of fits that were not refined further

-
plot(f_saem_1[["sfo_path_1", "tc"]])
+
+

Appendix +

+
+

Plots of fits that were not refined further +

+
+plot(f_saem_1[["sfo_path_1", "tc"]])
-SFO pathway fit with two-component error -

+SFO pathway fit with two-component error

SFO pathway fit with two-component error

-
plot(f_saem_1[["fomc_path_1", "tc"]])
+
+plot(f_saem_1[["fomc_path_1", "tc"]])
-FOMC pathway fit with two-component error -

+FOMC pathway fit with two-component error

FOMC pathway fit with two-component error

-
plot(f_saem_1[["sforb_path_1", "tc"]])
+
+plot(f_saem_1[["sforb_path_1", "tc"]])
-HS pathway fit with two-component error -

+HS pathway fit with two-component error

HS pathway fit with two-component error

-
-

Hierarchical fit listings

-
-

Pathway 1

+
+

Hierarchical fit listings +

+
+

Pathway 1 +


 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 18:31:33 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:35:03 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - k_cyan * cyan
@@ -2548,7 +2266,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 480.873 s
+Fitted in 445.08 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2653,17 +2371,17 @@ JCZ38  14.46  48.05
 J9Z38 103.86 345.00
 JSE76 143.91 478.04
 
-
-

+ +


 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 18:32:28 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:34:47 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - k_cyan * cyan
@@ -2676,7 +2394,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 534.75 s
+Fitted in 428.46 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -2783,17 +2501,17 @@ JCZ38  15.81  52.52
 J9Z38 107.97 358.68
 JSE76 114.20 379.35
 
-
-

+ +


 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 18:33:51 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:35:21 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -2808,7 +2526,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 618.676 s
+Fitted in 462.739 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -2928,17 +2646,17 @@ JCZ38  20.53   68.19       NA
 J9Z38 140.07  465.32       NA
 JSE76 318.86 1059.22       NA
 
-
-

+ +


 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 18:34:01 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:35:31 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -2953,7 +2671,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 627.822 s
+Fitted in 472.067 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3066,17 +2784,17 @@ JCZ38  22.01  73.1       NA
 J9Z38 130.09 432.2       NA
 JSE76 210.98 700.9       NA
 
-
-

+ +


 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 18:33:18 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:36:02 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3095,7 +2813,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 584.724 s
+Fitted in 503.671 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3212,17 +2930,17 @@ JCZ38  22.34  74.22       NA      NA      NA
 J9Z38 119.92 398.36       NA      NA      NA
 JSE76 200.41 665.76       NA      NA      NA
 
-
-

+ +


 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 18:35:43 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:38:54 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -3241,7 +2959,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 729.575 s
+Fitted in 674.81 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3358,17 +3076,17 @@ JCZ38  22.20  73.75       NA      NA      NA
 J9Z38 108.23 359.53       NA      NA      NA
 JSE76 179.30 595.62       NA      NA      NA
 
-
-

+ +


 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 18:34:05 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:36:26 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -3386,7 +3104,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 632.71 s
+Fitted in 527.639 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3523,17 +3241,17 @@ JCZ38  22.98  76.33       NA           NA           NA
 J9Z38 116.28 386.29       NA           NA           NA
 JSE76 193.42 642.53       NA           NA           NA
 
-
-

+ +


 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 18:37:01 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:38:31 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -3551,7 +3269,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 807.852 s
+Fitted in 651.67 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3688,17 +3406,17 @@ JCZ38  22.34  74.2       NA           NA           NA
 J9Z38 110.14 365.9       NA           NA           NA
 JSE76 177.11 588.3       NA           NA           NA
 
-
-

+ +


 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 18:33:29 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:36:13 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan
@@ -3713,7 +3431,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 596.235 s
+Fitted in 514.353 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -3830,20 +3548,21 @@ JCZ38  22.27  73.98       NA      NA      NA
 J9Z38 113.09 375.69       NA      NA      NA
 JSE76 187.01 621.23       NA      NA      NA
 
-
-

+ +

-
-

Pathway 2

+
+

Pathway 2 +


 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 18:46:08 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:47:30 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -3858,7 +3577,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 536.687 s
+Fitted in 505.533 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -3999,17 +3718,17 @@ JCZ38   7.075  23.50       NA
 J9Z38 117.249 389.49       NA
 JSE76  14.169  47.07       NA
 
-
-

+ +


 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 18:47:06 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:48:20 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4029,7 +3748,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 594.209 s
+Fitted in 555.413 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -4190,17 +3909,17 @@ JCZ38  12.50  41.53       NA      NA      NA
 J9Z38 118.69 394.27       NA      NA      NA
 JSE76  24.32  80.78       NA      NA      NA
 
-
-

+ +


 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 18:49:43 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:51:02 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4220,7 +3939,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 751.883 s
+Fitted in 717.675 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4381,17 +4100,17 @@ JCZ38   8.93  29.66       NA      NA      NA
 J9Z38 110.45 366.89       NA      NA      NA
 JSE76  17.96  59.66       NA      NA      NA
 
-
-

+ +


 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 18:46:57 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:48:15 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4409,7 +4128,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 585.771 s
+Fitted in 550.772 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -4577,17 +4296,17 @@ JCZ38   7.203  23.93       NA           NA           NA
 J9Z38 131.918 438.22       NA           NA           NA
 JSE76  14.287  47.46       NA           NA           NA
 
-
-

+ +


 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 18:50:00 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 20:50:59 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -4605,7 +4324,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 767.874 s
+Fitted in 714.48 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4773,21 +4492,22 @@ JCZ38   8.535  28.35       NA           NA           NA
 J9Z38 105.517 350.52       NA           NA           NA
 JSE76  17.837  59.25       NA           NA           NA
 
-
-

+ +

-
-

Pathway 2, refined fits

+
+

Pathway 2, refined fits +


 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 19:03:52 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:04:10 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
@@ -4802,7 +4522,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 830.375 s
+Fitted in 786.038 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -4919,18 +4639,18 @@ JCZ38  12.03  39.96       NA
 J9Z38 111.14 369.19       NA
 JSE76  23.77  78.98       NA
 
-
-

+ +


 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 19:05:47 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:05:56 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -4950,7 +4670,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 945.728 s
+Fitted in 892.139 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -5085,18 +4805,18 @@ JCZ38  13.04  43.33       NA      NA      NA
 J9Z38 120.93 401.73       NA      NA      NA
 JSE76  26.39  87.68       NA      NA      NA
 
-
-

+ +


 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 19:05:49 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:02 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -5116,7 +4836,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 947.743 s
+Fitted in 898.534 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -5251,18 +4971,18 @@ JCZ38  11.49  38.18       NA      NA      NA
 J9Z38 107.55 357.28       NA      NA      NA
 JSE76  27.20  90.36       NA      NA      NA
 
-
-

+ +


 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 19:05:38 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:05:52 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -5280,7 +5000,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 936.368 s
+Fitted in 888.333 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Constant variance 
@@ -5422,18 +5142,18 @@ JCZ38  12.92  42.93       NA           NA           NA
 J9Z38 114.71 381.07       NA           NA           NA
 JSE76  26.04  86.51       NA           NA           NA
 
-
-

+ +


 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 19:05:52 2025 
-Date of summary: Thu Feb 13 19:05:53 2025 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:21 2025 
+Date of summary: Mon May 12 21:06:22 2025 
 
 Equations:
 d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
@@ -5451,7 +5171,7 @@ Data:
 
 Model predictions using solution type deSolve 
 
-Fitted in 950.661 s
+Fitted in 916.619 s
 Using 300, 100 iterations and 10 chains
 
 Variance model: Two-component variance function 
@@ -5593,19 +5313,20 @@ JCZ38  11.06  36.75       NA           NA           NA
 J9Z38 106.71 354.49       NA           NA           NA
 JSE76  25.44  84.51       NA           NA           NA
 
-
-

+ +

-
-

Session info

-
R version 4.4.2 (2024-10-31)
+

+
Session info
+

+
R version 4.5.0 (2025-04-11)
 Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
 BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0  LAPACK version 3.11.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -5623,75 +5344,52 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
-[5] rmarkdown_2.29  nvimcom_0.9-167
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
 
 loaded via a namespace (and not attached):
- [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
- [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
- [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    processx_3.8.4   
-[13] pkgbuild_1.4.5    deSolve_1.40      mclust_6.1.1      ps_1.8.1         
-[17] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
-[21] jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4       munsell_0.5.1    
-[25] cachem_1.1.0      yaml_2.3.10       inline_0.3.20     tools_4.4.2      
-[29] colorout_1.3-2    dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1    
-[33] vctrs_0.6.5       R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4  
-[37] MASS_7.3-61       pkgconfig_2.0.3   callr_3.7.6       pillar_1.9.0     
-[41] bslib_0.8.0       gtable_0.3.6      glue_1.8.0        xfun_0.49        
-[45] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
-[49] nlme_3.1-166      compiler_4.4.2    readxl_1.4.3     

+ [1] sass_0.4.9        generics_0.1.3    lattice_0.22-6    digest_0.6.37    
+ [5] magrittr_2.0.3    evaluate_1.0.3    grid_4.5.0        fastmap_1.2.0    
+ [9] cellranger_1.1.0  jsonlite_1.9.0    processx_3.8.6    pkgbuild_1.4.6   
+[13] deSolve_1.40      mclust_6.1.1      ps_1.9.0          gridExtra_2.3    
+[17] scales_1.3.0      codetools_0.2-20  textshaping_1.0.0 jquerylib_0.1.4  
+[21] cli_3.6.4         rlang_1.1.5       munsell_0.5.1     cachem_1.1.0     
+[25] yaml_2.3.10       inline_0.3.21     tools_4.5.0       dplyr_1.1.4      
+[29] colorspace_2.1-1  ggplot2_3.5.1     vctrs_0.6.5       R6_2.6.1         
+[33] zoo_1.8-13        lifecycle_1.0.4   fs_1.6.5          htmlwidgets_1.6.4
+[37] MASS_7.3-65       ragg_1.3.3        pkgconfig_2.0.3   desc_1.4.3       
+[41] callr_3.7.6       pkgdown_2.1.1     pillar_1.10.1     bslib_0.9.0      
+[45] gtable_0.3.6      glue_1.8.0        systemfonts_1.2.1 xfun_0.51        
+[49] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
+[53] nlme_3.1-168      compiler_4.5.0    readxl_1.4.4
-
-

Hardware info

+
+

Hardware info +

CPU model: AMD Ryzen 9 7950X 16-Core Processor
-
MemTotal:       64927788 kB
+
MemTotal:       64927780 kB
- - - - + - +
+

Developed by Johannes Ranke.

+
- +
+

Site built with pkgdown 2.1.1.

+
- - - - - + diff --git a/docs/articles/prebuilt/2022_dmta_parent.html b/docs/articles/prebuilt/2022_dmta_parent.html index 14f12c0e..10035c99 100644 --- a/docs/articles/prebuilt/2022_dmta_parent.html +++ b/docs/articles/prebuilt/2022_dmta_parent.html @@ -1,396 +1,100 @@ - - - + - - - - - - - - - -Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + +Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P • mkin + + + + + - + Skip to contents + + +
-
npar AIC BIC Lik
dfop_path_2 const
Hierarchical SFO path 1 fit with constant variance Hierarchical SFO path 1 fit with two-component error Hierarchical FOMC path 1 fit with constant variance Hierarchical FOMC path 1 fit with two-component error Hierarchical DFOP path 1 fit with constant variance Hierarchical DFOP path 1 fit with two-component error Hierarchical SFORB path 1 fit with constant variance Hierarchical SFORB path 1 fit with two-component error Hierarchical HS path 1 fit with constant variance Hierarchical FOMC path 2 fit with two-component error Hierarchical DFOP path 2 fit with constant variance Hierarchical DFOP path 2 fit with two-component error Hierarchical SFORB path 2 fit with constant variance Hierarchical SFORB path 2 fit with two-component error Hierarchical FOMC path 2 fit with reduced random effects, two-component error Hierarchical DFOP path 2 fit with reduced random effects, constant variance Hierarchical DFOP path 2 fit with reduced random effects, two-component error Hierarchical SFORB path 2 fit with reduced random effects, constant variance Hierarchical SFORB path 2 fit with reduced random effects, two-component error
+
+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")
+}
+
- - + - - + @@ -502,14 +208,12 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Calke
time DMTA
0
- +
- - + - - + @@ -577,14 +281,12 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Borstel
time DMTA
0.000000
- +
- - + - - + @@ -732,14 +434,12 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Flaach
time DMTA
0.0000000
- +
- - + - - + @@ -839,14 +539,12 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset BBA 2.2
time DMTA
0.0000000
- +
- - + - - + @@ -946,14 +644,12 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset BBA 2.3
time DMTA
0.0000000
- +
- - + - - + @@ -1150,24 +846,25 @@ dmta_ds[["Elliot 2"]] <- NULL
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()
+
+ @@ -1175,8 +872,7 @@ status(f_sep_const) |> kable() - - + @@ -1221,11 +917,11 @@ 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()
+
+ @@ -1233,8 +929,7 @@ status(f_sep_tc) |> kable() - - + @@ -1278,8 +973,9 @@ status(f_sep_tc) |> kable() 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 @@ -1291,18 +987,18 @@ 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()
+
+ - - + @@ -1328,17 +1024,16 @@ 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)
+
+ - - + @@ -1404,22 +1099,22 @@ 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()
+
+ - - + @@ -1450,32 +1145,34 @@ 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))
+
--------++++++++ - - + @@ -1484,8 +1181,7 @@ achieved with the argument test = TRUE to the - - + @@ -1513,35 +1209,35 @@ 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'

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

Plot of the final NLHM DFOP fit

Finally, a summary report of the fit is produced.

-
summary(f_saem_dfop_tc_no_ranef_k2)
+
+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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:46 2025 
+Date of summary: Mon May 12 21:06:46 2025 
 
 Equations:
 d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1553,7 +1249,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.778 s
+Fitted in 3.953 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -1615,8 +1311,9 @@ 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). @@ -1626,12 +1323,13 @@ 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 -

+Scaled parameters from the multistart runs, full model

Scaled parameters from the multistart runs, full model

@@ -1642,34 +1340,36 @@ 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 -

+Scaled parameters from the multistart runs, reduced model

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 -

+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

+
+

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 @@ -1681,35 +1381,39 @@ 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:      3.3 
-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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:38 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - k_DMTA * DMTA
@@ -1719,7 +1423,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 0.792 s
+Fitted in 0.793 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -1771,17 +1475,17 @@ Estimated disappearance times:
       DT50  DT90
 DMTA 12.24 40.65
 
-
-

+ +


 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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:40 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - k_DMTA * DMTA
@@ -1791,7 +1495,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.245 s
+Fitted in 2.462 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -1845,17 +1549,17 @@ Estimated disappearance times:
       DT50  DT90
 DMTA 12.24 40.65
 
-
-

+ +


 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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:39 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
@@ -1865,7 +1569,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.409 s
+Fitted in 1.408 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -1922,17 +1626,17 @@ Estimated disappearance times:
       DT50  DT90 DT50back
 DMTA 11.41 42.53     12.8
 
-
-

+ +


 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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:40 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
@@ -1942,7 +1646,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.811 s
+Fitted in 2.735 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -2001,17 +1705,17 @@ Estimated disappearance times:
       DT50  DT90 DT50back
 DMTA 11.05 42.81    12.89
 
-
-

+ +


 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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:39 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -2023,7 +1727,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 1.638 s
+Fitted in 1.769 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -2085,17 +1789,17 @@ 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:      3.3 
-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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:41 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -2107,7 +1811,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.024 s
+Fitted in 3.069 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -2171,17 +1875,17 @@ 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:      3.3 
-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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:39 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
@@ -2191,7 +1895,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 2.301 s
+Fitted in 1.996 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Constant variance 
@@ -2253,17 +1957,17 @@ 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:      3.3 
-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 
+mkin version used for pre-fitting:  1.2.10 
+R version used for fitting:         4.5.0 
+Date of fit:     Mon May 12 21:06:41 2025 
+Date of summary: Mon May 12 21:07:51 2025 
 
 Equations:
 d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
@@ -2273,7 +1977,7 @@ Data:
 
 Model predictions using solution type analytical 
 
-Fitted in 3.264 s
+Fitted in 3.389 s
 Using 300, 100 iterations and 9 chains
 
 Variance model: Two-component variance function 
@@ -2337,69 +2041,63 @@ 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 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 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 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 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 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 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 constant variance

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

+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 4.4.2 (2024-10-31)
+

+
Session info
+

+
R version 4.5.0 (2025-04-11)
 Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
 BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0  LAPACK version 3.11.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -2417,73 +2115,50 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
-[5] rmarkdown_2.29  nvimcom_0.9-167
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
 
 loaded via a namespace (and not attached):
- [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

+ [1] gtable_0.3.6      jsonlite_1.9.0    dplyr_1.1.4       compiler_4.5.0   
+ [5] tidyselect_1.2.1  gridExtra_2.3     jquerylib_0.1.4   systemfonts_1.2.1
+ [9] scales_1.3.0      textshaping_1.0.0 yaml_2.3.10       fastmap_1.2.0    
+[13] lattice_0.22-6    ggplot2_3.5.1     R6_2.6.1          generics_0.1.3   
+[17] lmtest_0.9-40     MASS_7.3-65       htmlwidgets_1.6.4 tibble_3.2.1     
+[21] desc_1.4.3        munsell_0.5.1     bslib_0.9.0       pillar_1.10.1    
+[25] rlang_1.1.5       cachem_1.1.0      xfun_0.51         fs_1.6.5         
+[29] sass_0.4.9        cli_3.6.4         pkgdown_2.1.1     magrittr_2.0.3   
+[33] digest_0.6.37     grid_4.5.0        mclust_6.1.1      lifecycle_1.0.4  
+[37] nlme_3.1-168      vctrs_0.6.5       evaluate_1.0.3    glue_1.8.0       
+[41] codetools_0.2-20  ragg_1.3.3        zoo_1.8-13        colorspace_2.1-1 
+[45] tools_4.5.0       pkgconfig_2.0.3   htmltools_0.5.8.1
-
-

Hardware info

+
+

Hardware info +

CPU model: AMD Ryzen 9 7950X 16-Core Processor
-
MemTotal:       64927788 kB
+
MemTotal:       64927780 kB
- - - - +
- - - +
+

Site built with pkgdown 2.1.1.

+
- - - - - + diff --git a/docs/articles/prebuilt/2022_dmta_pathway.html b/docs/articles/prebuilt/2022_dmta_pathway.html index c9f87cd8..d2ef55fb 100644 --- a/docs/articles/prebuilt/2022_dmta_pathway.html +++ b/docs/articles/prebuilt/2022_dmta_pathway.html @@ -1,396 +1,100 @@ - - - + - - - - - - - - - -Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + +Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P • mkin + + + + + - + Skip to contents + + +
-

Testing hierarchical pathway kinetics with -residue data on dimethenamid and dimethenamid-P

-

Johannes Ranke

-

Last change on 20 April 2023, last compiled on 13 -Februar 2025

-
+
+
-
-true -
+

Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P

+

Johannes +Ranke

+ +

Last change on 20 April 2023, +last compiled on 12 Mai 2025

+ + Source: vignettes/prebuilt/2022_dmta_pathway.rmd +
2022_dmta_pathway.rmd
+
-
-

Introduction

+ + +
+

Introduction +

The purpose of this document is to test demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS, with parallel formation of two or more metabolites @@ -399,7 +103,7 @@ 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 1.2.9, which is currently under +

The mkin package is used in version 1.2.10, which is currently under development. 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 @@ -408,26 +112,28 @@ 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()
-
-# We need to start a new cluster after defining a compiled model that is
-# saved as a DLL to the user directory, therefore we define a function
-# This is used again after defining the pathway model
-start_cluster <- function(n_cores) {
-  if (Sys.info()["sysname"] == "Windows") {
-    ret <- makePSOCKcluster(n_cores)
-  } else {
-    ret <- makeForkCluster(n_cores)
-  }
-  return(ret)
-}
+
+library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+n_cores <- detectCores()
+
+# We need to start a new cluster after defining a compiled model that is
+# saved as a DLL to the user directory, therefore we define a function
+# This is used again after defining the pathway model
+start_cluster <- function(n_cores) {
+  if (Sys.info()["sysname"] == "Windows") {
+    ret <- makePSOCKcluster(n_cores)
+  } else {
+    ret <- makeForkCluster(n_cores)
+  }
+  return(ret)
+}
-
-

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 @@ -448,41 +154,41 @@ 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$name == "DMTAP", "name"] <-  "DMTA"              # Rename DMTAP to DMTA
-  ds_i <- subset(ds_i, select = c("name", "time", "value")) # Select data
-  ds_i$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$name == "DMTAP", "name"] <-  "DMTA"              # Rename DMTAP to DMTA
+  ds_i <- subset(ds_i, select = c("name", "time", "value")) # Select data
+  ds_i$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),
-      booktabs = TRUE, row.names = FALSE))
-    cat("\n\\clearpage\n")
-}
-
npar AICChisq Df Pr(>Chisq)
f_saem_dfop_tc_no_ranef_k2
Hierarchical mkin fit of the SFO model with error model const Hierarchical mkin fit of the SFO model with error model tc Hierarchical mkin fit of the FOMC model with error model const Hierarchical mkin fit of the FOMC model with error model tc Hierarchical mkin fit of the DFOP model with error model const Hierarchical mkin fit of the DFOP model with error model tc Hierarchical mkin fit of the HS model with error model const Hierarchical mkin fit of the HS model with error model tc
+
+for (ds_name in names(dmta_ds)) {
+  print(
+    kable(mkin_long_to_wide(dmta_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+    cat("\n\\clearpage\n")
+}
+
- - + - - + @@ -535,17 +241,15 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Calke
time DMTA M23 M27 M31
0
- +
- - + - - + @@ -661,17 +365,15 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Borstel
time DMTA M23 M27 M31
0.000000
- +
- - + - - + @@ -927,17 +629,15 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Flaach
time DMTA M23 M27 M31
0.0000000
- +
- - + - - + @@ -1109,17 +809,15 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset BBA 2.2
time DMTA M23 M27 M31
0.0000000
- +
- - + - - + @@ -1291,17 +989,15 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset BBA 2.3
time DMTA M23 M27 M31
0.0000000
- +
- - + - - + @@ -1642,8 +1338,9 @@ dmta_ds[["Elliot 2"]] <- NULL
Dataset Elliot
time DMTA M23 M27 M31
0.000000
-
-

Separate evaluations

+
+

Separate evaluations +

As a first step to obtain suitable starting parameters for the NLHM fits, we do separate fits of several variants of the pathway model used previously (Ranke et al. 2021), varying @@ -1651,71 +1348,71 @@ the kinetic model for the parent compound. Because the SFORB model often provides faster convergence than the DFOP model, and can sometimes be fitted where the DFOP model results in errors, it is included in the set of parent models tested here.

-
if (!dir.exists("dmta_dlls")) dir.create("dmta_dlls")
-m_sfo_path_1 <- mkinmod(
-  DMTA = mkinsub("SFO", c("M23", "M27", "M31")),
-  M23 = mkinsub("SFO"),
-  M27 = mkinsub("SFO"),
-  M31 = mkinsub("SFO", "M27", sink = FALSE),
-  name = "m_sfo_path", dll_dir = "dmta_dlls",
-  unload = TRUE, overwrite = TRUE,
-  quiet = TRUE
-)
-m_fomc_path_1 <- mkinmod(
-  DMTA = mkinsub("FOMC", c("M23", "M27", "M31")),
-  M23 = mkinsub("SFO"),
-  M27 = mkinsub("SFO"),
-  M31 = mkinsub("SFO", "M27", sink = FALSE),
-  name = "m_fomc_path", dll_dir = "dmta_dlls",
-  unload = TRUE, overwrite = TRUE,
-  quiet = TRUE
-)
-m_dfop_path_1 <- mkinmod(
-  DMTA = mkinsub("DFOP", c("M23", "M27", "M31")),
-  M23 = mkinsub("SFO"),
-  M27 = mkinsub("SFO"),
-  M31 = mkinsub("SFO", "M27", sink = FALSE),
-  name = "m_dfop_path", dll_dir = "dmta_dlls",
-  unload = TRUE, overwrite = TRUE,
-  quiet = TRUE
-)
-m_sforb_path_1 <- mkinmod(
-  DMTA = mkinsub("SFORB", c("M23", "M27", "M31")),
-  M23 = mkinsub("SFO"),
-  M27 = mkinsub("SFO"),
-  M31 = mkinsub("SFO", "M27", sink = FALSE),
-  name = "m_sforb_path", dll_dir = "dmta_dlls",
-  unload = TRUE, overwrite = TRUE,
-  quiet = TRUE
-)
-m_hs_path_1 <- mkinmod(
-  DMTA = mkinsub("HS", c("M23", "M27", "M31")),
-  M23 = mkinsub("SFO"),
-  M27 = mkinsub("SFO"),
-  M31 = mkinsub("SFO", "M27", sink = FALSE),
-  name = "m_hs_path", dll_dir = "dmta_dlls",
-  unload = TRUE, overwrite = TRUE,
-  quiet = TRUE
-)
-cl <- start_cluster(n_cores)
-
-deg_mods_1 <- list(
-  sfo_path_1 = m_sfo_path_1,
-  fomc_path_1 = m_fomc_path_1,
-  dfop_path_1 = m_dfop_path_1,
-  sforb_path_1 = m_sforb_path_1,
-  hs_path_1 = m_hs_path_1)
-
-sep_1_const <- mmkin(
-  deg_mods_1,
-  dmta_ds,
-  error_model = "const",
-  quiet = TRUE)
-
-status(sep_1_const) |> kable()
- - - +
+if (!dir.exists("dmta_dlls")) dir.create("dmta_dlls")
+m_sfo_path_1 <- mkinmod(
+  DMTA = mkinsub("SFO", c("M23", "M27", "M31")),
+  M23 = mkinsub("SFO"),
+  M27 = mkinsub("SFO"),
+  M31 = mkinsub("SFO", "M27", sink = FALSE),
+  name = "m_sfo_path", dll_dir = "dmta_dlls",
+  unload = TRUE, overwrite = TRUE,
+  quiet = TRUE
+)
+m_fomc_path_1 <- mkinmod(
+  DMTA = mkinsub("FOMC", c("M23", "M27", "M31")),
+  M23 = mkinsub("SFO"),
+  M27 = mkinsub("SFO"),
+  M31 = mkinsub("SFO", "M27", sink = FALSE),
+  name = "m_fomc_path", dll_dir = "dmta_dlls",
+  unload = TRUE, overwrite = TRUE,
+  quiet = TRUE
+)
+m_dfop_path_1 <- mkinmod(
+  DMTA = mkinsub("DFOP", c("M23", "M27", "M31")),
+  M23 = mkinsub("SFO"),
+  M27 = mkinsub("SFO"),
+  M31 = mkinsub("SFO", "M27", sink = FALSE),
+  name = "m_dfop_path", dll_dir = "dmta_dlls",
+  unload = TRUE, overwrite = TRUE,
+  quiet = TRUE
+)
+m_sforb_path_1 <- mkinmod(
+  DMTA = mkinsub("SFORB", c("M23", "M27", "M31")),
+  M23 = mkinsub("SFO"),
+  M27 = mkinsub("SFO"),
+  M31 = mkinsub("SFO", "M27", sink = FALSE),
+  name = "m_sforb_path", dll_dir = "dmta_dlls",
+  unload = TRUE, overwrite = TRUE,
+  quiet = TRUE
+)
+m_hs_path_1 <- mkinmod(
+  DMTA = mkinsub("HS", c("M23", "M27", "M31")),
+  M23 = mkinsub("SFO"),
+  M27 = mkinsub("SFO"),
+  M31 = mkinsub("SFO", "M27", sink = FALSE),
+  name = "m_hs_path", dll_dir = "dmta_dlls",
+  unload = TRUE, overwrite = TRUE,
+  quiet = TRUE
+)
+cl <- start_cluster(n_cores)
+
+deg_mods_1 <- list(
+  sfo_path_1 = m_sfo_path_1,
+  fomc_path_1 = m_fomc_path_1,
+  dfop_path_1 = m_dfop_path_1,
+  sforb_path_1 = m_sforb_path_1,
+  hs_path_1 = m_hs_path_1)
+
+sep_1_const <- mmkin(
+  deg_mods_1,
+  dmta_ds,
+  error_model = "const",
+  quiet = TRUE)
+
+status(sep_1_const) |> kable()
+
+ @@ -1723,8 +1420,7 @@ status(sep_1_const) |> kable() - - + @@ -1777,11 +1473,11 @@ status(sep_1_const) |> kable() constant variance converged (status OK). Most fits with DFOP or SFORB for the parent converged as well. The fits with HS for the parent did not converge with default settings.

-
sep_1_tc <- update(sep_1_const, error_model = "tc")
-status(sep_1_tc) |> kable()
-
Calke Borstel BBA 2.2 BBA 2.3 Elliot
sfo_path_1
- - +
+sep_1_tc <- update(sep_1_const, error_model = "tc")
+status(sep_1_tc) |> kable()
+
+ @@ -1789,8 +1485,7 @@ status(sep_1_tc) |> kable() - - + @@ -1845,24 +1540,25 @@ different data sets when applying the DFOP and SFORB model and some additional convergence problems when using the FOMC model for the parent.

-
-

Hierarchichal model fits

+
+

Hierarchichal model fits +

The following code fits two sets of the corresponding hierarchical models to the data, one assuming constant variance, and one assuming two-component error.

-
saem_1 <- mhmkin(list(sep_1_const, sep_1_tc))
+
+saem_1 <- mhmkin(list(sep_1_const, sep_1_tc))

The run time for these fits was around two hours on five year old hardware. After a recent hardware upgrade these fits complete in less than twenty minutes.

-
status(saem_1) |> kable()
-
Calke Borstel BBA 2.2 BBA 2.3 Elliot
sfo_path_1
- - +
+status(saem_1) |> kable()
+
+ - - + @@ -1893,17 +1589,16 @@ than twenty minutes.

const tc
sfo_path_1

According to the status function, all fits terminated successfully.

-
anova(saem_1) |> kable(digits = 1)
- - - +
+anova(saem_1) |> kable(digits = 1)
+
+ - - + @@ -1990,22 +1685,22 @@ assume a discontinuity, so the SFORB model is preferable from a mechanistic viewpoint. In addition, the information criteria AIC and BIC are very similar for HS and SFORB. Therefore, the SFORB model is selected here for further refinements.

-
-

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(saem_1) |> kable()
-
npar AIC BIC Lik
sfo_path_1 const
- - +
+illparms(saem_1) |> kable()
+
+ - - + @@ -2044,22 +1739,22 @@ two-component error, the random effect for the rate constant from reversibly bound DMTA to the free DMTA (k_DMTA_bound_free) is not well-defined. Therefore, the fit is updated without assuming a random effect for this parameter.

-
saem_sforb_path_1_tc_reduced <- update(saem_1[["sforb_path_1", "tc"]],
-  no_random_effect = "log_k_DMTA_bound_free")
-illparms(saem_sforb_path_1_tc_reduced)
+
+saem_sforb_path_1_tc_reduced <- update(saem_1[["sforb_path_1", "tc"]],
+  no_random_effect = "log_k_DMTA_bound_free")
+illparms(saem_sforb_path_1_tc_reduced)

As expected, no ill-defined parameters remain. The model comparison below shows that the reduced model is preferable.

-
anova(saem_1[["sforb_path_1", "tc"]], saem_sforb_path_1_tc_reduced) |> kable(digits = 1)
-
const tc
sfo_path_1
- - +
+anova(saem_1[["sforb_path_1", "tc"]], saem_sforb_path_1_tc_reduced) |> kable(digits = 1)
+
+ - - + @@ -2078,8 +1773,9 @@ below shows that the reduced model is preferable.

npar AIC BIC Lik
saem_sforb_path_1_tc_reduced

The convergence plot of the refined fit is shown below.

-
plot(saem_sforb_path_1_tc_reduced$so, plot.type = "convergence")
-

+
+plot(saem_sforb_path_1_tc_reduced$so, plot.type = "convergence")
+

For some parameters, for example for f_DMTA_ilr_1 and f_DMTA_ilr_2, i.e. for two of the parameters determining the formation fractions of the parallel formation of the three @@ -2091,15 +1787,18 @@ the parameter estimates very much, and it is proposed that the fit is acceptable. No numeric convergence criterion is implemented in saemix.

-
-

Alternative check of parameter identifiability

+
+

Alternative check of parameter identifiability +

As an alternative check of parameter identifiability (Duchesne et al. 2021), multistart runs were performed on the basis of the refined fit shown above.

-
saem_sforb_path_1_tc_reduced_multi <- multistart(saem_sforb_path_1_tc_reduced,
-  n = 32, cores = 10)
+
+saem_sforb_path_1_tc_reduced_multi <- multistart(saem_sforb_path_1_tc_reduced,
+  n = 32, cores = 10)
 
   (subscript) logical subscript too long
-
print(saem_sforb_path_1_tc_reduced_multi)
+
+print(saem_sforb_path_1_tc_reduced_multi)
<multistart> object with 32 fits:
  E OK 
  7 25 
@@ -2112,11 +1811,11 @@ the SAEM algorithm leads to parameter combinations for the degradation
 model that the numerical integration routine cannot cope with. Because
 of this variation of initial parameters, some of the model fits take up
 to two times more time than the original fit.

-
par(mar = c(12.1, 4.1, 2.1, 2.1))
-parplot(saem_sforb_path_1_tc_reduced_multi, ylim = c(0.5, 2), las = 2)

+
+par(mar = c(12.1, 4.1, 2.1, 2.1))
+parplot(saem_sforb_path_1_tc_reduced_multi, ylim = c(0.5, 2), las = 2)

 

-Parameter boxplots for the multistart runs that succeeded
-

+Parameter boxplots for the multistart runs that succeeded

 Parameter boxplots for the multistart runs that succeeded
 

 

@@ -2126,103 +1825,114 @@ independent of the starting parameters, and there are no remaining
 ill-defined parameters.
-
-

Plots of selected fits

+
+

Plots of selected fits +

The SFORB pathway fits with full and reduced parameter distribution model are shown below.

-
plot(saem_1[["sforb_path_1", "tc"]])
+
+plot(saem_1[["sforb_path_1", "tc"]])
-SFORB pathway fit with two-component error -

+SFORB pathway fit with two-component error

SFORB pathway fit with two-component error

-
plot(saem_sforb_path_1_tc_reduced)
+
+plot(saem_sforb_path_1_tc_reduced)
-SFORB pathway fit with two-component error, reduced parameter model -

+SFORB pathway fit with two-component error, reduced parameter model

SFORB pathway fit with two-component error, reduced parameter model

Plots of the remaining fits and listings for all successful fits are shown in the Appendix.

-
stopCluster(cl)
+
-
-

Conclusions

+
+

Conclusions +

Pathway fits with SFO, FOMC, DFOP, SFORB and HS models for the parent compound could be successfully performed.

-
-

Acknowledgements

+
+

Acknowledgements +

The helpful comments by Janina Wöltjen of the German Environment Agency on earlier versions of this document 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.
Ranke, Johannes, Janina Wöltjen, Jana Schmidt, and Emmanuelle Comets. 2021. “Taking Kinetic Evaluations of Degradation Data to the Next Level with Nonlinear Mixed-Effects Models.” Environments -8 (8). https://doi.org/10.3390/environments8080071. +8 (8). https://doi.org/10.3390/environments8080071.
-
-

Appendix

-
-

Plots of hierarchical fits not selected for refinement

-
plot(saem_1[["sfo_path_1", "tc"]])
+
+

Appendix +

+
+

Plots of hierarchical fits not selected for refinement +

+
+plot(saem_1[["sfo_path_1", "tc"]])
-SFO pathway fit with two-component error -

+SFO pathway fit with two-component error

SFO pathway fit with two-component error

-
plot(saem_1[["fomc_path_1", "tc"]])
+
+plot(saem_1[["fomc_path_1", "tc"]])
-FOMC pathway fit with two-component error -

+FOMC pathway fit with two-component error

FOMC pathway fit with two-component error

-
plot(saem_1[["sforb_path_1", "tc"]])
+
+plot(saem_1[["sforb_path_1", "tc"]])
-HS pathway fit with two-component error -

+HS pathway fit with two-component error

HS pathway fit with two-component error

-
-

Hierarchical model fit listings

-
-

Fits with random effects for all degradation parameters

+
+

Hierarchical model fit listings +

+
+

Fits with random effects for all degradation parameters +

-
-

Improved fit of the SFORB pathway model with two-component -error

+
+

Improved fit of the SFORB pathway model with two-component +error +

-
-

Session info

-
R version 4.4.2 (2024-10-31)
+

+
Session info
+

+
R version 4.5.0 (2025-04-11)
 Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
 BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0  LAPACK version 3.11.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -2240,75 +1950,52 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
-[5] rmarkdown_2.29  nvimcom_0.9-167
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
 
 loaded via a namespace (and not attached):
- [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
- [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
- [9] fastmap_1.2.0     jsonlite_1.8.9    processx_3.8.4    pkgbuild_1.4.5   
-[13] deSolve_1.40      mclust_6.1.1      ps_1.8.1          gridExtra_2.3    
-[17] fansi_1.0.6       scales_1.3.0      codetools_0.2-20  jquerylib_0.1.4  
-[21] cli_3.6.3         rlang_1.1.4       munsell_0.5.1     cachem_1.1.0     
-[25] yaml_2.3.10       tools_4.4.2       inline_0.3.20     colorout_1.3-2   
-[29] dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1     vctrs_0.6.5      
-[33] R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4   MASS_7.3-61      
-[37] pkgconfig_2.0.3   callr_3.7.6       pillar_1.9.0      bslib_0.8.0      
-[41] gtable_0.3.6      glue_1.8.0        xfun_0.49         tibble_3.2.1     
-[45] lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1 nlme_3.1-166     
-[49] compiler_4.4.2   

+ [1] sass_0.4.9        generics_0.1.3    lattice_0.22-6    digest_0.6.37    
+ [5] magrittr_2.0.3    evaluate_1.0.3    grid_4.5.0        fastmap_1.2.0    
+ [9] jsonlite_1.9.0    processx_3.8.6    pkgbuild_1.4.6    deSolve_1.40     
+[13] mclust_6.1.1      ps_1.9.0          gridExtra_2.3     scales_1.3.0     
+[17] codetools_0.2-20  textshaping_1.0.0 jquerylib_0.1.4   cli_3.6.4        
+[21] rlang_1.1.5       munsell_0.5.1     cachem_1.1.0      yaml_2.3.10      
+[25] tools_4.5.0       inline_0.3.21     dplyr_1.1.4       colorspace_2.1-1 
+[29] ggplot2_3.5.1     vctrs_0.6.5       R6_2.6.1          zoo_1.8-13       
+[33] lifecycle_1.0.4   fs_1.6.5          htmlwidgets_1.6.4 MASS_7.3-65      
+[37] ragg_1.3.3        pkgconfig_2.0.3   desc_1.4.3        callr_3.7.6      
+[41] pkgdown_2.1.1     pillar_1.10.1     bslib_0.9.0       gtable_0.3.6     
+[45] glue_1.8.0        systemfonts_1.2.1 xfun_0.51         tibble_3.2.1     
+[49] lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1 nlme_3.1-168     
+[53] compiler_4.5.0
-
-

Hardware info

+
+

Hardware info +

CPU model: AMD Ryzen 9 7950X 16-Core Processor
-
MemTotal:       64927788 kB
+
MemTotal:       64927780 kB
- - - - +
- +
+

Developed by Johannes Ranke.

+
- +
+

Site built with pkgdown 2.1.1.

+
- - - - - + diff --git a/docs/articles/prebuilt/2023_mesotrione_parent.html b/docs/articles/prebuilt/2023_mesotrione_parent.html index 8bb993dc..92df6e51 100644 --- a/docs/articles/prebuilt/2023_mesotrione_parent.html +++ b/docs/articles/prebuilt/2023_mesotrione_parent.html @@ -1,374 +1,100 @@ - - - + - - - - - - - - - -Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + +Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione • mkin + + + + + - + Skip to contents + + +
-

Testing covariate modelling in hierarchical -parent degradation kinetics with residue data on mesotrione

-

Johannes Ranke

-

Last change on 4 August 2023, last compiled on 13 -Februar 2025

-
+
+
-
-true -
+

Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione

+

Johannes +Ranke

+ +

Last change on 4 August 2023, +last compiled on 12 Mai 2025

+ + Source: vignettes/prebuilt/2023_mesotrione_parent.rmd +
2023_mesotrione_parent.rmd
+
-
-

Introduction

+ + +
+

Introduction +

The purpose of this document is to test demonstrate how nonlinear hierarchical models (NLHM) based on the parent degradation models SFO, FOMC, DFOP and HS can be fitted with the mkin package, also considering @@ -377,7 +103,7 @@ parameters. Because in some other case studies, the SFORB parameterisation of biexponential decline has shown some advantages over the DFOP parameterisation, SFORB was included in the list of tested models as well.

-

The mkin package is used in version 1.2.9, which is contains the +

The mkin package is used in version 1.2.10, which is contains the functions that were used for 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.

@@ -385,33 +111,35 @@ 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)
-}
-
-

Test data

-
data_file <- system.file(
-  "testdata", "mesotrione_soil_efsa_2016.xlsx", package = "mkin")
-meso_ds <- read_spreadsheet(data_file, parent_only = TRUE)
+
+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)
+}
+
+

Test data +

+
+data_file <- system.file(
+  "testdata", "mesotrione_soil_efsa_2016.xlsx", package = "mkin")
+meso_ds <- read_spreadsheet(data_file, parent_only = TRUE)

The following tables show the covariate data and the 18 datasets that were read in from the spreadsheet file.

-
pH <- attr(meso_ds, "covariates")
-kable(pH, caption = "Covariate data")
- +
+pH <- attr(meso_ds, "covariates")
+kable(pH, caption = "Covariate data")
+
- - + - - + @@ -487,20 +215,19 @@ kable(pH, caption = "Covariate data")
Covariate data
pH
Richmond
-
for (ds_name in names(meso_ds)) {
-  print(
-    kable(mkin_long_to_wide(meso_ds[[ds_name]]),
-      caption = paste("Dataset", ds_name),
-      booktabs = TRUE, row.names = FALSE))
-}
- +
+for (ds_name in names(meso_ds)) {
+  print(
+    kable(mkin_long_to_wide(meso_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+}
+
- - + - - + @@ -592,14 +319,12 @@ kable(pH, caption = "Covariate data")
Dataset Richmond
time meso
0.000000
- +
- - + - - + @@ -635,14 +360,12 @@ kable(pH, caption = "Covariate data")
Dataset Richmond 2
time meso
0.000000
- +
- - + - - + @@ -678,14 +401,12 @@ kable(pH, caption = "Covariate data")
Dataset ERTC
time meso
0.000000
- +
- - + - - + @@ -717,14 +438,12 @@ kable(pH, caption = "Covariate data")
Dataset Toulouse
time meso
0.000000
- +
- - + - - + @@ -752,14 +471,12 @@ kable(pH, caption = "Covariate data")
Dataset Picket Piece
time meso
0.000000
- +
- - + - - + @@ -783,14 +500,12 @@ kable(pH, caption = "Covariate data")
Dataset 721
time meso
0.00000
- +
- - + - - + @@ -814,14 +529,12 @@ kable(pH, caption = "Covariate data")
Dataset 722
time meso
0.00000
- +
- - + - - + @@ -845,14 +558,12 @@ kable(pH, caption = "Covariate data")
Dataset 723
time meso
0.00000
- +
- - + - - + @@ -876,14 +587,12 @@ kable(pH, caption = "Covariate data")
Dataset 724
time meso
0.000000
- +
- - + - - + @@ -907,14 +616,12 @@ kable(pH, caption = "Covariate data")
Dataset 725
time meso
0.00000
- +
- - + - - + @@ -938,14 +645,12 @@ kable(pH, caption = "Covariate data")
Dataset 727
time meso
0.00000
- +
- - + - - + @@ -969,14 +674,12 @@ kable(pH, caption = "Covariate data")
Dataset 728
time meso
0.00000
- +
- - + - - + @@ -1000,14 +703,12 @@ kable(pH, caption = "Covariate data")
Dataset 729
time meso
0.00000
- +
- - + - - + @@ -1031,14 +732,12 @@ kable(pH, caption = "Covariate data")
Dataset 730
time meso
0.00000
- +
- - + - - + @@ -1062,14 +761,12 @@ kable(pH, caption = "Covariate data")
Dataset 731
time meso
0.00000
- +
- - + - - + @@ -1093,14 +790,12 @@ kable(pH, caption = "Covariate data")
Dataset 732
time meso
0.00000
- +
- - + - - + @@ -1124,14 +819,12 @@ kable(pH, caption = "Covariate data")
Dataset 741
time meso
0.00000
- +
- - + - - + @@ -1157,32 +850,33 @@ kable(pH, caption = "Covariate data")
Dataset 742
time meso
0.00000
-
-

Separate evaluations

+
+

Separate evaluations +

In order to obtain suitable starting parameters for the NLHM fits, separate fits of the five 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", "SFORB", "HS")
-f_sep_const <- mmkin(
-  deg_mods,
-  meso_ds,
-  error_model = "const",
-  cluster = cl,
-  quiet = TRUE)
-
status(f_sep_const[, 1:5]) |> kable()
- - - +
+deg_mods <- c("SFO", "FOMC", "DFOP", "SFORB", "HS")
+f_sep_const <- mmkin(
+  deg_mods,
+  meso_ds,
+  error_model = "const",
+  cluster = cl,
+  quiet = TRUE)
+
+status(f_sep_const[, 1:5]) |> kable()
+
+ - - + @@ -1226,26 +920,26 @@ f_sep_const <- mmkin(
Richmond Richmond 2 ERTC Toulouse Picket Piece
SFO
-
status(f_sep_const[, 6:18]) |> kable()
- +
+status(f_sep_const[, 6:18]) |> kable()
+
--------------++++++++++++++ - - + @@ -1260,8 +954,7 @@ f_sep_const <- mmkin( - - + @@ -1348,19 +1041,19 @@ f_sep_const <- mmkin(

In the tables above, OK indicates convergence and C indicates failure to converge. Most separate fits with constant variance converged, with the exception of two FOMC fits, one SFORB fit and one HS fit.

-
f_sep_tc <- update(f_sep_const, error_model = "tc")
-
status(f_sep_tc[, 1:5]) |> kable()
-
721 722732 741 742
SFO
- - +
+f_sep_tc <- update(f_sep_const, error_model = "tc")
+
+status(f_sep_tc[, 1:5]) |> kable()
+
+ - - + @@ -1404,26 +1097,26 @@ the exception of two FOMC fits, one SFORB fit and one HS fit.

Richmond Richmond 2 ERTC Toulouse Picket Piece
SFO
-
status(f_sep_tc[, 6:18]) |> kable()
- +
+status(f_sep_tc[, 6:18]) |> kable()
+
--------------++++++++++++++ - - + @@ -1438,8 +1131,7 @@ the exception of two FOMC fits, one SFORB fit and one HS fit.

- - + @@ -1527,21 +1219,21 @@ the exception of two FOMC fits, one SFORB fit and one HS fit.

converge is larger, with convergence problems appearing for a number of non-SFO fits.

-
-

Hierarchical model fits without covariate effect

+
+

Hierarchical model fits without covariate effect +

The following code fits hierarchical kinetic models for the ten combinations of the five different degradation models with the two different error models in parallel.

-
f_saem_1 <- mhmkin(list(f_sep_const, f_sep_tc), cluster = cl)
-status(f_saem_1) |> kable()
-
721 722 732 741 742
SFO
- - +
+f_saem_1 <- mhmkin(list(f_sep_const, f_sep_tc), cluster = cl)
+status(f_saem_1) |> kable()
+
+ - - + @@ -1571,17 +1263,16 @@ status(f_saem_1) |> kable()
const tc
SFO

All fits terminate without errors (status OK).

-
anova(f_saem_1) |> kable(digits = 1)
- - - +
+anova(f_saem_1) |> kable(digits = 1)
+
+ - - + @@ -1660,20 +1351,19 @@ consistently preferable to the corresponding fits with two-component error for these data. This is confirmed by the fact that the parameter b.1 (the relative standard deviation in the fits obtained with the saemix package), is ill-defined in all fits.

-
illparms(f_saem_1) |> kable()
-
npar AIC BIC Lik
SFO const
+
+illparms(f_saem_1) |> kable()
+
---+++ - - + - - + @@ -1705,16 +1395,15 @@ with the saemix package), is ill-defined in all fits.

For obtaining fits with only well-defined random effects, we update the set of fits, excluding random effects that were ill-defined according to the illparms function.

-
f_saem_2 <- update(f_saem_1, no_random_effect = illparms(f_saem_1))
-status(f_saem_2) |> kable()
-
const tc
SFO
- - +
+f_saem_2 <- update(f_saem_1, no_random_effect = illparms(f_saem_1))
+status(f_saem_2) |> kable()
+
+ - - + @@ -1744,15 +1433,14 @@ status(f_saem_2) |> kable()
const tc
SFO

The updated fits terminate without errors.

-
illparms(f_saem_2) |> kable()
- - - +
+illparms(f_saem_2) |> kable()
+
+ - - + @@ -1783,8 +1471,9 @@ status(f_saem_2) |> kable()
const tc
SFO

No ill-defined errors remain in the fits with constant variance.

-
-

Hierarchical model fits with covariate effect

+
+

Hierarchical model fits with covariate effect +

In the following sections, hierarchical fits including a model for the influence of pH on selected degradation parameters are shown for all parent models. Constant variance is selected as the error model based on @@ -1793,20 +1482,21 @@ in the fits without pH influence are excluded. A potential influence of the soil pH is only included for parameters with a well-defined random effect, because experience has shown that only for such parameters a significant pH effect could be found.

-
-

SFO

-
sfo_pH <- saem(f_sep_const["SFO", ], no_random_effect = "meso_0", covariates = pH,
-  covariate_models = list(log_k_meso ~ pH))
-
summary(sfo_pH)$confint_trans |> kable(digits = 2)
- - - +
+

SFO +

+
+sfo_pH <- saem(f_sep_const["SFO", ], no_random_effect = "meso_0", covariates = pH,
+  covariate_models = list(log_k_meso ~ pH))
+
+summary(sfo_pH)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -1844,23 +1534,26 @@ significant pH effect could be found.

beta_pH(log_k_meso). Its confidence interval does not include zero, indicating that the influence of soil pH on the log of the degradation rate constant is significantly greater than zero.

-
anova(f_saem_2[["SFO", "const"]], sfo_pH, test = TRUE)
+
+anova(f_saem_2[["SFO", "const"]], sfo_pH, test = TRUE)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
                            npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)    
-f_saem_2[["SFO", "const"]]    4 797.56 801.12 -394.78                         
+f_saem_2[["SFO", "const"]]    4 797.56 801.12 -394.78                         
 sfo_pH                        5 783.09 787.54 -386.54 16.473  1  4.934e-05 ***
 ---
-Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The comparison with the SFO fit without covariate effect confirms that considering the soil pH improves the model, both by comparison of AIC and BIC and by the likelihood ratio test.

-
plot(sfo_pH)
-

+
+plot(sfo_pH)
+

Endpoints for a model with covariates are by default calculated for the median of the covariate values. This quantile can be adapted, or a specific covariate value can be given as shown below.

-
endpoints(sfo_pH)
+
+endpoints(sfo_pH)
$covariates
       pH
 50% 5.75
@@ -1868,7 +1561,8 @@ specific covariate value can be given as shown below.

 $distimes
          DT50     DT90
 meso 18.52069 61.52441
-
endpoints(sfo_pH, covariate_quantile = 0.9)
+
+endpoints(sfo_pH, covariate_quantile = 0.9)
$covariates
       pH
 90% 7.13
@@ -1876,7 +1570,8 @@ meso 18.52069 61.52441
$distimes DT50 DT90 meso 8.237019 27.36278 -
endpoints(sfo_pH, covariates = c(pH = 7.0))
+
+endpoints(sfo_pH, covariates = c(pH = 7.0))
$covariates
      pH
 User  7
@@ -1885,20 +1580,21 @@ $distimes
         DT50    DT90
 meso 8.89035 29.5331
-
-

FOMC

-
fomc_pH <- saem(f_sep_const["FOMC", ], no_random_effect = "meso_0", covariates = pH,
-  covariate_models = list(log_alpha ~ pH))
-
summary(fomc_pH)$confint_trans |> kable(digits = 2)
-
est. lower upper
meso_0
- - +
+

FOMC +

+
+fomc_pH <- saem(f_sep_const["FOMC", ], no_random_effect = "meso_0", covariates = pH,
+  covariate_models = list(log_alpha ~ pH))
+
+summary(fomc_pH)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -1951,34 +1647,36 @@ that the model with covariate influence is preferable. However, the random effect for alpha is not well-defined any more after inclusion of the covariate effect (the confidence interval of SD.log_alpha includes zero).

-
illparms(fomc_pH)
-
[1] "sd(log_alpha)"
+
+illparms(fomc_pH)
+
[1] "sd(log_alpha)"

Therefore, the model is updated without this random effect, and no ill-defined parameters remain.

-
fomc_pH_2 <- update(fomc_pH, no_random_effect = c("meso_0", "log_alpha"))
-illparms(fomc_pH_2)
-
anova(f_saem_2[["FOMC", "const"]], fomc_pH, fomc_pH_2, test = TRUE)
+
+fomc_pH_2 <- update(fomc_pH, no_random_effect = c("meso_0", "log_alpha"))
+illparms(fomc_pH_2)
+
+anova(f_saem_2[["FOMC", "const"]], fomc_pH, fomc_pH_2, test = TRUE)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
                             npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)    
-f_saem_2[["FOMC", "const"]]    5 783.25 787.71 -386.63                         
+f_saem_2[["FOMC", "const"]]    5 783.25 787.71 -386.63                         
 fomc_pH_2                      6 767.49 772.83 -377.75 17.762  1  2.503e-05 ***
 fomc_pH                        7 770.07 776.30 -378.04  0.000  1          1    
 ---
-Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model comparison indicates that including pH dependence significantly improves the fit, and that the reduced model with covariate influence results in the most preferable FOMC fit.

-
summary(fomc_pH_2)$confint_trans |> kable(digits = 2)
-
est. lower upper
meso_0
- - +
+summary(fomc_pH_2)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2018,9 +1716,11 @@ results in the most preferable FOMC fit.

est. lower upper
meso_0
-
plot(fomc_pH_2)
-

-
endpoints(fomc_pH_2)
+
+plot(fomc_pH_2)
+

+
+endpoints(fomc_pH_2)
$covariates
       pH
 50% 5.75
@@ -2028,7 +1728,8 @@ results in the most preferable FOMC fit.

 $distimes
          DT50     DT90 DT50back
 meso 17.30248 82.91343 24.95943
-
endpoints(fomc_pH_2, covariates = c(pH = 7))
+
+endpoints(fomc_pH_2, covariates = c(pH = 7))
$covariates
      pH
 User  7
@@ -2037,21 +1738,21 @@ $distimes
          DT50     DT90 DT50back
 meso 6.986239 27.02927 8.136621
-
-

DFOP

+
+

DFOP +

In the DFOP fits without covariate effects, random effects for two degradation parameters (k2 and g) were identifiable.

-
summary(f_saem_2[["DFOP", "const"]])$confint_trans |> kable(digits = 2)
- - - +
+summary(f_saem_2[["DFOP", "const"]])$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2101,23 +1802,23 @@ identifiable.

excluding the same random effects as in the refined DFOP fit without covariate influence, and including covariate models for the two identifiable parameters k2 and g.

-
dfop_pH <- saem(f_sep_const["DFOP", ], no_random_effect = c("meso_0", "log_k1"),
-  covariates = pH,
-  covariate_models = list(log_k2 ~ pH, g_qlogis ~ pH))
+
+dfop_pH <- saem(f_sep_const["DFOP", ], no_random_effect = c("meso_0", "log_k1"),
+  covariates = pH,
+  covariate_models = list(log_k2 ~ pH, g_qlogis ~ pH))

The corresponding parameters for the influence of soil pH are beta_pH(log_k2) for the influence of soil pH on k2, and beta_pH(g_qlogis) for its influence on g.

-
summary(dfop_pH)$confint_trans |> kable(digits = 2)
-
est. lower upper
meso_0
- - +
+summary(dfop_pH)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2175,49 +1876,55 @@ identifiable parameters k2 and g.

est. lower upper
meso_0
-
illparms(dfop_pH)
-
[1] "sd(g_qlogis)"
+
+illparms(dfop_pH)
+
[1] "sd(g_qlogis)"

Confidence intervals for neither of them include zero, indicating a significant difference from zero. However, the random effect for g is now ill-defined. The fit is updated without this ill-defined random effect.

-
dfop_pH_2 <- update(dfop_pH,
-  no_random_effect = c("meso_0", "log_k1", "g_qlogis"))
-illparms(dfop_pH_2)
-
[1] "beta_pH(g_qlogis)"
+
+dfop_pH_2 <- update(dfop_pH,
+  no_random_effect = c("meso_0", "log_k1", "g_qlogis"))
+illparms(dfop_pH_2)
+
[1] "beta_pH(g_qlogis)"

Now, the slope parameter for the pH effect on g is ill-defined. Therefore, another attempt is made without the corresponding covariate model.

-
dfop_pH_3 <- saem(f_sep_const["DFOP", ], no_random_effect = c("meso_0", "log_k1"),
-  covariates = pH,
-  covariate_models = list(log_k2 ~ pH))
-illparms(dfop_pH_3)
-
[1] "sd(g_qlogis)"
+
+dfop_pH_3 <- saem(f_sep_const["DFOP", ], no_random_effect = c("meso_0", "log_k1"),
+  covariates = pH,
+  covariate_models = list(log_k2 ~ pH))
+illparms(dfop_pH_3)
+
[1] "sd(g_qlogis)"

As the random effect for g is again ill-defined, the fit is repeated without it.

-
dfop_pH_4 <- update(dfop_pH_3, no_random_effect = c("meso_0", "log_k1", "g_qlogis"))
-illparms(dfop_pH_4)
+
+dfop_pH_4 <- update(dfop_pH_3, no_random_effect = c("meso_0", "log_k1", "g_qlogis"))
+illparms(dfop_pH_4)

While no ill-defined parameters remain, model comparison suggests that the previous model dfop_pH_2 with two pH dependent parameters is preferable, based on information criteria as well as based on the likelihood ratio test.

-
anova(f_saem_2[["DFOP", "const"]], dfop_pH, dfop_pH_2, dfop_pH_3, dfop_pH_4)
+
+anova(f_saem_2[["DFOP", "const"]], dfop_pH, dfop_pH_2, dfop_pH_3, dfop_pH_4)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
                             npar    AIC    BIC     Lik
-f_saem_2[["DFOP", "const"]]    7 782.94 789.18 -384.47
+f_saem_2[["DFOP", "const"]]    7 782.94 789.18 -384.47
 dfop_pH_4                      7 767.35 773.58 -376.68
 dfop_pH_2                      8 765.14 772.26 -374.57
 dfop_pH_3                      8 769.00 776.12 -376.50
 dfop_pH                        9 769.10 777.11 -375.55
-
anova(dfop_pH_2, dfop_pH_4, test = TRUE)
+
+anova(dfop_pH_2, dfop_pH_4, test = TRUE)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
           npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)  
 dfop_pH_4    7 767.35 773.58 -376.68                       
 dfop_pH_2    8 765.14 772.26 -374.57 4.2153  1    0.04006 *
 ---
-Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

When focussing on parameter identifiability using the test if the confidence interval includes zero, dfop_pH_4 would still be the preferred model. However, it should be kept in mind that parameter @@ -2226,9 +1933,11 @@ likelihood. As the confidence interval of the random effect for g only marginally includes zero, it is suggested that this is acceptable, and that dfop_pH_2 can be considered the most preferable model.

-
plot(dfop_pH_2)
-

-
endpoints(dfop_pH_2)
+
+plot(dfop_pH_2)
+

+
+endpoints(dfop_pH_2)
$covariates
       pH
 50% 5.75
@@ -2236,7 +1945,8 @@ most preferable model.

 $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
 meso 18.36876 73.51841 22.13125 4.191901 23.98672
-
endpoints(dfop_pH_2, covariates = c(pH = 7))
+
+endpoints(dfop_pH_2, covariates = c(pH = 7))
$covariates
      pH
 User  7
@@ -2245,21 +1955,22 @@ $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
 meso 8.346428 28.34437 8.532507 4.191901 8.753618
-
-

SFORB

-
sforb_pH <- saem(f_sep_const["SFORB", ], no_random_effect = c("meso_free_0", "log_k_meso_free_bound"),
-  covariates = pH,
-  covariate_models = list(log_k_meso_free ~ pH, log_k_meso_bound_free ~ pH))
-
summary(sforb_pH)$confint_trans |> kable(digits = 2)
- - - +
+

SFORB +

+
+sforb_pH <- saem(f_sep_const["SFORB", ], no_random_effect = c("meso_free_0", "log_k_meso_free_bound"),
+  covariates = pH,
+  covariate_models = list(log_k_meso_free ~ pH, log_k_meso_bound_free ~ pH))
+
+summary(sforb_pH)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2325,39 +2036,41 @@ effect on this parameter (SD.log_k_meso_bound_free) includes zero.

Using the illparms function, these ill-defined parameters can be found more conveniently.

-
illparms(sforb_pH)
-
[1] "sd(log_k_meso_bound_free)"      "beta_pH(log_k_meso_bound_free)"
+
+illparms(sforb_pH)
+
[1] "sd(log_k_meso_bound_free)"      "beta_pH(log_k_meso_bound_free)"

To remove the ill-defined parameters, a second variant of the SFORB model with pH influence is fitted. No ill-defined parameters remain.

-
sforb_pH_2 <- update(sforb_pH,
-  no_random_effect = c("meso_free_0", "log_k_meso_free_bound", "log_k_meso_bound_free"),
-  covariate_models = list(log_k_meso_free ~ pH))
-illparms(sforb_pH_2)
+
+sforb_pH_2 <- update(sforb_pH,
+  no_random_effect = c("meso_free_0", "log_k_meso_free_bound", "log_k_meso_bound_free"),
+  covariate_models = list(log_k_meso_free ~ pH))
+illparms(sforb_pH_2)

The model comparison of the SFORB fits includes the refined model without covariate effect, and both versions of the SFORB fit with covariate effect.

-
anova(f_saem_2[["SFORB", "const"]], sforb_pH, sforb_pH_2, test = TRUE)
+
+anova(f_saem_2[["SFORB", "const"]], sforb_pH, sforb_pH_2, test = TRUE)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
                              npar    AIC    BIC     Lik   Chisq Df Pr(>Chisq)  
-f_saem_2[["SFORB", "const"]]    7 783.40 789.63 -384.70                        
+f_saem_2[["SFORB", "const"]]    7 783.40 789.63 -384.70                        
 sforb_pH_2                      7 770.94 777.17 -378.47 12.4616  0             
 sforb_pH                        9 768.81 776.83 -375.41  6.1258  2    0.04675 *
 ---
-Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The first model including pH influence is preferable based on information criteria and the likelihood ratio test. However, as it is not fully identifiable, the second model is selected.

-
summary(sforb_pH_2)$confint_trans |> kable(digits = 2)
-
est. lower upper
meso_free_0
- - +
+summary(sforb_pH_2)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2403,9 +2116,11 @@ not fully identifiable, the second model is selected.

est. lower upper
meso_free_0
-
plot(sforb_pH_2)
-

-
endpoints(sforb_pH_2)
+
+plot(sforb_pH_2)
+

+
+endpoints(sforb_pH_2)
$covariates
       pH
 50% 5.75
@@ -2421,7 +2136,8 @@ $SFORB
 $distimes
          DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
 meso 16.86549 73.15824 22.02282     7.119554     26.33839
-
endpoints(sforb_pH_2, covariates = c(pH = 7))
+
+endpoints(sforb_pH_2, covariates = c(pH = 7))
$covariates
      pH
 User  7
@@ -2438,21 +2154,22 @@ $distimes
          DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
 meso 7.932495 36.93311 11.11797     5.205671        18.26
-
-

HS

-
hs_pH <- saem(f_sep_const["HS", ], no_random_effect = c("meso_0"),
-  covariates = pH,
-  covariate_models = list(log_k1 ~ pH, log_k2 ~ pH, log_tb ~ pH))
-
summary(hs_pH)$confint_trans |> kable(digits = 2)
- - - +
+

HS +

+
+hs_pH <- saem(f_sep_const["HS", ], no_random_effect = c("meso_0"),
+  covariates = pH,
+  covariate_models = list(log_k1 ~ pH, log_k2 ~ pH, log_tb ~ pH))
+
+summary(hs_pH)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2522,37 +2239,39 @@ meso 7.932495 36.93311 11.11797 5.205671 18.26
est. lower upper
meso_0
-
illparms(hs_pH)
-
[1] "sd(log_tb)"      "beta_pH(log_tb)"
+
+illparms(hs_pH)
+
[1] "sd(log_tb)"      "beta_pH(log_tb)"

According to the output of the illparms function, the random effect on the break time tb cannot reliably be quantified, neither can the influence of soil pH on tb. The fit is repeated without the corresponding covariate model, and no ill-defined parameters remain.

-
hs_pH_2 <- update(hs_pH, covariate_models = list(log_k1 ~ pH, log_k2 ~ pH))
-illparms(hs_pH_2)
+
+hs_pH_2 <- update(hs_pH, covariate_models = list(log_k1 ~ pH, log_k2 ~ pH))
+illparms(hs_pH_2)

Model comparison confirms that this model is preferable to the fit without covariate influence, and also to the first version with covariate influence.

-
anova(f_saem_2[["HS", "const"]], hs_pH, hs_pH_2, test = TRUE)
+
+anova(f_saem_2[["HS", "const"]], hs_pH, hs_pH_2, test = TRUE)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
                           npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)    
-f_saem_2[["HS", "const"]]    8 780.08 787.20 -382.04                         
+f_saem_2[["HS", "const"]]    8 780.08 787.20 -382.04                         
 hs_pH_2                     10 766.47 775.37 -373.23 17.606  2  0.0001503 ***
 hs_pH                       11 769.80 779.59 -373.90  0.000  1  1.0000000    
 ---
-Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
-
summary(hs_pH_2)$confint_trans |> kable(digits = 2)
- - - +Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 +
+summary(hs_pH_2)$confint_trans |> kable(digits = 2)
+
+ - - + @@ -2616,9 +2335,11 @@ Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.&
est. lower upper
meso_0
-
plot(hs_pH_2)
-

-
endpoints(hs_pH_2)
+
+plot(hs_pH_2)
+

+
+endpoints(hs_pH_2)
$covariates
       pH
 50% 5.75
@@ -2626,7 +2347,8 @@ Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.&
 $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
 meso 14.68725 82.45287 24.82079 14.68725 29.29299
-
endpoints(hs_pH_2, covariates = c(pH = 7))
+
+endpoints(hs_pH_2, covariates = c(pH = 7))
$covariates
      pH
 User  7
@@ -2635,11 +2357,13 @@ $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
 meso 8.298536 38.85371 11.69613 8.298536 15.71561
-
-

Comparison across parent models

+
+

Comparison across parent models +

After model reduction for all models with pH influence, they are compared with each other.

-
anova(sfo_pH, fomc_pH_2, dfop_pH_2, dfop_pH_4, sforb_pH_2, hs_pH_2)
+
+anova(sfo_pH, fomc_pH_2, dfop_pH_2, dfop_pH_4, sforb_pH_2, hs_pH_2)
Data: 116 observations of 1 variable(s) grouped in 18 datasets
 
            npar    AIC    BIC     Lik
@@ -2654,7 +2378,8 @@ hs_pH_2      10 766.47 775.37 -373.23
selected as the best fit.

The endpoints resulting from this model are listed below. Please refer to the Appendix for a detailed listing.

-
endpoints(dfop_pH_2)
+
+endpoints(dfop_pH_2)
$covariates
       pH
 50% 5.75
@@ -2662,7 +2387,8 @@ refer to the Appendix for a detailed listing.

 $distimes
          DT50     DT90 DT50back  DT50_k1  DT50_k2
 meso 18.36876 73.51841 22.13125 4.191901 23.98672
-
endpoints(dfop_pH_2, covariates = c(pH = 7))
+
+endpoints(dfop_pH_2, covariates = c(pH = 7))
$covariates
      pH
 User  7
@@ -2672,34 +2398,40 @@ $distimes
 meso 8.346428 28.34437 8.532507 4.191901 8.753618
-
-

Conclusions

+
+

Conclusions +

These evaluations demonstrate that covariate effects can be included for all types of parent degradation models. These models can then be further refined to make them fully identifiable.

-
-

Appendix

-
-

Hierarchical fit listings

-
-

Fits without covariate effects

+
+

Appendix +

+
+

Hierarchical fit listings +

+
+

Fits without covariate effects +

-
-

Fits with covariate effects

+
+

Fits with covariate effects +

-
-

Session info

-
R version 4.4.2 (2024-10-31)
+

+
Session info
+

+
R version 4.5.0 (2025-04-11)
 Platform: x86_64-pc-linux-gnu
 Running under: Debian GNU/Linux 12 (bookworm)
 
 Matrix products: default
 BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
-LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0  LAPACK version 3.11.0
 
 locale:
  [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
@@ -2717,74 +2449,51 @@ attached base packages:
 [8] base     
 
 other attached packages:
-[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
-[5] rmarkdown_2.29  nvimcom_0.9-167
+[1] rmarkdown_2.29  nvimcom_0.9-167 saemix_3.3      npde_3.5       
+[5] knitr_1.49      mkin_1.2.10    
 
 loaded via a namespace (and not attached):
- [1] gtable_0.3.6      jsonlite_1.8.9    dplyr_1.1.4       compiler_4.4.2   
- [5] tidyselect_1.2.1  colorout_1.3-2    gridExtra_2.3     jquerylib_0.1.4  
- [9] scales_1.3.0      readxl_1.4.3      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        cellranger_1.1.0  codetools_0.2-20  zoo_1.8-12       
-[41] fansi_1.0.6       colorspace_2.1-1  tools_4.4.2       pkgconfig_2.0.3  
-[45] htmltools_0.5.8.1

+ [1] gtable_0.3.6      jsonlite_1.9.0    dplyr_1.1.4       compiler_4.5.0   
+ [5] tidyselect_1.2.1  gridExtra_2.3     jquerylib_0.1.4   systemfonts_1.2.1
+ [9] scales_1.3.0      textshaping_1.0.0 readxl_1.4.4      yaml_2.3.10      
+[13] fastmap_1.2.0     lattice_0.22-6    ggplot2_3.5.1     R6_2.6.1         
+[17] generics_0.1.3    lmtest_0.9-40     MASS_7.3-65       htmlwidgets_1.6.4
+[21] tibble_3.2.1      desc_1.4.3        munsell_0.5.1     bslib_0.9.0      
+[25] pillar_1.10.1     rlang_1.1.5       cachem_1.1.0      xfun_0.51        
+[29] fs_1.6.5          sass_0.4.9        cli_3.6.4         pkgdown_2.1.1    
+[33] magrittr_2.0.3    digest_0.6.37     grid_4.5.0        mclust_6.1.1     
+[37] lifecycle_1.0.4   nlme_3.1-168      vctrs_0.6.5       evaluate_1.0.3   
+[41] glue_1.8.0        cellranger_1.1.0  codetools_0.2-20  ragg_1.3.3       
+[45] zoo_1.8-13        colorspace_2.1-1  tools_4.5.0       pkgconfig_2.0.3  
+[49] htmltools_0.5.8.1
-
-

Hardware info

+
+

Hardware info +

CPU model: AMD Ryzen 9 7950X 16-Core Processor
-
MemTotal:       64927788 kB
+
MemTotal:       64927780 kB
- - - - +
- +
+

Developed by Johannes Ranke.

+
- +
+

Site built with pkgdown 2.1.1.

+
- - - - - + diff --git a/docs/articles/twa.html b/docs/articles/twa.html index 19bc4761..6901a28f 100644 --- a/docs/articles/twa.html +++ b/docs/articles/twa.html @@ -20,7 +20,7 @@ mkin - 1.2.9 + 1.2.10 

 print(p5a)
@@ -170,7 +170,7 @@ same.

## 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)
@@ -221,7 +221,7 @@ same.

## 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)
@@ -272,7 +272,7 @@ same.

## 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)
@@ -331,7 +331,7 @@ lower value for the rate constant is used here.

## 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)
@@ -386,7 +386,7 @@ lower value for the rate constant is used here.

## 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)
@@ -440,7 +440,7 @@ suggest a simple exponential decline.

## 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)
@@ -498,7 +498,7 @@ in PestDF and g in mkin. In mkin, it is restricted to the interval from 
## 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)
@@ -558,7 +558,7 @@ difference in IORE model parameters between PestDF and mkin.

## 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)
@@ -624,7 +624,7 @@ overparameterisation.

## 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)
@@ -681,7 +681,7 @@ overparameterisation.

## 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)
@@ -732,7 +732,7 @@ overparameterisation.

## 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)
@@ -787,7 +787,7 @@ overparameterisation.

## 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)
@@ -844,7 +844,7 @@ same results in mkin and PestDF.

## 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)
@@ -893,7 +893,7 @@ same results in mkin and PestDF.

## 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)
@@ -950,7 +950,7 @@ mkin and PestDF.

## 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)
diff --git a/docs/articles/web_only/benchmarks.html b/docs/articles/web_only/benchmarks.html index 3566be42..52e657cb 100644 --- a/docs/articles/web_only/benchmarks.html +++ b/docs/articles/web_only/benchmarks.html @@ -20,7 +20,7 @@ mkin - 1.2.9 + 1.2.10