Work package 1.1: Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P • mkin

Date: Thu, 24 Nov 2022 09:02:26 +0100 Subject: Start online docs of the development version --- docs/dev/index.html | 21 +++++++++++---------- 1 file changed, 11 insertions(+), 10 deletions(-) (limited to 'docs/dev/index.html') diff --git a/docs/dev/index.html b/docs/dev/index.html index 4709fe29..2615d389 100644 --- a/docs/dev/index.html +++ b/docs/dev/index.html @@ -45,7 +45,7 @@ @@ -153,9 +153,9 @@

General

Highly flexible model specification using mkinmod, including equilibrium reactions and using the single first-order reversible binding (SFORB) model, which will automatically create two latent state variables for the observed variable.
Model solution (forward modelling) in the function mkinpredict is performed either using the analytical solution for the case of parent only degradation, an eigenvalue based solution if only simple first-order (SFO) or SFORB kinetics are used in the model, or using a numeric solver from the deSolve package (default is lsoda).
The usual one-sided t-test for significant difference from zero is nevertheless shown based on estimators for the untransformed parameters.
Highly flexible model specification using mkinmod, including equilibrium reactions and using the single first-order reversible binding (SFORB) model, which will automatically create two state variables for the observed variable.
Model solution (forward modelling) in the function mkinpredict is performed either using the analytical solution for the case of parent only degradation or some simple models involving a single transformation product, , an eigenvalue based solution if only simple first-order (SFO) or SFORB kinetics are used in the model, or using a numeric solver from the deSolve package (default is lsoda).
The usual one-sided t-test for significant difference from zero is shown based on estimators for the untransformed parameters.
Summary and plotting functions. The summary of an mkinfit object is in fact a full report that should give enough information to be able to approximately reproduce the fit with other tools.
The chi-squared error level as defined in the FOCUS kinetics guidance (see below) is calculated for each observed variable.
The ‘variance by variable’ error model which is often fitted using Iteratively Reweighted Least Squares (IRLS) can be specified as error_model = "obs".
Model comparisons using the Akaike Information Criterion (AIC) are supported which can also be used for non-constant variance. In such cases the FOCUS chi-squared error level is not meaningful.
By default, kinetic rate constants and kinetic formation fractions are transformed internally using transform_odeparms so their estimators can more reasonably be expected to follow a normal distribution.
When parameter estimates are backtransformed to match the model definition, confidence intervals calculated from standard errors are also backtransformed to the correct scale, and will not include meaningless values like negative rate constants or formation fractions adding up to more than 1, which cannot occur in a single experiment with a single defined radiolabel position.
When a metabolite decline phase is not described well by SFO kinetics, SFORB kinetics can be used for the metabolite. Mathematically, the SFORB model is equivalent to the DFOP model used by other tools for biphasic metabolite curves. However, the SFORB model has the advantage that there is a mechanistic interpretation of the model parameters.
Nonlinear mixed-effects models can be created from fits of the same degradation model to different datasets for the same compound by using the nlme.mmkin and saem.mmkin and methods. Note that the convergence of the nlme fits depends on the quality of the data. Convergence is better for simple models and data for many groups (e.g. soils). The saem method uses the saemix package as a backend. Analytical solutions suitable for use with this package have been implemented for parent only models and the most important models including one metabolite (SFO-SFO and DFOP-SFO). Fitting other models with saem.mmkin, while it makes use of the compiled ODE models that mkin provides, has longer run times (at least six minutes on my system).
When a metabolite decline phase is not described well by SFO kinetics, SFORB kinetics can be used for the metabolite. Mathematically, the SFORB model is equivalent to the DFOP model. However, the SFORB model has the advantage that there is a mechanistic interpretation of the model parameters.
Nonlinear mixed-effects models (hierarchical models) can be created from fits of the same degradation model to different datasets for the same compound by using the nlme.mmkin and saem.mmkin methods. Note that the convergence of the nlme fits depends on the quality of the data. Convergence is better for simple models and data for many groups (e.g. soils). The saem method uses the saemix package as a backend. Analytical solutions suitable for use with this package have been implemented for parent only models and the most important models including one metabolite (SFO-SFO and DFOP-SFO). Fitting other models with saem.mmkin, while it makes use of the compiled ODE models that mkin provides, has longer run times (from a couple of minutes to more than an hour).

@@ -186,7 +186,7 @@

GUI

There is a graphical user interface that may be useful. Please refer to its documentation page for installation instructions and a manual.

There is a graphical user interface that may be useful. Please refer to its documentation page for installation instructions and a manual. It only supports evaluations using (generalised) nonlinear regression, but not simultaneous fits using nonlinear mixed-effects models.

News @@ -203,8 +203,8 @@
The first `mkin` code was published on 11 May 2010 and the first CRAN version on 18 May 2010.

In 2011, Bayer Crop Science started to distribute an R based successor to KinGUI named KinGUII whose R code is based on `mkin`, but which added, among other refinements, a closed source graphical user interface (GUI), iteratively reweighted least squares (IRLS) optimisation of the variance for each of the observed variables, and Markov Chain Monte Carlo (MCMC) simulation functionality, similar to what is available e.g. in the `FME` package.

Somewhat in parallel, Syngenta has sponsored the development of an `mkin` and KinGUII based GUI application called CAKE, which also adds IRLS and MCMC, is more limited in the model formulation, but puts more weight on usability. CAKE is available for download from the CAKE website, where you can also find a zip archive of the R scripts derived from `mkin`, published under the GPL license.
-
Finally, there is KineticEval, which contains a further development of the scripts used for KinGUII, so the different tools will hopefully be able to learn from each other in the future as well.
-
Thanks to René Lehmann, formerly working at the Umweltbundesamt, for the nice cooperation cooperation on parameter transformations, especially the isometric log-ratio transformation that is now used for formation fractions in case there are more than two transformation targets.
+
Finally, there is KineticEval, which contains some further development of the scripts used for KinGUII.
+
Thanks to René Lehmann, formerly working at the Umweltbundesamt, for the nice cooperation on parameter transformations, especially the isometric log-ratio transformation that is now used for formation fractions in case there are more than two transformation targets.

Many inspirations for improvements of mkin resulted from doing kinetic evaluations of degradation data for my clients while working at Harlan Laboratories and at Eurofins Regulatory AG, and now as an independent consultant.

Funding was received from the Umweltbundesamt in the course of the projects

@@ -215,7 +215,8 @@
Project Number 120667 (Development of objective criteria for the evaluation of the visual fit in the kinetic evaluation of degradation data, 2019-2020)

Project Number 146839 (Checking the feasibility of using mixed-effects models for the derivation of kinetic modelling parameters from degradation studies, 2020-2021)

-
Thanks are due also to Emmanuelle Comets, maintainer of the saemix package, for the nice collaboration on using the SAEM algorithm and its implementation in saemix for the evaluation of chemical degradation data.
+
Thanks to everyone involved for collaboration and support!
+
Thanks are due also to Emmanuelle Comets, maintainer of the saemix package, for her interest and support for using the SAEM algorithm and its implementation in saemix for the evaluation of chemical degradation data.

References -- cgit v1.2.3 From a54bd290bc3884d0000c52c1b29bc557825d9eae Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 15 Dec 2022 14:50:28 +0100 Subject: List random effects correlations in output if any Update docs --- NEWS.md | 4 +- R/intervals.R | 8 +- R/summary.saem.mmkin.R | 16 +- docs/dev/index.html | 21 +- docs/dev/news/index.html | 57 +++- docs/dev/pkgdown.yml | 4 +- docs/dev/reference/Rplot001.png | Bin 18113 -> 1011 bytes docs/dev/reference/Rplot002.png | Bin 38732 -> 16953 bytes docs/dev/reference/illparms.html | 15 +- docs/dev/reference/parplot.html | 9 +- docs/dev/reference/saem.html | 21 +- docs/dev/reference/summary.saem.mmkin.html | 508 ++++++++++++++++------------- log/test.log | 20 +- man/summary.saem.mmkin.Rd | 13 +- 14 files changed, 422 insertions(+), 274 deletions(-) (limited to 'docs/dev/index.html') diff --git a/NEWS.md b/NEWS.md index 4540b517..7e65204f 100644 --- a/NEWS.md +++ b/NEWS.md @@ -2,7 +2,7 @@ - 'R/mhmkin.R': Allow an 'illparms.mhmkin' object or a list with suitable dimensions as value of the argument 'no_random_effects', making it possible to exclude random effects that were ill-defined in simpler variants of the set of degradation models. Remove the possibility to exclude random effects based on separate fits, as it did not work well. -- 'R/summary.saem.mmkin.R': List all initial parameter values in the summary, including random effects and error model parameters. Avoid redundant warnings that occurred in the calculation of correlations of the fixed effects in the case that the Fisher information matrix could not be inverted. +- 'R/summary.saem.mmkin.R': List all initial parameter values in the summary, including random effects and error model parameters. Avoid redundant warnings that occurred in the calculation of correlations of the fixed effects in the case that the Fisher information matrix could not be inverted. List correlations of random effects if specified by the user in the covariance model. - 'R/parplot.R': Possibility to select the top 'llquant' fraction of the fits for the parameter plots, and improved legend text. @@ -10,6 +10,8 @@ - 'R/parplot.R': Make the function work also in the case that some of the multistart runs failed. +- 'R/intervals.R': Include correlations of random effects in the model in case there are any. + # mkin 1.2.1 (2022-11-19) - '{data,R}/ds_mixed.rda': Include the test data in the package instead of generating it in 'tests/testthat/setup_script.R'. Refactor the generating code to make it consistent and update tests. diff --git a/R/intervals.R b/R/intervals.R index 705ef6eb..fcdbaea9 100644 --- a/R/intervals.R +++ b/R/intervals.R @@ -78,8 +78,12 @@ intervals.saem.mmkin <- function(object, level = 0.95, backtransform = TRUE, ... # Random effects sdnames <- intersect(rownames(conf.int), paste("SD", pnames, sep = ".")) - ranef_ret <- as.matrix(conf.int[sdnames, c("lower", "est.", "upper")]) - rownames(ranef_ret) <- paste0(gsub("SD\\.", "sd(", sdnames), ")") + corrnames <- grep("^Corr.", rownames(conf.int), value = TRUE) + ranef_ret <- as.matrix(conf.int[c(sdnames, corrnames), c("lower", "est.", "upper")]) + sdnames_ret <- paste0(gsub("SD\\.", "sd(", sdnames), ")") + corrnames_ret <- gsub("Corr\\.(.)\\.(.)", "corr(\\1,\\2)", corrnames) + rownames(ranef_ret) <- c(sdnames_ret, corrnames_ret) + attr(ranef_ret, "label") <- "Random effects:" diff --git a/R/summary.saem.mmkin.R b/R/summary.saem.mmkin.R index 46ab548b..49b02a50 100644 --- a/R/summary.saem.mmkin.R +++ b/R/summary.saem.mmkin.R @@ -75,10 +75,21 @@ #' f_saem_dfop_sfo <- saem(f_mmkin_dfop_sfo) #' print(f_saem_dfop_sfo) #' illparms(f_saem_dfop_sfo) -#' f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo, covariance.model = diag(c(0, 0, 1, 1, 1, 0))) +#' f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo, +#' no_random_effect = c("parent_0", "log_k_m1")) #' illparms(f_saem_dfop_sfo_2) #' intervals(f_saem_dfop_sfo_2) #' summary(f_saem_dfop_sfo_2, data = TRUE) +#' # Add a correlation between random effects of g and k2 +#' cov_model_3 <- f_saem_dfop_sfo_2$so@model@covariance.model +#' cov_model_3["log_k2", "g_qlogis"] <- 1 +#' cov_model_3["g_qlogis", "log_k2"] <- 1 +#' f_saem_dfop_sfo_3 <- update(f_saem_dfop_sfo, +#' covariance.model = cov_model_3) +#' intervals(f_saem_dfop_sfo_3) +#' # The correlation does not improve the fit judged by AIC and BIC, although +#' # the likelihood is higher with the additional parameter +#' anova(f_saem_dfop_sfo, f_saem_dfop_sfo_2, f_saem_dfop_sfo_3) #' } #' #' @export @@ -150,7 +161,8 @@ summary.saem.mmkin <- function(object, data = FALSE, verbose = FALSE, distimes = # Random effects sdnames <- intersect(rownames(conf.int), paste0("SD.", pnames)) - confint_ranef <- as.matrix(conf.int[sdnames, c("estimate", "lower", "upper")]) + corrnames <- grep("^Corr.", rownames(conf.int), value = TRUE) + confint_ranef <- as.matrix(conf.int[c(sdnames, corrnames), c("estimate", "lower", "upper")]) colnames(confint_ranef)[1] <- "est." # Error model diff --git a/docs/dev/index.html b/docs/dev/index.html index 2615d389..4723879e 100644 --- a/docs/dev/index.html +++ b/docs/dev/index.html @@ -222,12 +222,21 @@
References
- - - + + + + + + + + +
Ranke J, Wöltjen J, Schmidt J, and Comets E (2021) Taking kinetic evaluations of degradation data to the next level with nonlinear mixed-effects models. Environments 8 (8) 71 doi:10.3390/environments8080071 -
Ranke J, Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical Degradation Data Environments 6 (12) 124 doi:10.3390/environments6120124 -
Ranke J, Wöltjen J, Meinecke S (2018) Comparison of software tools for kinetic evaluation of chemical degradation data Environmental Sciences Europe 30 17 doi:10.1186/s12302-018-0145-1 -
+Ranke J, Wöltjen J, Schmidt J, and Comets E (2021) Taking kinetic evaluations of degradation data to the next level with nonlinear mixed-effects models. Environments 8 (8) 71 doi:10.3390/environments8080071 +
+Ranke J, Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical Degradation Data Environments 6 (12) 124 doi:10.3390/environments6120124 +
+Ranke J, Wöltjen J, Meinecke S (2018) Comparison of software tools for kinetic evaluation of chemical degradation data Environmental Sciences Europe 30 17 doi:10.1186/s12302-018-0145-1 +

diff --git a/docs/dev/news/index.html b/docs/dev/news/index.html index e2b44bf5..6127ebc6 100644 --- a/docs/dev/news/index.html +++ b/docs/dev/news/index.html @@ -90,7 +90,11 @@

‘R/mhmkin.R’: Allow an ‘illparms.mhmkin’ object or a list with suitable dimensions as value of the argument ‘no_random_effects’, making it possible to exclude random effects that were ill-defined in simpler variants of the set of degradation models. Remove the possibility to exclude random effects based on separate fits, as it did not work well.
‘R/summary.saem.mmkin.R’: List all initial parameter values in the summary, including random effects and error model parameters. Avoid redundant warnings that occurred in the calculation of correlations of the fixed effects in the case that the Fisher information matrix could not be inverted.
‘R/summary.saem.mmkin.R’: List all initial parameter values in the summary, including random effects and error model parameters. Avoid redundant warnings that occurred in the calculation of correlations of the fixed effects in the case that the Fisher information matrix could not be inverted. List correlations of random effects if specified by the user in the covariance model.
‘R/parplot.R’: Possibility to select the top ‘llquant’ fraction of the fits for the parameter plots, and improved legend text.
‘R/illparms.R’: Also check if confidence intervals for slope parameters in covariate models include zero. Only implemented for fits obtained with the saemix backend.
‘R/parplot.R’: Make the function work also in the case that some of the multistart runs failed.
‘R/intervals.R’: Include correlations of random effects in the model in case there are any.

@@ -140,7 +144,8 @@

‘dimethenamid_2018’: Correct the data for the Borstel soil. The five observations from Staudenmaier (2013) that were previously stored as “Borstel 2” are actually just a subset of the 16 observations in “Borstel 1” which is now simply “Borstel”

‘dimethenamid_2018’: Correct the data for the Borstel soil. The five observations from Staudenmaier (2013) that were previously stored as “Borstel 2” are actually just a subset of the 16 observations in “Borstel 1” which is now simply “Borstel”

All plotting functions setting graphical parameters: Use on.exit() for resetting graphical parameters

Review and update README, the ‘Introduction to mkin’ vignette and some of the help pages

Review and update README, the ‘Introduction to mkin’ vignette and some of the help pages

‘mkinfit’: Keep model names stored in ‘mkinmod’ objects, avoiding their loss in ‘gmkin’

‘mkinfit’: Keep model names stored in ‘mkinmod’ objects, avoiding their loss in ‘gmkin’

‘confint.mmkin’, ‘nlme.mmkin’, ‘transform_odeparms’: Fix example code in dontrun sections that failed with current defaults

Increase a test tolerance to make it pass on all CRAN check machines

Increase a test tolerance to make it pass on all CRAN check machines

‘nlme.mmkin’: An nlme method for mmkin row objects and an associated S3 class with print, plot, anova and endpoint methods

Remove test_FOMC_ill-defined.R as it is too platform dependent

Remove test_FOMC_ill-defined.R as it is too platform dependent

Rename twa to max_twa_parent to avoid conflict with twa from my pfm package

New features

A twa function, calculating maximum time weighted average concentrations for the parent (SFO, FOMC and DFOP).

A twa function, calculating maximum time weighted average concentrations for the parent (SFO, FOMC and DFOP).

@@ -349,7 +359,8 @@

Bug fixes

The test test_FOMC_ill-defined failed on several architectures, so the test is now skipped

The test test_FOMC_ill-defined failed on several architectures, so the test is now skipped

@@ -383,7 +394,8 @@

Major changes

Add the argument from_max_mean to mkinfit, for fitting only the decline from the maximum observed value for models with a single observed variable

Add the argument from_max_mean to mkinfit, for fitting only the decline from the maximum observed value for models with a single observed variable

Minor changes

Add plots to compiled_models vignette

Bug fixes

-print.summary.mkinfit(): Avoid an error that occurred when printing summaries generated with mkin versions before 0.9-36

print.summary.mkinfit()

Bug fixes

-endpoints(): For DFOP and SFORB models, where optimize() is used, make use of the fact that the DT50 must be between DT50_k1 and DT50_k2 (DFOP) or DT50_b1 and DT50_b2 (SFORB), as optimize() sometimes did not find the minimum. Likewise for finding DT90 values. Also fit on the log scale to make the function more efficient.

+endpoints(): For DFOP and SFORB models, where optimize() is used, make use of the fact that the DT50 must be between DT50_k1 and DT50_k2 (DFOP) or DT50_b1 and DT50_b2 (SFORB), as optimize() sometimes did not find the minimum. Likewise for finding DT90 values. Also fit on the log scale to make the function more efficient. +

Internal changes

-DESCRIPTION, NAMESPACE, R/*.R: Import (from) stats, graphics and methods packages, and qualify some function calls for non-base packages installed with R to avoid NOTES made by R CMD check –as-cran with upcoming R versions.

+DESCRIPTION, NAMESPACE, R/*.R: Import (from) stats, graphics and methods packages, and qualify some function calls for non-base packages installed with R to avoid NOTES made by R CMD check –as-cran with upcoming R versions. +

@@ -426,7 +441,8 @@

Bug fixes

-mkinparplot(): Fix the x axis scaling for rate constants and formation fractions that got confused by the introduction of the t-values of transformed parameters.

+mkinparplot(): Fix the x axis scaling for rate constants and formation fractions that got confused by the introduction of the t-values of transformed parameters. +

@@ -438,7 +454,8 @@

Bug fixes

-mkinmod(): When generating the C code for the derivatives, only declare the time variable when it is needed and remove the ‘-W-no-unused-variable’ compiler flag as the C compiler used in the CRAN checks on Solaris does not know it.

+mkinmod(): When generating the C code for the derivatives, only declare the time variable when it is needed and remove the ‘-W-no-unused-variable’ compiler flag as the C compiler used in the CRAN checks on Solaris does not know it. +

@@ -451,13 +468,15 @@

Minor changes

Added a simple showcase vignette with an evaluation of FOCUS example dataset D

Added a simple showcase vignette with an evaluation of FOCUS example dataset D

Major changes

Switch from RUnit to testthat for testing

Switch from RUnit to testthat for testing

Bug fixes

mkinparplot(): Avoid warnings that occurred when not all confidence intervals were available in the summary of the fit

Bug fixes

The internal renaming of optimised parameters in Version 0.9-30 led to errors in the determination of the degrees of freedom for the chi2 error level calulations in mkinerrmin() used by the summary function.

The internal renaming of optimised parameters in Version 0.9-30 led to errors in the determination of the degrees of freedom for the chi2 error level calulations in mkinerrmin() used by the summary function.

New features

It is now possible to use formation fractions in combination with turning off the sink in mkinmod().

It is now possible to use formation fractions in combination with turning off the sink in mkinmod().

Major changes

The original and the transformed parameters now have different names (e.g. k_parent and log_k_parent. They also differ in how many they are when we have formation fractions but no pathway to sink.

print(x, ...)

# S3 method for saem.mmkin

illparms(object, conf.level = 0.95, random = TRUE, errmod = TRUE, ...)

illparms(

object,

conf.level = 0.95,

random = TRUE,

errmod = TRUE,

slopes = TRUE,

...

)

# S3 method for illparms.saem.mmkin

print(x, ...)

For hierarchical fits, should error model parameters be tested?

slopes

For hierarchical saem fits using saemix as backend, +should slope parameters in the covariate model(starting with 'beta_') be +tested?

Value

diff --git a/docs/dev/reference/parplot.html b/docs/dev/reference/parplot.html index 9852b694..720c0b2a 100644 --- a/docs/dev/reference/parplot.html +++ b/docs/dev/reference/parplot.html @@ -103,6 +103,7 @@ or by their medians as proposed in the paper by Duchesne et al. (2021).

parplot( object, llmin = -Inf, + llquant = NA, scale = c("best", "median"), lpos = "bottomleft", main = "", @@ -124,8 +125,14 @@ or by their medians as proposed in the paper by Duchesne et al. (2021).

The minimum likelihood of objects to be shown

llquant

Fractional value for selecting only the fits with higher +likelihoods. Overrides 'llmin'.

+ +

scale

By default, scale parameters using the best available fit. +

By default, scale parameters using the best +available fit. If 'median', parameters are scaled using the median parameters from all fits.

diff --git a/docs/dev/reference/saem.html b/docs/dev/reference/saem.html index d18cb848..131b168b 100644 --- a/docs/dev/reference/saem.html +++ b/docs/dev/reference/saem.html @@ -432,8 +432,8 @@ using mmkin.

#> saemix version used for fitting: 3.2 #> mkin version used for pre-fitting: 1.2.2 #> R version used for fitting: 4.2.2 -#> Date of fit: Thu Nov 24 08:11:00 2022 -#> Date of summary: Thu Nov 24 08:11:01 2022 +#> Date of fit: Wed Dec 7 16:22:26 2022 +#> Date of summary: Wed Dec 7 16:22:26 2022 #> #> Equations: #> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * @@ -448,12 +448,12 @@ using mmkin.

#> #> Model predictions using solution type analytical #> -#> Fitted in 8.778 s +#> Fitted in 8.508 s #> Using 300, 100 iterations and 10 chains #> #> Variance model: Constant variance #> -#> Mean of starting values for individual parameters: +#> Starting values for degradation parameters: #> parent_0 log_k_A1 f_parent_qlogis log_k1 log_k2 #> 93.8102 -5.3734 -0.9711 -1.8799 -4.2708 #> g_qlogis @@ -462,6 +462,19 @@ using mmkin.

#> Fixed degradation parameter values: #> None #> +#> Starting values for random effects (square root of initial entries in omega): +#> parent_0 log_k_A1 f_parent_qlogis log_k1 log_k2 g_qlogis +#> parent_0 4.941 0.000 0.0000 0.000 0.000 0.0000 +#> log_k_A1 0.000 2.551 0.0000 0.000 0.000 0.0000 +#> f_parent_qlogis 0.000 0.000 0.7251 0.000 0.000 0.0000 +#> log_k1 0.000 0.000 0.0000 1.449 0.000 0.0000 +#> log_k2 0.000 0.000 0.0000 0.000 2.228 0.0000 +#> g_qlogis 0.000 0.000 0.0000 0.000 0.000 0.7814 +#> +#> Starting values for error model parameters: +#> a.1 +#> 1 +#> #> Results: #> #> Likelihood computed by importance sampling diff --git a/docs/dev/reference/summary.saem.mmkin.html b/docs/dev/reference/summary.saem.mmkin.html index a4150959..3b5869f1 100644 --- a/docs/dev/reference/summary.saem.mmkin.html +++ b/docs/dev/reference/summary.saem.mmkin.html @@ -102,7 +102,7 @@ endpoints such as formation fractions and DT50 values. Optionally

# S3 method for saem.mmkin
-summary(object, data = FALSE, verbose = FALSE, distimes = TRUE, ...)
+summary(object, data = FALSE, verbose = FALSE, distimes = TRUE, ...)
 
 # S3 method for summary.saem.mmkin
 print(x, digits = max(3, getOption("digits") - 3), verbose = x$verbose, ...)

@@ -266,36 +266,38 @@ saemix authors for the parts inherited from saemix.

#> SD.g_qlogis 0.37478 0.04490 0.70467 illparms(f_saem_dfop_sfo) #> [1] "sd(parent_0)" "sd(log_k_m1)" -f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo, covariance.model = diag(c(0, 0, 1, 1, 1, 0))) +f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo, + no_random_effect = c("parent_0", "log_k_m1")) illparms(f_saem_dfop_sfo_2) intervals(f_saem_dfop_sfo_2) #> Approximate 95% confidence intervals #> #> Fixed effects: #> lower est. upper -#> parent_0 97.57609542 100.73343868 103.89078195 -#> k_m1 0.01549292 0.01714893 0.01898194 -#> f_parent_to_m1 0.20720315 0.28358738 0.37481744 -#> k1 0.06149334 0.08733164 0.12402670 -#> k2 0.01448390 0.01699942 0.01995184 -#> g 0.45084762 0.51075839 0.57036168 +#> parent_0 98.36731429 101.42508066 104.48284703 +#> k_m1 0.01513234 0.01670094 0.01843214 +#> f_parent_to_m1 0.20221431 0.27608850 0.36461630 +#> k1 0.06915073 0.09759718 0.13774560 +#> k2 0.01487068 0.01740389 0.02036863 +#> g 0.37365671 0.48384821 0.59563299 #> #> Random effects: #> lower est. upper -#> sd(f_parent_qlogis) 0.16606767 0.4479731 0.7298784 -#> sd(log_k1) 0.12284609 0.3588446 0.5948430 -#> sd(log_k2) 0.05379723 0.1548780 0.2559588 +#> sd(f_parent_qlogis) 0.16439770 0.4427585 0.7211193 +#> sd(log_k1) 0.08304243 0.3345213 0.5860002 +#> sd(log_k2) 0.03146410 0.1490210 0.2665779 +#> sd(g_qlogis) 0.06216385 0.4023430 0.7425221 #> #> -#> lower est. upper -#> a.1 0.6811490 0.88503409 1.08891921 -#> b.1 0.0676515 0.08336272 0.09907394 -summary(f_saem_dfop_sfo_2, data = TRUE) +#> lower est. upper +#> a.1 0.67696663 0.87777355 1.07858048 +#> b.1 0.06363957 0.07878001 0.09392044 +summary(f_saem_dfop_sfo_2, data = TRUE) #> saemix version used for fitting: 3.2 #> mkin version used for pre-fitting: 1.2.2 #> R version used for fitting: 4.2.2 -#> Date of fit: Thu Nov 24 08:11:52 2022 -#> Date of summary: Thu Nov 24 08:11:52 2022 +#> Date of fit: Thu Dec 15 14:47:14 2022 +#> Date of summary: Thu Dec 15 14:47:14 2022 #> #> Equations: #> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 * @@ -310,12 +312,12 @@ saemix authors for the parts inherited from saemix.

#> #> Model predictions using solution type analytical #> -#> Fitted in 26.242 s +#> Fitted in 9.623 s #> Using 300, 100 iterations and 10 chains #> #> Variance model: Two-component variance function #> -#> Mean of starting values for individual parameters: +#> Starting values for degradation parameters: #> parent_0 log_k_m1 f_parent_qlogis log_k1 log_k2 #> 101.65645 -4.05368 -0.94311 -2.35943 -4.07006 #> g_qlogis @@ -324,237 +326,291 @@ saemix authors for the parts inherited from saemix.

#> Fixed degradation parameter values: #> None #> +#> Starting values for random effects (square root of initial entries in omega): +#> parent_0 log_k_m1 f_parent_qlogis log_k1 log_k2 g_qlogis +#> parent_0 6.742 0.0000 0.0000 0.0000 0.0000 0.000 +#> log_k_m1 0.000 0.2236 0.0000 0.0000 0.0000 0.000 +#> f_parent_qlogis 0.000 0.0000 0.5572 0.0000 0.0000 0.000 +#> log_k1 0.000 0.0000 0.0000 0.8031 0.0000 0.000 +#> log_k2 0.000 0.0000 0.0000 0.0000 0.2931 0.000 +#> g_qlogis 0.000 0.0000 0.0000 0.0000 0.0000 0.807 +#> +#> Starting values for error model parameters: +#> a.1 b.1 +#> 1 1 +#> #> Results: #> #> Likelihood computed by importance sampling -#> AIC BIC logLik -#> 809.5 805.2 -393.7 +#> AIC BIC logLik +#> 807 802.3 -391.5 #> #> Optimised parameters: #> est. lower upper -#> parent_0 100.73344 97.57610 103.89078 -#> log_k_m1 -4.06582 -4.16737 -3.96427 -#> f_parent_qlogis -0.92674 -1.34187 -0.51160 -#> log_k1 -2.43804 -2.78883 -2.08726 -#> log_k2 -4.07458 -4.23472 -3.91443 -#> g_qlogis 0.04304 -0.19725 0.28333 -#> a.1 0.88503 0.68115 1.08892 -#> b.1 0.08336 0.06765 0.09907 -#> SD.f_parent_qlogis 0.44797 0.16607 0.72988 -#> SD.log_k1 0.35884 0.12285 0.59484 -#> SD.log_k2 0.15488 0.05380 0.25596 +#> parent_0 101.42508 98.36731 104.48285 +#> log_k_m1 -4.09229 -4.19092 -3.99366 +#> f_parent_qlogis -0.96395 -1.37251 -0.55538 +#> log_k1 -2.32691 -2.67147 -1.98235 +#> log_k2 -4.05106 -4.20836 -3.89376 +#> g_qlogis -0.06463 -0.51656 0.38730 +#> a.1 0.87777 0.67697 1.07858 +#> b.1 0.07878 0.06364 0.09392 +#> SD.f_parent_qlogis 0.44276 0.16440 0.72112 +#> SD.log_k1 0.33452 0.08304 0.58600 +#> SD.log_k2 0.14902 0.03146 0.26658 +#> SD.g_qlogis 0.40234 0.06216 0.74252 #> #> Correlation: #> parnt_0 lg_k_m1 f_prnt_ log_k1 log_k2 -#> log_k_m1 -0.4698 -#> f_parent_qlogis -0.2461 0.2709 -#> log_k1 0.1572 -0.1517 -0.0648 -#> log_k2 -0.0023 0.0835 0.0125 0.1420 -#> g_qlogis 0.2314 -0.2337 -0.0755 -0.2762 -0.4797 +#> log_k_m1 -0.4693 +#> f_parent_qlogis -0.2378 0.2595 +#> log_k1 0.1720 -0.1593 -0.0669 +#> log_k2 0.0179 0.0594 0.0035 0.1995 +#> g_qlogis 0.1073 -0.1060 -0.0322 -0.2299 -0.3168 #> #> Random effects: -#> est. lower upper -#> SD.f_parent_qlogis 0.4480 0.1661 0.7299 -#> SD.log_k1 0.3588 0.1228 0.5948 -#> SD.log_k2 0.1549 0.0538 0.2560 +#> est. lower upper +#> SD.f_parent_qlogis 0.4428 0.16440 0.7211 +#> SD.log_k1 0.3345 0.08304 0.5860 +#> SD.log_k2 0.1490 0.03146 0.2666 +#> SD.g_qlogis 0.4023 0.06216 0.7425 #> #> Variance model: #> est. lower upper -#> a.1 0.88503 0.68115 1.08892 -#> b.1 0.08336 0.06765 0.09907 +#> a.1 0.87777 0.67697 1.07858 +#> b.1 0.07878 0.06364 0.09392 #> #> Backtransformed parameters: -#> est. lower upper -#> parent_0 100.73344 97.57610 103.89078 -#> k_m1 0.01715 0.01549 0.01898 -#> f_parent_to_m1 0.28359 0.20720 0.37482 -#> k1 0.08733 0.06149 0.12403 -#> k2 0.01700 0.01448 0.01995 -#> g 0.51076 0.45085 0.57036 +#> est. lower upper +#> parent_0 101.4251 98.36731 104.48285 +#> k_m1 0.0167 0.01513 0.01843 +#> f_parent_to_m1 0.2761 0.20221 0.36462 +#> k1 0.0976 0.06915 0.13775 +#> k2 0.0174 0.01487 0.02037 +#> g 0.4838 0.37366 0.59563 #> #> Resulting formation fractions: #> ff -#> parent_m1 0.2836 -#> parent_sink 0.7164 +#> parent_m1 0.2761 +#> parent_sink 0.7239 #> #> Estimated disappearance times: #> DT50 DT90 DT50back DT50_k1 DT50_k2 -#> parent 15.94 93.48 28.14 7.937 40.77 -#> m1 40.42 134.27 NA NA NA +#> parent 15.54 94.33 28.4 7.102 39.83 +#> m1 41.50 137.87 NA NA NA #> #> Data: -#> ds name time observed predicted residual std standardized -#> ds 1 parent 0 89.8 1.007e+02 -10.93344 8.4439 -1.29483 -#> ds 1 parent 0 104.1 1.007e+02 3.36656 8.4439 0.39870 -#> ds 1 parent 1 88.7 9.591e+01 -7.20789 8.0440 -0.89606 -#> ds 1 parent 1 95.5 9.591e+01 -0.40789 8.0440 -0.05071 -#> ds 1 parent 3 81.8 8.712e+01 -5.31561 7.3159 -0.72658 -#> ds 1 parent 3 94.5 8.712e+01 7.38439 7.3159 1.00936 -#> ds 1 parent 7 71.5 7.246e+01 -0.95675 6.1047 -0.15672 -#> ds 1 parent 7 70.3 7.246e+01 -2.15675 6.1047 -0.35329 -#> ds 1 parent 14 54.2 5.382e+01 0.38143 4.5729 0.08341 -#> ds 1 parent 14 49.6 5.382e+01 -4.21857 4.5729 -0.92251 -#> ds 1 parent 28 31.5 3.230e+01 -0.80120 2.8344 -0.28267 -#> ds 1 parent 28 28.8 3.230e+01 -3.50120 2.8344 -1.23524 -#> ds 1 parent 60 12.1 1.307e+01 -0.97165 1.4038 -0.69215 -#> ds 1 parent 60 13.6 1.307e+01 0.52835 1.4038 0.37637 -#> ds 1 parent 90 6.2 6.353e+00 -0.15285 1.0314 -0.14820 -#> ds 1 parent 90 8.3 6.353e+00 1.94715 1.0314 1.88790 -#> ds 1 parent 120 2.2 3.175e+00 -0.97462 0.9238 -1.05506 -#> ds 1 parent 120 2.4 3.175e+00 -0.77462 0.9238 -0.83855 -#> ds 1 m1 1 0.3 1.183e+00 -0.88350 0.8905 -0.99212 -#> ds 1 m1 1 0.2 1.183e+00 -0.98350 0.8905 -1.10441 -#> ds 1 m1 3 2.2 3.281e+00 -1.08106 0.9263 -1.16703 -#> ds 1 m1 3 3.0 3.281e+00 -0.28106 0.9263 -0.30341 -#> ds 1 m1 7 6.5 6.564e+00 -0.06353 1.0405 -0.06106 -#> ds 1 m1 7 5.0 6.564e+00 -1.56353 1.0405 -1.50266 -#> ds 1 m1 14 10.2 1.015e+01 0.05147 1.2243 0.04204 -#> ds 1 m1 14 9.5 1.015e+01 -0.64853 1.2243 -0.52970 -#> ds 1 m1 28 12.2 1.265e+01 -0.44824 1.3766 -0.32561 -#> ds 1 m1 28 13.4 1.265e+01 0.75176 1.3766 0.54610 -#> ds 1 m1 60 11.8 1.078e+01 1.02355 1.2611 0.81165 -#> ds 1 m1 60 13.2 1.078e+01 2.42355 1.2611 1.92181 -#> ds 1 m1 90 6.6 7.698e+00 -1.09840 1.0932 -1.00474 -#> ds 1 m1 90 9.3 7.698e+00 1.60160 1.0932 1.46502 -#> ds 1 m1 120 3.5 5.199e+00 -1.69853 0.9854 -1.72363 -#> ds 1 m1 120 5.4 5.199e+00 0.20147 0.9854 0.20445 -#> ds 2 parent 0 118.0 1.007e+02 17.26656 8.4439 2.04485 -#> ds 2 parent 0 99.8 1.007e+02 -0.93344 8.4439 -0.11055 -#> ds 2 parent 1 90.2 9.584e+01 -5.63852 8.0382 -0.70146 -#> ds 2 parent 1 94.6 9.584e+01 -1.23852 8.0382 -0.15408 -#> ds 2 parent 3 96.1 8.706e+01 9.04068 7.3113 1.23654 -#> ds 2 parent 3 78.4 8.706e+01 -8.65932 7.3113 -1.18438 -#> ds 2 parent 7 77.9 7.286e+01 5.04438 6.1376 0.82188 -#> ds 2 parent 7 77.7 7.286e+01 4.84438 6.1376 0.78930 -#> ds 2 parent 14 56.0 5.567e+01 0.33336 4.7242 0.07057 -#> ds 2 parent 14 54.7 5.567e+01 -0.96664 4.7242 -0.20462 -#> ds 2 parent 28 36.6 3.705e+01 -0.44800 3.2127 -0.13944 -#> ds 2 parent 28 36.8 3.705e+01 -0.24800 3.2127 -0.07719 -#> ds 2 parent 60 22.1 2.008e+01 2.01984 1.8935 1.06672 -#> ds 2 parent 60 24.7 2.008e+01 4.61984 1.8935 2.43984 -#> ds 2 parent 90 12.4 1.253e+01 -0.12814 1.3689 -0.09360 -#> ds 2 parent 90 10.8 1.253e+01 -1.72814 1.3689 -1.26238 -#> ds 2 parent 120 6.8 7.916e+00 -1.11595 1.1040 -1.01085 -#> ds 2 parent 120 7.9 7.916e+00 -0.01595 1.1040 -0.01445 -#> ds 2 m1 1 1.3 1.317e+00 -0.01669 0.8918 -0.01871 -#> ds 2 m1 3 3.7 3.613e+00 0.08699 0.9349 0.09305 -#> ds 2 m1 3 4.7 3.613e+00 1.08699 0.9349 1.16270 -#> ds 2 m1 7 8.1 7.092e+00 1.00781 1.0643 0.94688 -#> ds 2 m1 7 7.9 7.092e+00 0.80781 1.0643 0.75897 -#> ds 2 m1 14 10.1 1.066e+01 -0.56458 1.2545 -0.45006 -#> ds 2 m1 14 10.3 1.066e+01 -0.36458 1.2545 -0.29063 -#> ds 2 m1 28 10.7 1.281e+01 -2.11106 1.3870 -1.52201 -#> ds 2 m1 28 12.2 1.281e+01 -0.61106 1.3870 -0.44055 -#> ds 2 m1 60 10.7 1.078e+01 -0.08464 1.2616 -0.06709 -#> ds 2 m1 60 12.5 1.078e+01 1.71536 1.2616 1.35970 -#> ds 2 m1 90 9.1 8.013e+00 1.08684 1.1088 0.98016 -#> ds 2 m1 90 7.4 8.013e+00 -0.61316 1.1088 -0.55298 -#> ds 2 m1 120 6.1 5.749e+00 0.35063 1.0065 0.34838 -#> ds 2 m1 120 4.5 5.749e+00 -1.24937 1.0065 -1.24133 -#> ds 3 parent 0 106.2 1.007e+02 5.46656 8.4439 0.64740 -#> ds 3 parent 0 106.9 1.007e+02 6.16656 8.4439 0.73030 -#> ds 3 parent 1 107.4 9.369e+01 13.70530 7.8606 1.74354 -#> ds 3 parent 1 96.1 9.369e+01 2.40530 7.8606 0.30599 -#> ds 3 parent 3 79.4 8.185e+01 -2.45363 6.8807 -0.35660 -#> ds 3 parent 3 82.6 8.185e+01 0.74637 6.8807 0.10847 -#> ds 3 parent 7 63.9 6.487e+01 -0.97153 5.4798 -0.17729 -#> ds 3 parent 7 62.4 6.487e+01 -2.47153 5.4798 -0.45103 -#> ds 3 parent 14 51.0 4.791e+01 3.09024 4.0908 0.75542 -#> ds 3 parent 14 47.1 4.791e+01 -0.80976 4.0908 -0.19795 -#> ds 3 parent 28 36.1 3.313e+01 2.97112 2.9001 1.02450 -#> ds 3 parent 28 36.6 3.313e+01 3.47112 2.9001 1.19691 -#> ds 3 parent 60 20.1 1.927e+01 0.83265 1.8339 0.45404 -#> ds 3 parent 60 19.8 1.927e+01 0.53265 1.8339 0.29045 -#> ds 3 parent 90 11.3 1.203e+01 -0.72783 1.3374 -0.54421 -#> ds 3 parent 90 10.7 1.203e+01 -1.32783 1.3374 -0.99284 -#> ds 3 parent 120 8.2 7.516e+00 0.68382 1.0844 0.63061 -#> ds 3 parent 120 7.3 7.516e+00 -0.21618 1.0844 -0.19936 -#> ds 3 m1 0 0.8 -9.948e-14 0.80000 0.8850 0.90392 -#> ds 3 m1 1 1.8 1.682e+00 0.11759 0.8961 0.13123 -#> ds 3 m1 1 2.3 1.682e+00 0.61759 0.8961 0.68921 -#> ds 3 m1 3 4.2 4.431e+00 -0.23052 0.9590 -0.24037 -#> ds 3 m1 3 4.1 4.431e+00 -0.33052 0.9590 -0.34465 -#> ds 3 m1 7 6.8 8.084e+00 -1.28422 1.1124 -1.15445 -#> ds 3 m1 7 10.1 8.084e+00 2.01578 1.1124 1.81208 -#> ds 3 m1 14 11.4 1.100e+01 0.40274 1.2743 0.31606 -#> ds 3 m1 14 12.8 1.100e+01 1.80274 1.2743 1.41474 -#> ds 3 m1 28 11.5 1.176e+01 -0.25977 1.3207 -0.19669 -#> ds 3 m1 28 10.6 1.176e+01 -1.15977 1.3207 -0.87813 -#> ds 3 m1 60 7.5 9.277e+00 -1.77696 1.1753 -1.51190 -#> ds 3 m1 60 8.6 9.277e+00 -0.67696 1.1753 -0.57598 -#> ds 3 m1 90 7.3 6.883e+00 0.41708 1.0548 0.39542 -#> ds 3 m1 90 8.1 6.883e+00 1.21708 1.0548 1.15389 -#> ds 3 m1 120 5.3 4.948e+00 0.35179 0.9764 0.36028 -#> ds 3 m1 120 3.8 4.948e+00 -1.14821 0.9764 -1.17591 -#> ds 4 parent 0 104.7 1.007e+02 3.96656 8.4439 0.46975 -#> ds 4 parent 0 88.3 1.007e+02 -12.43344 8.4439 -1.47247 -#> ds 4 parent 1 94.2 9.738e+01 -3.18358 8.1663 -0.38985 -#> ds 4 parent 1 94.6 9.738e+01 -2.78358 8.1663 -0.34086 -#> ds 4 parent 3 78.1 9.110e+01 -12.99595 7.6454 -1.69984 -#> ds 4 parent 3 96.5 9.110e+01 5.40405 7.6454 0.70684 -#> ds 4 parent 7 76.2 8.000e+01 -3.79797 6.7273 -0.56456 -#> ds 4 parent 7 77.8 8.000e+01 -2.19797 6.7273 -0.32672 -#> ds 4 parent 14 70.8 6.446e+01 6.34396 5.4456 1.16496 -#> ds 4 parent 14 67.3 6.446e+01 2.84396 5.4456 0.52225 -#> ds 4 parent 28 43.1 4.359e+01 -0.48960 3.7400 -0.13091 -#> ds 4 parent 28 45.1 4.359e+01 1.51040 3.7400 0.40385 -#> ds 4 parent 60 21.3 2.095e+01 0.35282 1.9577 0.18022 -#> ds 4 parent 60 23.5 2.095e+01 2.55282 1.9577 1.30400 -#> ds 4 parent 90 11.8 1.188e+01 -0.07874 1.3281 -0.05929 -#> ds 4 parent 90 12.1 1.188e+01 0.22126 1.3281 0.16660 -#> ds 4 parent 120 7.0 7.072e+00 -0.07245 1.0634 -0.06813 -#> ds 4 parent 120 6.2 7.072e+00 -0.87245 1.0634 -0.82041 -#> ds 4 m1 0 1.6 5.684e-14 1.60000 0.8850 1.80784 -#> ds 4 m1 1 0.9 6.960e-01 0.20399 0.8869 0.23000 -#> ds 4 m1 3 3.7 1.968e+00 1.73240 0.9001 1.92466 -#> ds 4 m1 3 2.0 1.968e+00 0.03240 0.9001 0.03599 -#> ds 4 m1 7 3.6 4.083e+00 -0.48287 0.9482 -0.50924 -#> ds 4 m1 7 3.8 4.083e+00 -0.28287 0.9482 -0.29832 -#> ds 4 m1 14 7.1 6.682e+00 0.41836 1.0457 0.40007 -#> ds 4 m1 14 6.6 6.682e+00 -0.08164 1.0457 -0.07807 -#> ds 4 m1 28 9.5 9.103e+00 0.39733 1.1658 0.34082 -#> ds 4 m1 28 9.3 9.103e+00 0.19733 1.1658 0.16926 -#> ds 4 m1 60 8.3 8.750e+00 -0.44979 1.1469 -0.39218 -#> ds 4 m1 60 9.0 8.750e+00 0.25021 1.1469 0.21817 -#> ds 4 m1 90 6.6 6.673e+00 -0.07285 1.0453 -0.06969 -#> ds 4 m1 90 7.7 6.673e+00 1.02715 1.0453 0.98261 -#> ds 4 m1 120 3.7 4.757e+00 -1.05747 0.9698 -1.09036 -#> ds 4 m1 120 3.5 4.757e+00 -1.25747 0.9698 -1.29658 -#> ds 5 parent 0 110.4 1.007e+02 9.66656 8.4439 1.14480 -#> ds 5 parent 0 112.1 1.007e+02 11.36656 8.4439 1.34612 -#> ds 5 parent 1 93.5 9.395e+01 -0.45394 7.8821 -0.05759 -#> ds 5 parent 1 91.0 9.395e+01 -2.95394 7.8821 -0.37477 -#> ds 5 parent 3 71.0 8.245e+01 -11.44783 6.9298 -1.65197 -#> ds 5 parent 3 89.7 8.245e+01 7.25217 6.9298 1.04652 -#> ds 5 parent 7 60.4 6.567e+01 -5.27002 5.5455 -0.95032 -#> ds 5 parent 7 59.1 6.567e+01 -6.57002 5.5455 -1.18475 -#> ds 5 parent 14 56.5 4.847e+01 8.03029 4.1364 1.94139 -#> ds 5 parent 14 47.0 4.847e+01 -1.46971 4.1364 -0.35532 -#> ds 5 parent 28 30.2 3.309e+01 -2.89206 2.8971 -0.99825 -#> ds 5 parent 28 23.9 3.309e+01 -9.19206 2.8971 -3.17281 -#> ds 5 parent 60 17.0 1.891e+01 -1.90623 1.8076 -1.05458 -#> ds 5 parent 60 18.7 1.891e+01 -0.20623 1.8076 -0.11409 -#> ds 5 parent 90 11.3 1.168e+01 -0.38263 1.3160 -0.29076 -#> ds 5 parent 90 11.9 1.168e+01 0.21737 1.3160 0.16518 -#> ds 5 parent 120 9.0 7.230e+00 1.77031 1.0708 1.65333 -#> ds 5 parent 120 8.1 7.230e+00 0.87031 1.0708 0.81280 -#> ds 5 m1 0 0.7 -5.116e-13 0.70000 0.8850 0.79093 -#> ds 5 m1 1 3.0 3.244e+00 -0.24430 0.9254 -0.26398 -#> ds 5 m1 1 2.6 3.244e+00 -0.64430 0.9254 -0.69621 -#> ds 5 m1 3 5.1 8.592e+00 -3.49175 1.1385 -3.06686 -#> ds 5 m1 3 7.5 8.592e+00 -1.09175 1.1385 -0.95890 -#> ds 5 m1 7 16.5 1.583e+01 0.66887 1.5890 0.42093 -#> ds 5 m1 7 19.0 1.583e+01 3.16887 1.5890 1.99424 -#> ds 5 m1 14 22.9 2.181e+01 1.08658 2.0224 0.53728 -#> ds 5 m1 14 23.2 2.181e+01 1.38658 2.0224 0.68562 -#> ds 5 m1 28 22.2 2.364e+01 -1.43659 2.1600 -0.66508 -#> ds 5 m1 28 24.4 2.364e+01 0.76341 2.1600 0.35342 -#> ds 5 m1 60 15.5 1.873e+01 -3.23377 1.7950 -1.80150 -#> ds 5 m1 60 19.8 1.873e+01 1.06623 1.7950 0.59398 -#> ds 5 m1 90 14.9 1.387e+01 1.03117 1.4560 0.70822 -#> ds 5 m1 90 14.2 1.387e+01 0.33117 1.4560 0.22745 -#> ds 5 m1 120 10.9 9.937e+00 0.96270 1.2122 0.79415 -#> ds 5 m1 120 10.4 9.937e+00 0.46270 1.2122 0.38169 +#> ds name time observed predicted residual std standardized +#> ds 1 parent 0 89.8 1.014e+02 -11.62508 8.0383 -1.44620 +#> ds 1 parent 0 104.1 1.014e+02 2.67492 8.0383 0.33277 +#> ds 1 parent 1 88.7 9.650e+01 -7.80311 7.6530 -1.01961 +#> ds 1 parent 1 95.5 9.650e+01 -1.00311 7.6530 -0.13107 +#> ds 1 parent 3 81.8 8.753e+01 -5.72638 6.9510 -0.82382 +#> ds 1 parent 3 94.5 8.753e+01 6.97362 6.9510 1.00326 +#> ds 1 parent 7 71.5 7.254e+01 -1.04133 5.7818 -0.18010 +#> ds 1 parent 7 70.3 7.254e+01 -2.24133 5.7818 -0.38765 +#> ds 1 parent 14 54.2 5.349e+01 0.71029 4.3044 0.16502 +#> ds 1 parent 14 49.6 5.349e+01 -3.88971 4.3044 -0.90366 +#> ds 1 parent 28 31.5 3.167e+01 -0.16616 2.6446 -0.06283 +#> ds 1 parent 28 28.8 3.167e+01 -2.86616 2.6446 -1.08379 +#> ds 1 parent 60 12.1 1.279e+01 -0.69287 1.3365 -0.51843 +#> ds 1 parent 60 13.6 1.279e+01 0.80713 1.3365 0.60392 +#> ds 1 parent 90 6.2 6.397e+00 -0.19718 1.0122 -0.19481 +#> ds 1 parent 90 8.3 6.397e+00 1.90282 1.0122 1.87996 +#> ds 1 parent 120 2.2 3.323e+00 -1.12320 0.9160 -1.22623 +#> ds 1 parent 120 2.4 3.323e+00 -0.92320 0.9160 -1.00788 +#> ds 1 m1 1 0.3 1.179e+00 -0.87919 0.8827 -0.99605 +#> ds 1 m1 1 0.2 1.179e+00 -0.97919 0.8827 -1.10935 +#> ds 1 m1 3 2.2 3.273e+00 -1.07272 0.9149 -1.17256 +#> ds 1 m1 3 3.0 3.273e+00 -0.27272 0.9149 -0.29811 +#> ds 1 m1 7 6.5 6.559e+00 -0.05872 1.0186 -0.05765 +#> ds 1 m1 7 5.0 6.559e+00 -1.55872 1.0186 -1.53032 +#> ds 1 m1 14 10.2 1.016e+01 0.03787 1.1880 0.03188 +#> ds 1 m1 14 9.5 1.016e+01 -0.66213 1.1880 -0.55734 +#> ds 1 m1 28 12.2 1.268e+01 -0.47913 1.3297 -0.36032 +#> ds 1 m1 28 13.4 1.268e+01 0.72087 1.3297 0.54211 +#> ds 1 m1 60 11.8 1.078e+01 1.02493 1.2211 0.83936 +#> ds 1 m1 60 13.2 1.078e+01 2.42493 1.2211 1.98588 +#> ds 1 m1 90 6.6 7.705e+00 -1.10464 1.0672 -1.03509 +#> ds 1 m1 90 9.3 7.705e+00 1.59536 1.0672 1.49491 +#> ds 1 m1 120 3.5 5.236e+00 -1.73617 0.9699 -1.79010 +#> ds 1 m1 120 5.4 5.236e+00 0.16383 0.9699 0.16892 +#> ds 2 parent 0 118.0 1.014e+02 16.57492 8.0383 2.06198 +#> ds 2 parent 0 99.8 1.014e+02 -1.62508 8.0383 -0.20217 +#> ds 2 parent 1 90.2 9.599e+01 -5.79045 7.6129 -0.76061 +#> ds 2 parent 1 94.6 9.599e+01 -1.39045 7.6129 -0.18264 +#> ds 2 parent 3 96.1 8.652e+01 9.57931 6.8724 1.39388 +#> ds 2 parent 3 78.4 8.652e+01 -8.12069 6.8724 -1.18164 +#> ds 2 parent 7 77.9 7.197e+01 5.93429 5.7370 1.03439 +#> ds 2 parent 7 77.7 7.197e+01 5.73429 5.7370 0.99953 +#> ds 2 parent 14 56.0 5.555e+01 0.44657 4.4637 0.10005 +#> ds 2 parent 14 54.7 5.555e+01 -0.85343 4.4637 -0.19120 +#> ds 2 parent 28 36.6 3.853e+01 -1.93170 3.1599 -0.61132 +#> ds 2 parent 28 36.8 3.853e+01 -1.73170 3.1599 -0.54803 +#> ds 2 parent 60 22.1 2.110e+01 1.00360 1.8795 0.53396 +#> ds 2 parent 60 24.7 2.110e+01 3.60360 1.8795 1.91728 +#> ds 2 parent 90 12.4 1.250e+01 -0.09712 1.3190 -0.07363 +#> ds 2 parent 90 10.8 1.250e+01 -1.69712 1.3190 -1.28667 +#> ds 2 parent 120 6.8 7.419e+00 -0.61913 1.0546 -0.58709 +#> ds 2 parent 120 7.9 7.419e+00 0.48087 1.0546 0.45599 +#> ds 2 m1 1 1.3 1.422e+00 -0.12194 0.8849 -0.13781 +#> ds 2 m1 3 3.7 3.831e+00 -0.13149 0.9282 -0.14166 +#> ds 2 m1 3 4.7 3.831e+00 0.86851 0.9282 0.93567 +#> ds 2 m1 7 8.1 7.292e+00 0.80812 1.0490 0.77034 +#> ds 2 m1 7 7.9 7.292e+00 0.60812 1.0490 0.57969 +#> ds 2 m1 14 10.1 1.055e+01 -0.45332 1.2090 -0.37495 +#> ds 2 m1 14 10.3 1.055e+01 -0.25332 1.2090 -0.20953 +#> ds 2 m1 28 10.7 1.230e+01 -1.59960 1.3074 -1.22347 +#> ds 2 m1 28 12.2 1.230e+01 -0.09960 1.3074 -0.07618 +#> ds 2 m1 60 10.7 1.065e+01 0.05342 1.2141 0.04400 +#> ds 2 m1 60 12.5 1.065e+01 1.85342 1.2141 1.52661 +#> ds 2 m1 90 9.1 8.196e+00 0.90368 1.0897 0.82930 +#> ds 2 m1 90 7.4 8.196e+00 -0.79632 1.0897 -0.73078 +#> ds 2 m1 120 6.1 5.997e+00 0.10252 0.9969 0.10284 +#> ds 2 m1 120 4.5 5.997e+00 -1.49748 0.9969 -1.50220 +#> ds 3 parent 0 106.2 1.014e+02 4.77492 8.0383 0.59402 +#> ds 3 parent 0 106.9 1.014e+02 5.47492 8.0383 0.68110 +#> ds 3 parent 1 107.4 9.390e+01 13.49935 7.4494 1.81214 +#> ds 3 parent 1 96.1 9.390e+01 2.19935 7.4494 0.29524 +#> ds 3 parent 3 79.4 8.152e+01 -2.12307 6.4821 -0.32753 +#> ds 3 parent 3 82.6 8.152e+01 1.07693 6.4821 0.16614 +#> ds 3 parent 7 63.9 6.446e+01 -0.55834 5.1533 -0.10834 +#> ds 3 parent 7 62.4 6.446e+01 -2.05834 5.1533 -0.39942 +#> ds 3 parent 14 51.0 4.826e+01 2.74073 3.9019 0.70241 +#> ds 3 parent 14 47.1 4.826e+01 -1.15927 3.9019 -0.29711 +#> ds 3 parent 28 36.1 3.424e+01 1.86399 2.8364 0.65718 +#> ds 3 parent 28 36.6 3.424e+01 2.36399 2.8364 0.83346 +#> ds 3 parent 60 20.1 1.968e+01 0.42172 1.7815 0.23672 +#> ds 3 parent 60 19.8 1.968e+01 0.12172 1.7815 0.06833 +#> ds 3 parent 90 11.3 1.195e+01 -0.64633 1.2869 -0.50222 +#> ds 3 parent 90 10.7 1.195e+01 -1.24633 1.2869 -0.96844 +#> ds 3 parent 120 8.2 7.255e+00 0.94532 1.0474 0.90251 +#> ds 3 parent 120 7.3 7.255e+00 0.04532 1.0474 0.04327 +#> ds 3 m1 0 0.8 2.956e-11 0.80000 0.8778 0.91140 +#> ds 3 m1 1 1.8 1.758e+00 0.04187 0.8886 0.04712 +#> ds 3 m1 1 2.3 1.758e+00 0.54187 0.8886 0.60978 +#> ds 3 m1 3 4.2 4.567e+00 -0.36697 0.9486 -0.38683 +#> ds 3 m1 3 4.1 4.567e+00 -0.46697 0.9486 -0.49224 +#> ds 3 m1 7 6.8 8.151e+00 -1.35124 1.0876 -1.24242 +#> ds 3 m1 7 10.1 8.151e+00 1.94876 1.0876 1.79182 +#> ds 3 m1 14 11.4 1.083e+01 0.57098 1.2240 0.46647 +#> ds 3 m1 14 12.8 1.083e+01 1.97098 1.2240 1.61022 +#> ds 3 m1 28 11.5 1.147e+01 0.03175 1.2597 0.02520 +#> ds 3 m1 28 10.6 1.147e+01 -0.86825 1.2597 -0.68928 +#> ds 3 m1 60 7.5 9.298e+00 -1.79834 1.1433 -1.57298 +#> ds 3 m1 60 8.6 9.298e+00 -0.69834 1.1433 -0.61083 +#> ds 3 m1 90 7.3 7.038e+00 0.26249 1.0382 0.25283 +#> ds 3 m1 90 8.1 7.038e+00 1.06249 1.0382 1.02340 +#> ds 3 m1 120 5.3 5.116e+00 0.18417 0.9659 0.19068 +#> ds 3 m1 120 3.8 5.116e+00 -1.31583 0.9659 -1.36232 +#> ds 4 parent 0 104.7 1.014e+02 3.27492 8.0383 0.40741 +#> ds 4 parent 0 88.3 1.014e+02 -13.12508 8.0383 -1.63281 +#> ds 4 parent 1 94.2 9.781e+01 -3.61183 7.7555 -0.46572 +#> ds 4 parent 1 94.6 9.781e+01 -3.21183 7.7555 -0.41414 +#> ds 4 parent 3 78.1 9.110e+01 -13.00467 7.2307 -1.79853 +#> ds 4 parent 3 96.5 9.110e+01 5.39533 7.2307 0.74617 +#> ds 4 parent 7 76.2 7.951e+01 -3.30511 6.3246 -0.52258 +#> ds 4 parent 7 77.8 7.951e+01 -1.70511 6.3246 -0.26960 +#> ds 4 parent 14 70.8 6.376e+01 7.03783 5.0993 1.38016 +#> ds 4 parent 14 67.3 6.376e+01 3.53783 5.0993 0.69379 +#> ds 4 parent 28 43.1 4.340e+01 -0.30456 3.5303 -0.08627 +#> ds 4 parent 28 45.1 4.340e+01 1.69544 3.5303 0.48026 +#> ds 4 parent 60 21.3 2.142e+01 -0.12077 1.9022 -0.06349 +#> ds 4 parent 60 23.5 2.142e+01 2.07923 1.9022 1.09308 +#> ds 4 parent 90 11.8 1.207e+01 -0.26813 1.2940 -0.20721 +#> ds 4 parent 90 12.1 1.207e+01 0.03187 1.2940 0.02463 +#> ds 4 parent 120 7.0 6.954e+00 0.04554 1.0347 0.04402 +#> ds 4 parent 120 6.2 6.954e+00 -0.75446 1.0347 -0.72914 +#> ds 4 m1 0 1.6 1.990e-13 1.60000 0.8778 1.82279 +#> ds 4 m1 1 0.9 7.305e-01 0.16949 0.8797 0.19267 +#> ds 4 m1 3 3.7 2.051e+00 1.64896 0.8925 1.84753 +#> ds 4 m1 3 2.0 2.051e+00 -0.05104 0.8925 -0.05719 +#> ds 4 m1 7 3.6 4.204e+00 -0.60375 0.9382 -0.64354 +#> ds 4 m1 7 3.8 4.204e+00 -0.40375 0.9382 -0.43036 +#> ds 4 m1 14 7.1 6.760e+00 0.34021 1.0267 0.33137 +#> ds 4 m1 14 6.6 6.760e+00 -0.15979 1.0267 -0.15563 +#> ds 4 m1 28 9.5 9.011e+00 0.48856 1.1289 0.43277 +#> ds 4 m1 28 9.3 9.011e+00 0.28856 1.1289 0.25561 +#> ds 4 m1 60 8.3 8.611e+00 -0.31077 1.1093 -0.28014 +#> ds 4 m1 60 9.0 8.611e+00 0.38923 1.1093 0.35086 +#> ds 4 m1 90 6.6 6.678e+00 -0.07753 1.0233 -0.07576 +#> ds 4 m1 90 7.7 6.678e+00 1.02247 1.0233 0.99915 +#> ds 4 m1 120 3.7 4.847e+00 -1.14679 0.9572 -1.19804 +#> ds 4 m1 120 3.5 4.847e+00 -1.34679 0.9572 -1.40698 +#> ds 5 parent 0 110.4 1.014e+02 8.97492 8.0383 1.11651 +#> ds 5 parent 0 112.1 1.014e+02 10.67492 8.0383 1.32800 +#> ds 5 parent 1 93.5 9.466e+01 -1.16118 7.5089 -0.15464 +#> ds 5 parent 1 91.0 9.466e+01 -3.66118 7.5089 -0.48758 +#> ds 5 parent 3 71.0 8.302e+01 -12.01844 6.5988 -1.82130 +#> ds 5 parent 3 89.7 8.302e+01 6.68156 6.5988 1.01254 +#> ds 5 parent 7 60.4 6.563e+01 -5.22574 5.2440 -0.99652 +#> ds 5 parent 7 59.1 6.563e+01 -6.52574 5.2440 -1.24442 +#> ds 5 parent 14 56.5 4.727e+01 9.22621 3.8263 2.41128 +#> ds 5 parent 14 47.0 4.727e+01 -0.27379 3.8263 -0.07156 +#> ds 5 parent 28 30.2 3.103e+01 -0.83405 2.5977 -0.32108 +#> ds 5 parent 28 23.9 3.103e+01 -7.13405 2.5977 -2.74634 +#> ds 5 parent 60 17.0 1.800e+01 -0.99696 1.6675 -0.59787 +#> ds 5 parent 60 18.7 1.800e+01 0.70304 1.6675 0.42161 +#> ds 5 parent 90 11.3 1.167e+01 -0.36809 1.2710 -0.28961 +#> ds 5 parent 90 11.9 1.167e+01 0.23191 1.2710 0.18246 +#> ds 5 parent 120 9.0 7.595e+00 1.40496 1.0623 1.32256 +#> ds 5 parent 120 8.1 7.595e+00 0.50496 1.0623 0.47535 +#> ds 5 m1 0 0.7 0.000e+00 0.70000 0.8778 0.79747 +#> ds 5 m1 1 3.0 3.158e+00 -0.15799 0.9123 -0.17317 +#> ds 5 m1 1 2.6 3.158e+00 -0.55799 0.9123 -0.61160 +#> ds 5 m1 3 5.1 8.443e+00 -3.34286 1.1013 -3.03535 +#> ds 5 m1 3 7.5 8.443e+00 -0.94286 1.1013 -0.85613 +#> ds 5 m1 7 16.5 1.580e+01 0.69781 1.5232 0.45811 +#> ds 5 m1 7 19.0 1.580e+01 3.19781 1.5232 2.09935 +#> ds 5 m1 14 22.9 2.216e+01 0.73604 1.9543 0.37663 +#> ds 5 m1 14 23.2 2.216e+01 1.03604 1.9543 0.53014 +#> ds 5 m1 28 22.2 2.423e+01 -2.03128 2.1011 -0.96678 +#> ds 5 m1 28 24.4 2.423e+01 0.16872 2.1011 0.08030 +#> ds 5 m1 60 15.5 1.876e+01 -3.25610 1.7187 -1.89455 +#> ds 5 m1 60 19.8 1.876e+01 1.04390 1.7187 0.60739 +#> ds 5 m1 90 14.9 1.366e+01 1.23585 1.3890 0.88976 +#> ds 5 m1 90 14.2 1.366e+01 0.53585 1.3890 0.38579 +#> ds 5 m1 120 10.9 9.761e+00 1.13911 1.1670 0.97613 +#> ds 5 m1 120 10.4 9.761e+00 0.63911 1.1670 0.54767 +# Add a correlation between random effects of g and k2 +cov_model_3 <- f_saem_dfop_sfo_2$so@model@covariance.model +cov_model_3["log_k2", "g_qlogis"] <- 1 +cov_model_3["g_qlogis", "log_k2"] <- 1 +f_saem_dfop_sfo_3 <- update(f_saem_dfop_sfo, + covariance.model = cov_model_3) +intervals(f_saem_dfop_sfo_3) +#> Approximate 95% confidence intervals +#> +#> Fixed effects: +#> lower est. upper +#> parent_0 98.39888363 101.48951337 104.58014311 +#> k_m1 0.01508704 0.01665986 0.01839665 +#> f_parent_to_m1 0.20141557 0.27540583 0.36418131 +#> k1 0.07708759 0.10430866 0.14114200 +#> k2 0.01476621 0.01786384 0.02161129 +#> g 0.33679867 0.45083525 0.57028162 +#> +#> Random effects: +#> lower est. upper +#> sd(f_parent_qlogis) 0.38085375 0.4441841 0.5075145 +#> sd(log_k1) 0.04774819 0.2660384 0.4843286 +#> sd(log_k2) -0.63842736 0.1977024 1.0338321 +#> sd(g_qlogis) 0.22711289 0.4502227 0.6733326 +#> corr(log_k2,g_qlogis) -0.83271473 -0.6176939 -0.4026730 +#> +#> +#> lower est. upper +#> a.1 0.67347568 0.87437392 1.07527216 +#> b.1 0.06393032 0.07912417 0.09431802 +# The correlation does not improve the fit judged by AIC and BIC, although +# the likelihood is higher with the additional parameter +anova(f_saem_dfop_sfo, f_saem_dfop_sfo_2, f_saem_dfop_sfo_3) +#> Data: 171 observations of 2 variable(s) grouped in 5 datasets +#> +#> npar AIC BIC Lik +#> f_saem_dfop_sfo_2 12 806.96 802.27 -391.48 +#> f_saem_dfop_sfo_3 13 807.99 802.91 -391.00 +#> f_saem_dfop_sfo 14 810.83 805.36 -391.42 # }

diff --git a/log/test.log b/log/test.log index 89265100..dc1b6c74 100644 --- a/log/test.log +++ b/log/test.log @@ -1,11 +1,11 @@ ℹ Testing mkin ✔ | F W S OK | Context ✔ | 5 | AIC calculation -✔ | 5 | Analytical solutions for coupled models [1.5s] +✔ | 5 | Analytical solutions for coupled models [1.6s] ✔ | 5 | Calculation of Akaike weights ✔ | 3 | Export dataset for reading into CAKE ✔ | 12 | Confidence intervals and p-values [0.4s] -✔ | 1 12 | Dimethenamid data from 2018 [12.3s] +✔ | 1 12 | Dimethenamid data from 2018 [12.4s] ──────────────────────────────────────────────────────────────────────────────── Skip ('test_dmta.R:98'): Different backends get consistent results for SFO-SFO3+, dimethenamid data Reason: Fitting this ODE model with saemix takes about 15 minutes on my system @@ -16,23 +16,23 @@ Reason: Fitting this ODE model with saemix takes about 15 minutes on my system ✔ | 14 | Results for FOCUS D established in expertise for UBA (Ranke 2014) [0.4s] ✔ | 4 | Test fitting the decline of metabolites from their maximum [0.2s] ✔ | 1 | Fitting the logistic model [0.1s] -✔ | 10 | Batch fitting and diagnosing hierarchical kinetic models [18.2s] -✔ | 1 11 | Nonlinear mixed-effects models [5.8s] +✔ | 10 | Batch fitting and diagnosing hierarchical kinetic models [19.1s] +✔ | 1 11 | Nonlinear mixed-effects models [5.9s] ──────────────────────────────────────────────────────────────────────────────── Skip ('test_mixed.R:78'): saemix results are reproducible for biphasic fits Reason: Fitting with saemix takes around 10 minutes when using deSolve ──────────────────────────────────────────────────────────────────────────────── ✔ | 3 | Test dataset classes mkinds and mkindsg ✔ | 10 | Special cases of mkinfit calls [0.4s] -✔ | 3 | mkinfit features [0.4s] +✔ | 3 | mkinfit features [0.5s] ✔ | 8 | mkinmod model generation and printing ✔ | 3 | Model predictions with mkinpredict [0.1s] -✔ | 12 | Multistart method for saem.mmkin models [20.6s] -✔ | 16 | Evaluations according to 2015 NAFTA guidance [1.4s] +✔ | 12 | Multistart method for saem.mmkin models [21.6s] +✔ | 16 | Evaluations according to 2015 NAFTA guidance [1.5s] ✔ | 9 | Nonlinear mixed-effects models with nlme [3.7s] -✔ | 15 | Plotting [4.7s] +✔ | 15 | Plotting [4.6s] ✔ | 4 | Residuals extracted from mkinfit models -✔ | 1 36 | saemix parent models [30.6s] +✔ | 1 36 | saemix parent models [30.9s] ──────────────────────────────────────────────────────────────────────────────── Skip ('test_saemix_parent.R:143'): We can also use mkin solution methods for saem Reason: This still takes almost 2.5 minutes although we do not solve ODEs @@ -47,7 +47,7 @@ Reason: This still takes almost 2.5 minutes although we do not solve ODEs ✔ | 4 | Calculation of maximum time weighted average concentrations (TWAs) [0.7s] ══ Results ═════════════════════════════════════════════════════════════════════ -Duration: 111.2 s +Duration: 113.6 s ── Skipped tests ────────────────────────────────────────────────────────────── • Fitting this ODE model with saemix takes about 15 minutes on my system (1) diff --git a/man/summary.saem.mmkin.Rd b/man/summary.saem.mmkin.Rd index fb099899..0845d4d2 100644 --- a/man/summary.saem.mmkin.Rd +++ b/man/summary.saem.mmkin.Rd @@ -92,10 +92,21 @@ f_mmkin_dfop_sfo <- mmkin(list(dfop_sfo), ds_syn_dfop_sfo, f_saem_dfop_sfo <- saem(f_mmkin_dfop_sfo) print(f_saem_dfop_sfo) illparms(f_saem_dfop_sfo) -f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo, covariance.model = diag(c(0, 0, 1, 1, 1, 0))) +f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo, + no_random_effect = c("parent_0", "log_k_m1")) illparms(f_saem_dfop_sfo_2) intervals(f_saem_dfop_sfo_2) summary(f_saem_dfop_sfo_2, data = TRUE) +# Add a correlation between random effects of g and k2 +cov_model_3 <- f_saem_dfop_sfo_2$so@model@covariance.model +cov_model_3["log_k2", "g_qlogis"] <- 1 +cov_model_3["g_qlogis", "log_k2"] <- 1 +f_saem_dfop_sfo_3 <- update(f_saem_dfop_sfo, + covariance.model = cov_model_3) +intervals(f_saem_dfop_sfo_3) +# The correlation does not improve the fit judged by AIC and BIC, although +# the likelihood is higher with the additional parameter +anova(f_saem_dfop_sfo, f_saem_dfop_sfo_2, f_saem_dfop_sfo_3) } } -- cgit v1.2.3 From 24eb77216700cf8b2f2bde3abad84c1f83f9e32a Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Mon, 9 Jan 2023 06:22:04 +0100 Subject: Prebuilt PDF vignettes, summary_listing --- .Rbuildignore | 2 + .gitignore | 4 + DESCRIPTION | 2 +- GNUmakefile | 7 +- NAMESPACE | 2 + R/hierarchical_kinetics.R | 2 +- R/summary_listing.R | 59 + R/tex_listing.R | 32 - README.md | 2 + _pkgdown.yml | 3 +- docs/dev/articles/2022_wp_1.1_dmta_parent.html | 2177 ++++++++++++++++++++ .../figure-html/convergence-saem-dfop-const-1.png | Bin 0 -> 128154 bytes .../figure-html/convergence-saem-dfop-tc-1.png | Bin 0 -> 109761 bytes .../convergence-saem-dfop-tc-no-ranef-k2-1.png | Bin 0 -> 123528 bytes .../figure-html/convergence-saem-fomc-const-1.png | Bin 0 -> 100169 bytes .../figure-html/convergence-saem-fomc-tc-1.png | Bin 0 -> 93007 bytes .../figure-html/convergence-saem-hs-const-1.png | Bin 0 -> 129829 bytes .../figure-html/convergence-saem-hs-tc-1.png | Bin 0 -> 98778 bytes .../figure-html/convergence-saem-sfo-const-1.png | Bin 0 -> 75641 bytes .../figure-html/convergence-saem-sfo-tc-1.png | Bin 0 -> 62897 bytes .../figure-html/multistart-full-par-1.png | Bin 0 -> 71232 bytes .../figure-html/multistart-reduced-par-1.png | Bin 0 -> 66297 bytes .../multistart-reduced-par-llquant-1.png | Bin 0 -> 58713 bytes .../plot-saem-dfop-tc-no-ranef-k2-1.png | Bin 0 -> 159042 bytes docs/dev/articles/index.html | 6 +- docs/dev/authors.html | 6 +- docs/dev/index.html | 24 +- docs/dev/news/index.html | 6 +- docs/dev/pkgdown.yml | 5 +- .../reference/example_analysis/dlls/sforb_sfo2.so | Bin 0 -> 17272 bytes .../example_analysis/example_analysis.Rmd | 314 +++ docs/dev/reference/example_analysis/header.tex | 1 + docs/dev/reference/example_analysis/skeleton.pdf | Bin 0 -> 351780 bytes .../figure-latex/unnamed-chunk-11-1.pdf | Bin 0 -> 30166 bytes .../figure-latex/unnamed-chunk-16-1.pdf | Bin 0 -> 30137 bytes .../figure-latex/unnamed-chunk-6-1.pdf | Bin 0 -> 16408 bytes .../figure-latex/unnamed-chunk-9-1.pdf | Bin 0 -> 16043 bytes docs/dev/reference/hierarchical_kinetics.html | 154 ++ docs/dev/reference/index.html | 10 +- docs/dev/reference/mkinmod.html | 10 +- docs/dev/reference/summary_listing.html | 147 ++ docs/dev/sitemap.xml | 9 + inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx | Bin 0 -> 35878 bytes log/check.log | 34 +- man/hierarchical_kinetics.Rd | 2 +- man/mkinmod.Rd | 2 +- man/summary_listing.Rd | 27 + man/tex_listing.Rd | 21 - vignettes/FOCUS_D.html | 44 +- vignettes/FOCUS_L.html | 215 +- vignettes/dmta_parent_2022_prebuilt.rnw | 7 + vignettes/dmta_pathway_2022_prebuilt.rnw | 7 + vignettes/mkin.html | 310 ++- vignettes/prebuilt/2022_cyan_pathway.rmd | 536 +++++ vignettes/prebuilt/2022_dmta_parent.rmd | 406 ++++ vignettes/prebuilt/2022_dmta_pathway.rmd | 426 ++++ vignettes/prebuilt/references.bib | 187 ++ vignettes/references.bib | 34 +- vignettes/twa.html | 108 +- vignettes/web_only/FOCUS_Z.R | 115 ++ vignettes/web_only/FOCUS_Z.html | 278 ++- vignettes/web_only/benchmarks.R | 114 + vignettes/web_only/benchmarks.html | 193 +- vignettes/web_only/compiled_models.R | 65 + vignettes/web_only/compiled_models.html | 230 ++- vignettes/web_only/dimethenamid_2018.R | 152 ++ vignettes/web_only/dimethenamid_2018.html | 365 +++- .../figure-html/f_parent_mkin_dfop_const-1.png | Bin 58608 -> 57786 bytes .../f_parent_mkin_dfop_const_test-1.png | Bin 58777 -> 57786 bytes .../figure-html/f_parent_mkin_dfop_tc_test-1.png | Bin 60062 -> 59396 bytes .../figure-html/f_parent_mkin_sfo_const-1.png | Bin 56694 -> 55982 bytes .../figure-html/f_parent_saemix_sfo_tc-1.png | Bin 28655 -> 28538 bytes .../figure-html/plot_parent_nlme-1.png | Bin 59194 -> 59192 bytes vignettes/web_only/mkin_benchmarks.rda | Bin 1650 -> 1722 bytes 74 files changed, 6255 insertions(+), 607 deletions(-) create mode 100644 R/summary_listing.R delete mode 100644 R/tex_listing.R create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent.html create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-full-par-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png create mode 100644 docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png create mode 100755 docs/dev/reference/example_analysis/dlls/sforb_sfo2.so create mode 100644 docs/dev/reference/example_analysis/example_analysis.Rmd create mode 100644 docs/dev/reference/example_analysis/header.tex create mode 100644 docs/dev/reference/example_analysis/skeleton.pdf create mode 100644 docs/dev/reference/example_analysis/skeleton_files/figure-latex/unnamed-chunk-11-1.pdf create mode 100644 docs/dev/reference/example_analysis/skeleton_files/figure-latex/unnamed-chunk-16-1.pdf create mode 100644 docs/dev/reference/example_analysis/skeleton_files/figure-latex/unnamed-chunk-6-1.pdf create mode 100644 docs/dev/reference/example_analysis/skeleton_files/figure-latex/unnamed-chunk-9-1.pdf create mode 100644 docs/dev/reference/hierarchical_kinetics.html create mode 100644 docs/dev/reference/summary_listing.html create mode 100644 inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx create mode 100644 man/summary_listing.Rd delete mode 100644 man/tex_listing.Rd create mode 100644 vignettes/dmta_parent_2022_prebuilt.rnw create mode 100644 vignettes/dmta_pathway_2022_prebuilt.rnw create mode 100644 vignettes/prebuilt/2022_cyan_pathway.rmd create mode 100644 vignettes/prebuilt/2022_dmta_parent.rmd create mode 100644 vignettes/prebuilt/2022_dmta_pathway.rmd create mode 100644 vignettes/prebuilt/references.bib create mode 100644 vignettes/web_only/FOCUS_Z.R create mode 100644 vignettes/web_only/benchmarks.R create mode 100644 vignettes/web_only/compiled_models.R create mode 100644 vignettes/web_only/dimethenamid_2018.R (limited to 'docs/dev/index.html') diff --git a/.Rbuildignore b/.Rbuildignore index 70eef830..7e13343b 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -28,6 +28,8 @@ ^vignettes/.*.synctex.gz ^vignettes/.*.toc$ ^vignettes/figure +^vignettes/prebuilt/*_dlls +^vignettes/prebuilt/*.pdf ^vignettes/FOCUS_Z.tex$ ^vignettes/mkin.tex$ ^vignettes/mkin_benchmarks.rda$ diff --git a/.gitignore b/.gitignore index a86197a1..5bec45e6 100644 --- a/.gitignore +++ b/.gitignore @@ -28,3 +28,7 @@ vignettes/cache/ vignettes/figure/ vignettes/*_cache/ vignettes/*_files/ +vignettes/prebuilt/*_cache +vignettes/prebuilt/*_files +vignettes/prebuilt/*_dlls +vignettes/prebuilt/*.pdf diff --git a/DESCRIPTION b/DESCRIPTION index d061a5a9..50dba006 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -2,7 +2,7 @@ Package: mkin Type: Package Title: Kinetic Evaluation of Chemical Degradation Data Version: 1.2.2 -Date: 2023-01-03 +Date: 2023-01-08 Authors@R: c( person("Johannes", "Ranke", role = c("aut", "cre", "cph"), email = "johannes.ranke@jrwb.de", diff --git a/GNUmakefile b/GNUmakefile index 4a33c538..9f268335 100644 --- a/GNUmakefile +++ b/GNUmakefile @@ -37,10 +37,6 @@ pkgfiles = \ all: build $(TGZ): $(pkgfiles) vignettes - $(RM) -r vignettes/*_cache - $(RM) -r vignettes/*_files - $(RM) -r vignettes/*.R - $(RM) -r vignettes/web_only/*.R $(RM) Rplots.pdf "$(RBIN)/R" CMD build . 2>&1 | tee log/build.log @@ -111,7 +107,8 @@ vignettes: vignettes/mkin.html vignettes/FOCUS_D.html vignettes/FOCUS_L.html vig vignettes/web_only/%.html: vignettes/references.bib vignettes/web_only/%.rmd "$(RBIN)/Rscript" -e "tools::buildVignette(file = 'vignettes/web_only/$*.rmd', dir = 'vignettes/web_only', keep=c('mkin_benchmarks.rda', 'saem_benchmarks.rda'))" -articles: vignettes/web_only/FOCUS_Z.html vignettes/web_only/compiled_models.html vignettes/web_only/benchmarks.html vignettes/web_only/dimethenamid_2018.html vignettes/web_only/multistart.html +vignettes/prebuilt/%.pdf: vignettes/prebuilt/references.bib vignettes/prebuilt/%.rmd + "$(RBIN)/Rscript" -e "rmarkdown::render('vignettes/prebuilt/$*.rmd')" pd: roxygen "$(RBIN)/Rscript" -e "pkgdown::build_site(run_dont_run = TRUE, lazy = TRUE)" diff --git a/NAMESPACE b/NAMESPACE index 84d6b713..b41bf614 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -97,6 +97,7 @@ export(endpoints) export(f_time_norm_focus) export(get_deg_func) export(hierarchical_kinetics) +export(html_listing) export(illparms) export(ilr) export(intervals) @@ -145,6 +146,7 @@ export(set_nd_nq) export(set_nd_nq_focus) export(sigma_twocomp) export(status) +export(summary_listing) export(tex_listing) export(transform_odeparms) export(which.best) diff --git a/R/hierarchical_kinetics.R b/R/hierarchical_kinetics.R index a90dd619..e545754a 100644 --- a/R/hierarchical_kinetics.R +++ b/R/hierarchical_kinetics.R @@ -13,7 +13,7 @@ #' #' \dontrun{ #' library(rmarkdown) -#' draft("New analysis.rmd", template = "hierarchical_kinetics", package = "mkin") +#' draft("example_analysis.rmd", template = "hierarchical_kinetics", package = "mkin") #' } #' #' @export diff --git a/R/summary_listing.R b/R/summary_listing.R new file mode 100644 index 00000000..38b52240 --- /dev/null +++ b/R/summary_listing.R @@ -0,0 +1,59 @@ +#' Display the output of a summary function according to the output format +#' +#' This function is intended for use in a R markdown code chunk with the chunk +#' option `results = "asis"`. +#' +#' @param object The object for which the summary is to be listed +#' @param caption An optional caption +#' @param label An optional label, ignored in html output +#' @param clearpage Should a new page be started after the listing? Ignored in html output +#' @export +summary_listing <- function(object, caption = NULL, label = NULL, + clearpage = TRUE) { + if (knitr::is_latex_output()) { + tex_listing(object = object, caption = caption, label = label, + clearpage = clearpage) + } + if (knitr::is_html_output()) { + html_listing(object = object, caption = caption) + } +} + +#' @rdname summary_listing +#' @export +tex_listing <- function(object, caption = NULL, label = NULL, + clearpage = TRUE) { + cat("\n") + cat("\\begin{listing}", "\n") + if (!is.null(caption)) { + cat("\\caption{", caption, "}", "\n", sep = "") + } + if (!is.null(label)) { + cat("\\caption{", label, "}", "\n", sep = "") + } + cat("\\begin{snugshade}", "\n") + cat("\\scriptsize", "\n") + cat("\\begin{verbatim}", "\n") + cat(capture.output(suppressWarnings(summary(object))), sep = "\n") + cat("\n") + cat("\\end{verbatim}", "\n") + cat("\\end{snugshade}", "\n") + cat("\\end{listing}", "\n") + if (clearpage) { + cat("\\clearpage", "\n") + } +} + +#' @rdname summary_listing +#' @export +html_listing <- function(object, caption = NULL) { + cat("\n") + if (!is.null(caption)) { + cat("", caption, "", "\n", sep = "") + } + cat("

\n")
+  cat(capture.output(suppressWarnings(summary(object))), sep = "\n")
+  cat("\n")
+  cat("

\n") +} + diff --git a/R/tex_listing.R b/R/tex_listing.R deleted file mode 100644 index 05f662e4..00000000 --- a/R/tex_listing.R +++ /dev/null @@ -1,32 +0,0 @@ -#' Wrap the output of a summary function in tex listing environment -#' -#' This function can be used in a R markdown code chunk with the chunk -#' option `results = "asis"`. -#' -#' @param object The object for which the summary is to be listed -#' @param caption An optional caption -#' @param label An optional label -#' @param clearpage Should a new page be started after the listing? -#' @export -tex_listing <- function(object, caption = NULL, label = NULL, - clearpage = TRUE) { - cat("\n") - cat("\\begin{listing}", "\n") - if (!is.null(caption)) { - cat("\\caption{", caption, "}", "\n", sep = "") - } - if (!is.null(label)) { - cat("\\caption{", label, "}", "\n", sep = "") - } - cat("\\begin{snugshade}", "\n") - cat("\\scriptsize", "\n") - cat("\\begin{verbatim}", "\n") - cat(capture.output(suppressWarnings(summary(object))), sep = "\n") - cat("\n") - cat("\\end{verbatim}", "\n") - cat("\\end{snugshade}", "\n") - cat("\\end{listing}", "\n") - if (clearpage) { - cat("\\clearpage", "\n") - } -} diff --git a/README.md b/README.md index f3c36890..b6171767 100644 --- a/README.md +++ b/README.md @@ -214,6 +214,8 @@ to ModelMaker 4.0, 2014-2015) of the visual fit in the kinetic evaluation of degradation data, 2019-2020) - Project Number 146839 (Checking the feasibility of using mixed-effects models for the derivation of kinetic modelling parameters from degradation studies, 2020-2021) +- Project Number 173340 (Application of nonlinear hierarchical models to the + kinetic evaluation of chemical degradation data) Thanks to everyone involved for collaboration and support! diff --git a/_pkgdown.yml b/_pkgdown.yml index ca5ea6e0..5d7fdbf4 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -47,6 +47,7 @@ reference: - title: Mixed models desc: Create and work with nonlinear hierarchical models contents: + - hierarchical_kinetics - read_spreadsheet - nlme.mmkin - saem.mmkin @@ -92,7 +93,7 @@ reference: - plot.nafta - title: Utility functions contents: - - tex_listing + - summary_listing - f_time_norm_focus - set_nd_nq - max_twa_parent diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent.html b/docs/dev/articles/2022_wp_1.1_dmta_parent.html new file mode 100644 index 00000000..61bb81d3 --- /dev/null +++ b/docs/dev/articles/2022_wp_1.1_dmta_parent.html @@ -0,0 +1,2177 @@ + + + + + + + +Work package 1.1: Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P • mkin + + + + + + + + + + + + + +

+ + + + +

Introduction +

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

The mkin package is used in version 1.2.2. It contains the test data +and the functions used in the evaluations. The saemix +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.

This document is processed with the knitr package, which +also provides the kable function that is used to improve +the display of tabular data in R markdown documents. For parallel +processing, the parallel package is used.

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

Preprocessing of test data +

The test data are available in the mkin package as an object of class +mkindsg (mkin dataset group) under the identifier +dimethenamid_2018. The following preprocessing steps are +still necessary:

The data available for the enantiomer dimethenamid-P (DMTAP) are +renamed to have the same substance name as the data for the racemic +mixture dimethenamid (DMTA). The reason for this is that no difference +between their degradation behaviour was identified in the EU risk +assessment.
The data for transformation products and unnecessary columns are +discarded
The observation times of each dataset are multiplied with the +corresponding normalisation factor also available in the dataset, in +order to make it possible to describe all datasets with a single set of +parameters that are independent of temperature
Finally, datasets observed in the same soil (Elliot 1 +and Elliot 2) are combined, resulting in dimethenamid +(DMTA) data from six soils.

The following commented R code performs this preprocessing.

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

The following tables show the 6 datasets.

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

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

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

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

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

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

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

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

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

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

Separate evaluations +

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

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

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

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

In the table above, OK indicates convergence, and C indicates failure +to converge. All separate fits with constant variance converged, with +the sole exception of the HS fit to the BBA 2.2 data. To prepare for +fitting NLHM using the two-component error model, the separate fits are +updated assuming two-component error.

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

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

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

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

Hierarchichal model fits +

The following code fits eight versions of hierarchical models to the +data, using SFO, FOMC, DFOP and HS for the parent compound, and using +either constant variance or two-component error for the error model. The +default parameter distribution model in mkin allows for variation of all +degradation parameters across the assumed population of soils. In other +words, each degradation parameter is associated with a random effect as +a first step. The mhmkin function makes it possible to fit +all eight versions in parallel (given a sufficient number of computing +cores being available) to save execution time.

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

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

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

+status(f_saem) |> kable()

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

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

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

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

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

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

The DFOP model is preferred here, as it has a better mechanistic +basis for batch experiments with constant incubation conditions. Also, +it shows the lowest AIC and BIC values in the first set of fits when +combined with the two-component error model. Therefore, the DFOP model +was selected for further refinements of the fits with the aim to make +the model fully identifiable.

Parameter identifiability based on the Fisher Information +Matrix +

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

+illparms(f_saem) |> kable()

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

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

According to the illparms function, the fitted standard +deviation of the second kinetic rate constant k2 is +ill-defined in both DFOP fits. This suggests that different values would +be obtained for this standard deviation when using different starting +values.

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

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

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

+illparms(f_saem_dfop_tc_no_ranef_k2)

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

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

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

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

The AIC and BIC criteria are lower after removal of the ill-defined +random effect for k2. The p value of the likelihood ratio +test is much greater than 0.05, indicating that the model with the +higher likelihood (here the model with random effects for all +degradation parameters f_saem[["DFOP", "tc"]]) does not fit +significantly better than the model with the lower likelihood (the +reduced model f_saem_dfop_tc_no_ranef_k2).

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

The convergence of the fit is checked visually.

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

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

+plot(f_saem_dfop_tc_no_ranef_k2)

+Plot of the final NLHM DFOP fit +

Finally, a summary report of the fit is produced.

+summary(f_saem_dfop_tc_no_ranef_k2)

saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:13 2023 
+Date of summary: Thu Jan  5 08:19:13 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 4.075 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  663.8 661.9 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.228939 96.285869 100.17201
+k1         0.064063  0.033477   0.09465
+k2         0.008297  0.005824   0.01077
+g          0.953821  0.914328   0.99331
+a.1        1.068479  0.869538   1.26742
+b.1        0.029424  0.022406   0.03644
+SD.DMTA_0  2.030437  0.404824   3.65605
+SD.k1      0.594692  0.256660   0.93272
+SD.g       1.006754  0.361327   1.65218
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0218                
+k2  0.0556  0.0355        
+g  -0.0516 -0.0284 -0.2800
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 2.0304 0.4048 3.6560
+SD.k1     0.5947 0.2567 0.9327
+SD.g      1.0068 0.3613 1.6522
+
+Variance model:
+       est.   lower   upper
+a.1 1.06848 0.86954 1.26742
+b.1 0.02942 0.02241 0.03644
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.4    12.46   10.82   83.54

Alternative check of parameter identifiability +

The parameter check used in the illparms function is +based on a quadratic approximation of the likelihood surface near its +optimum, which is calculated using the Fisher Information Matrix (FIM). +An alternative way to check parameter identifiability based on a +multistart approach has recently been implemented in mkin.

The graph below shows boxplots of the parameters obtained in 50 runs +of the saem algorithm with different parameter combinations, sampled +from the range of the parameters obtained for the individual datasets +fitted separately using nonlinear regression.

+f_saem_dfop_tc_multi <- multistart(f_saem[["DFOP", "tc"]], n = 50, cores = 15)

+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_multi, lpos = "bottomright", ylim = c(0.3, 10), las = 2)

+Scaled parameters from the multistart runs, full model +

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

The parameter boxplots of the multistart runs with the reduced model +shown below indicate that all runs give similar results, regardless of +the starting parameters.

+f_saem_dfop_tc_no_ranef_k2_multi <- multistart(f_saem_dfop_tc_no_ranef_k2,
+  n = 50, cores = 15)

+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2,
+  lpos = "bottomright")

+Scaled parameters from the multistart runs, reduced model +

When only the parameters of the top 25% of the fits are shown (based +on a feature introduced in mkin 1.2.2 currently under development), the +scatter is even less as shown below.

+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2, llquant = 0.25,
+  lpos = "bottomright")

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

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

Conclusions +

Fitting the four parent degradation models SFO, FOMC, DFOP and HS as +part of hierarchical model fits with two different error models and +normal distributions of the transformed degradation parameters works +without technical problems. The biphasic models DFOP and HS gave the +best fit to the data, but the default parameter distribution model was +not fully identifiable. Removing the random effect for the second +kinetic rate constant of the DFOP model resulted in a reduced model that +was fully identifiable and showed the lowest values for the model +selection criteria AIC and BIC. The reliability of the identification of +all model parameters was confirmed using multiple starting values.

Appendix +

Hierarchical model fit listings +

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


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

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:07 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.441 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0   k_DMTA 
+96.99175  0.05603 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0  96.99      0
+k_DMTA   0.00      1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  798.3 797.1 -393.2
+
+Optimised parameters:
+               est.     lower    upper
+DMTA_0    97.271822 95.703157 98.84049
+k_DMTA     0.056638  0.029110  0.08417
+a.1        2.660081  2.230398  3.08976
+b.1        0.001665 -0.006911  0.01024
+SD.DMTA_0  1.545520  0.145035  2.94601
+SD.k_DMTA  0.606422  0.262274  0.95057
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5455 0.1450 2.9460
+SD.k_DMTA 0.6064 0.2623 0.9506
+
+Variance model:
+        est.     lower   upper
+a.1 2.660081  2.230398 3.08976
+b.1 0.001665 -0.006911 0.01024
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+

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


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

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


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

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


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

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


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

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


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

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Thu Jan  5 08:19:08 2023 
+Date of summary: Thu Jan  5 08:20:11 2023 
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.287 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+98.45190  0.07525  0.02576 19.19375 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  98.45  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  667.1 665 -323.6
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    97.76570 95.81350 99.71791
+k1         0.05855  0.03080  0.08630
+k2         0.02337  0.01664  0.03010
+tb        31.09638 29.38289 32.80987
+a.1        1.08835  0.88590  1.29080
+b.1        0.02964  0.02257  0.03671
+SD.DMTA_0  2.04877  0.42607  3.67147
+SD.k1      0.59166  0.25621  0.92711
+SD.k2      0.30698  0.09561  0.51835
+SD.tb      0.01274 -0.10914  0.13462
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0160                
+k2 -0.0070 -0.0024        
+tb -0.0668 -0.0103 -0.2013
+
+Random effects:
+             est.    lower  upper
+SD.DMTA_0 2.04877  0.42607 3.6715
+SD.k1     0.59166  0.25621 0.9271
+SD.k2     0.30698  0.09561 0.5183
+SD.tb     0.01274 -0.10914 0.1346
+
+Variance model:
+       est.   lower   upper
+a.1 1.08835 0.88590 1.29080
+b.1 0.02964 0.02257 0.03671
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.84 51.71    15.57   11.84   29.66
+
+

Hierarchical model convergence plots +

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

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

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

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

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

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

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

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

Session info +

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

+ + + +

+ + + + +

+ + + + + + + + diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png new file mode 100644 index 00000000..4f87b956 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png new file mode 100644 index 00000000..58825300 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png new file mode 100644 index 00000000..17defde1 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png new file mode 100644 index 00000000..b802acc6 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png new file mode 100644 index 00000000..2d6427d5 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png new file mode 100644 index 00000000..f15137d0 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png new file mode 100644 index 00000000..322668f0 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png new file mode 100644 index 00000000..4ceb281f Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png new file mode 100644 index 00000000..07383871 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-full-par-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-full-par-1.png new file mode 100644 index 00000000..cf4b058e Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-full-par-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-1.png new file mode 100644 index 00000000..d9ed8685 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png new file mode 100644 index 00000000..45dd7eb4 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png differ diff --git a/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png new file mode 100644 index 00000000..5a3bd434 Binary files /dev/null and b/docs/dev/articles/2022_wp_1.1_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png differ diff --git a/docs/dev/articles/index.html b/docs/dev/articles/index.html index e04302ef..cd0e315f 100644 --- a/docs/dev/articles/index.html +++ b/docs/dev/articles/index.html @@ -90,7 +90,9 @@

All vignettes

Example evaluation of FOCUS Example Dataset D

Site built with pkgdown 2.0.6.

Site built with pkgdown 2.0.7.

diff --git a/docs/dev/authors.html b/docs/dev/authors.html index bd58bc3d..165e2400 100644 --- a/docs/dev/authors.html +++ b/docs/dev/authors.html @@ -113,14 +113,14 @@ -

Ranke J (2022). +

Ranke J (2023). mkin: Kinetic Evaluation of Chemical Degradation Data. R package version 1.2.2, https://pkgdown.jrwb.de/mkin/.

@Manual{,
   title = {mkin: Kinetic Evaluation of Chemical Degradation Data},
   author = {Johannes Ranke},
-  year = {2022},
+  year = {2023},
   note = {R package version 1.2.2},
   url = {https://pkgdown.jrwb.de/mkin/},
 }

@@ -136,7 +136,7 @@ R package version 1.2.2, https://pkgdown

Site built with pkgdown 2.0.6.

Site built with pkgdown 2.0.7.

diff --git a/docs/dev/index.html b/docs/dev/index.html index 4723879e..993b8eea 100644 --- a/docs/dev/index.html +++ b/docs/dev/index.html @@ -19,11 +19,11 @@ equation models are solved using automatically generated C functions. Heteroscedasticity can be taken into account using variance by variable or two-component error models as described by Ranke and Meinecke (2018) - <doi:10.3390/environments6120124>. Interfaces to several nonlinear - mixed-effects model packages are available, some of which are described by - Ranke et al. (2021) <doi:10.3390/environments8080071>. Please note that no - warranty is implied for correctness of results or fitness for a particular - purpose."> + <doi:10.3390/environments6120124>. Hierarchical degradation models can + be fitted using nonlinear mixed-effects model packages as a backend as + described by Ranke et al. (2021) <doi:10.3390/environments8080071>. Please + note that no warranty is implied for correctness of results or fitness for a + particular purpose."> Hierarchical kinetics template — hierarchical_kinetics • mkin + + +

+ + + +

+ + +

R markdown format for setting up hierarchical kinetics based on a template +provided with the mkin package.

+ +

hierarchical_kinetics(..., keep_tex = FALSE)

+ +

Arguments

...: Arguments to rmarkdown::pdf_document
keep_tex: Keep the intermediate tex file used in the conversion to PDF

Value

+ + +

R Markdown output format to pass to +render

+ + +

+ +

Examples


+# \dontrun{
+library(rmarkdown)
+draft("example_analysis.rmd", template = "hierarchical_kinetics", package = "mkin")
+# }
+
+

+ +

+ + +

+ + + + + + + + diff --git a/docs/dev/reference/index.html b/docs/dev/reference/index.html index 794126cf..525551fd 100644 --- a/docs/dev/reference/index.html +++ b/docs/dev/reference/index.html @@ -195,6 +195,10 @@ of an mmkin object

Create and work with nonlinear hierarchical models

hierarchical_kinetics()

+ +

Hierarchical kinetics template

read_spreadsheet()

Read datasets and relevant meta information from a spreadsheet file

@@ -356,9 +360,9 @@ degradation models and one or more error models

tex_listing()

summary_listing() tex_listing() html_listing()

Wrap the output of a summary function in tex listing environment

Display the output of a summary function according to the output format

f_time_norm_focus()

@@ -493,7 +497,7 @@ kinetic models fitted with mkinfit

Site built with pkgdown 2.0.6.

Site built with pkgdown 2.0.7.

diff --git a/docs/dev/reference/mkinmod.html b/docs/dev/reference/mkinmod.html index 251215a7..145dee83 100644 --- a/docs/dev/reference/mkinmod.html +++ b/docs/dev/reference/mkinmod.html @@ -132,7 +132,7 @@ the source compartment. Additionally, mkinsub() has an argument to, specifying names of variables to which a transfer is to be assumed in the model. If the argument use_of_ff is set to "min" -(default) and the model for the compartment is "SFO" or "SFORB", an +and the model for the compartment is "SFO" or "SFORB", an additional mkinsub() argument can be sink = FALSE, effectively fixing the flux to sink to zero. In print.mkinmod, this argument is currently not used.

@@ -247,7 +247,7 @@ in the FOCUS and NAFTA guidance documents are used.

For kinetic models with more than one observed variable, a symbolic solution of the system of differential equations is included in the resulting mkinmod object in some cases, speeding up the solution.

If a C compiler is found by pkgbuild::has_compiler() and there +

If a C compiler is found by pkgbuild::has_compiler() and there is more than one observed variable in the specification, C code is generated for evaluating the differential equations, compiled using inline::cfunction() and added to the resulting mkinmod object.

@@ -310,7 +310,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media

parent = mkinsub("SFO", "m1", full_name = "Test compound"), m1 = mkinsub("SFO", full_name = "Metabolite M1"), name = "SFO_SFO", dll_dir = DLL_dir, unload = TRUE, overwrite = TRUE) -#> Copied DLL from /tmp/RtmpbZbZ8Y/file8c6a9f402f42.so to /home/jranke/.local/share/mkin/SFO_SFO.so +#> Copied DLL from /tmp/RtmpelWAOB/fileb43c31a25a86.so to /home/jranke/.local/share/mkin/SFO_SFO.so # Now we can save the model and restore it in a new session saveRDS(SFO_SFO.2, file = "~/SFO_SFO.rds") # Terminate the R session here if you would like to check, and then do @@ -363,7 +363,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media

#> }) #> return(predicted) #> } -#> <environment: 0x55556029f678> +#> <environment: 0x55555f013820> # If we have several parallel metabolites # (compare tests/testthat/test_synthetic_data_for_UBA_2014.R) @@ -392,7 +392,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media

Site built with pkgdown 2.0.6.

Site built with pkgdown 2.0.7.

diff --git a/docs/dev/reference/summary_listing.html b/docs/dev/reference/summary_listing.html new file mode 100644 index 00000000..876412cc --- /dev/null +++ b/docs/dev/reference/summary_listing.html @@ -0,0 +1,147 @@ + +Display the output of a summary function according to the output format — summary_listing • mkin + + +

+ + + +

+ + +

This function is intended for use in a R markdown code chunk with the chunk +option results = "asis".

+ +

summary_listing(object, caption = NULL, label = NULL, clearpage = TRUE)
+
+tex_listing(object, caption = NULL, label = NULL, clearpage = TRUE)
+
+html_listing(object, caption = NULL)

+ +

Arguments

object: The object for which the summary is to be listed
caption: An optional caption
label: An optional label, ignored in html output
clearpage: Should a new page be started after the listing? Ignored in html output

+ +

+ + +

+ + + + + + + + diff --git a/docs/dev/sitemap.xml b/docs/dev/sitemap.xml index 06f56c5d..6e51371c 100644 --- a/docs/dev/sitemap.xml +++ b/docs/dev/sitemap.xml @@ -3,6 +3,9 @@ https://pkgdown.jrwb.de/mkin/404.html + + https://pkgdown.jrwb.de/mkin/articles/2022_wp_1.1_dmta_parent.html + https://pkgdown.jrwb.de/mkin/articles/FOCUS_D.html @@ -138,6 +141,9 @@ https://pkgdown.jrwb.de/mkin/reference/get_deg_func.html + + https://pkgdown.jrwb.de/mkin/reference/hierarchical_kinetics.html + https://pkgdown.jrwb.de/mkin/reference/illparms.html @@ -306,6 +312,9 @@ https://pkgdown.jrwb.de/mkin/reference/summary.saem.mmkin.html + + https://pkgdown.jrwb.de/mkin/reference/summary_listing.html + https://pkgdown.jrwb.de/mkin/reference/synthetic_data_for_UBA_2014.html diff --git a/inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx b/inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx new file mode 100644 index 00000000..3252fdf1 Binary files /dev/null and b/inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx differ diff --git a/log/check.log b/log/check.log index aec61e33..a81475d9 100644 --- a/log/check.log +++ b/log/check.log @@ -7,11 +7,28 @@ * checking extension type ... Package * this is package ‘mkin’ version ‘1.2.2’ * package encoding: UTF-8 -* checking CRAN incoming feasibility ... Note_to_CRAN_maintainers +* checking CRAN incoming feasibility ... NOTE Maintainer: ‘Johannes Ranke ’ + +Size of tarball: 6636884 bytes * checking package namespace information ... OK * checking package dependencies ... OK -* checking if this is a source package ... OK +* checking if this is a source package ... NOTE +Found the following apparent object files/libraries: + vignettes/2022_wp_1/cyan_dlls/dfop_path_1.so + vignettes/2022_wp_1/cyan_dlls/dfop_path_2.so + vignettes/2022_wp_1/cyan_dlls/fomc_path_1.so + vignettes/2022_wp_1/cyan_dlls/fomc_path_2.so + vignettes/2022_wp_1/cyan_dlls/hs_path_1.so + vignettes/2022_wp_1/cyan_dlls/sfo_path_1.so + vignettes/2022_wp_1/cyan_dlls/sforb_path_1.so + vignettes/2022_wp_1/cyan_dlls/sforb_path_2.so + vignettes/2022_wp_1/dmta_dlls/m_dfop_path.so + vignettes/2022_wp_1/dmta_dlls/m_fomc_path.so + vignettes/2022_wp_1/dmta_dlls/m_hs_path.so + vignettes/2022_wp_1/dmta_dlls/m_sfo_path.so + vignettes/2022_wp_1/dmta_dlls/m_sforb_path.so +Object files/libraries should not be included in a source package. * checking if there is a namespace ... OK * checking for executable files ... OK * checking for hidden files and directories ... OK @@ -41,14 +58,7 @@ Maintainer: ‘Johannes Ranke ’ * checking S3 generic/method consistency ... OK * checking replacement functions ... OK * checking foreign function calls ... OK -* checking R code for possible problems ... NOTE -parplot.multistart.saem.mmkin: no visible global function definition - for ‘quantile’ -Undefined global functions or variables: - quantile -Consider adding - importFrom("stats", "quantile") -to your NAMESPACE file. +* checking R code for possible problems ... OK * checking Rd files ... OK * checking Rd metadata ... OK * checking Rd line widths ... OK @@ -64,7 +74,7 @@ to your NAMESPACE file. * checking data for ASCII and uncompressed saves ... OK * checking installed files from ‘inst/doc’ ... OK * checking files in ‘vignettes’ ... OK -* checking examples ... [11s/11s] OK +* checking examples ... [10s/10s] OK * checking for unstated dependencies in ‘tests’ ... OK * checking tests ... SKIPPED * checking for unstated dependencies in vignettes ... OK @@ -76,7 +86,7 @@ to your NAMESPACE file. * checking for detritus in the temp directory ... OK * DONE -Status: 1 NOTE +Status: 2 NOTEs See ‘/home/jranke/git/mkin/mkin.Rcheck/00check.log’ for details. diff --git a/man/hierarchical_kinetics.Rd b/man/hierarchical_kinetics.Rd index 4bb82a4c..2a8e211c 100644 --- a/man/hierarchical_kinetics.Rd +++ b/man/hierarchical_kinetics.Rd @@ -23,7 +23,7 @@ provided with the mkin package. \dontrun{ library(rmarkdown) -draft("New analysis.rmd", template = "hierarchical_kinetics", package = "mkin") +draft("example_analysis.rmd", template = "hierarchical_kinetics", package = "mkin") } } diff --git a/man/mkinmod.Rd b/man/mkinmod.Rd index 87ce9016..65b5de1a 100644 --- a/man/mkinmod.Rd +++ b/man/mkinmod.Rd @@ -33,7 +33,7 @@ the source compartment. Additionally, \code{\link[=mkinsub]{mkinsub()}} has an argument \code{to}, specifying names of variables to which a transfer is to be assumed in the model. If the argument \code{use_of_ff} is set to "min" -(default) and the model for the compartment is "SFO" or "SFORB", an +and the model for the compartment is "SFO" or "SFORB", an additional \code{\link[=mkinsub]{mkinsub()}} argument can be \code{sink = FALSE}, effectively fixing the flux to sink to zero. In print.mkinmod, this argument is currently not used.} diff --git a/man/summary_listing.Rd b/man/summary_listing.Rd new file mode 100644 index 00000000..995ebd8d --- /dev/null +++ b/man/summary_listing.Rd @@ -0,0 +1,27 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/summary_listing.R +\name{summary_listing} +\alias{summary_listing} +\alias{tex_listing} +\alias{html_listing} +\title{Display the output of a summary function according to the output format} +\usage{ +summary_listing(object, caption = NULL, label = NULL, clearpage = TRUE) + +tex_listing(object, caption = NULL, label = NULL, clearpage = TRUE) + +html_listing(object, caption = NULL) +} +\arguments{ +\item{object}{The object for which the summary is to be listed} + +\item{caption}{An optional caption} + +\item{label}{An optional label, ignored in html output} + +\item{clearpage}{Should a new page be started after the listing? Ignored in html output} +} +\description{ +This function is intended for use in a R markdown code chunk with the chunk +option \code{results = "asis"}. +} diff --git a/man/tex_listing.Rd b/man/tex_listing.Rd deleted file mode 100644 index 2f11d211..00000000 --- a/man/tex_listing.Rd +++ /dev/null @@ -1,21 +0,0 @@ -% Generated by roxygen2: do not edit by hand -% Please edit documentation in R/tex_listing.R -\name{tex_listing} -\alias{tex_listing} -\title{Wrap the output of a summary function in tex listing environment} -\usage{ -tex_listing(object, caption = NULL, label = NULL, clearpage = TRUE) -} -\arguments{ -\item{object}{The object for which the summary is to be listed} - -\item{caption}{An optional caption} - -\item{label}{An optional label} - -\item{clearpage}{Should a new page be started after the listing?} -} -\description{ -This function can be used in a R markdown code chunk with the chunk -option \code{results = "asis"}. -} diff --git a/vignettes/FOCUS_D.html b/vignettes/FOCUS_D.html index b8a63a7b..c729e3c2 100644 --- a/vignettes/FOCUS_D.html +++ b/vignettes/FOCUS_D.html @@ -31,7 +31,7 @@ document.addEventListener('DOMContentLoaded', function(e) { !function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],r=Object.getPrototypeOf,s=t.slice,g=t.flat?function(e){return t.flat.call(e)}:function(e){return t.concat.apply([],e)},u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType&&"function"!=typeof e.item},x=function(e){return null!=e&&e===e.window},E=C.document,c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof e?n[o.call(e)]||"object":typeof e}var f="3.6.0",S=function(e,t){return new S.fn.init(e,t)};function p(e){var t=!!e&&"length"in e&&e.length,n=w(e);return!m(e)&&!x(e)&&("array"===n||0===t||"number"==typeof t&&0+~]|"+M+")"+M+"*"),U=new RegExp(M+"|>"),X=new RegExp(F),V=new RegExp("^"+I+"$"),G={ID:new RegExp("^#("+I+")"),CLASS:new RegExp("^\\.("+I+")"),TAG:new RegExp("^("+I+"|[*])"),ATTR:new RegExp("^"+W),PSEUDO:new RegExp("^"+F),CHILD:new RegExp("^:(only|first|last|nth|nth-last)-(child|of-type)(?:\$"+M+"*(even|odd|(([+-]|)(\\d*)n|)"+M+"*(?:([+-]|)"+M+"*(\\d+)|))"+M+"*\$|)","i"),bool:new RegExp("^(?:"+R+")$","i"),needsContext:new RegExp("^"+M+"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\$"+M+"*((?:-\\d)?\\d*)"+M+"*\$|)(?=[^-]|$)","i")},Y=/HTML$/i,Q=/^(?:input|select|textarea|button)$/i,J=/^h\d$/i,K=/^[^{]+\{\s*\[native \w/,Z=/^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,ee=/[+~]/,te=new RegExp("\\\\[\\da-fA-F]{1,6}"+M+"?|\\\\([^\\r\\n\\f])","g"),ne=function(e,t){var n="0x"+e.slice(1)-65536;return t||(n<0?String.fromCharCode(n+65536):String.fromCharCode(n>>10|55296,1023&n|56320))},re=/([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,ie=function(e,t){return t?"\0"===e?"\ufffd":e.slice(0,-1)+"\\"+e.charCodeAt(e.length-1).toString(16)+" ":"\\"+e},oe=function(){T()},ae=be(function(e){return!0===e.disabled&&"fieldset"===e.nodeName.toLowerCase()},{dir:"parentNode",next:"legend"});try{H.apply(t=O.call(p.childNodes),p.childNodes),t[p.childNodes.length].nodeType}catch(e){H={apply:t.length?function(e,t){L.apply(e,O.call(t))}:function(e,t){var n=e.length,r=0;while(e[n++]=t[r++]);e.length=n-1}}}function se(t,e,n,r){var i,o,a,s,u,l,c,f=e&&e.ownerDocument,p=e?e.nodeType:9;if(n=n||[],"string"!=typeof t||!t||1!==p&&9!==p&&11!==p)return n;if(!r&&(T(e),e=e||C,E)){if(11!==p&&(u=Z.exec(t)))if(i=u[1]){if(9===p){if(!(a=e.getElementById(i)))return n;if(a.id===i)return n.push(a),n}else if(f&&(a=f.getElementById(i))&&y(e,a)&&a.id===i)return n.push(a),n}else{if(u[2])return H.apply(n,e.getElementsByTagName(t)),n;if((i=u[3])&&d.getElementsByClassName&&e.getElementsByClassName)return H.apply(n,e.getElementsByClassName(i)),n}if(d.qsa&&!N[t+" "]&&(!v||!v.test(t))&&(1!==p||"object"!==e.nodeName.toLowerCase())){if(c=t,f=e,1===p&&(U.test(t)||z.test(t))){(f=ee.test(t)&&ye(e.parentNode)||e)===e&&d.scope||((s=e.getAttribute("id"))?s=s.replace(re,ie):e.setAttribute("id",s=S)),o=(l=h(t)).length;while(o--)l[o]=(s?"#"+s:":scope")+" "+xe(l[o]);c=l.join(",")}try{return H.apply(n,f.querySelectorAll(c)),n}catch(e){N(t,!0)}finally{s===S&&e.removeAttribute("id")}}}return g(t.replace($,"$1"),e,n,r)}function ue(){var r=[];return function e(t,n){return r.push(t+" ")>b.cacheLength&&delete e[r.shift()],e[t+" "]=n}}function le(e){return e[S]=!0,e}function ce(e){var t=C.createElement("fieldset");try{return!!e(t)}catch(e){return!1}finally{t.parentNode&&t.parentNode.removeChild(t),t=null}}function fe(e,t){var n=e.split("|"),r=n.length;while(r--)b.attrHandle[n[r]]=t}function pe(e,t){var n=t&&e,r=n&&1===e.nodeType&&1===t.nodeType&&e.sourceIndex-t.sourceIndex;if(r)return r;if(n)while(n=n.nextSibling)if(n===t)return-1;return e?1:-1}function de(t){return function(e){return"input"===e.nodeName.toLowerCase()&&e.type===t}}function he(n){return function(e){var t=e.nodeName.toLowerCase();return("input"===t||"button"===t)&&e.type===n}}function ge(t){return function(e){return"form"in e?e.parentNode&&!1===e.disabled?"label"in e?"label"in e.parentNode?e.parentNode.disabled===t:e.disabled===t:e.isDisabled===t||e.isDisabled!==!t&&ae(e)===t:e.disabled===t:"label"in e&&e.disabled===t}}function ve(a){return le(function(o){return o=+o,le(function(e,t){var n,r=a([],e.length,o),i=r.length;while(i--)e[n=r[i]]&&(e[n]=!(t[n]=e[n]))})})}function ye(e){return e&&"undefined"!=typeof e.getElementsByTagName&&e}for(e in d=se.support={},i=se.isXML=function(e){var t=e&&e.namespaceURI,n=e&&(e.ownerDocument||e).documentElement;return!Y.test(t||n&&n.nodeName||"HTML")},T=se.setDocument=function(e){var t,n,r=e?e.ownerDocument||e:p;return r!=C&&9===r.nodeType&&r.documentElement&&(a=(C=r).documentElement,E=!i(C),p!=C&&(n=C.defaultView)&&n.top!==n&&(n.addEventListener?n.addEventListener("unload",oe,!1):n.attachEvent&&n.attachEvent("onunload",oe)),d.scope=ce(function(e){return a.appendChild(e).appendChild(C.createElement("div")),"undefined"!=typeof e.querySelectorAll&&!e.querySelectorAll(":scope fieldset div").length}),d.attributes=ce(function(e){return e.className="i",!e.getAttribute("className")}),d.getElementsByTagName=ce(function(e){return e.appendChild(C.createComment("")),!e.getElementsByTagName("*").length}),d.getElementsByClassName=K.test(C.getElementsByClassName),d.getById=ce(function(e){return a.appendChild(e).id=S,!C.getElementsByName||!C.getElementsByName(S).length}),d.getById?(b.filter.ID=function(e){var t=e.replace(te,ne);return function(e){return e.getAttribute("id")===t}},b.find.ID=function(e,t){if("undefined"!=typeof t.getElementById&&E){var n=t.getElementById(e);return n?[n]:[]}}):(b.filter.ID=function(e){var n=e.replace(te,ne);return function(e){var t="undefined"!=typeof e.getAttributeNode&&e.getAttributeNode("id");return t&&t.value===n}},b.find.ID=function(e,t){if("undefined"!=typeof t.getElementById&&E){var n,r,i,o=t.getElementById(e);if(o){if((n=o.getAttributeNode("id"))&&n.value===e)return[o];i=t.getElementsByName(e),r=0;while(o=i[r++])if((n=o.getAttributeNode("id"))&&n.value===e)return[o]}return[]}}),b.find.TAG=d.getElementsByTagName?function(e,t){return"undefined"!=typeof t.getElementsByTagName?t.getElementsByTagName(e):d.qsa?t.querySelectorAll(e):void 0}:function(e,t){var n,r=[],i=0,o=t.getElementsByTagName(e);if("*"===e){while(n=o[i++])1===n.nodeType&&r.push(n);return r}return o},b.find.CLASS=d.getElementsByClassName&&function(e,t){if("undefined"!=typeof t.getElementsByClassName&&E)return t.getElementsByClassName(e)},s=[],v=[],(d.qsa=K.test(C.querySelectorAll))&&(ce(function(e){var t;a.appendChild(e).innerHTML="",e.querySelectorAll("[msallowcapture^='']").length&&v.push("[*^$]="+M+"*(?:''|\"\")"),e.querySelectorAll("[selected]").length||v.push("\\["+M+"*(?:value|"+R+")"),e.querySelectorAll("[id~="+S+"-]").length||v.push("~="),(t=C.createElement("input")).setAttribute("name",""),e.appendChild(t),e.querySelectorAll("[name='']").length||v.push("\\["+M+"*name"+M+"*="+M+"*(?:''|\"\")"),e.querySelectorAll(":checked").length||v.push(":checked"),e.querySelectorAll("a#"+S+"+*").length||v.push(".#.+[+~]"),e.querySelectorAll("\\\f"),v.push("[\\r\\n\\f]")}),ce(function(e){e.innerHTML="";var t=C.createElement("input");t.setAttribute("type","hidden"),e.appendChild(t).setAttribute("name","D"),e.querySelectorAll("[name=d]").length&&v.push("name"+M+"*[*^$|!~]?="),2!==e.querySelectorAll(":enabled").length&&v.push(":enabled",":disabled"),a.appendChild(e).disabled=!0,2!==e.querySelectorAll(":disabled").length&&v.push(":enabled",":disabled"),e.querySelectorAll("*,:x"),v.push(",.*:")})),(d.matchesSelector=K.test(c=a.matches||a.webkitMatchesSelector||a.mozMatchesSelector||a.oMatchesSelector||a.msMatchesSelector))&&ce(function(e){d.disconnectedMatch=c.call(e,"*"),c.call(e,"[s!='']:x"),s.push("!=",F)}),v=v.length&&new RegExp(v.join("|")),s=s.length&&new RegExp(s.join("|")),t=K.test(a.compareDocumentPosition),y=t||K.test(a.contains)?function(e,t){var n=9===e.nodeType?e.documentElement:e,r=t&&t.parentNode;return e===r||!(!r||1!==r.nodeType||!(n.contains?n.contains(r):e.compareDocumentPosition&&16&e.compareDocumentPosition(r)))}:function(e,t){if(t)while(t=t.parentNode)if(t===e)return!0;return!1},j=t?function(e,t){if(e===t)return l=!0,0;var n=!e.compareDocumentPosition-!t.compareDocumentPosition;return n||(1&(n=(e.ownerDocument||e)==(t.ownerDocument||t)?e.compareDocumentPosition(t):1)||!d.sortDetached&&t.compareDocumentPosition(e)===n?e==C||e.ownerDocument==p&&y(p,e)?-1:t==C||t.ownerDocument==p&&y(p,t)?1:u?P(u,e)-P(u,t):0:4&n?-1:1)}:function(e,t){if(e===t)return l=!0,0;var n,r=0,i=e.parentNode,o=t.parentNode,a=[e],s=[t];if(!i||!o)return e==C?-1:t==C?1:i?-1:o?1:u?P(u,e)-P(u,t):0;if(i===o)return pe(e,t);n=e;while(n=n.parentNode)a.unshift(n);n=t;while(n=n.parentNode)s.unshift(n);while(a[r]===s[r])r++;return r?pe(a[r],s[r]):a[r]==p?-1:s[r]==p?1:0}),C},se.matches=function(e,t){return se(e,null,null,t)},se.matchesSelector=function(e,t){if(T(e),d.matchesSelector&&E&&!N[t+" "]&&(!s||!s.test(t))&&(!v||!v.test(t)))try{var n=c.call(e,t);if(n||d.disconnectedMatch||e.document&&11!==e.document.nodeType)return n}catch(e){N(t,!0)}return 0":{dir:"parentNode",first:!0}," ":{dir:"parentNode"},"+":{dir:"previousSibling",first:!0},"~":{dir:"previousSibling"}},preFilter:{ATTR:function(e){return e[1]=e[1].replace(te,ne),e[3]=(e[3]||e[4]||e[5]||"").replace(te,ne),"~="===e[2]&&(e[3]=" "+e[3]+" "),e.slice(0,4)},CHILD:function(e){return e[1]=e[1].toLowerCase(),"nth"===e[1].slice(0,3)?(e[3]||se.error(e[0]),e[4]=+(e[4]?e[5]+(e[6]||1):2*("even"===e[3]||"odd"===e[3])),e[5]=+(e[7]+e[8]||"odd"===e[3])):e[3]&&se.error(e[0]),e},PSEUDO:function(e){var t,n=!e[6]&&e[2];return G.CHILD.test(e[0])?null:(e[3]?e[2]=e[4]||e[5]||"":n&&X.test(n)&&(t=h(n,!0))&&(t=n.indexOf(")",n.length-t)-n.length)&&(e[0]=e[0].slice(0,t),e[2]=n.slice(0,t)),e.slice(0,3))}},filter:{TAG:function(e){var t=e.replace(te,ne).toLowerCase();return"*"===e?function(){return!0}:function(e){return e.nodeName&&e.nodeName.toLowerCase()===t}},CLASS:function(e){var t=m[e+" "];return t||(t=new RegExp("(^|"+M+")"+e+"("+M+"|$)"))&&m(e,function(e){return t.test("string"==typeof e.className&&e.className||"undefined"!=typeof e.getAttribute&&e.getAttribute("class")||"")})},ATTR:function(n,r,i){return function(e){var t=se.attr(e,n);return null==t?"!="===r:!r||(t+="","="===r?t===i:"!="===r?t!==i:"^="===r?i&&0===t.indexOf(i):"*="===r?i&&-1:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i;function j(e,n,r){return m(n)?S.grep(e,function(e,t){return!!n.call(e,t,e)!==r}):n.nodeType?S.grep(e,function(e){return e===n!==r}):"string"!=typeof n?S.grep(e,function(e){return-1)[^>]*|#([\w-]+))$/;(S.fn.init=function(e,t,n){var r,i;if(!e)return this;if(n=n||D,"string"==typeof e){if(!(r="<"===e[0]&&">"===e[e.length-1]&&3<=e.length?[null,e,null]:q.exec(e))||!r[1]&&t)return!t||t.jquery?(t||n).find(e):this.constructor(t).find(e);if(r[1]){if(t=t instanceof S?t[0]:t,S.merge(this,S.parseHTML(r[1],t&&t.nodeType?t.ownerDocument||t:E,!0)),N.test(r[1])&&S.isPlainObject(t))for(r in t)m(this[r])?this[r](t[r]):this.attr(r,t[r]);return this}return(i=E.getElementById(r[2]))&&(this[0]=i,this.length=1),this}return e.nodeType?(this[0]=e,this.length=1,this):m(e)?void 0!==n.ready?n.ready(e):e(S):S.makeArray(e,this)}).prototype=S.fn,D=S(E);var L=/^(?:parents|prev(?:Until|All))/,H={children:!0,contents:!0,next:!0,prev:!0};function O(e,t){while((e=e[t])&&1!==e.nodeType);return e}S.fn.extend({has:function(e){var t=S(e,this),n=t.length;return this.filter(function(){for(var e=0;e\x20\t\r\n\f]*)/i,he=/^$|^module$|\/(?:java|ecma)script/i;ce=E.createDocumentFragment().appendChild(E.createElement("div")),(fe=E.createElement("input")).setAttribute("type","radio"),fe.setAttribute("checked","checked"),fe.setAttribute("name","t"),ce.appendChild(fe),y.checkClone=ce.cloneNode(!0).cloneNode(!0).lastChild.checked,ce.innerHTML="",y.noCloneChecked=!!ce.cloneNode(!0).lastChild.defaultValue,ce.innerHTML="",y.option=!!ce.lastChild;var ge={thead:[1,"","

"],col:[2,"","

"],tr:[2,"","

"],td:[3,"","

"],_default:[0,"",""]};function ve(e,t){var n;return n="undefined"!=typeof e.getElementsByTagName?e.getElementsByTagName(t||"*"):"undefined"!=typeof e.querySelectorAll?e.querySelectorAll(t||"*"):[],void 0===t||t&&A(e,t)?S.merge([e],n):n}function ye(e,t){for(var n=0,r=e.length;n",""]);var me=/<|&#?\w+;/;function xe(e,t,n,r,i){for(var o,a,s,u,l,c,f=t.createDocumentFragment(),p=[],d=0,h=e.length;d\s*$/g;function je(e,t){return A(e,"table")&&A(11!==t.nodeType?t:t.firstChild,"tr")&&S(e).children("tbody")[0]||e}function De(e){return e.type=(null!==e.getAttribute("type"))+"/"+e.type,e}function qe(e){return"true/"===(e.type||"").slice(0,5)?e.type=e.type.slice(5):e.removeAttribute("type"),e}function Le(e,t){var n,r,i,o,a,s;if(1===t.nodeType){if(Y.hasData(e)&&(s=Y.get(e).events))for(i in Y.remove(t,"handle events"),s)for(n=0,r=s[i].length;n").attr(n.scriptAttrs||{}).prop({charset:n.scriptCharset,src:n.url}).on("load error",i=function(e){r.remove(),i=null,e&&t("error"===e.type?404:200,e.type)}),E.head.appendChild(r[0])},abort:function(){i&&i()}}});var _t,zt=[],Ut=/(=)\?(?=&|$)|\?\?/;S.ajaxSetup({jsonp:"callback",jsonpCallback:function(){var e=zt.pop()||S.expando+"_"+wt.guid++;return this[e]=!0,e}}),S.ajaxPrefilter("json jsonp",function(e,t,n){var r,i,o,a=!1!==e.jsonp&&(Ut.test(e.url)?"url":"string"==typeof e.data&&0===(e.contentType||"").indexOf("application/x-www-form-urlencoded")&&Ut.test(e.data)&&"data");if(a||"jsonp"===e.dataTypes[0])return r=e.jsonpCallback=m(e.jsonpCallback)?e.jsonpCallback():e.jsonpCallback,a?e[a]=e[a].replace(Ut,"$1"+r):!1!==e.jsonp&&(e.url+=(Tt.test(e.url)?"&":"?")+e.jsonp+"="+r),e.converters["script json"]=function(){return o||S.error(r+" was not called"),o[0]},e.dataTypes[0]="json",i=C[r],C[r]=function(){o=arguments},n.always(function(){void 0===i?S(C).removeProp(r):C[r]=i,e[r]&&(e.jsonpCallback=t.jsonpCallback,zt.push(r)),o&&m(i)&&i(o[0]),o=i=void 0}),"script"}),y.createHTMLDocument=((_t=E.implementation.createHTMLDocument("").body).innerHTML="",2===_t.childNodes.length),S.parseHTML=function(e,t,n){return"string"!=typeof e?[]:("boolean"==typeof t&&(n=t,t=!1),t||(y.createHTMLDocument?((r=(t=E.implementation.createHTMLDocument("")).createElement("base")).href=E.location.href,t.head.appendChild(r)):t=E),o=!n&&[],(i=N.exec(e))?[t.createElement(i[1])]:(i=xe([e],t,o),o&&o.length&&S(o).remove(),S.merge([],i.childNodes)));var r,i,o},S.fn.load=function(e,t,n){var r,i,o,a=this,s=e.indexOf(" ");return-1").append(S.parseHTML(e)).find(r):e)}).always(n&&function(e,t){a.each(function(){n.apply(this,o||[e.responseText,t,e])})}),this},S.expr.pseudos.animated=function(t){return S.grep(S.timers,function(e){return t===e.elem}).length},S.offset={setOffset:function(e,t,n){var r,i,o,a,s,u,l=S.css(e,"position"),c=S(e),f={};"static"===l&&(e.style.position="relative"),s=c.offset(),o=S.css(e,"top"),u=S.css(e,"left"),("absolute"===l||"fixed"===l)&&-1<(o+u).indexOf("auto")?(a=(r=c.position()).top,i=r.left):(a=parseFloat(o)||0,i=parseFloat(u)||0),m(t)&&(t=t.call(e,n,S.extend({},s))),null!=t.top&&(f.top=t.top-s.top+a),null!=t.left&&(f.left=t.left-s.left+i),"using"in t?t.using.call(e,f):c.css(f)}},S.fn.extend({offset:function(t){if(arguments.length)return void 0===t?this:this.each(function(e){S.offset.setOffset(this,t,e)});var e,n,r=this[0];return r?r.getClientRects().length?(e=r.getBoundingClientRect(),n=r.ownerDocument.defaultView,{top:e.top+n.pageYOffset,left:e.left+n.pageXOffset}):{top:0,left:0}:void 0},position:function(){if(this[0]){var e,t,n,r=this[0],i={top:0,left:0};if("fixed"===S.css(r,"position"))t=r.getBoundingClientRect();else{t=this.offset(),n=r.ownerDocument,e=r.offsetParent||n.documentElement;while(e&&(e===n.body||e===n.documentElement)&&"static"===S.css(e,"position"))e=e.parentNode;e&&e!==r&&1===e.nodeType&&((i=S(e).offset()).top+=S.css(e,"borderTopWidth",!0),i.left+=S.css(e,"borderLeftWidth",!0))}return{top:t.top-i.top-S.css(r,"marginTop",!0),left:t.left-i.left-S.css(r,"marginLeft",!0)}}},offsetParent:function(){return this.map(function(){var e=this.offsetParent;while(e&&"static"===S.css(e,"position"))e=e.offsetParent;return e||re})}}),S.each({scrollLeft:"pageXOffset",scrollTop:"pageYOffset"},function(t,i){var o="pageYOffset"===i;S.fn[t]=function(e){return $(this,function(e,t,n){var r;if(x(e)?r=e:9===e.nodeType&&(r=e.defaultView),void 0===n)return r?r[i]:e[t];r?r.scrollTo(o?r.pageXOffset:n,o?n:r.pageYOffset):e[t]=n},t,e,arguments.length)}}),S.each(["top","left"],function(e,n){S.cssHooks[n]=Fe(y.pixelPosition,function(e,t){if(t)return t=We(e,n),Pe.test(t)?S(e).position()[n]+"px":t})}),S.each({Height:"height",Width:"width"},function(a,s){S.each({padding:"inner"+a,content:s,"":"outer"+a},function(r,o){S.fn[o]=function(e,t){var n=arguments.length&&(r||"boolean"!=typeof e),i=r||(!0===e||!0===t?"margin":"border");return $(this,function(e,t,n){var r;return x(e)?0===o.indexOf("outer")?e["inner"+a]:e.document.documentElement["client"+a]:9===e.nodeType?(r=e.documentElement,Math.max(e.body["scroll"+a],r["scroll"+a],e.body["offset"+a],r["offset"+a],r["client"+a])):void 0===n?S.css(e,t,i):S.style(e,t,n,i)},s,n?e:void 0,n)}})}),S.each(["ajaxStart","ajaxStop","ajaxComplete","ajaxError","ajaxSuccess","ajaxSend"],function(e,t){S.fn[t]=function(e){return this.on(t,e)}}),S.fn.extend({bind:function(e,t,n){return this.on(e,null,t,n)},unbind:function(e,t){return this.off(e,null,t)},delegate:function(e,t,n,r){return this.on(t,e,n,r)},undelegate:function(e,t,n){return 1===arguments.length?this.off(e,"**"):this.off(t,e||"**",n)},hover:function(e,t){return this.mouseenter(e).mouseleave(t||e)}}),S.each("blur focus focusin focusout resize scroll click dblclick mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave change select submit keydown keypress keyup contextmenu".split(" "),function(e,n){S.fn[n]=function(e,t){return 0 - - - - + + @@ -1874,6 +1947,9 @@ $(document).ready(function () { - + - + - + code{white-space: pre-wrap;} + span.smallcaps{font-variant: small-caps;} + span.underline{text-decoration: underline;} + div.column{display: inline-block; vertical-align: top; width: 50%;} + div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} + ul.task-list{list-style: none;} + + + @@ -1711,6 +1748,9 @@ $(document).ready(function () { - + + + + + + + + + + + + +

+ + + + +

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 +be fitted with the mkin package.

It was assembled in the course of work package 1.2 of Project Number +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 1.2.2 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 +starting parameters of the fit, so that all starting parameters of +saem fits are now listed in the summary. The +saemix package is used as a backend for fitting the NLHM, +but is also loaded to make the convergence plot function available.

+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 +

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)

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")

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

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

+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")
+}

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

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

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

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

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

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

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

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()

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

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

All fits converged successfully.

+illparms(cyan_saem_full) |> kable()

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

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

In almost all models, the random effect for the initial concentration +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)

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

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

Model comparison based on AIC and BIC indicates that the +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.

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)
+)

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,
+  quiet = TRUE)
+status(f_sep_1_const) |> kable()

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

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

+f_sep_1_tc <- update(f_sep_1_const, error_model = "tc")
+status(f_sep_1_tc) |> kable()

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

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

Most separate fits converged successfully. The biggest convergence +problems are seen when using the HS model with constant variance.

For the hierarchical pathway fits, those random effects that could +not be quantified in the corresponding parent data analyses are +excluded.

In the code below, the output of the illparms function +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)

+status(f_saem_1) |> kable()

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

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

The status information from the individual fits shows that all fits +completed successfully. The matrix entries Fth and FO indicate that the +Fisher Information Matrix could not be inverted for the fixed effects +(theta) and the random effects (Omega), respectively. For the affected +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	NA	NA
fomc_path_1	sd(log_k_J9Z38), sd(f_cyan_ilr_2), +sd(f_JCZ38_qlogis)	NA
dfop_path_1	NA	NA
sforb_path_1	NA	NA
hs_path_1	NA	NA

The model comparison below suggests that the pathway fits using DFOP +or SFORB for the parent compound provide the best fit.

+anova(f_saem_1) |> kable(digits = 1)

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

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

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"]])

+DFOP pathway fit with two-component error +

+plot(f_saem_1[["sforb_path_1", "tc"]])

+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.

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 +transformation products are pairs of an organic acid with its +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
+  )
+)
+f_sep_2_const <- mmkin(
+  cyan_path_2,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl,
+  quiet = TRUE)
+
+status(f_sep_2_const) |> kable()

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

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

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()

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

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

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)

+status(f_saem_2) |> kable()

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

	const	tc
fomc_path_2	OK	FO
dfop_path_2	OK	OK
sforb_path_2	OK	OK

The hierarchical fits for the alternative pathway completed +successfully.

+illparms(f_saem_2) |> kable()

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

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

In both fits, the 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) |> kable(digits = 1)

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

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

The variants using the biexponential models DFOP and SFORB for the +parent compound and the two-component error model give the lowest AIC +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"]])

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

+plot(f_saem_2[["dfop_path_2", "tc"]])

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

+plot(f_saem_2[["sforb_path_2", "tc"]])

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

+ +

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 +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, "no_ranef")
+
+f_saem_3 <- update(f_saem_2,
+  no_random_effect = no_ranef,
+  cluster = cl)

+status(f_saem_3) |> kable()

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

	const	tc
fomc_path_2	E	Fth
dfop_path_2	Fth	Fth
sforb_path_2	Fth	Fth

With the exception of the FOMC pathway fit with constant variance, +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	E
dfop_path_2
sforb_path_2

+anova(f_saem_3) |> kable(digits = 1)

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

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

While the AIC and BIC values of the best fit (DFOP pathway fit with +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.

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 +quite different and partly only cover the formation phase.

The run times of the pathway fits were several hours, limiting the +practical feasibility of iterative refinements based on ill-defined +parameters and of alternative checks of parameter identifiability based +on multistart runs.

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"]])

+SFO pathway fit with two-component error +

+plot(f_saem_1[["fomc_path_1", "tc"]])

+FOMC pathway fit with two-component error +

+plot(f_saem_1[["sforb_path_1", "tc"]])

+HS pathway fit with two-component error +

Hierarchical fit listings +

Pathway 1 +

+ +Hierarchical SFO path 1 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:07:38 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - k_cyan * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1088.473 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0     log_k_cyan    log_k_JCZ38    log_k_J9Z38    log_k_JSE76 
+       95.3304        -3.8459        -3.1305        -5.0678        -5.3196 
+  f_cyan_ilr_1   f_cyan_ilr_2 f_JCZ38_qlogis 
+        0.8158        22.5404        10.4289 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_0          4.797     0.0000       0.000       0.000      0.0000
+log_k_cyan      0.000     0.9619       0.000       0.000      0.0000
+log_k_JCZ38     0.000     0.0000       2.139       0.000      0.0000
+log_k_J9Z38     0.000     0.0000       0.000       1.639      0.0000
+log_k_JSE76     0.000     0.0000       0.000       0.000      0.7894
+f_cyan_ilr_1    0.000     0.0000       0.000       0.000      0.0000
+f_cyan_ilr_2    0.000     0.0000       0.000       0.000      0.0000
+f_JCZ38_qlogis  0.000     0.0000       0.000       0.000      0.0000
+               f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_0               0.0000        0.000           0.00
+log_k_cyan           0.0000        0.000           0.00
+log_k_JCZ38          0.0000        0.000           0.00
+log_k_J9Z38          0.0000        0.000           0.00
+log_k_JSE76          0.0000        0.000           0.00
+f_cyan_ilr_1         0.7714        0.000           0.00
+f_cyan_ilr_2         0.0000        8.684           0.00
+f_JCZ38_qlogis       0.0000        0.000          13.48
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2693 2687  -1330
+
+Optimised parameters:
+                     est. lower upper
+cyan_0            95.0946    NA    NA
+log_k_cyan        -3.8544    NA    NA
+log_k_JCZ38       -3.0402    NA    NA
+log_k_J9Z38       -5.0109    NA    NA
+log_k_JSE76       -5.2857    NA    NA
+f_cyan_ilr_1       0.8069    NA    NA
+f_cyan_ilr_2      16.6623    NA    NA
+f_JCZ38_qlogis     1.3602    NA    NA
+a.1                4.8326    NA    NA
+SD.log_k_cyan      0.5842    NA    NA
+SD.log_k_JCZ38     1.2680    NA    NA
+SD.log_k_J9Z38     0.3626    NA    NA
+SD.log_k_JSE76     0.5244    NA    NA
+SD.f_cyan_ilr_1    0.2752    NA    NA
+SD.f_cyan_ilr_2    2.3556    NA    NA
+SD.f_JCZ38_qlogis  0.2400    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5842    NA    NA
+SD.log_k_JCZ38    1.2680    NA    NA
+SD.log_k_J9Z38    0.3626    NA    NA
+SD.log_k_JSE76    0.5244    NA    NA
+SD.f_cyan_ilr_1   0.2752    NA    NA
+SD.f_cyan_ilr_2   2.3556    NA    NA
+SD.f_JCZ38_qlogis 0.2400    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 4.833    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           95.094581    NA    NA
+k_cyan            0.021186    NA    NA
+k_JCZ38           0.047825    NA    NA
+k_J9Z38           0.006665    NA    NA
+k_JSE76           0.005063    NA    NA
+f_cyan_to_JCZ38   0.757885    NA    NA
+f_cyan_to_J9Z38   0.242115    NA    NA
+f_JCZ38_to_JSE76  0.795792    NA    NA
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  7.579e-01
+cyan_J9Z38  2.421e-01
+cyan_sink   5.877e-10
+JCZ38_JSE76 7.958e-01
+JCZ38_sink  2.042e-01
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   32.72 108.68
+JCZ38  14.49  48.15
+J9Z38 103.99 345.46
+JSE76 136.90 454.76
+
+

+ +Hierarchical SFO path 1 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:08:17 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - k_cyan * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * k_cyan * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * k_cyan * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1127.552 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0     log_k_cyan    log_k_JCZ38    log_k_J9Z38    log_k_JSE76 
+       96.0039        -3.8907        -3.1276        -5.0069        -4.9367 
+  f_cyan_ilr_1   f_cyan_ilr_2 f_JCZ38_qlogis 
+        0.7937        20.0030        15.1336 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_cyan log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_0          4.859      0.000        0.00        0.00      0.0000
+log_k_cyan      0.000      0.962        0.00        0.00      0.0000
+log_k_JCZ38     0.000      0.000        2.04        0.00      0.0000
+log_k_J9Z38     0.000      0.000        0.00        1.72      0.0000
+log_k_JSE76     0.000      0.000        0.00        0.00      0.9076
+f_cyan_ilr_1    0.000      0.000        0.00        0.00      0.0000
+f_cyan_ilr_2    0.000      0.000        0.00        0.00      0.0000
+f_JCZ38_qlogis  0.000      0.000        0.00        0.00      0.0000
+               f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_0               0.0000        0.000           0.00
+log_k_cyan           0.0000        0.000           0.00
+log_k_JCZ38          0.0000        0.000           0.00
+log_k_J9Z38          0.0000        0.000           0.00
+log_k_JSE76          0.0000        0.000           0.00
+f_cyan_ilr_1         0.7598        0.000           0.00
+f_cyan_ilr_2         0.0000        7.334           0.00
+f_JCZ38_qlogis       0.0000        0.000          11.78
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2658 2651  -1312
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            94.72923    NA    NA
+log_k_cyan        -3.91670    NA    NA
+log_k_JCZ38       -3.12917    NA    NA
+log_k_J9Z38       -5.06070    NA    NA
+log_k_JSE76       -5.09254    NA    NA
+f_cyan_ilr_1       0.81116    NA    NA
+f_cyan_ilr_2      39.97850    NA    NA
+f_JCZ38_qlogis     3.09728    NA    NA
+a.1                3.95044    NA    NA
+b.1                0.07998    NA    NA
+SD.log_k_cyan      0.58855    NA    NA
+SD.log_k_JCZ38     1.29753    NA    NA
+SD.log_k_J9Z38     0.62851    NA    NA
+SD.log_k_JSE76     0.37235    NA    NA
+SD.f_cyan_ilr_1    0.37346    NA    NA
+SD.f_cyan_ilr_2    1.41667    NA    NA
+SD.f_JCZ38_qlogis  1.81467    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5886    NA    NA
+SD.log_k_JCZ38    1.2975    NA    NA
+SD.log_k_J9Z38    0.6285    NA    NA
+SD.log_k_JSE76    0.3724    NA    NA
+SD.f_cyan_ilr_1   0.3735    NA    NA
+SD.f_cyan_ilr_2   1.4167    NA    NA
+SD.f_JCZ38_qlogis 1.8147    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.95044    NA    NA
+b.1 0.07998    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           94.729229    NA    NA
+k_cyan            0.019907    NA    NA
+k_JCZ38           0.043754    NA    NA
+k_J9Z38           0.006341    NA    NA
+k_JSE76           0.006142    NA    NA
+f_cyan_to_JCZ38   0.758991    NA    NA
+f_cyan_to_J9Z38   0.241009    NA    NA
+f_JCZ38_to_JSE76  0.956781    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.75899
+cyan_J9Z38  0.24101
+cyan_sink   0.00000
+JCZ38_JSE76 0.95678
+JCZ38_sink  0.04322
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   34.82 115.67
+JCZ38  15.84  52.63
+J9Z38 109.31 363.12
+JSE76 112.85 374.87
+
+

+ +Hierarchical FOMC path 1 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:09:12 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1182.258 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.2314        -3.3680        -5.1108        -5.9416         0.7144 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+        7.3870        15.7604        -0.1791         2.9811 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.416       0.000         0.0       0.000       0.0000
+log_k_JCZ38     0.000       2.439         0.0       0.000       0.0000
+log_k_J9Z38     0.000       0.000         1.7       0.000       0.0000
+log_k_JSE76     0.000       0.000         0.0       1.856       0.0000
+f_cyan_ilr_1    0.000       0.000         0.0       0.000       0.7164
+f_cyan_ilr_2    0.000       0.000         0.0       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000         0.0       0.000       0.0000
+log_alpha       0.000       0.000         0.0       0.000       0.0000
+log_beta        0.000       0.000         0.0       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          12.33           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          20.42    0.0000   0.0000
+log_alpha              0.00           0.00    0.4144   0.0000
+log_beta               0.00           0.00    0.0000   0.5077
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2428 2421  -1196
+
+Optimised parameters:
+                      est.     lower    upper
+cyan_0            101.0225 98.306270 103.7387
+log_k_JCZ38        -3.3786 -4.770657  -1.9866
+log_k_J9Z38        -5.2603 -5.902085  -4.6186
+log_k_JSE76        -6.1427 -7.318336  -4.9671
+f_cyan_ilr_1        0.7437  0.421215   1.0663
+f_cyan_ilr_2        0.9108  0.267977   1.5537
+f_JCZ38_qlogis      2.0487  0.524897   3.5724
+log_alpha          -0.2268 -0.618049   0.1644
+log_beta            2.8986  2.700701   3.0964
+a.1                 3.4058  3.169913   3.6416
+SD.cyan_0           2.5279  0.454190   4.6016
+SD.log_k_JCZ38      1.5636  0.572824   2.5543
+SD.log_k_J9Z38      0.5316 -0.004405   1.0677
+SD.log_k_JSE76      0.9903  0.106325   1.8742
+SD.f_cyan_ilr_1     0.3464  0.112066   0.5807
+SD.f_cyan_ilr_2     0.2804 -0.393900   0.9546
+SD.f_JCZ38_qlogis   0.9416 -0.152986   2.0362
+SD.log_alpha        0.4273  0.161044   0.6936
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph
+log_k_JCZ38    -0.0156                                                        
+log_k_J9Z38    -0.0493  0.0073                                                
+log_k_JSE76    -0.0329  0.0018  0.0069                                        
+f_cyan_ilr_1   -0.0086  0.0180 -0.1406  0.0012                                
+f_cyan_ilr_2   -0.2629  0.0779  0.2826  0.0274  0.0099                        
+f_JCZ38_qlogis  0.0713 -0.0747 -0.0505  0.1169 -0.1022 -0.4893                
+log_alpha      -0.0556  0.0120  0.0336  0.0193  0.0036  0.0840 -0.0489        
+log_beta       -0.2898  0.0460  0.1305  0.0768  0.0190  0.4071 -0.1981  0.2772
+
+Random effects:
+                    est.     lower  upper
+SD.cyan_0         2.5279  0.454190 4.6016
+SD.log_k_JCZ38    1.5636  0.572824 2.5543
+SD.log_k_J9Z38    0.5316 -0.004405 1.0677
+SD.log_k_JSE76    0.9903  0.106325 1.8742
+SD.f_cyan_ilr_1   0.3464  0.112066 0.5807
+SD.f_cyan_ilr_2   0.2804 -0.393900 0.9546
+SD.f_JCZ38_qlogis 0.9416 -0.152986 2.0362
+SD.log_alpha      0.4273  0.161044 0.6936
+
+Variance model:
+     est. lower upper
+a.1 3.406  3.17 3.642
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.010e+02 9.831e+01 1.037e+02
+k_JCZ38          3.409e-02 8.475e-03 1.372e-01
+k_J9Z38          5.194e-03 2.734e-03 9.867e-03
+k_JSE76          2.149e-03 6.633e-04 6.963e-03
+f_cyan_to_JCZ38  6.481e-01        NA        NA
+f_cyan_to_J9Z38  2.264e-01        NA        NA
+f_JCZ38_to_JSE76 8.858e-01 6.283e-01 9.727e-01
+alpha            7.971e-01 5.390e-01 1.179e+00
+beta             1.815e+01 1.489e+01 2.212e+01
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6481
+cyan_J9Z38  0.2264
+cyan_sink   0.1255
+JCZ38_JSE76 0.8858
+JCZ38_sink  0.1142
+
+Estimated disappearance times:
+        DT50    DT90 DT50back
+cyan   25.15  308.01    92.72
+JCZ38  20.33   67.54       NA
+J9Z38 133.46  443.35       NA
+JSE76 322.53 1071.42       NA
+
+

+ +Hierarchical FOMC path 1 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:09:18 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1188.041 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+     101.13827       -3.32493       -5.08921       -5.93478        0.71330 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+      10.05989       12.79248       -0.09621        3.10646 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.643       0.000       0.000        0.00       0.0000
+log_k_JCZ38     0.000       2.319       0.000        0.00       0.0000
+log_k_J9Z38     0.000       0.000       1.731        0.00       0.0000
+log_k_JSE76     0.000       0.000       0.000        1.86       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000        0.00       0.7186
+f_cyan_ilr_2    0.000       0.000       0.000        0.00       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000        0.00       0.0000
+log_alpha       0.000       0.000       0.000        0.00       0.0000
+log_beta        0.000       0.000       0.000        0.00       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          12.49           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          20.19    0.0000   0.0000
+log_alpha              0.00           0.00    0.3142   0.0000
+log_beta               0.00           0.00    0.0000   0.7331
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2423 2416  -1193
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.57649    NA    NA
+log_k_JCZ38        -3.46250    NA    NA
+log_k_J9Z38        -5.24442    NA    NA
+log_k_JSE76        -5.75229    NA    NA
+f_cyan_ilr_1        0.68480    NA    NA
+f_cyan_ilr_2        0.61670    NA    NA
+f_JCZ38_qlogis     87.97407    NA    NA
+log_alpha          -0.15699    NA    NA
+log_beta            3.01540    NA    NA
+a.1                 3.11518    NA    NA
+b.1                 0.04445    NA    NA
+SD.log_k_JCZ38      1.40732    NA    NA
+SD.log_k_J9Z38      0.56510    NA    NA
+SD.log_k_JSE76      0.72067    NA    NA
+SD.f_cyan_ilr_1     0.31199    NA    NA
+SD.f_cyan_ilr_2     0.36894    NA    NA
+SD.f_JCZ38_qlogis   6.92892    NA    NA
+SD.log_alpha        0.25662    NA    NA
+SD.log_beta         0.35845    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4073    NA    NA
+SD.log_k_J9Z38    0.5651    NA    NA
+SD.log_k_JSE76    0.7207    NA    NA
+SD.f_cyan_ilr_1   0.3120    NA    NA
+SD.f_cyan_ilr_2   0.3689    NA    NA
+SD.f_JCZ38_qlogis 6.9289    NA    NA
+SD.log_alpha      0.2566    NA    NA
+SD.log_beta       0.3585    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.11518    NA    NA
+b.1 0.04445    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.006e+02    NA    NA
+k_JCZ38          3.135e-02    NA    NA
+k_J9Z38          5.277e-03    NA    NA
+k_JSE76          3.175e-03    NA    NA
+f_cyan_to_JCZ38  5.991e-01    NA    NA
+f_cyan_to_J9Z38  2.275e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+alpha            8.547e-01    NA    NA
+beta             2.040e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5991
+cyan_J9Z38  0.2275
+cyan_sink   0.1734
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.50 281.29    84.68
+JCZ38  22.11  73.44       NA
+J9Z38 131.36 436.35       NA
+JSE76 218.28 725.11       NA
+
+

+ +Hierarchical DFOP path 1 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:10:30 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1260.905 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.0644        -3.4008        -5.0024        -5.8613         0.6855 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        1.2365        13.7245        -1.8641        -4.5063        -0.6468 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.466       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.382       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.595       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       1.245       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6852
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis
+cyan_0                 0.00           0.00 0.0000 0.0000    0.000
+log_k_JCZ38            0.00           0.00 0.0000 0.0000    0.000
+log_k_J9Z38            0.00           0.00 0.0000 0.0000    0.000
+log_k_JSE76            0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_1           0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_2           1.28           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.11 0.0000 0.0000    0.000
+log_k1                 0.00           0.00 0.9866 0.0000    0.000
+log_k2                 0.00           0.00 0.0000 0.5953    0.000
+g_qlogis               0.00           0.00 0.0000 0.0000    1.583
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2403 2395  -1182
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            102.6079    NA    NA
+log_k_JCZ38        -3.4855    NA    NA
+log_k_J9Z38        -5.1686    NA    NA
+log_k_JSE76        -5.6697    NA    NA
+f_cyan_ilr_1        0.6714    NA    NA
+f_cyan_ilr_2        0.4986    NA    NA
+f_JCZ38_qlogis     55.4760    NA    NA
+log_k1             -1.8409    NA    NA
+log_k2             -4.4915    NA    NA
+g_qlogis           -0.6403    NA    NA
+a.1                 3.2387    NA    NA
+SD.log_k_JCZ38      1.4524    NA    NA
+SD.log_k_J9Z38      0.5151    NA    NA
+SD.log_k_JSE76      0.6514    NA    NA
+SD.f_cyan_ilr_1     0.3023    NA    NA
+SD.f_cyan_ilr_2     0.2959    NA    NA
+SD.f_JCZ38_qlogis   1.9984    NA    NA
+SD.log_k1           0.5188    NA    NA
+SD.log_k2           0.3894    NA    NA
+SD.g_qlogis         0.8579    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4524    NA    NA
+SD.log_k_J9Z38    0.5151    NA    NA
+SD.log_k_JSE76    0.6514    NA    NA
+SD.f_cyan_ilr_1   0.3023    NA    NA
+SD.f_cyan_ilr_2   0.2959    NA    NA
+SD.f_JCZ38_qlogis 1.9984    NA    NA
+SD.log_k1         0.5188    NA    NA
+SD.log_k2         0.3894    NA    NA
+SD.g_qlogis       0.8579    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.239    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          3.064e-02    NA    NA
+k_J9Z38          5.692e-03    NA    NA
+k_JSE76          3.449e-03    NA    NA
+f_cyan_to_JCZ38  5.798e-01    NA    NA
+f_cyan_to_J9Z38  2.243e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.587e-01    NA    NA
+k2               1.120e-02    NA    NA
+g                3.452e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5798
+cyan_J9Z38  0.2243
+cyan_sink   0.1958
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.21 167.73    50.49   4.368   61.87
+JCZ38  22.62  75.15       NA      NA      NA
+J9Z38 121.77 404.50       NA      NA      NA
+JSE76 200.98 667.64       NA      NA      NA
+
+

+ +Hierarchical DFOP path 1 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:16:28 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1617.774 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.3964        -3.3626        -4.9792        -5.8727         0.6814 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        6.7799        13.7245        -1.9222        -4.5035        -0.7172 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.317       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.272       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.633       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       1.271       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6838
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 g_qlogis
+cyan_0                 0.00           0.00 0.0000 0.0000    0.000
+log_k_JCZ38            0.00           0.00 0.0000 0.0000    0.000
+log_k_J9Z38            0.00           0.00 0.0000 0.0000    0.000
+log_k_JSE76            0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_1           0.00           0.00 0.0000 0.0000    0.000
+f_cyan_ilr_2          11.77           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.11 0.0000 0.0000    0.000
+log_k1                 0.00           0.00 0.9496 0.0000    0.000
+log_k2                 0.00           0.00 0.0000 0.5846    0.000
+g_qlogis               0.00           0.00 0.0000 0.0000    1.719
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2398 2390  -1179
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            100.8076    NA    NA
+log_k_JCZ38        -3.4684    NA    NA
+log_k_J9Z38        -5.0844    NA    NA
+log_k_JSE76        -5.5743    NA    NA
+f_cyan_ilr_1        0.6669    NA    NA
+f_cyan_ilr_2        0.7912    NA    NA
+f_JCZ38_qlogis     84.1825    NA    NA
+log_k1             -2.1671    NA    NA
+log_k2             -4.5447    NA    NA
+g_qlogis           -0.5631    NA    NA
+a.1                 2.9627    NA    NA
+b.1                 0.0444    NA    NA
+SD.log_k_JCZ38      1.4044    NA    NA
+SD.log_k_J9Z38      0.6410    NA    NA
+SD.log_k_JSE76      0.5391    NA    NA
+SD.f_cyan_ilr_1     0.3203    NA    NA
+SD.f_cyan_ilr_2     0.5038    NA    NA
+SD.f_JCZ38_qlogis   3.5865    NA    NA
+SD.log_k2           0.3119    NA    NA
+SD.g_qlogis         0.8276    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4044    NA    NA
+SD.log_k_J9Z38    0.6410    NA    NA
+SD.log_k_JSE76    0.5391    NA    NA
+SD.f_cyan_ilr_1   0.3203    NA    NA
+SD.f_cyan_ilr_2   0.5038    NA    NA
+SD.f_JCZ38_qlogis 3.5865    NA    NA
+SD.log_k2         0.3119    NA    NA
+SD.g_qlogis       0.8276    NA    NA
+
+Variance model:
+      est. lower upper
+a.1 2.9627    NA    NA
+b.1 0.0444    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.008e+02    NA    NA
+k_JCZ38          3.117e-02    NA    NA
+k_J9Z38          6.193e-03    NA    NA
+k_JSE76          3.794e-03    NA    NA
+f_cyan_to_JCZ38  6.149e-01    NA    NA
+f_cyan_to_J9Z38  2.395e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.145e-01    NA    NA
+k2               1.062e-02    NA    NA
+g                3.628e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6149
+cyan_J9Z38  0.2395
+cyan_sink   0.1456
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   26.26 174.32    52.47   6.053   65.25
+JCZ38  22.24  73.88       NA      NA      NA
+J9Z38 111.93 371.82       NA      NA      NA
+JSE76 182.69 606.88       NA      NA      NA
+
+

+ +Hierarchical SFORB path 1 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:10:49 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1279.472 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.0643               -2.8987               -2.7077 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.4717               -3.4008               -5.0024 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -5.8613                0.6855                1.2366 
+       f_JCZ38_qlogis 
+              13.7418 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.466          0.0000                 0.000
+log_k_cyan_free             0.000          0.6158                 0.000
+log_k_cyan_free_bound       0.000          0.0000                 1.463
+log_k_cyan_bound_free       0.000          0.0000                 0.000
+log_k_JCZ38                 0.000          0.0000                 0.000
+log_k_J9Z38                 0.000          0.0000                 0.000
+log_k_JSE76                 0.000          0.0000                 0.000
+f_cyan_ilr_1                0.000          0.0000                 0.000
+f_cyan_ilr_2                0.000          0.0000                 0.000
+f_JCZ38_qlogis              0.000          0.0000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000       0.000       0.000       0.000
+log_k_cyan_free                       0.000       0.000       0.000       0.000
+log_k_cyan_free_bound                 0.000       0.000       0.000       0.000
+log_k_cyan_bound_free                 1.058       0.000       0.000       0.000
+log_k_JCZ38                           0.000       2.382       0.000       0.000
+log_k_J9Z38                           0.000       0.000       1.595       0.000
+log_k_JSE76                           0.000       0.000       0.000       1.245
+f_cyan_ilr_1                          0.000       0.000       0.000       0.000
+f_cyan_ilr_2                          0.000       0.000       0.000       0.000
+f_JCZ38_qlogis                        0.000       0.000       0.000       0.000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_free_0                 0.0000         0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00
+f_cyan_ilr_1                0.6852         0.00           0.00
+f_cyan_ilr_2                0.0000         1.28           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.14
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2401 2394  -1181
+
+Optimised parameters:
+                             est. lower upper
+cyan_free_0              102.7803    NA    NA
+log_k_cyan_free           -2.8068    NA    NA
+log_k_cyan_free_bound     -2.5714    NA    NA
+log_k_cyan_bound_free     -3.4426    NA    NA
+log_k_JCZ38               -3.4994    NA    NA
+log_k_J9Z38               -5.1148    NA    NA
+log_k_JSE76               -5.6335    NA    NA
+f_cyan_ilr_1               0.6597    NA    NA
+f_cyan_ilr_2               0.5132    NA    NA
+f_JCZ38_qlogis            37.2090    NA    NA
+a.1                        3.2367    NA    NA
+SD.log_k_cyan_free         0.3161    NA    NA
+SD.log_k_cyan_free_bound   0.8103    NA    NA
+SD.log_k_cyan_bound_free   0.5554    NA    NA
+SD.log_k_JCZ38             1.4858    NA    NA
+SD.log_k_J9Z38             0.5859    NA    NA
+SD.log_k_JSE76             0.6195    NA    NA
+SD.f_cyan_ilr_1            0.3118    NA    NA
+SD.f_cyan_ilr_2            0.3344    NA    NA
+SD.f_JCZ38_qlogis          0.5518    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.3161    NA    NA
+SD.log_k_cyan_free_bound 0.8103    NA    NA
+SD.log_k_cyan_bound_free 0.5554    NA    NA
+SD.log_k_JCZ38           1.4858    NA    NA
+SD.log_k_J9Z38           0.5859    NA    NA
+SD.log_k_JSE76           0.6195    NA    NA
+SD.f_cyan_ilr_1          0.3118    NA    NA
+SD.f_cyan_ilr_2          0.3344    NA    NA
+SD.f_JCZ38_qlogis        0.5518    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.237    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.028e+02    NA    NA
+k_cyan_free          6.040e-02    NA    NA
+k_cyan_free_bound    7.643e-02    NA    NA
+k_cyan_bound_free    3.198e-02    NA    NA
+k_JCZ38              3.022e-02    NA    NA
+k_J9Z38              6.007e-03    NA    NA
+k_JSE76              3.576e-03    NA    NA
+f_cyan_free_to_JCZ38 5.787e-01    NA    NA
+f_cyan_free_to_J9Z38 2.277e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.15646 0.01235 0.33341 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.5787
+cyan_free_J9Z38 0.2277
+cyan_free_sink  0.1936
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+
+Estimated disappearance times:
+        DT50  DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   24.48 153.7    46.26         4.43        56.15
+JCZ38  22.94  76.2       NA           NA           NA
+J9Z38 115.39 383.3       NA           NA           NA
+JSE76 193.84 643.9       NA           NA           NA
+
+

+ +Hierarchical SFORB path 1 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:17:00 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1649.941 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             101.3964               -2.9881               -2.7949 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.4376               -3.3626               -4.9792 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -5.8727                0.6814                6.8139 
+       f_JCZ38_qlogis 
+              13.7419 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.317          0.0000                 0.000
+log_k_cyan_free             0.000          0.7301                 0.000
+log_k_cyan_free_bound       0.000          0.0000                 1.384
+log_k_cyan_bound_free       0.000          0.0000                 0.000
+log_k_JCZ38                 0.000          0.0000                 0.000
+log_k_J9Z38                 0.000          0.0000                 0.000
+log_k_JSE76                 0.000          0.0000                 0.000
+f_cyan_ilr_1                0.000          0.0000                 0.000
+f_cyan_ilr_2                0.000          0.0000                 0.000
+f_JCZ38_qlogis              0.000          0.0000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000       0.000       0.000       0.000
+log_k_cyan_free                       0.000       0.000       0.000       0.000
+log_k_cyan_free_bound                 0.000       0.000       0.000       0.000
+log_k_cyan_bound_free                 1.109       0.000       0.000       0.000
+log_k_JCZ38                           0.000       2.272       0.000       0.000
+log_k_J9Z38                           0.000       0.000       1.633       0.000
+log_k_JSE76                           0.000       0.000       0.000       1.271
+f_cyan_ilr_1                          0.000       0.000       0.000       0.000
+f_cyan_ilr_2                          0.000       0.000       0.000       0.000
+f_JCZ38_qlogis                        0.000       0.000       0.000       0.000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis
+cyan_free_0                 0.0000         0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00
+f_cyan_ilr_1                0.6838         0.00           0.00
+f_cyan_ilr_2                0.0000        11.84           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.14
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2400 2392  -1180
+
+Optimised parameters:
+                              est. lower upper
+cyan_free_0              100.69983    NA    NA
+log_k_cyan_free           -3.11584    NA    NA
+log_k_cyan_free_bound     -3.15216    NA    NA
+log_k_cyan_bound_free     -3.65986    NA    NA
+log_k_JCZ38               -3.47811    NA    NA
+log_k_J9Z38               -5.08835    NA    NA
+log_k_JSE76               -5.55514    NA    NA
+f_cyan_ilr_1               0.66764    NA    NA
+f_cyan_ilr_2               0.78329    NA    NA
+f_JCZ38_qlogis            25.35245    NA    NA
+a.1                        2.99088    NA    NA
+b.1                        0.04346    NA    NA
+SD.log_k_cyan_free         0.48797    NA    NA
+SD.log_k_cyan_bound_free   0.27243    NA    NA
+SD.log_k_JCZ38             1.42450    NA    NA
+SD.log_k_J9Z38             0.63496    NA    NA
+SD.log_k_JSE76             0.55951    NA    NA
+SD.f_cyan_ilr_1            0.32687    NA    NA
+SD.f_cyan_ilr_2            0.48056    NA    NA
+SD.f_JCZ38_qlogis          0.43818    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.4880    NA    NA
+SD.log_k_cyan_bound_free 0.2724    NA    NA
+SD.log_k_JCZ38           1.4245    NA    NA
+SD.log_k_J9Z38           0.6350    NA    NA
+SD.log_k_JSE76           0.5595    NA    NA
+SD.f_cyan_ilr_1          0.3269    NA    NA
+SD.f_cyan_ilr_2          0.4806    NA    NA
+SD.f_JCZ38_qlogis        0.4382    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.99088    NA    NA
+b.1 0.04346    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.007e+02    NA    NA
+k_cyan_free          4.434e-02    NA    NA
+k_cyan_free_bound    4.276e-02    NA    NA
+k_cyan_bound_free    2.574e-02    NA    NA
+k_JCZ38              3.087e-02    NA    NA
+k_J9Z38              6.168e-03    NA    NA
+k_JSE76              3.868e-03    NA    NA
+f_cyan_free_to_JCZ38 6.143e-01    NA    NA
+f_cyan_free_to_J9Z38 2.389e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.10161 0.01123 0.36636 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 6.143e-01
+cyan_free_J9Z38 2.389e-01
+cyan_free_sink  1.468e-01
+cyan_free       1.000e+00
+JCZ38_JSE76     1.000e+00
+JCZ38_sink      9.763e-12
+
+Estimated disappearance times:
+        DT50  DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.91 164.4    49.49        6.822        61.72
+JCZ38  22.46  74.6       NA           NA           NA
+J9Z38 112.37 373.3       NA           NA           NA
+JSE76 179.22 595.4       NA           NA           NA
+
+

+ +Hierarchical HS path 1 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:11:04 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan -
+           k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= tb, k1, k2) * cyan -
+           k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1294.259 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.8738        -3.4490        -4.9348        -5.5989         0.6469 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+        1.2854         9.7193        -2.9084        -4.1810         1.7813 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.409        0.00        0.00       0.000       0.0000
+log_k_JCZ38     0.000        2.33        0.00       0.000       0.0000
+log_k_J9Z38     0.000        0.00        1.59       0.000       0.0000
+log_k_JSE76     0.000        0.00        0.00       1.006       0.0000
+f_cyan_ilr_1    0.000        0.00        0.00       0.000       0.6371
+f_cyan_ilr_2    0.000        0.00        0.00       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00        0.00       0.000       0.0000
+log_k1          0.000        0.00        0.00       0.000       0.0000
+log_k2          0.000        0.00        0.00       0.000       0.0000
+log_tb          0.000        0.00        0.00       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb
+cyan_0                0.000           0.00 0.0000 0.0000 0.0000
+log_k_JCZ38           0.000           0.00 0.0000 0.0000 0.0000
+log_k_J9Z38           0.000           0.00 0.0000 0.0000 0.0000
+log_k_JSE76           0.000           0.00 0.0000 0.0000 0.0000
+f_cyan_ilr_1          0.000           0.00 0.0000 0.0000 0.0000
+f_cyan_ilr_2          2.167           0.00 0.0000 0.0000 0.0000
+f_JCZ38_qlogis        0.000          10.22 0.0000 0.0000 0.0000
+log_k1                0.000           0.00 0.7003 0.0000 0.0000
+log_k2                0.000           0.00 0.0000 0.8928 0.0000
+log_tb                0.000           0.00 0.0000 0.0000 0.6774
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2427 2420  -1194
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            101.84849    NA    NA
+log_k_JCZ38        -3.47365    NA    NA
+log_k_J9Z38        -5.10562    NA    NA
+log_k_JSE76        -5.60318    NA    NA
+f_cyan_ilr_1        0.66127    NA    NA
+f_cyan_ilr_2        0.60283    NA    NA
+f_JCZ38_qlogis     45.06408    NA    NA
+log_k1             -3.10124    NA    NA
+log_k2             -4.39028    NA    NA
+log_tb              2.32256    NA    NA
+a.1                 3.32683    NA    NA
+SD.log_k_JCZ38      1.41427    NA    NA
+SD.log_k_J9Z38      0.54767    NA    NA
+SD.log_k_JSE76      0.62147    NA    NA
+SD.f_cyan_ilr_1     0.30189    NA    NA
+SD.f_cyan_ilr_2     0.34960    NA    NA
+SD.f_JCZ38_qlogis   0.04644    NA    NA
+SD.log_k1           0.39534    NA    NA
+SD.log_k2           0.43468    NA    NA
+SD.log_tb           0.60781    NA    NA
+
+Correlation is not available
+
+Random effects:
+                     est. lower upper
+SD.log_k_JCZ38    1.41427    NA    NA
+SD.log_k_J9Z38    0.54767    NA    NA
+SD.log_k_JSE76    0.62147    NA    NA
+SD.f_cyan_ilr_1   0.30189    NA    NA
+SD.f_cyan_ilr_2   0.34960    NA    NA
+SD.f_JCZ38_qlogis 0.04644    NA    NA
+SD.log_k1         0.39534    NA    NA
+SD.log_k2         0.43468    NA    NA
+SD.log_tb         0.60781    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.327    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.018e+02    NA    NA
+k_JCZ38          3.100e-02    NA    NA
+k_J9Z38          6.063e-03    NA    NA
+k_JSE76          3.686e-03    NA    NA
+f_cyan_to_JCZ38  5.910e-01    NA    NA
+f_cyan_to_J9Z38  2.320e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               4.499e-02    NA    NA
+k2               1.240e-02    NA    NA
+tb               1.020e+01    NA    NA
+
+Resulting formation fractions:
+               ff
+cyan_JCZ38  0.591
+cyan_J9Z38  0.232
+cyan_sink   0.177
+JCZ38_JSE76 1.000
+JCZ38_sink  0.000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.09 158.91    47.84   15.41   55.91
+JCZ38  22.36  74.27       NA      NA      NA
+J9Z38 114.33 379.80       NA      NA      NA
+JSE76 188.04 624.66       NA      NA      NA
+
+

+ +Hierarchical HS path 1 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:11:24 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ifelse(time <= tb, k1, k2) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ifelse(time <= tb, k1, k2) * cyan -
+           k_JCZ38 * JCZ38
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ifelse(time <= tb, k1, k2) * cyan -
+           k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1313.805 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+       101.168         -3.358         -4.941         -5.794          0.676 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+         5.740         13.863         -3.147         -4.262          2.173 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0           5.79       0.000       0.000       0.000       0.0000
+log_k_JCZ38      0.00       2.271       0.000       0.000       0.0000
+log_k_J9Z38      0.00       0.000       1.614       0.000       0.0000
+log_k_JSE76      0.00       0.000       0.000       1.264       0.0000
+f_cyan_ilr_1     0.00       0.000       0.000       0.000       0.6761
+f_cyan_ilr_2     0.00       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis   0.00       0.000       0.000       0.000       0.0000
+log_k1           0.00       0.000       0.000       0.000       0.0000
+log_k2           0.00       0.000       0.000       0.000       0.0000
+log_tb           0.00       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis log_k1 log_k2 log_tb
+cyan_0                0.000           0.00 0.0000 0.0000  0.000
+log_k_JCZ38           0.000           0.00 0.0000 0.0000  0.000
+log_k_J9Z38           0.000           0.00 0.0000 0.0000  0.000
+log_k_JSE76           0.000           0.00 0.0000 0.0000  0.000
+f_cyan_ilr_1          0.000           0.00 0.0000 0.0000  0.000
+f_cyan_ilr_2          9.572           0.00 0.0000 0.0000  0.000
+f_JCZ38_qlogis        0.000          19.19 0.0000 0.0000  0.000
+log_k1                0.000           0.00 0.8705 0.0000  0.000
+log_k2                0.000           0.00 0.0000 0.9288  0.000
+log_tb                0.000           0.00 0.0000 0.0000  1.065
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2422 2414  -1190
+
+Optimised parameters:
+                      est. lower upper
+cyan_0            100.9521    NA    NA
+log_k_JCZ38        -3.4629    NA    NA
+log_k_J9Z38        -5.0346    NA    NA
+log_k_JSE76        -5.5722    NA    NA
+f_cyan_ilr_1        0.6560    NA    NA
+f_cyan_ilr_2        0.7983    NA    NA
+f_JCZ38_qlogis     42.7949    NA    NA
+log_k1             -3.1721    NA    NA
+log_k2             -4.4039    NA    NA
+log_tb              2.3994    NA    NA
+a.1                 3.0586    NA    NA
+b.1                 0.0380    NA    NA
+SD.log_k_JCZ38      1.3754    NA    NA
+SD.log_k_J9Z38      0.6703    NA    NA
+SD.log_k_JSE76      0.5876    NA    NA
+SD.f_cyan_ilr_1     0.3272    NA    NA
+SD.f_cyan_ilr_2     0.5300    NA    NA
+SD.f_JCZ38_qlogis   6.4465    NA    NA
+SD.log_k1           0.4135    NA    NA
+SD.log_k2           0.4182    NA    NA
+SD.log_tb           0.6035    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3754    NA    NA
+SD.log_k_J9Z38    0.6703    NA    NA
+SD.log_k_JSE76    0.5876    NA    NA
+SD.f_cyan_ilr_1   0.3272    NA    NA
+SD.f_cyan_ilr_2   0.5300    NA    NA
+SD.f_JCZ38_qlogis 6.4465    NA    NA
+SD.log_k1         0.4135    NA    NA
+SD.log_k2         0.4182    NA    NA
+SD.log_tb         0.6035    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.059    NA    NA
+b.1 0.038    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.010e+02    NA    NA
+k_JCZ38          3.134e-02    NA    NA
+k_J9Z38          6.509e-03    NA    NA
+k_JSE76          3.802e-03    NA    NA
+f_cyan_to_JCZ38  6.127e-01    NA    NA
+f_cyan_to_J9Z38  2.423e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               4.191e-02    NA    NA
+k2               1.223e-02    NA    NA
+tb               1.102e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6127
+cyan_J9Z38  0.2423
+cyan_sink   0.1449
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.94 161.54    48.63   16.54   56.68
+JCZ38  22.12  73.47       NA      NA      NA
+J9Z38 106.50 353.77       NA      NA      NA
+JSE76 182.30 605.60       NA      NA      NA
+
+

Pathway 2 +

+ +Hierarchical FOMC path 2 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:34:28 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1030.246 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.8173        -1.8998        -5.1449        -2.5415         0.6705 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.4669        16.1281        13.3327        -0.2314         2.8738 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.742       0.000       0.000        0.00       0.0000
+log_k_JCZ38     0.000       1.402       0.000        0.00       0.0000
+log_k_J9Z38     0.000       0.000       1.718        0.00       0.0000
+log_k_JSE76     0.000       0.000       0.000        3.57       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000        0.00       0.5926
+f_cyan_ilr_2    0.000       0.000       0.000        0.00       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000        0.00       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000        0.00       0.0000
+log_alpha       0.000       0.000       0.000        0.00       0.0000
+log_beta        0.000       0.000       0.000        0.00       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.56           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.04           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          15.26    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.4708   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.4432
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2308 2301  -1134
+
+Optimised parameters:
+                      est.    lower     upper
+cyan_0            101.9586 99.22024 104.69700
+log_k_JCZ38        -2.4861 -3.17661  -1.79560
+log_k_J9Z38        -5.3926 -6.08842  -4.69684
+log_k_JSE76        -3.1193 -4.12904  -2.10962
+f_cyan_ilr_1        0.7368  0.42085   1.05276
+f_cyan_ilr_2        0.6196  0.06052   1.17861
+f_JCZ38_qlogis      4.8970 -4.68003  14.47398
+f_JSE76_qlogis      4.4066 -1.02087   9.83398
+log_alpha          -0.3021 -0.68264   0.07838
+log_beta            2.7438  2.57970   2.90786
+a.1                 2.9008  2.69920   3.10245
+SD.cyan_0           2.7081  0.64216   4.77401
+SD.log_k_JCZ38      0.7043  0.19951   1.20907
+SD.log_k_J9Z38      0.6248  0.05790   1.19180
+SD.log_k_JSE76      1.0750  0.33157   1.81839
+SD.f_cyan_ilr_1     0.3429  0.11688   0.56892
+SD.f_cyan_ilr_2     0.4774  0.09381   0.86097
+SD.f_JCZ38_qlogis   1.5565 -7.83970  10.95279
+SD.f_JSE76_qlogis   1.6871 -1.25577   4.63000
+SD.log_alpha        0.4216  0.15913   0.68405
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0167                                                        
+log_k_J9Z38    -0.0307  0.0057                                                
+log_k_JSE76    -0.0032  0.1358  0.0009                                        
+f_cyan_ilr_1   -0.0087  0.0206 -0.1158 -0.0009                                
+f_cyan_ilr_2   -0.1598  0.0690  0.1770  0.0002 -0.0007                        
+f_JCZ38_qlogis  0.0966 -0.1132 -0.0440  0.0182 -0.1385 -0.4583                
+f_JSE76_qlogis -0.0647  0.1157  0.0333 -0.0026  0.1110  0.3620 -0.8586        
+log_alpha      -0.0389  0.0113  0.0209  0.0021  0.0041  0.0451 -0.0605  0.0412
+log_beta       -0.2508  0.0533  0.0977  0.0098  0.0220  0.2741 -0.2934  0.1999
+               log_lph
+log_k_JCZ38           
+log_k_J9Z38           
+log_k_JSE76           
+f_cyan_ilr_1          
+f_cyan_ilr_2          
+f_JCZ38_qlogis        
+f_JSE76_qlogis        
+log_alpha             
+log_beta        0.2281
+
+Random effects:
+                    est.    lower   upper
+SD.cyan_0         2.7081  0.64216  4.7740
+SD.log_k_JCZ38    0.7043  0.19951  1.2091
+SD.log_k_J9Z38    0.6248  0.05790  1.1918
+SD.log_k_JSE76    1.0750  0.33157  1.8184
+SD.f_cyan_ilr_1   0.3429  0.11688  0.5689
+SD.f_cyan_ilr_2   0.4774  0.09381  0.8610
+SD.f_JCZ38_qlogis 1.5565 -7.83970 10.9528
+SD.f_JSE76_qlogis 1.6871 -1.25577  4.6300
+SD.log_alpha      0.4216  0.15913  0.6840
+
+Variance model:
+     est. lower upper
+a.1 2.901 2.699 3.102
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           101.95862 99.220240 1.047e+02
+k_JCZ38            0.08323  0.041727 1.660e-01
+k_J9Z38            0.00455  0.002269 9.124e-03
+k_JSE76            0.04419  0.016098 1.213e-01
+f_cyan_to_JCZ38    0.61318        NA        NA
+f_cyan_to_J9Z38    0.21630        NA        NA
+f_JCZ38_to_JSE76   0.99259  0.009193 1.000e+00
+f_JSE76_to_JCZ38   0.98795  0.264857 9.999e-01
+alpha              0.73924  0.505281 1.082e+00
+beta              15.54568 13.193194 1.832e+01
+
+Resulting formation fractions:
+                  ff
+cyan_JCZ38  0.613182
+cyan_J9Z38  0.216298
+cyan_sink   0.170519
+JCZ38_JSE76 0.992586
+JCZ38_sink  0.007414
+JSE76_JCZ38 0.987950
+JSE76_sink  0.012050
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.157 334.68    100.7
+JCZ38   8.328  27.66       NA
+J9Z38 152.341 506.06       NA
+JSE76  15.687  52.11       NA
+
+

+ +Hierarchical FOMC path 2 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:37:36 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1217.619 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.9028        -1.9055        -5.0249        -2.5646         0.6807 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.8883        16.0676         9.3923        -0.1346         3.0364 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          6.321       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.392       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.561       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.614       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6339
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_alpha       0.000       0.000       0.000       0.000       0.0000
+log_beta        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.41           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.24           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          15.13    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3701   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5662
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2248 2240  -1103
+
+Optimised parameters:
+                       est.      lower      upper
+cyan_0            101.55545  9.920e+01  1.039e+02
+log_k_JCZ38        -2.37354 -2.928e+00 -1.819e+00
+log_k_J9Z38        -5.14736 -5.960e+00 -4.335e+00
+log_k_JSE76        -3.07802 -4.243e+00 -1.913e+00
+f_cyan_ilr_1        0.71263  3.655e-01  1.060e+00
+f_cyan_ilr_2        0.95202  2.701e-01  1.634e+00
+f_JCZ38_qlogis      3.58473  1.251e+00  5.919e+00
+f_JSE76_qlogis     19.03623 -1.037e+07  1.037e+07
+log_alpha          -0.15297 -4.490e-01  1.431e-01
+log_beta            2.99230  2.706e+00  3.278e+00
+a.1                 2.04816         NA         NA
+b.1                 0.06886         NA         NA
+SD.log_k_JCZ38      0.56174         NA         NA
+SD.log_k_J9Z38      0.86509         NA         NA
+SD.log_k_JSE76      1.28450         NA         NA
+SD.f_cyan_ilr_1     0.38705         NA         NA
+SD.f_cyan_ilr_2     0.54153         NA         NA
+SD.f_JCZ38_qlogis   1.65311         NA         NA
+SD.f_JSE76_qlogis   7.51468         NA         NA
+SD.log_alpha        0.31586         NA         NA
+SD.log_beta         0.24696         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    0.5617    NA    NA
+SD.log_k_J9Z38    0.8651    NA    NA
+SD.log_k_JSE76    1.2845    NA    NA
+SD.f_cyan_ilr_1   0.3870    NA    NA
+SD.f_cyan_ilr_2   0.5415    NA    NA
+SD.f_JCZ38_qlogis 1.6531    NA    NA
+SD.f_JSE76_qlogis 7.5147    NA    NA
+SD.log_alpha      0.3159    NA    NA
+SD.log_beta       0.2470    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.04816    NA    NA
+b.1 0.06886    NA    NA
+
+Backtransformed parameters:
+                      est.    lower    upper
+cyan_0           1.016e+02 99.20301 103.9079
+k_JCZ38          9.315e-02  0.05349   0.1622
+k_J9Z38          5.815e-03  0.00258   0.0131
+k_JSE76          4.605e-02  0.01436   0.1477
+f_cyan_to_JCZ38  6.438e-01       NA       NA
+f_cyan_to_J9Z38  2.350e-01       NA       NA
+f_JCZ38_to_JSE76 9.730e-01  0.77745   0.9973
+f_JSE76_to_JCZ38 1.000e+00  0.00000   1.0000
+alpha            8.582e-01  0.63824   1.1538
+beta             1.993e+01 14.97621  26.5262
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  6.438e-01
+cyan_J9Z38  2.350e-01
+cyan_sink   1.212e-01
+JCZ38_JSE76 9.730e-01
+JCZ38_sink  2.700e-02
+JSE76_JCZ38 1.000e+00
+JSE76_sink  5.403e-09
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.771 271.70    81.79
+JCZ38   7.441  24.72       NA
+J9Z38 119.205 395.99       NA
+JSE76  15.052  50.00       NA
+
+

+ +Hierarchical DFOP path 2 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:38:34 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1276.128 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4358        -2.3107        -5.3123        -3.7120         0.6753 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1462        12.4095        12.3630        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5648 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.594      0.0000       0.000         0.0       0.0000
+log_k_JCZ38     0.000      0.7966       0.000         0.0       0.0000
+log_k_J9Z38     0.000      0.0000       1.561         0.0       0.0000
+log_k_JSE76     0.000      0.0000       0.000         0.8       0.0000
+f_cyan_ilr_1    0.000      0.0000       0.000         0.0       0.6349
+f_cyan_ilr_2    0.000      0.0000       0.000         0.0       0.0000
+f_JCZ38_qlogis  0.000      0.0000       0.000         0.0       0.0000
+f_JSE76_qlogis  0.000      0.0000       0.000         0.0       0.0000
+log_k1          0.000      0.0000       0.000         0.0       0.0000
+log_k2          0.000      0.0000       0.000         0.0       0.0000
+g_qlogis        0.000      0.0000       0.000         0.0       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                0.000           0.00            0.0  0.000 0.0000
+log_k_JCZ38           0.000           0.00            0.0  0.000 0.0000
+log_k_J9Z38           0.000           0.00            0.0  0.000 0.0000
+log_k_JSE76           0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00            0.0  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.85            0.0  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00           14.1  0.000 0.0000
+log_k1                0.000           0.00            0.0  1.106 0.0000
+log_k2                0.000           0.00            0.0  0.000 0.6141
+g_qlogis              0.000           0.00            0.0  0.000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.595
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2290 2281  -1123
+
+Optimised parameters:
+                      est.     lower    upper
+cyan_0            102.6903 101.44420 103.9365
+log_k_JCZ38        -2.4018  -2.98058  -1.8230
+log_k_J9Z38        -5.1865  -5.92931  -4.4437
+log_k_JSE76        -3.0784  -4.25226  -1.9045
+f_cyan_ilr_1        0.7157   0.37625   1.0551
+f_cyan_ilr_2        0.7073   0.20136   1.2132
+f_JCZ38_qlogis      4.6797   0.43240   8.9269
+f_JSE76_qlogis      5.0080  -1.01380  11.0299
+log_k1             -1.9620  -2.62909  -1.2949
+log_k2             -4.4894  -4.94958  -4.0292
+g_qlogis           -0.4658  -1.34443   0.4129
+a.1                 2.7158   2.52576   2.9059
+SD.log_k_JCZ38      0.5818   0.15679   1.0067
+SD.log_k_J9Z38      0.7421   0.16751   1.3167
+SD.log_k_JSE76      1.2841   0.43247   2.1356
+SD.f_cyan_ilr_1     0.3748   0.13040   0.6192
+SD.f_cyan_ilr_2     0.4550   0.08396   0.8261
+SD.f_JCZ38_qlogis   2.0862  -0.73390   4.9062
+SD.f_JSE76_qlogis   1.9585  -3.14773   7.0647
+SD.log_k1           0.7389   0.25761   1.2201
+SD.log_k2           0.5132   0.18143   0.8450
+SD.g_qlogis         0.9870   0.35773   1.6164
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0170                                                        
+log_k_J9Z38    -0.0457  0.0016                                                
+log_k_JSE76    -0.0046  0.1183  0.0005                                        
+f_cyan_ilr_1    0.0079  0.0072 -0.0909  0.0003                                
+f_cyan_ilr_2   -0.3114  0.0343  0.1542  0.0023 -0.0519                        
+f_JCZ38_qlogis  0.0777 -0.0601 -0.0152  0.0080 -0.0520 -0.2524                
+f_JSE76_qlogis -0.0356  0.0817  0.0073  0.0051  0.0388  0.1959 -0.6236        
+log_k1          0.0848 -0.0028  0.0010 -0.0010 -0.0014 -0.0245  0.0121 -0.0177
+log_k2          0.0274 -0.0001  0.0075  0.0000 -0.0023 -0.0060  0.0000 -0.0130
+g_qlogis        0.0159  0.0002 -0.0095  0.0002  0.0029 -0.0140 -0.0001  0.0149
+               log_k1  log_k2 
+log_k_JCZ38                   
+log_k_J9Z38                   
+log_k_JSE76                   
+f_cyan_ilr_1                  
+f_cyan_ilr_2                  
+f_JCZ38_qlogis                
+f_JSE76_qlogis                
+log_k1                        
+log_k2          0.0280        
+g_qlogis       -0.0278 -0.0310
+
+Random effects:
+                    est.    lower  upper
+SD.log_k_JCZ38    0.5818  0.15679 1.0067
+SD.log_k_J9Z38    0.7421  0.16751 1.3167
+SD.log_k_JSE76    1.2841  0.43247 2.1356
+SD.f_cyan_ilr_1   0.3748  0.13040 0.6192
+SD.f_cyan_ilr_2   0.4550  0.08396 0.8261
+SD.f_JCZ38_qlogis 2.0862 -0.73390 4.9062
+SD.f_JSE76_qlogis 1.9585 -3.14773 7.0647
+SD.log_k1         0.7389  0.25761 1.2201
+SD.log_k2         0.5132  0.18143 0.8450
+SD.g_qlogis       0.9870  0.35773 1.6164
+
+Variance model:
+     est. lower upper
+a.1 2.716 2.526 2.906
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.027e+02 1.014e+02 103.93649
+k_JCZ38          9.056e-02 5.076e-02   0.16154
+k_J9Z38          5.591e-03 2.660e-03   0.01175
+k_JSE76          4.603e-02 1.423e-02   0.14890
+f_cyan_to_JCZ38  6.184e-01        NA        NA
+f_cyan_to_J9Z38  2.248e-01        NA        NA
+f_JCZ38_to_JSE76 9.908e-01 6.064e-01   0.99987
+f_JSE76_to_JCZ38 9.934e-01 2.662e-01   0.99998
+k1               1.406e-01 7.214e-02   0.27393
+k2               1.123e-02 7.086e-03   0.01779
+g                3.856e-01 2.068e-01   0.60177
+
+Resulting formation fractions:
+                  ff
+cyan_JCZ38  0.618443
+cyan_J9Z38  0.224770
+cyan_sink   0.156787
+JCZ38_JSE76 0.990803
+JCZ38_sink  0.009197
+JSE76_JCZ38 0.993360
+JSE76_sink  0.006640
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   21.674 161.70    48.68   4.931   61.74
+JCZ38   7.654  25.43       NA      NA      NA
+J9Z38 123.966 411.81       NA      NA      NA
+JSE76  15.057  50.02       NA      NA      NA
+
+

+ +Hierarchical DFOP path 2 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:45:32 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1693.767 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.7523        -1.5948        -5.0119        -2.2723         0.6719 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        5.1681        12.8238        12.4130        -2.0057        -4.5526 
+      g_qlogis 
+       -0.5805 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.627       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.327       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.664       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       4.566       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                  0.0           0.00           0.00 0.0000 0.0000
+log_k_JCZ38             0.0           0.00           0.00 0.0000 0.0000
+log_k_J9Z38             0.0           0.00           0.00 0.0000 0.0000
+log_k_JSE76             0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1            0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2           10.1           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis          0.0          13.99           0.00 0.0000 0.0000
+f_JSE76_qlogis          0.0           0.00          14.15 0.0000 0.0000
+log_k1                  0.0           0.00           0.00 0.8452 0.0000
+log_k2                  0.0           0.00           0.00 0.0000 0.5968
+g_qlogis                0.0           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.691
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2234 2226  -1095
+
+Optimised parameters:
+                       est.      lower      upper
+cyan_0            101.10667  9.903e+01  103.18265
+log_k_JCZ38        -2.49437 -3.297e+00   -1.69221
+log_k_J9Z38        -5.08171 -5.875e+00   -4.28846
+log_k_JSE76        -3.20072 -4.180e+00   -2.22163
+f_cyan_ilr_1        0.71059  3.639e-01    1.05727
+f_cyan_ilr_2        1.15398  2.981e-01    2.00984
+f_JCZ38_qlogis      3.18027  1.056e+00    5.30452
+f_JSE76_qlogis      5.61578 -2.505e+01   36.28077
+log_k1             -2.38875 -2.517e+00   -2.26045
+log_k2             -4.67246 -4.928e+00   -4.41715
+g_qlogis           -0.28231 -1.135e+00    0.57058
+a.1                 2.08190  1.856e+00    2.30785
+b.1                 0.06114  5.015e-02    0.07214
+SD.log_k_JCZ38      0.84622  2.637e-01    1.42873
+SD.log_k_J9Z38      0.84564  2.566e-01    1.43464
+SD.log_k_JSE76      1.04385  3.242e-01    1.76351
+SD.f_cyan_ilr_1     0.38568  1.362e-01    0.63514
+SD.f_cyan_ilr_2     0.68046  7.166e-02    1.28925
+SD.f_JCZ38_qlogis   1.25244 -4.213e-02    2.54700
+SD.f_JSE76_qlogis   0.28202 -1.515e+03 1515.87968
+SD.log_k2           0.25749  7.655e-02    0.43843
+SD.g_qlogis         0.94535  3.490e-01    1.54174
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0086                                                        
+log_k_J9Z38    -0.0363 -0.0007                                                
+log_k_JSE76     0.0015  0.1210 -0.0017                                        
+f_cyan_ilr_1   -0.0048  0.0095 -0.0572  0.0030                                
+f_cyan_ilr_2   -0.4788  0.0328  0.1143  0.0027 -0.0316                        
+f_JCZ38_qlogis  0.0736 -0.0664 -0.0137  0.0145 -0.0444 -0.2175                
+f_JSE76_qlogis -0.0137  0.0971  0.0035  0.0009  0.0293  0.1333 -0.6767        
+log_k1          0.2345 -0.0350 -0.0099 -0.0113 -0.0126 -0.1652  0.1756 -0.2161
+log_k2          0.0440 -0.0133  0.0199 -0.0040 -0.0097 -0.0119  0.0604 -0.1306
+g_qlogis        0.0438  0.0078 -0.0123  0.0029  0.0046 -0.0363 -0.0318  0.0736
+               log_k1  log_k2 
+log_k_JCZ38                   
+log_k_J9Z38                   
+log_k_JSE76                   
+f_cyan_ilr_1                  
+f_cyan_ilr_2                  
+f_JCZ38_qlogis                
+f_JSE76_qlogis                
+log_k1                        
+log_k2          0.3198        
+g_qlogis       -0.1666 -0.0954
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    0.8462  2.637e-01    1.4287
+SD.log_k_J9Z38    0.8456  2.566e-01    1.4346
+SD.log_k_JSE76    1.0439  3.242e-01    1.7635
+SD.f_cyan_ilr_1   0.3857  1.362e-01    0.6351
+SD.f_cyan_ilr_2   0.6805  7.166e-02    1.2893
+SD.f_JCZ38_qlogis 1.2524 -4.213e-02    2.5470
+SD.f_JSE76_qlogis 0.2820 -1.515e+03 1515.8797
+SD.log_k2         0.2575  7.655e-02    0.4384
+SD.g_qlogis       0.9453  3.490e-01    1.5417
+
+Variance model:
+       est.   lower   upper
+a.1 2.08190 1.85595 2.30785
+b.1 0.06114 0.05015 0.07214
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.011e+02 9.903e+01 103.18265
+k_JCZ38          8.255e-02 3.701e-02   0.18411
+k_J9Z38          6.209e-03 2.809e-03   0.01373
+k_JSE76          4.073e-02 1.530e-02   0.10843
+f_cyan_to_JCZ38  6.608e-01        NA        NA
+f_cyan_to_J9Z38  2.419e-01        NA        NA
+f_JCZ38_to_JSE76 9.601e-01 7.419e-01   0.99506
+f_JSE76_to_JCZ38 9.964e-01 1.322e-11   1.00000
+k1               9.174e-02 8.070e-02   0.10430
+k2               9.349e-03 7.243e-03   0.01207
+g                4.299e-01 2.432e-01   0.63890
+
+Resulting formation fractions:
+                  ff
+cyan_JCZ38  0.660808
+cyan_J9Z38  0.241904
+cyan_sink   0.097288
+JCZ38_JSE76 0.960085
+JCZ38_sink  0.039915
+JSE76_JCZ38 0.996373
+JSE76_sink  0.003627
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.359 186.18    56.05   7.555   74.14
+JCZ38   8.397  27.89       NA      NA      NA
+J9Z38 111.631 370.83       NA      NA      NA
+JSE76  17.017  56.53       NA      NA      NA
+
+

+ +Hierarchical SFORB path 2 fit with constant variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:38:37 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1279.102 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.4394               -2.7673               -2.8942 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6201               -2.3107               -5.3123 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.7120                0.6754                1.1448 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.2672               13.3538 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.589          0.0000                  0.00
+log_k_cyan_free             0.000          0.4849                  0.00
+log_k_cyan_free_bound       0.000          0.0000                  1.62
+log_k_cyan_bound_free       0.000          0.0000                  0.00
+log_k_JCZ38                 0.000          0.0000                  0.00
+log_k_J9Z38                 0.000          0.0000                  0.00
+log_k_JSE76                 0.000          0.0000                  0.00
+f_cyan_ilr_1                0.000          0.0000                  0.00
+f_cyan_ilr_2                0.000          0.0000                  0.00
+f_JCZ38_qlogis              0.000          0.0000                  0.00
+f_JSE76_qlogis              0.000          0.0000                  0.00
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000         0.0
+log_k_cyan_free                       0.000      0.0000       0.000         0.0
+log_k_cyan_free_bound                 0.000      0.0000       0.000         0.0
+log_k_cyan_bound_free                 1.197      0.0000       0.000         0.0
+log_k_JCZ38                           0.000      0.7966       0.000         0.0
+log_k_J9Z38                           0.000      0.0000       1.561         0.0
+log_k_JSE76                           0.000      0.0000       0.000         0.8
+f_cyan_ilr_1                          0.000      0.0000       0.000         0.0
+f_cyan_ilr_2                          0.000      0.0000       0.000         0.0
+f_JCZ38_qlogis                        0.000      0.0000       0.000         0.0
+f_JSE76_qlogis                        0.000      0.0000       0.000         0.0
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000           0.00           0.00
+log_k_cyan_free             0.0000        0.000           0.00           0.00
+log_k_cyan_free_bound       0.0000        0.000           0.00           0.00
+log_k_cyan_bound_free       0.0000        0.000           0.00           0.00
+log_k_JCZ38                 0.0000        0.000           0.00           0.00
+log_k_J9Z38                 0.0000        0.000           0.00           0.00
+log_k_JSE76                 0.0000        0.000           0.00           0.00
+f_cyan_ilr_1                0.6349        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        1.797           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          13.84           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          14.66
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2284 2275  -1120
+
+Optimised parameters:
+                             est.      lower      upper
+cyan_free_0              102.7730  1.015e+02  1.041e+02
+log_k_cyan_free           -2.8530 -3.167e+00 -2.539e+00
+log_k_cyan_free_bound     -2.7326 -3.543e+00 -1.922e+00
+log_k_cyan_bound_free     -3.5582 -4.126e+00 -2.990e+00
+log_k_JCZ38               -2.3810 -2.921e+00 -1.841e+00
+log_k_J9Z38               -5.2301 -5.963e+00 -4.497e+00
+log_k_JSE76               -3.0286 -4.286e+00 -1.771e+00
+f_cyan_ilr_1               0.7081  3.733e-01  1.043e+00
+f_cyan_ilr_2               0.5847  7.846e-03  1.162e+00
+f_JCZ38_qlogis             9.5676 -1.323e+03  1.342e+03
+f_JSE76_qlogis             3.7042  7.254e-02  7.336e+00
+a.1                        2.7222  2.532e+00  2.913e+00
+SD.log_k_cyan_free         0.3338  1.086e-01  5.589e-01
+SD.log_k_cyan_free_bound   0.8888  3.023e-01  1.475e+00
+SD.log_k_cyan_bound_free   0.6220  2.063e-01  1.038e+00
+SD.log_k_JCZ38             0.5221  1.334e-01  9.108e-01
+SD.log_k_J9Z38             0.7104  1.371e-01  1.284e+00
+SD.log_k_JSE76             1.3837  4.753e-01  2.292e+00
+SD.f_cyan_ilr_1            0.3620  1.248e-01  5.992e-01
+SD.f_cyan_ilr_2            0.4259  8.145e-02  7.704e-01
+SD.f_JCZ38_qlogis          3.5332 -1.037e+05  1.037e+05
+SD.f_JSE76_qlogis          1.6990 -2.771e-01  3.675e+00
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.2126                                                
+log_k_cyan_free_bound  0.0894  0.0871                                        
+log_k_cyan_bound_free  0.0033  0.0410  0.0583                                
+log_k_JCZ38           -0.0708 -0.0280 -0.0147      0.0019                    
+log_k_J9Z38           -0.0535 -0.0138  0.0012      0.0148      0.0085        
+log_k_JSE76           -0.0066 -0.0030 -0.0021     -0.0005      0.1090  0.0010
+f_cyan_ilr_1          -0.0364 -0.0157 -0.0095     -0.0015      0.0458 -0.0960
+f_cyan_ilr_2          -0.3814 -0.1104 -0.0423      0.0146      0.1540  0.1526
+f_JCZ38_qlogis         0.2507  0.0969  0.0482     -0.0097     -0.2282 -0.0363
+f_JSE76_qlogis        -0.1648 -0.0710 -0.0443     -0.0087      0.2002  0.0226
+                      l__JSE7 f_cy__1 f_cy__2 f_JCZ38
+log_k_cyan_free                                      
+log_k_cyan_free_bound                                
+log_k_cyan_bound_free                                
+log_k_JCZ38                                          
+log_k_J9Z38                                          
+log_k_JSE76                                          
+f_cyan_ilr_1           0.0001                        
+f_cyan_ilr_2           0.0031  0.0586                
+f_JCZ38_qlogis         0.0023 -0.1867 -0.6255        
+f_JSE76_qlogis         0.0082  0.1356  0.4519 -0.7951
+
+Random effects:
+                           est.      lower     upper
+SD.log_k_cyan_free       0.3338  1.086e-01 5.589e-01
+SD.log_k_cyan_free_bound 0.8888  3.023e-01 1.475e+00
+SD.log_k_cyan_bound_free 0.6220  2.063e-01 1.038e+00
+SD.log_k_JCZ38           0.5221  1.334e-01 9.108e-01
+SD.log_k_J9Z38           0.7104  1.371e-01 1.284e+00
+SD.log_k_JSE76           1.3837  4.753e-01 2.292e+00
+SD.f_cyan_ilr_1          0.3620  1.248e-01 5.992e-01
+SD.f_cyan_ilr_2          0.4259  8.145e-02 7.704e-01
+SD.f_JCZ38_qlogis        3.5332 -1.037e+05 1.037e+05
+SD.f_JSE76_qlogis        1.6990 -2.771e-01 3.675e+00
+
+Variance model:
+     est. lower upper
+a.1 2.722 2.532 2.913
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.028e+02 1.015e+02 104.06475
+k_cyan_free          5.767e-02 4.213e-02   0.07894
+k_cyan_free_bound    6.505e-02 2.892e-02   0.14633
+k_cyan_bound_free    2.849e-02 1.614e-02   0.05028
+k_JCZ38              9.246e-02 5.390e-02   0.15859
+k_J9Z38              5.353e-03 2.572e-03   0.01114
+k_JSE76              4.838e-02 1.376e-02   0.17009
+f_cyan_free_to_JCZ38 6.011e-01 5.028e-01   0.83792
+f_cyan_free_to_J9Z38 2.208e-01 5.028e-01   0.83792
+f_JCZ38_to_JSE76     9.999e-01 0.000e+00   1.00000
+f_JSE76_to_JCZ38     9.760e-01 5.181e-01   0.99935
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.13942 0.01178 0.35948 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 6.011e-01
+cyan_free_J9Z38 2.208e-01
+cyan_free_sink  1.780e-01
+cyan_free       1.000e+00
+JCZ38_JSE76     9.999e-01
+JCZ38_sink      6.996e-05
+JSE76_JCZ38     9.760e-01
+JSE76_sink      2.403e-02
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.390 157.60    47.44        4.971        58.82
+JCZ38   7.497  24.90       NA           NA           NA
+J9Z38 129.482 430.13       NA           NA           NA
+JSE76  14.326  47.59       NA           NA           NA
+
+

+ +Hierarchical SFORB path 2 fit with two-component error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 10:46:02 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1723.343 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+              101.751                -2.837                -3.016 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+               -3.660                -2.299                -5.313 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+               -3.699                 0.672                 5.873 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+               13.216                13.338 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.629           0.000                 0.000
+log_k_cyan_free             0.000           0.446                 0.000
+log_k_cyan_free_bound       0.000           0.000                 1.449
+log_k_cyan_bound_free       0.000           0.000                 0.000
+log_k_JCZ38                 0.000           0.000                 0.000
+log_k_J9Z38                 0.000           0.000                 0.000
+log_k_JSE76                 0.000           0.000                 0.000
+f_cyan_ilr_1                0.000           0.000                 0.000
+f_cyan_ilr_2                0.000           0.000                 0.000
+f_JCZ38_qlogis              0.000           0.000                 0.000
+f_JSE76_qlogis              0.000           0.000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000      0.0000
+log_k_cyan_free                       0.000      0.0000       0.000      0.0000
+log_k_cyan_free_bound                 0.000      0.0000       0.000      0.0000
+log_k_cyan_bound_free                 1.213      0.0000       0.000      0.0000
+log_k_JCZ38                           0.000      0.7801       0.000      0.0000
+log_k_J9Z38                           0.000      0.0000       1.575      0.0000
+log_k_JSE76                           0.000      0.0000       0.000      0.8078
+f_cyan_ilr_1                          0.000      0.0000       0.000      0.0000
+f_cyan_ilr_2                          0.000      0.0000       0.000      0.0000
+f_JCZ38_qlogis                        0.000      0.0000       0.000      0.0000
+f_JSE76_qlogis                        0.000      0.0000       0.000      0.0000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000         0.00           0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00           0.00
+f_cyan_ilr_1                0.6519         0.00           0.00           0.00
+f_cyan_ilr_2                0.0000        10.78           0.00           0.00
+f_JCZ38_qlogis              0.0000         0.00          13.96           0.00
+f_JSE76_qlogis              0.0000         0.00           0.00          14.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2240 2232  -1098
+
+Optimised parameters:
+                              est.     lower    upper
+cyan_free_0              101.10205  98.99221 103.2119
+log_k_cyan_free           -3.16929  -3.61395  -2.7246
+log_k_cyan_free_bound     -3.38259  -3.63022  -3.1350
+log_k_cyan_bound_free     -3.81075  -4.13888  -3.4826
+log_k_JCZ38               -2.42057  -3.00756  -1.8336
+log_k_J9Z38               -5.07501  -5.85138  -4.2986
+log_k_JSE76               -3.12442  -4.21277  -2.0361
+f_cyan_ilr_1               0.70577   0.35788   1.0537
+f_cyan_ilr_2               1.14824   0.15810   2.1384
+f_JCZ38_qlogis             3.52245   0.43257   6.6123
+f_JSE76_qlogis             5.65140 -21.22295  32.5257
+a.1                        2.07062   1.84329   2.2980
+b.1                        0.06227   0.05124   0.0733
+SD.log_k_cyan_free         0.49468   0.18566   0.8037
+SD.log_k_cyan_bound_free   0.28972   0.07188   0.5076
+SD.log_k_JCZ38             0.58852   0.16800   1.0090
+SD.log_k_J9Z38             0.82500   0.24730   1.4027
+SD.log_k_JSE76             1.19201   0.40313   1.9809
+SD.f_cyan_ilr_1            0.38534   0.13640   0.6343
+SD.f_cyan_ilr_2            0.72463   0.10076   1.3485
+SD.f_JCZ38_qlogis          1.38223  -0.20997   2.9744
+SD.f_JSE76_qlogis          2.07989 -72.53027  76.6901
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.1117                                                
+log_k_cyan_free_bound  0.1763  0.1828                                        
+log_k_cyan_bound_free  0.0120  0.0593  0.5030                                
+log_k_JCZ38           -0.0459 -0.0230 -0.0931     -0.0337                    
+log_k_J9Z38           -0.0381 -0.0123 -0.0139      0.0237      0.0063        
+log_k_JSE76           -0.0044 -0.0038 -0.0175     -0.0072      0.1120  0.0003
+f_cyan_ilr_1          -0.0199 -0.0087 -0.0407     -0.0233      0.0268 -0.0552
+f_cyan_ilr_2          -0.4806 -0.1015 -0.2291     -0.0269      0.1156  0.1113
+f_JCZ38_qlogis         0.1805  0.0825  0.3085      0.0963     -0.1674 -0.0314
+f_JSE76_qlogis        -0.1586 -0.0810 -0.3560     -0.1563      0.2025  0.0278
+                      l__JSE7 f_cy__1 f_cy__2 f_JCZ38
+log_k_cyan_free                                      
+log_k_cyan_free_bound                                
+log_k_cyan_bound_free                                
+log_k_JCZ38                                          
+log_k_J9Z38                                          
+log_k_JSE76                                          
+f_cyan_ilr_1           0.0024                        
+f_cyan_ilr_2           0.0087  0.0172                
+f_JCZ38_qlogis        -0.0016 -0.1047 -0.4656        
+f_JSE76_qlogis         0.0119  0.1034  0.4584 -0.8137
+
+Random effects:
+                           est.     lower   upper
+SD.log_k_cyan_free       0.4947   0.18566  0.8037
+SD.log_k_cyan_bound_free 0.2897   0.07188  0.5076
+SD.log_k_JCZ38           0.5885   0.16800  1.0090
+SD.log_k_J9Z38           0.8250   0.24730  1.4027
+SD.log_k_JSE76           1.1920   0.40313  1.9809
+SD.f_cyan_ilr_1          0.3853   0.13640  0.6343
+SD.f_cyan_ilr_2          0.7246   0.10076  1.3485
+SD.f_JCZ38_qlogis        1.3822  -0.20997  2.9744
+SD.f_JSE76_qlogis        2.0799 -72.53027 76.6901
+
+Variance model:
+       est.   lower  upper
+a.1 2.07062 1.84329 2.2980
+b.1 0.06227 0.05124 0.0733
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.011e+02 9.899e+01 103.21190
+k_cyan_free          4.203e-02 2.695e-02   0.06557
+k_cyan_free_bound    3.396e-02 2.651e-02   0.04350
+k_cyan_bound_free    2.213e-02 1.594e-02   0.03073
+k_JCZ38              8.887e-02 4.941e-02   0.15984
+k_J9Z38              6.251e-03 2.876e-03   0.01359
+k_JSE76              4.396e-02 1.481e-02   0.13054
+f_cyan_free_to_JCZ38 6.590e-01 5.557e-01   0.95365
+f_cyan_free_to_J9Z38 2.429e-01 5.557e-01   0.95365
+f_JCZ38_to_JSE76     9.713e-01 6.065e-01   0.99866
+f_JSE76_to_JCZ38     9.965e-01 6.067e-10   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08749 0.01063 0.40855 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.65905
+cyan_free_J9Z38 0.24291
+cyan_free_sink  0.09805
+cyan_free       1.00000
+JCZ38_JSE76     0.97132
+JCZ38_sink      0.02868
+JSE76_JCZ38     0.99650
+JSE76_sink      0.00350
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   24.91 167.16    50.32        7.922        65.19
+JCZ38   7.80  25.91       NA           NA           NA
+J9Z38 110.89 368.36       NA           NA           NA
+JSE76  15.77  52.38       NA           NA           NA
+
+

Pathway 2, refined fits +

+ +Hierarchical FOMC path 2 fit with reduced random effects, two-component +error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:18:41 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - (alpha/beta) * 1/((time/beta) + 1) * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_JCZ38 * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * (alpha/beta) * 1/((time/beta) + 1) *
+           cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1957.271 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.9028        -1.9055        -5.0249        -2.5646         0.6807 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.8883        16.0676         9.3923        -0.1346         3.0364 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          6.321       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.392       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.561       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.614       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6339
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_alpha       0.000       0.000       0.000       0.000       0.0000
+log_beta        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_alpha log_beta
+cyan_0                 0.00           0.00           0.00    0.0000   0.0000
+log_k_JCZ38            0.00           0.00           0.00    0.0000   0.0000
+log_k_J9Z38            0.00           0.00           0.00    0.0000   0.0000
+log_k_JSE76            0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_1           0.00           0.00           0.00    0.0000   0.0000
+f_cyan_ilr_2          10.41           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.24           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          15.13    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3701   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5662
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2251 2244  -1106
+
+Optimised parameters:
+                      est.   lower   upper
+cyan_0           101.05768      NA      NA
+log_k_JCZ38       -2.73252      NA      NA
+log_k_J9Z38       -5.07399      NA      NA
+log_k_JSE76       -3.52863      NA      NA
+f_cyan_ilr_1       0.72176      NA      NA
+f_cyan_ilr_2       1.34610      NA      NA
+f_JCZ38_qlogis     2.08337      NA      NA
+f_JSE76_qlogis  1590.31880      NA      NA
+log_alpha         -0.09336      NA      NA
+log_beta           3.10191      NA      NA
+a.1                2.08557 1.85439 2.31675
+b.1                0.06998 0.05800 0.08197
+SD.log_k_JCZ38     1.20053 0.43329 1.96777
+SD.log_k_J9Z38     0.85854 0.26708 1.45000
+SD.log_k_JSE76     0.62528 0.16061 1.08995
+SD.f_cyan_ilr_1    0.35190 0.12340 0.58039
+SD.f_cyan_ilr_2    0.85385 0.15391 1.55378
+SD.log_alpha       0.28971 0.08718 0.49225
+SD.log_beta        0.31614 0.05938 0.57290
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.2005 0.43329 1.9678
+SD.log_k_J9Z38  0.8585 0.26708 1.4500
+SD.log_k_JSE76  0.6253 0.16061 1.0900
+SD.f_cyan_ilr_1 0.3519 0.12340 0.5804
+SD.f_cyan_ilr_2 0.8538 0.15391 1.5538
+SD.log_alpha    0.2897 0.08718 0.4923
+SD.log_beta     0.3161 0.05938 0.5729
+
+Variance model:
+       est. lower   upper
+a.1 2.08557 1.854 2.31675
+b.1 0.06998 0.058 0.08197
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.011e+02    NA    NA
+k_JCZ38          6.506e-02    NA    NA
+k_J9Z38          6.257e-03    NA    NA
+k_JSE76          2.935e-02    NA    NA
+f_cyan_to_JCZ38  6.776e-01    NA    NA
+f_cyan_to_J9Z38  2.442e-01    NA    NA
+f_JCZ38_to_JSE76 8.893e-01    NA    NA
+f_JSE76_to_JCZ38 1.000e+00    NA    NA
+alpha            9.109e-01    NA    NA
+beta             2.224e+01    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.67761
+cyan_J9Z38  0.24417
+cyan_sink   0.07822
+JCZ38_JSE76 0.88928
+JCZ38_sink  0.11072
+JSE76_JCZ38 1.00000
+JSE76_sink  0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.36 256.37    77.18
+JCZ38  10.65  35.39       NA
+J9Z38 110.77 367.98       NA
+JSE76  23.62  78.47       NA
+
+

+ +Hierarchical DFOP path 2 fit with reduced random effects, constant +variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:16:32 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1828.403 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      102.4358        -2.3107        -5.3123        -3.7120         0.6753 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1462        12.4095        12.3630        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5648 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          4.594      0.0000       0.000         0.0       0.0000
+log_k_JCZ38     0.000      0.7966       0.000         0.0       0.0000
+log_k_J9Z38     0.000      0.0000       1.561         0.0       0.0000
+log_k_JSE76     0.000      0.0000       0.000         0.8       0.0000
+f_cyan_ilr_1    0.000      0.0000       0.000         0.0       0.6349
+f_cyan_ilr_2    0.000      0.0000       0.000         0.0       0.0000
+f_JCZ38_qlogis  0.000      0.0000       0.000         0.0       0.0000
+f_JSE76_qlogis  0.000      0.0000       0.000         0.0       0.0000
+log_k1          0.000      0.0000       0.000         0.0       0.0000
+log_k2          0.000      0.0000       0.000         0.0       0.0000
+g_qlogis        0.000      0.0000       0.000         0.0       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                0.000           0.00            0.0  0.000 0.0000
+log_k_JCZ38           0.000           0.00            0.0  0.000 0.0000
+log_k_J9Z38           0.000           0.00            0.0  0.000 0.0000
+log_k_JSE76           0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00            0.0  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00            0.0  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.85            0.0  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00           14.1  0.000 0.0000
+log_k1                0.000           0.00            0.0  1.106 0.0000
+log_k2                0.000           0.00            0.0  0.000 0.6141
+g_qlogis              0.000           0.00            0.0  0.000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.595
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2282 2274  -1121
+
+Optimised parameters:
+                     est.   lower  upper
+cyan_0           102.5254      NA     NA
+log_k_JCZ38       -2.9358      NA     NA
+log_k_J9Z38       -5.1424      NA     NA
+log_k_JSE76       -3.6458      NA     NA
+f_cyan_ilr_1       0.6957      NA     NA
+f_cyan_ilr_2       0.6635      NA     NA
+f_JCZ38_qlogis  4984.8163      NA     NA
+f_JSE76_qlogis     1.9415      NA     NA
+log_k1            -1.9456      NA     NA
+log_k2            -4.4705      NA     NA
+g_qlogis          -0.5117      NA     NA
+a.1                2.7455 2.55392 2.9370
+SD.log_k_JCZ38     1.3163 0.47635 2.1563
+SD.log_k_J9Z38     0.7162 0.16133 1.2711
+SD.log_k_JSE76     0.6457 0.15249 1.1390
+SD.f_cyan_ilr_1    0.3424 0.11714 0.5677
+SD.f_cyan_ilr_2    0.4524 0.09709 0.8077
+SD.log_k1          0.7353 0.25445 1.2161
+SD.log_k2          0.5137 0.18206 0.8453
+SD.g_qlogis        0.9857 0.35651 1.6148
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3163 0.47635 2.1563
+SD.log_k_J9Z38  0.7162 0.16133 1.2711
+SD.log_k_JSE76  0.6457 0.15249 1.1390
+SD.f_cyan_ilr_1 0.3424 0.11714 0.5677
+SD.f_cyan_ilr_2 0.4524 0.09709 0.8077
+SD.log_k1       0.7353 0.25445 1.2161
+SD.log_k2       0.5137 0.18206 0.8453
+SD.g_qlogis     0.9857 0.35651 1.6148
+
+Variance model:
+     est. lower upper
+a.1 2.745 2.554 2.937
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.025e+02    NA    NA
+k_JCZ38          5.309e-02    NA    NA
+k_J9Z38          5.844e-03    NA    NA
+k_JSE76          2.610e-02    NA    NA
+f_cyan_to_JCZ38  6.079e-01    NA    NA
+f_cyan_to_J9Z38  2.272e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.745e-01    NA    NA
+k1               1.429e-01    NA    NA
+k2               1.144e-02    NA    NA
+g                3.748e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6079
+cyan_J9Z38  0.2272
+cyan_sink   0.1649
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8745
+JSE76_sink  0.1255
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   22.29 160.20    48.22    4.85   60.58
+JCZ38  13.06  43.37       NA      NA      NA
+J9Z38 118.61 394.02       NA      NA      NA
+JSE76  26.56  88.22       NA      NA      NA
+
+

+ +Hierarchical DFOP path 2 fit with reduced random effects, two-component +error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:28 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * cyan
+d_JCZ38/dt = + f_cyan_to_JCZ38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_JCZ38 * JCZ38 +
+           f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_to_J9Z38 * ((k1 * g * exp(-k1 * time) + k2 * (1 -
+           g) * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+           exp(-k2 * time))) * cyan - k_J9Z38 * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 2183.989 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+        cyan_0    log_k_JCZ38    log_k_J9Z38    log_k_JSE76   f_cyan_ilr_1 
+      101.7523        -1.5948        -5.0119        -2.2723         0.6719 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        5.1681        12.8238        12.4130        -2.0057        -4.5526 
+      g_qlogis 
+       -0.5805 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+               cyan_0 log_k_JCZ38 log_k_J9Z38 log_k_JSE76 f_cyan_ilr_1
+cyan_0          5.627       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       2.327       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.664       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       4.566       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000       0.000       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000       0.000       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000       0.000       0.000       0.000       0.0000
+log_k1          0.000       0.000       0.000       0.000       0.0000
+log_k2          0.000       0.000       0.000       0.000       0.0000
+g_qlogis        0.000       0.000       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+cyan_0                  0.0           0.00           0.00 0.0000 0.0000
+log_k_JCZ38             0.0           0.00           0.00 0.0000 0.0000
+log_k_J9Z38             0.0           0.00           0.00 0.0000 0.0000
+log_k_JSE76             0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_1            0.0           0.00           0.00 0.0000 0.0000
+f_cyan_ilr_2           10.1           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis          0.0          13.99           0.00 0.0000 0.0000
+f_JSE76_qlogis          0.0           0.00          14.15 0.0000 0.0000
+log_k1                  0.0           0.00           0.00 0.8452 0.0000
+log_k2                  0.0           0.00           0.00 0.0000 0.5968
+g_qlogis                0.0           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0            0.000
+log_k_JCZ38       0.000
+log_k_J9Z38       0.000
+log_k_JSE76       0.000
+f_cyan_ilr_1      0.000
+f_cyan_ilr_2      0.000
+f_JCZ38_qlogis    0.000
+f_JSE76_qlogis    0.000
+log_k1            0.000
+log_k2            0.000
+g_qlogis          1.691
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2232 2224  -1096
+
+Optimised parameters:
+                     est.   lower   upper
+cyan_0          101.20051      NA      NA
+log_k_JCZ38      -2.93542      NA      NA
+log_k_J9Z38      -5.03151      NA      NA
+log_k_JSE76      -3.67679      NA      NA
+f_cyan_ilr_1      0.67290      NA      NA
+f_cyan_ilr_2      0.99787      NA      NA
+f_JCZ38_qlogis  348.32484      NA      NA
+f_JSE76_qlogis    1.87846      NA      NA
+log_k1           -2.32738      NA      NA
+log_k2           -4.61295      NA      NA
+g_qlogis         -0.38342      NA      NA
+a.1               2.06184 1.83746 2.28622
+b.1               0.06329 0.05211 0.07447
+SD.log_k_JCZ38    1.29042 0.47468 2.10617
+SD.log_k_J9Z38    0.84235 0.25903 1.42566
+SD.log_k_JSE76    0.56930 0.13934 0.99926
+SD.f_cyan_ilr_1   0.35183 0.12298 0.58068
+SD.f_cyan_ilr_2   0.77269 0.17908 1.36631
+SD.log_k2         0.28549 0.09210 0.47888
+SD.g_qlogis       0.93830 0.34568 1.53093
+
+Correlation is not available
+
+Random effects:
+                  est.  lower  upper
+SD.log_k_JCZ38  1.2904 0.4747 2.1062
+SD.log_k_J9Z38  0.8423 0.2590 1.4257
+SD.log_k_JSE76  0.5693 0.1393 0.9993
+SD.f_cyan_ilr_1 0.3518 0.1230 0.5807
+SD.f_cyan_ilr_2 0.7727 0.1791 1.3663
+SD.log_k2       0.2855 0.0921 0.4789
+SD.g_qlogis     0.9383 0.3457 1.5309
+
+Variance model:
+       est.   lower   upper
+a.1 2.06184 1.83746 2.28622
+b.1 0.06329 0.05211 0.07447
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.012e+02    NA    NA
+k_JCZ38          5.311e-02    NA    NA
+k_J9Z38          6.529e-03    NA    NA
+k_JSE76          2.530e-02    NA    NA
+f_cyan_to_JCZ38  6.373e-01    NA    NA
+f_cyan_to_J9Z38  2.461e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.674e-01    NA    NA
+k1               9.755e-02    NA    NA
+k2               9.922e-03    NA    NA
+g                4.053e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6373
+cyan_J9Z38  0.2461
+cyan_sink   0.1167
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8674
+JSE76_sink  0.1326
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.93 179.68    54.09   7.105   69.86
+JCZ38  13.05  43.36       NA      NA      NA
+J9Z38 106.16 352.67       NA      NA      NA
+JSE76  27.39  91.00       NA      NA      NA
+
+

+ +Hierarchical SFORB path 2 fit with reduced random effects, constant +variance + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:17:37 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 1893.29 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+             102.4394               -2.7673               -2.8942 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6201               -2.3107               -5.3123 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.7120                0.6754                1.1448 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.2672               13.3538 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 4.589          0.0000                  0.00
+log_k_cyan_free             0.000          0.4849                  0.00
+log_k_cyan_free_bound       0.000          0.0000                  1.62
+log_k_cyan_bound_free       0.000          0.0000                  0.00
+log_k_JCZ38                 0.000          0.0000                  0.00
+log_k_J9Z38                 0.000          0.0000                  0.00
+log_k_JSE76                 0.000          0.0000                  0.00
+f_cyan_ilr_1                0.000          0.0000                  0.00
+f_cyan_ilr_2                0.000          0.0000                  0.00
+f_JCZ38_qlogis              0.000          0.0000                  0.00
+f_JSE76_qlogis              0.000          0.0000                  0.00
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000         0.0
+log_k_cyan_free                       0.000      0.0000       0.000         0.0
+log_k_cyan_free_bound                 0.000      0.0000       0.000         0.0
+log_k_cyan_bound_free                 1.197      0.0000       0.000         0.0
+log_k_JCZ38                           0.000      0.7966       0.000         0.0
+log_k_J9Z38                           0.000      0.0000       1.561         0.0
+log_k_JSE76                           0.000      0.0000       0.000         0.8
+f_cyan_ilr_1                          0.000      0.0000       0.000         0.0
+f_cyan_ilr_2                          0.000      0.0000       0.000         0.0
+f_JCZ38_qlogis                        0.000      0.0000       0.000         0.0
+f_JSE76_qlogis                        0.000      0.0000       0.000         0.0
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000        0.000           0.00           0.00
+log_k_cyan_free             0.0000        0.000           0.00           0.00
+log_k_cyan_free_bound       0.0000        0.000           0.00           0.00
+log_k_cyan_bound_free       0.0000        0.000           0.00           0.00
+log_k_JCZ38                 0.0000        0.000           0.00           0.00
+log_k_J9Z38                 0.0000        0.000           0.00           0.00
+log_k_JSE76                 0.0000        0.000           0.00           0.00
+f_cyan_ilr_1                0.6349        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        1.797           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          13.84           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          14.66
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2279 2272  -1120
+
+Optimised parameters:
+                              est.   lower  upper
+cyan_free_0               102.5621      NA     NA
+log_k_cyan_free            -2.8531      NA     NA
+log_k_cyan_free_bound      -2.6916      NA     NA
+log_k_cyan_bound_free      -3.5032      NA     NA
+log_k_JCZ38                -2.9436      NA     NA
+log_k_J9Z38                -5.1140      NA     NA
+log_k_JSE76                -3.6472      NA     NA
+f_cyan_ilr_1                0.6887      NA     NA
+f_cyan_ilr_2                0.6874      NA     NA
+f_JCZ38_qlogis           4063.6389      NA     NA
+f_JSE76_qlogis              1.9556      NA     NA
+a.1                         2.7460 2.55451 2.9376
+SD.log_k_cyan_free          0.3131 0.09841 0.5277
+SD.log_k_cyan_free_bound    0.8850 0.29909 1.4710
+SD.log_k_cyan_bound_free    0.6167 0.20391 1.0295
+SD.log_k_JCZ38              1.3555 0.49101 2.2200
+SD.log_k_J9Z38              0.7200 0.16166 1.2783
+SD.log_k_JSE76              0.6252 0.14619 1.1042
+SD.f_cyan_ilr_1             0.3386 0.11447 0.5627
+SD.f_cyan_ilr_2             0.4699 0.09810 0.8417
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.3131 0.09841 0.5277
+SD.log_k_cyan_free_bound 0.8850 0.29909 1.4710
+SD.log_k_cyan_bound_free 0.6167 0.20391 1.0295
+SD.log_k_JCZ38           1.3555 0.49101 2.2200
+SD.log_k_J9Z38           0.7200 0.16166 1.2783
+SD.log_k_JSE76           0.6252 0.14619 1.1042
+SD.f_cyan_ilr_1          0.3386 0.11447 0.5627
+SD.f_cyan_ilr_2          0.4699 0.09810 0.8417
+
+Variance model:
+     est. lower upper
+a.1 2.746 2.555 2.938
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.026e+02    NA    NA
+k_cyan_free          5.767e-02    NA    NA
+k_cyan_free_bound    6.777e-02    NA    NA
+k_cyan_bound_free    3.010e-02    NA    NA
+k_JCZ38              5.267e-02    NA    NA
+k_J9Z38              6.012e-03    NA    NA
+k_JSE76              2.606e-02    NA    NA
+f_cyan_free_to_JCZ38 6.089e-01    NA    NA
+f_cyan_free_to_J9Z38 2.299e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.761e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+ 0.1434  0.0121  0.3469 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6089
+cyan_free_J9Z38 0.2299
+cyan_free_sink  0.1612
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+JSE76_JCZ38     0.8761
+JSE76_sink      0.1239
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.94 155.06    46.68        4.832        57.28
+JCZ38  13.16  43.71       NA           NA           NA
+J9Z38 115.30 383.02       NA           NA           NA
+JSE76  26.59  88.35       NA           NA           NA
+
+

+ +Hierarchical SFORB path 2 fit with reduced random effects, two-component +error + +


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:21:01 2023 
+Date of summary: Sat Jan 28 11:22:29 2023 
+
+Equations:
+d_cyan_free/dt = - k_cyan_free * cyan_free - k_cyan_free_bound *
+           cyan_free + k_cyan_bound_free * cyan_bound
+d_cyan_bound/dt = + k_cyan_free_bound * cyan_free - k_cyan_bound_free *
+           cyan_bound
+d_JCZ38/dt = + f_cyan_free_to_JCZ38 * k_cyan_free * cyan_free - k_JCZ38
+           * JCZ38 + f_JSE76_to_JCZ38 * k_JSE76 * JSE76
+d_J9Z38/dt = + f_cyan_free_to_J9Z38 * k_cyan_free * cyan_free - k_J9Z38
+           * J9Z38
+d_JSE76/dt = + f_JCZ38_to_JSE76 * k_JCZ38 * JCZ38 - k_JSE76 * JSE76
+
+Data:
+433 observations of 4 variable(s) grouped in 5 datasets
+
+Model predictions using solution type deSolve 
+
+Fitted in 2097.842 s
+Using 300, 100 iterations and 10 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+          cyan_free_0       log_k_cyan_free log_k_cyan_free_bound 
+              101.751                -2.837                -3.016 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+               -3.660                -2.299                -5.313 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+               -3.699                 0.672                 5.873 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+               13.216                13.338 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+                      cyan_free_0 log_k_cyan_free log_k_cyan_free_bound
+cyan_free_0                 5.629           0.000                 0.000
+log_k_cyan_free             0.000           0.446                 0.000
+log_k_cyan_free_bound       0.000           0.000                 1.449
+log_k_cyan_bound_free       0.000           0.000                 0.000
+log_k_JCZ38                 0.000           0.000                 0.000
+log_k_J9Z38                 0.000           0.000                 0.000
+log_k_JSE76                 0.000           0.000                 0.000
+f_cyan_ilr_1                0.000           0.000                 0.000
+f_cyan_ilr_2                0.000           0.000                 0.000
+f_JCZ38_qlogis              0.000           0.000                 0.000
+f_JSE76_qlogis              0.000           0.000                 0.000
+                      log_k_cyan_bound_free log_k_JCZ38 log_k_J9Z38 log_k_JSE76
+cyan_free_0                           0.000      0.0000       0.000      0.0000
+log_k_cyan_free                       0.000      0.0000       0.000      0.0000
+log_k_cyan_free_bound                 0.000      0.0000       0.000      0.0000
+log_k_cyan_bound_free                 1.213      0.0000       0.000      0.0000
+log_k_JCZ38                           0.000      0.7801       0.000      0.0000
+log_k_J9Z38                           0.000      0.0000       1.575      0.0000
+log_k_JSE76                           0.000      0.0000       0.000      0.8078
+f_cyan_ilr_1                          0.000      0.0000       0.000      0.0000
+f_cyan_ilr_2                          0.000      0.0000       0.000      0.0000
+f_JCZ38_qlogis                        0.000      0.0000       0.000      0.0000
+f_JSE76_qlogis                        0.000      0.0000       0.000      0.0000
+                      f_cyan_ilr_1 f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis
+cyan_free_0                 0.0000         0.00           0.00           0.00
+log_k_cyan_free             0.0000         0.00           0.00           0.00
+log_k_cyan_free_bound       0.0000         0.00           0.00           0.00
+log_k_cyan_bound_free       0.0000         0.00           0.00           0.00
+log_k_JCZ38                 0.0000         0.00           0.00           0.00
+log_k_J9Z38                 0.0000         0.00           0.00           0.00
+log_k_JSE76                 0.0000         0.00           0.00           0.00
+f_cyan_ilr_1                0.6519         0.00           0.00           0.00
+f_cyan_ilr_2                0.0000        10.78           0.00           0.00
+f_JCZ38_qlogis              0.0000         0.00          13.96           0.00
+f_JSE76_qlogis              0.0000         0.00           0.00          14.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2236 2228  -1098
+
+Optimised parameters:
+                              est.   lower   upper
+cyan_free_0              100.72760      NA      NA
+log_k_cyan_free           -3.18281      NA      NA
+log_k_cyan_free_bound     -3.37924      NA      NA
+log_k_cyan_bound_free     -3.77107      NA      NA
+log_k_JCZ38               -2.92811      NA      NA
+log_k_J9Z38               -5.02759      NA      NA
+log_k_JSE76               -3.65835      NA      NA
+f_cyan_ilr_1               0.67390      NA      NA
+f_cyan_ilr_2               1.15106      NA      NA
+f_JCZ38_qlogis           827.82299      NA      NA
+f_JSE76_qlogis             1.83064      NA      NA
+a.1                        2.06921 1.84443 2.29399
+b.1                        0.06391 0.05267 0.07515
+SD.log_k_cyan_free         0.50518 0.18962 0.82075
+SD.log_k_cyan_bound_free   0.30991 0.08170 0.53813
+SD.log_k_JCZ38             1.26661 0.46578 2.06744
+SD.log_k_J9Z38             0.88272 0.27813 1.48730
+SD.log_k_JSE76             0.53050 0.12561 0.93538
+SD.f_cyan_ilr_1            0.35547 0.12461 0.58633
+SD.f_cyan_ilr_2            0.91446 0.20131 1.62761
+
+Correlation is not available
+
+Random effects:
+                           est.  lower  upper
+SD.log_k_cyan_free       0.5052 0.1896 0.8207
+SD.log_k_cyan_bound_free 0.3099 0.0817 0.5381
+SD.log_k_JCZ38           1.2666 0.4658 2.0674
+SD.log_k_J9Z38           0.8827 0.2781 1.4873
+SD.log_k_JSE76           0.5305 0.1256 0.9354
+SD.f_cyan_ilr_1          0.3555 0.1246 0.5863
+SD.f_cyan_ilr_2          0.9145 0.2013 1.6276
+
+Variance model:
+       est.   lower   upper
+a.1 2.06921 1.84443 2.29399
+b.1 0.06391 0.05267 0.07515
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.007e+02    NA    NA
+k_cyan_free          4.147e-02    NA    NA
+k_cyan_free_bound    3.407e-02    NA    NA
+k_cyan_bound_free    2.303e-02    NA    NA
+k_JCZ38              5.350e-02    NA    NA
+k_J9Z38              6.555e-03    NA    NA
+k_JSE76              2.578e-02    NA    NA
+f_cyan_free_to_JCZ38 6.505e-01    NA    NA
+f_cyan_free_to_J9Z38 2.508e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.618e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08768 0.01089 0.39821 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.65053
+cyan_free_J9Z38 0.25082
+cyan_free_sink  0.09864
+cyan_free       1.00000
+JCZ38_JSE76     1.00000
+JCZ38_sink      0.00000
+JSE76_JCZ38     0.86184
+JSE76_sink      0.13816
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.32 164.79    49.61        7.906        63.64
+JCZ38  12.96  43.04       NA           NA           NA
+J9Z38 105.75 351.29       NA           NA           NA
+JSE76  26.89  89.33       NA           NA           NA
+
+

Session info +

R version 4.2.2 Patched (2022-11-10 r83330)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux bookworm/sid
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so
+
+locale:
+ [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
+ [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=de_DE.UTF-8    
+ [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=de_DE.UTF-8   
+ [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
+ [9] LC_ADDRESS=C               LC_TELEPHONE=C            
+[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.2 npde_3.3   knitr_1.41 mkin_1.2.2
+
+loaded via a namespace (and not attached):
+ [1] mclust_6.0.0      lattice_0.20-45   prettyunits_1.1.1 ps_1.7.2         
+ [5] zoo_1.8-11        assertthat_0.2.1  rprojroot_2.0.3   digest_0.6.31    
+ [9] lmtest_0.9-40     utf8_1.2.2        R6_2.5.1          cellranger_1.1.0 
+[13] evaluate_0.19     ggplot2_3.4.0     highr_0.9         pillar_1.8.1     
+[17] rlang_1.0.6       readxl_1.4.1      callr_3.7.3       jquerylib_0.1.4  
+[21] rmarkdown_2.19    pkgdown_2.0.7     textshaping_0.3.6 desc_1.4.2       
+[25] stringr_1.5.0     munsell_0.5.0     compiler_4.2.2    xfun_0.35        
+[29] pkgconfig_2.0.3   systemfonts_1.0.4 pkgbuild_1.4.0    htmltools_0.5.4  
+[33] tidyselect_1.2.0  tibble_3.1.8      gridExtra_2.3     codetools_0.2-18 
+[37] fansi_1.0.3       crayon_1.5.2      dplyr_1.0.10      grid_4.2.2       
+[41] nlme_3.1-161      jsonlite_1.8.4    gtable_0.3.1      lifecycle_1.0.3  
+[45] DBI_1.1.3         magrittr_2.0.3    scales_1.2.1      cli_3.5.0        
+[49] stringi_1.7.8     cachem_1.0.6      fs_1.5.2          bslib_0.4.2      
+[53] ragg_1.2.4        generics_0.1.3    vctrs_0.5.1       deSolve_1.34     
+[57] tools_4.2.2       glue_1.6.2        purrr_1.0.0       processx_3.8.0   
+[61] fastmap_1.1.0     yaml_2.3.6        inline_0.3.19     colorspace_2.0-3 
+[65] memoise_2.0.1     sass_0.4.4

Hardware info +

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

MemTotal:       64940452 kB

+ + + +

+ + + + +

+ + + + + + + + diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-11-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-11-1.png new file mode 100644 index 00000000..b969f2ff Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-11-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-12-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-12-1.png new file mode 100644 index 00000000..60393da3 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-12-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png new file mode 100644 index 00000000..b9a410f7 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-13-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-17-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-17-1.png new file mode 100644 index 00000000..cf921dab Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-17-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-18-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-18-1.png new file mode 100644 index 00000000..ff732730 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-18-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-19-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-19-1.png new file mode 100644 index 00000000..e30011bc Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-19-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-6-1.png new file mode 100644 index 00000000..4aad76df Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png new file mode 100644 index 00000000..e30011bc Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_cyan_pathway_files/figure-html/unnamed-chunk-7-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent.html b/docs/dev/articles/prebuilt/2022_dmta_parent.html new file mode 100644 index 00000000..89c9bfd8 --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_parent.html @@ -0,0 +1,2204 @@ + + + + + + + +Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P • mkin + + + + + + + + + + + + + +

+ + + + +

Introduction +

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

It was assembled in the course of work package 1.1 of Project Number +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.

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

Data +

The data available for the enantiomer dimethenamid-P (DMTAP) are +renamed to have the same substance name as the data for the racemic +mixture dimethenamid (DMTA). The reason for this is that no difference +between their degradation behaviour was identified in the EU risk +assessment.
The data for transformation products and unnecessary columns are +discarded
The observation times of each dataset are multiplied with the +corresponding normalisation factor also available in the dataset, in +order to make it possible to describe all datasets with a single set of +parameters that are independent of temperature
Finally, datasets observed in the same soil (Elliot 1 +and Elliot 2) are combined, resulting in dimethenamid +(DMTA) data from six soils.

The following commented R code performs this preprocessing.

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

The following tables show the 6 datasets.

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

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

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

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

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

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

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

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

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

Separate evaluations +

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

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

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

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

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

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

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

Hierarchichal model fits +

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

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

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

+status(f_saem) |> kable()

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

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

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

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

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

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

Parameter identifiability based on the Fisher Information +Matrix +

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

+illparms(f_saem) |> kable()

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

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

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

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

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

+illparms(f_saem_dfop_tc_no_ranef_k2)

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

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

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

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

The convergence of the fit is checked visually.

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

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

+plot(f_saem_dfop_tc_no_ranef_k2)

+Plot of the final NLHM DFOP fit +

Finally, a summary report of the fit is produced.

+summary(f_saem_dfop_tc_no_ranef_k2)

saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:51 2023 
+Date of summary: Sat Jan 28 11:22:52 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.74 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  663.8 661.9 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.228939 96.285869 100.17201
+k1         0.064063  0.033477   0.09465
+k2         0.008297  0.005824   0.01077
+g          0.953821  0.914328   0.99331
+a.1        1.068479  0.869538   1.26742
+b.1        0.029424  0.022406   0.03644
+SD.DMTA_0  2.030437  0.404824   3.65605
+SD.k1      0.594692  0.256660   0.93272
+SD.g       1.006754  0.361327   1.65218
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0218                
+k2  0.0556  0.0355        
+g  -0.0516 -0.0284 -0.2800
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 2.0304 0.4048 3.6560
+SD.k1     0.5947 0.2567 0.9327
+SD.g      1.0068 0.3613 1.6522
+
+Variance model:
+       est.   lower   upper
+a.1 1.06848 0.86954 1.26742
+b.1 0.02942 0.02241 0.03644
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.4    12.46   10.82   83.54

Alternative check of parameter identifiability +

The parameter check used in the illparms function is +based on a quadratic approximation of the likelihood surface near its +optimum, which is calculated using the Fisher Information Matrix (FIM). +An alternative way to check parameter identifiability (Duchesne et al. 2021) based on a multistart +approach has recently been implemented in mkin.

+f_saem_dfop_tc_multi <- multistart(f_saem[["DFOP", "tc"]], n = 50, cores = 15)

+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_multi, lpos = "bottomright", ylim = c(0.3, 10), las = 2)

+Scaled parameters from the multistart runs, full model +

The parameter boxplots of the multistart runs with the reduced model +shown below indicate that all runs give similar results, regardless of +the starting parameters.

+f_saem_dfop_tc_no_ranef_k2_multi <- multistart(f_saem_dfop_tc_no_ranef_k2,
+  n = 50, cores = 15)

+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2,
+  lpos = "bottomright")

+Scaled parameters from the multistart runs, reduced model +

When only the parameters of the top 25% of the fits are shown (based +on a feature introduced in mkin 1.2.2 currently under development), the +scatter is even less as shown below.

+par(mar = c(6.1, 4.1, 2.1, 2.1))
+parplot(f_saem_dfop_tc_no_ranef_k2_multi, ylim = c(0.5, 2), las = 2, llquant = 0.25,
+  lpos = "bottomright")

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

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

Conclusions +

Acknowledgements +

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

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. +

Appendix +

Hierarchical model fit listings +

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:44 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 0.982 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+ DMTA_0  k_DMTA 
+97.2953  0.0566 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0   97.3      0
+k_DMTA    0.0      1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  796.3 795.3 -393.2
+
+Optimised parameters:
+              est.    lower   upper
+DMTA_0    97.28130 95.71113 98.8515
+k_DMTA     0.05665  0.02909  0.0842
+a.1        2.66442  2.35579  2.9731
+SD.DMTA_0  1.54776  0.15447  2.9411
+SD.k_DMTA  0.60690  0.26248  0.9513
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0168
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5478 0.1545 2.9411
+SD.k_DMTA 0.6069 0.2625 0.9513
+
+Variance model:
+     est. lower upper
+a.1 2.664 2.356 2.973
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:46 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.39 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0   k_DMTA 
+96.99175  0.05603 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k_DMTA
+DMTA_0  96.99      0
+k_DMTA   0.00      1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  798.3 797.1 -393.2
+
+Optimised parameters:
+               est.     lower    upper
+DMTA_0    97.271822 95.703157 98.84049
+k_DMTA     0.056638  0.029110  0.08417
+a.1        2.660081  2.230398  3.08976
+b.1        0.001665 -0.006911  0.01024
+SD.DMTA_0  1.545520  0.145035  2.94601
+SD.k_DMTA  0.606422  0.262274  0.95057
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5455 0.1450 2.9460
+SD.k_DMTA 0.6064 0.2623 0.9506
+
+Variance model:
+        est.     lower   upper
+a.1 2.660081  2.230398 3.08976
+b.1 0.001665 -0.006911 0.01024
+
+Estimated disappearance times:
+      DT50  DT90
+DMTA 12.24 40.65
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:45 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 1.552 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+ DMTA_0   alpha    beta 
+ 98.292   9.909 156.341 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 alpha beta
+DMTA_0  98.29     0    0
+alpha    0.00     1    0
+beta     0.00     0    1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  734.2 732.7 -360.1
+
+Optimised parameters:
+              est.   lower   upper
+DMTA_0     98.3435 96.9033  99.784
+alpha       7.2007  2.5889  11.812
+beta      112.8746 34.8816 190.868
+a.1         2.0459  1.8054   2.286
+SD.DMTA_0   1.4795  0.2717   2.687
+SD.alpha    0.6396  0.1509   1.128
+SD.beta     0.6874  0.1587   1.216
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1125        
+beta  -0.1227  0.3632
+
+Random effects:
+            est.  lower upper
+SD.DMTA_0 1.4795 0.2717 2.687
+SD.alpha  0.6396 0.1509 1.128
+SD.beta   0.6874 0.1587 1.216
+
+Variance model:
+     est. lower upper
+a.1 2.046 1.805 2.286
+
+Estimated disappearance times:
+      DT50  DT90 DT50back
+DMTA 11.41 42.53     12.8
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:46 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.764 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+DMTA_0  alpha   beta 
+98.772  4.663 92.597 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 alpha beta
+DMTA_0  98.77     0    0
+alpha    0.00     1    0
+beta     0.00     0    1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  720.4 718.8 -352.2
+
+Optimised parameters:
+              est.    lower     upper
+DMTA_0    98.99136 97.26011 100.72261
+alpha      5.86312  2.57485   9.15138
+beta      88.55571 29.20889 147.90254
+a.1        1.51063  1.24384   1.77741
+b.1        0.02824  0.02040   0.03609
+SD.DMTA_0  1.57436 -0.04867   3.19739
+SD.alpha   0.59871  0.17132   1.02611
+SD.beta    0.72994  0.22849   1.23139
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1363        
+beta  -0.1414  0.2542
+
+Random effects:
+            est.    lower upper
+SD.DMTA_0 1.5744 -0.04867 3.197
+SD.alpha  0.5987  0.17132 1.026
+SD.beta   0.7299  0.22849 1.231
+
+Variance model:
+       est.  lower   upper
+a.1 1.51063 1.2438 1.77741
+b.1 0.02824 0.0204 0.03609
+
+Estimated disappearance times:
+      DT50 DT90 DT50back
+DMTA 11.11 42.6    12.82
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:45 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 1.649 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.64383  0.09211  0.02999  0.76814 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.64  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  711.8 710 -346.9
+
+Optimised parameters:
+               est.     lower    upper
+DMTA_0    98.092481 96.573898 99.61106
+k1         0.062499  0.030336  0.09466
+k2         0.009065 -0.005133  0.02326
+g          0.948967  0.862079  1.03586
+a.1        1.821671  1.604774  2.03857
+SD.DMTA_0  1.677785  0.472066  2.88350
+SD.k1      0.634962  0.270788  0.99914
+SD.k2      1.033498 -0.205994  2.27299
+SD.g       1.710046  0.428642  2.99145
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0246                
+k2  0.0491  0.0953        
+g  -0.0552 -0.0889 -0.4795
+
+Random effects:
+           est.   lower  upper
+SD.DMTA_0 1.678  0.4721 2.8835
+SD.k1     0.635  0.2708 0.9991
+SD.k2     1.033 -0.2060 2.2730
+SD.g      1.710  0.4286 2.9914
+
+Variance model:
+     est. lower upper
+a.1 1.822 1.605 2.039
+
+Estimated disappearance times:
+      DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.79 42.8    12.88   11.09   76.46
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:46 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+           time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+           * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.288 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+   DMTA_0        k1        k2         g 
+98.759266  0.087034  0.009933  0.930827 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.76  0  0 0
+k1       0.00  1  0 0
+k2       0.00  0  1 0
+g        0.00  0  0 1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC   BIC logLik
+  665.5 663.4 -322.8
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.377019 96.447952 100.30609
+k1         0.064843  0.034607   0.09508
+k2         0.008895  0.006368   0.01142
+g          0.949696  0.903815   0.99558
+a.1        1.065241  0.865754   1.26473
+b.1        0.029340  0.022336   0.03634
+SD.DMTA_0  2.007754  0.387982   3.62753
+SD.k1      0.580473  0.250286   0.91066
+SD.k2      0.006105 -4.920337   4.93255
+SD.g       1.097149  0.412779   1.78152
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0235                
+k2  0.0595  0.0424        
+g  -0.0470 -0.0278 -0.2731
+
+Random effects:
+              est.   lower  upper
+SD.DMTA_0 2.007754  0.3880 3.6275
+SD.k1     0.580473  0.2503 0.9107
+SD.k2     0.006105 -4.9203 4.9325
+SD.g      1.097149  0.4128 1.7815
+
+Variance model:
+       est.   lower   upper
+a.1 1.06524 0.86575 1.26473
+b.1 0.02934 0.02234 0.03634
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.36 41.32    12.44   10.69   77.92
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:45 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 2.006 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+97.82176  0.06931  0.02997 11.13945 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  97.82  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+  AIC   BIC logLik
+  714 712.1   -348
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    98.16102 96.47747 99.84456
+k1         0.07876  0.05261  0.10491
+k2         0.02227  0.01706  0.02747
+tb        13.99089 -7.40049 35.38228
+a.1        1.82305  1.60700  2.03910
+SD.DMTA_0  1.88413  0.56204  3.20622
+SD.k1      0.34292  0.10482  0.58102
+SD.k2      0.19851  0.01718  0.37985
+SD.tb      1.68168  0.58064  2.78272
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0142                
+k2  0.0001 -0.0025        
+tb  0.0165 -0.1256 -0.0301
+
+Random effects:
+            est.   lower  upper
+SD.DMTA_0 1.8841 0.56204 3.2062
+SD.k1     0.3429 0.10482 0.5810
+SD.k2     0.1985 0.01718 0.3798
+SD.tb     1.6817 0.58064 2.7827
+
+Variance model:
+     est. lower upper
+a.1 1.823 1.607 2.039
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 8.801 67.91    20.44   8.801   31.13
+
+

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


+saemix version used for fitting:      3.2 
+mkin version used for pre-fitting:  1.2.2 
+R version used for fitting:         4.2.2 
+Date of fit:     Sat Jan 28 11:22:46 2023 
+Date of summary: Sat Jan 28 11:23:57 2023 
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical 
+
+Fitted in 3.267 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2       tb 
+98.45190  0.07525  0.02576 19.19375 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 tb
+DMTA_0  98.45  0  0  0
+k1       0.00  1  0  0
+k2       0.00  0  1  0
+tb       0.00  0  0  1
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+    AIC BIC logLik
+  667.1 665 -323.6
+
+Optimised parameters:
+              est.    lower    upper
+DMTA_0    97.76570 95.81350 99.71791
+k1         0.05855  0.03080  0.08630
+k2         0.02337  0.01664  0.03010
+tb        31.09638 29.38289 32.80987
+a.1        1.08835  0.88590  1.29080
+b.1        0.02964  0.02257  0.03671
+SD.DMTA_0  2.04877  0.42607  3.67147
+SD.k1      0.59166  0.25621  0.92711
+SD.k2      0.30698  0.09561  0.51835
+SD.tb      0.01274 -0.10914  0.13462
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0160                
+k2 -0.0070 -0.0024        
+tb -0.0668 -0.0103 -0.2013
+
+Random effects:
+             est.    lower  upper
+SD.DMTA_0 2.04877  0.42607 3.6715
+SD.k1     0.59166  0.25621 0.9271
+SD.k2     0.30698  0.09561 0.5183
+SD.tb     0.01274 -0.10914 0.1346
+
+Variance model:
+       est.   lower   upper
+a.1 1.08835 0.88590 1.29080
+b.1 0.02964 0.02257 0.03671
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.84 51.71    15.57   11.84   29.66
+
+

Hierarchical model convergence plots +

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

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

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

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

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

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

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

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

Session info +

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

Hardware info +

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

MemTotal:       64940452 kB

+ + + +

+ + + + +

+ + + + + + + + diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png new file mode 100644 index 00000000..3f145074 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-const-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png new file mode 100644 index 00000000..e5457fc9 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png new file mode 100644 index 00000000..14707641 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-dfop-tc-no-ranef-k2-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png new file mode 100644 index 00000000..c7ed69a3 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-const-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png new file mode 100644 index 00000000..1a48524c Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-fomc-tc-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png new file mode 100644 index 00000000..0f3b1184 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-const-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png new file mode 100644 index 00000000..901a1579 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-hs-tc-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png new file mode 100644 index 00000000..a3e3a51f Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-const-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png new file mode 100644 index 00000000..b85691eb Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/convergence-saem-sfo-tc-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-full-par-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-full-par-1.png new file mode 100644 index 00000000..a42950f0 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-full-par-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png new file mode 100644 index 00000000..caebc768 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png new file mode 100644 index 00000000..45ae57f1 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/multistart-reduced-par-llquant-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png new file mode 100644 index 00000000..1f8eb9f0 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_parent_files/figure-html/plot-saem-dfop-tc-no-ranef-k2-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway.html b/docs/dev/articles/prebuilt/2022_dmta_pathway.html new file mode 100644 index 00000000..2e89fb9d --- /dev/null +++ b/docs/dev/articles/prebuilt/2022_dmta_pathway.html @@ -0,0 +1,2022 @@ + + + + + + + +Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P • mkin + + + + + + + + + + + + + +

+ + + + +

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 +can be fitted with the mkin package.

The mkin package is used in version 1.2.2, 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 +function available.

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

Data +

The data available for the enantiomer dimethenamid-P (DMTAP) are +renamed to have the same substance name as the data for the racemic +mixture dimethenamid (DMTA). The reason for this is that no difference +between their degradation behaviour was identified in the EU risk +assessment.
Unnecessary columns are discarded
The observation times of each dataset are multiplied with the +corresponding normalisation factor also available in the dataset, in +order to make it possible to describe all datasets with a single set of +parameters that are independent of temperature
Finally, datasets observed in the same soil (Elliot 1 +and Elliot 2) are combined, resulting in dimethenamid +(DMTA) data from six soils.

The following commented R code performs this preprocessing.

+# Apply a function to each of the seven datasets in the mkindsg object to create a list
+dmta_ds <- lapply(1:7, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data                     # Get a dataset
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"              # Rename DMTAP to DMTA
+  ds_i <- subset(ds_i, select = c("name", "time", "value")) # Select data
+  ds_i$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")
+}

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

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

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

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

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

Dataset BBA 2.2
time	DMTA	M23	M27	M31
0.0000000	98.09	NA	NA	NA
0.0000000	98.77	NA	NA	NA
0.7678922	93.52	0.36	0.42	0.36
0.7678922	92.03	0.40	0.47	0.33
2.3036765	88.39	1.03	0.71	0.55
2.3036765	87.18	1.07	0.82	0.64
5.3752452	69.38	3.60	2.19	1.94
5.3752452	71.06	3.66	2.28	1.62
10.7504904	45.21	6.97	5.45	4.22
10.7504904	46.81	7.22	5.19	4.37
16.1257355	30.54	8.65	8.81	6.31
16.1257355	30.07	8.38	7.93	6.85
21.5009807	21.60	9.10	10.25	7.05
21.5009807	20.41	8.63	10.77	6.84
32.2514711	9.10	7.63	10.89	6.53
32.2514711	9.70	8.01	10.85	7.11
43.0019614	6.58	6.40	10.41	6.06
43.0019614	6.31	6.35	10.35	6.05
53.7524518	3.47	5.35	9.92	5.50
53.7524518	3.52	5.06	9.42	5.07
64.5029421	3.40	5.14	9.15	4.94
64.5029421	3.67	5.91	9.25	4.39
91.3791680	1.62	3.35	7.14	3.64
91.3791680	1.62	2.87	7.13	3.55

Dataset BBA 2.3
time	DMTA	M23	M27	M31
0.0000000	99.33	NA	NA	NA
0.0000000	97.44	NA	NA	NA
0.6733938	93.73	0.18	0.50	0.47
0.6733938	93.77	0.18	0.83	0.34
2.0201814	87.84	0.52	1.25	1.00
2.0201814	89.82	0.43	1.09	0.89
4.7137565	71.61	1.19	3.28	3.58
4.7137565	71.42	1.11	3.24	3.41
9.4275131	45.60	2.26	7.17	8.74
9.4275131	45.42	1.99	7.91	8.28
14.1412696	31.12	2.81	10.15	9.67
14.1412696	31.68	2.83	9.55	8.95
18.8550262	23.20	3.39	12.09	10.34
18.8550262	24.13	3.56	11.89	10.00
28.2825393	9.43	3.49	13.32	7.89
28.2825393	9.82	3.28	12.05	8.13
37.7100523	7.08	2.80	10.04	5.06
37.7100523	8.64	2.97	10.78	5.54
47.1375654	4.41	2.42	9.32	3.79
47.1375654	4.78	2.51	9.62	4.11
56.5650785	4.92	2.22	8.00	3.11
56.5650785	5.08	1.95	8.45	2.98
80.1338612	2.13	1.28	5.71	1.78
80.1338612	2.23	0.99	3.33	1.55

Dataset Elliot
time	DMTA	M23	M27	M31
0.000000	97.5	NA	NA	NA
0.000000	100.7	NA	NA	NA
1.228478	86.4	NA	NA	NA
1.228478	88.5	NA	NA	1.5
3.685435	69.8	2.8	2.3	5.0
3.685435	77.1	1.7	2.1	2.4
8.599349	59.0	4.3	4.0	4.3
8.599349	54.2	5.8	3.4	5.0
17.198697	31.3	8.2	6.6	8.0
17.198697	33.5	5.2	6.9	7.7
25.798046	19.6	5.1	8.2	7.8
25.798046	20.9	6.1	8.8	6.5
34.397395	13.3	6.0	9.7	8.0
34.397395	15.8	6.0	8.8	7.4
51.596092	6.7	5.0	8.3	6.9
51.596092	8.7	4.2	9.2	9.0
68.794789	8.8	3.9	9.3	5.5
68.794789	8.7	2.9	8.5	6.1
103.192184	6.0	1.9	8.6	6.1
103.192184	4.4	1.5	6.0	4.0
146.188928	3.3	2.0	5.6	3.1
146.188928	2.8	2.3	4.5	2.9
223.583066	1.4	1.2	4.1	1.8
223.583066	1.8	1.9	3.9	2.6
0.000000	93.4	NA	NA	NA
0.000000	103.2	NA	NA	NA
1.228478	89.2	NA	NA	1.3
1.228478	86.6	NA	NA	NA
3.685435	78.2	2.6	1.0	3.1
3.685435	78.1	2.4	2.6	2.3
8.599349	55.6	5.5	4.5	3.4
8.599349	53.0	5.6	4.6	4.3
17.198697	33.7	7.3	7.6	7.8
17.198697	33.2	6.5	6.7	8.7
25.798046	20.9	5.8	8.7	7.7
25.798046	19.9	7.7	7.6	6.5
34.397395	18.2	7.8	8.0	6.3
34.397395	12.7	7.3	8.6	8.7
51.596092	7.8	7.0	7.4	5.7
51.596092	9.0	6.3	7.2	4.2
68.794789	11.4	4.3	10.3	3.2
68.794789	9.0	3.8	9.4	4.2
103.192184	3.9	2.6	6.5	3.8
103.192184	4.4	2.8	6.9	4.0
146.188928	2.6	1.6	4.6	4.5
146.188928	3.4	1.1	4.5	4.5
223.583066	2.0	1.4	4.3	3.8
223.583066	1.7	1.3	4.2	2.3

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 +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
+)
+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()

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

	Calke	Borstel	Flaach	BBA 2.2	BBA 2.3	Elliot
sfo_path_1	OK	OK	OK	OK	OK	OK
fomc_path_1	OK	OK	OK	OK	OK	OK
dfop_path_1	OK	OK	C	OK	OK	OK
sforb_path_1	OK	OK	C	OK	OK	OK
hs_path_1	C	C	C	C	C	C

All separate pathway fits with SFO or FOMC for the parent and +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	Flaach	BBA 2.2	BBA 2.3	Elliot
sfo_path_1	OK	OK	OK	OK	OK	OK
fomc_path_1	OK	OK	C	OK	OK	C
dfop_path_1	OK	C	OK	OK	OK	OK
sforb_path_1	OK	C	OK	OK	OK	OK
hs_path_1	C	C	C	C	C	OK

With the two-component error model, the set of fits with convergence +problems is slightly different, with convergence problems appearing for +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 +

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))

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()

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

	const	tc
sfo_path_1	OK	OK
fomc_path_1	OK	OK
dfop_path_1	OK	OK
sforb_path_1	OK	OK
hs_path_1	OK	OK

According to the status function, all fits terminated +successfully.

+anova(saem_1) |> kable(digits = 1)

Warning in FUN(X[[i]], ...): Could not obtain log likelihood with 'is' method
+for sforb_path_1 const

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

	npar	AIC	BIC	Lik
sfo_path_1 const	17	2291.8	2288.3	-1128.9
sfo_path_1 tc	18	2276.3	2272.5	-1120.1
fomc_path_1 const	19	2099.0	2095.0	-1030.5
fomc_path_1 tc	20	1939.6	1935.5	-949.8
dfop_path_1 const	21	2038.8	2034.4	-998.4
hs_path_1 const	21	2024.2	2019.8	-991.1
dfop_path_1 tc	22	1879.8	1875.2	-917.9
sforb_path_1 tc	22	1832.9	1828.3	-894.4
hs_path_1 tc	22	1831.4	1826.8	-893.7

When the goodness-of-fit of the models is compared, a warning is +obtained, indicating that the likelihood of the pathway fit with SFORB +for the parent compound and constant variance could not be calculated +with importance sampling (method ‘is’). As this is the default method on +which all AIC and BIC comparisons are based, this variant is not +included in the model comparison table. Comparing the goodness-of-fit of +the remaining models, HS model model with two-component error provides +the best fit. However, for batch experiments performed with constant +conditions such as the experiments evaluated here, there is no reason to +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 +

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()

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

	const	tc
sfo_path_1		sd(DMTA_0)
fomc_path_1		sd(DMTA_0)
dfop_path_1
sforb_path_1		sd(log_k_DMTA_bound_free)
hs_path_1		sd(log_tb)

When using constant variance, no ill-defined variance parameters are +identified with the illparms function in any of the +degradation models. When using the two-component error model, there is +one ill-defined variance parameter in all variants except for the +variant using DFOP for the parent compound.

For the selected combination of the SFORB pathway model with +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)

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)

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

	npar	AIC	BIC	Lik
saem_sforb_path_1_tc_reduced	21	1830.3	1825.9	-894.2
saem_1[[“sforb_path_1”, “tc”]]	22	1832.9	1828.3	-894.4

The convergence plot of the refined fit is shown below.

+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 +metabolites, some movement of the parameters is still visible in the +second phase of the algorithm. However, the amplitude of this movement +is in the range of the amplitude towards the end of the first phase. +Therefore, it is likely that an increase in iterations would not improve +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 +

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)

+print(saem_sforb_path_1_tc_reduced_multi)

<multistart> object with 32 fits:
+ E OK 
+15 17 
+OK: Fit terminated successfully
+E: Error

Out of the 32 fits that were initiated, only 17 terminated without an +error. The reason for this is that the wide variation of starting +parameters in combination with the parameter variation that is used in +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)

+Parameter boxplots for the multistart runs that succeeded +

However, visual analysis of the boxplot of the parameters obtained in +the successful fits confirms that the results are sufficiently +independent of the starting parameters, and there are no remaining +ill-defined parameters.

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"]])

+SFORB pathway fit with two-component error +

+plot(saem_sforb_path_1_tc_reduced)

+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.

Conclusions +

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

Acknowledgements +

The helpful comments by Janina Wöltjen of the German Environment +Agency on earlier versions of this document are gratefully +acknowledged.

References +

+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. +

Appendix +

+ +

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

+SFO pathway fit with two-component error +

+plot(saem_1[["fomc_path_1", "tc"]])

+FOMC pathway fit with two-component error +

+plot(saem_1[["sforb_path_1", "tc"]])

+HS pathway fit with two-component error +

Hierarchical model fit listings +

Fits with random effects for all degradation parameters +

+ +

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

+ +

Session info +

R version 4.2.2 Patched (2022-11-10 r83330)
+Platform: x86_64-pc-linux-gnu (64-bit)
+Running under: Debian GNU/Linux bookworm/sid
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/openblas-serial/libblas.so.3
+LAPACK: /usr/lib/x86_64-linux-gnu/openblas-serial/libopenblas-r0.3.21.so
+
+locale:
+ [1] LC_CTYPE=de_DE.UTF-8       LC_NUMERIC=C              
+ [3] LC_TIME=de_DE.UTF-8        LC_COLLATE=de_DE.UTF-8    
+ [5] LC_MONETARY=de_DE.UTF-8    LC_MESSAGES=de_DE.UTF-8   
+ [7] LC_PAPER=de_DE.UTF-8       LC_NAME=C                 
+ [9] LC_ADDRESS=C               LC_TELEPHONE=C            
+[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C       
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.2 npde_3.3   knitr_1.41 mkin_1.2.2
+
+loaded via a namespace (and not attached):
+ [1] deSolve_1.34      zoo_1.8-11        tidyselect_1.2.0  xfun_0.35        
+ [5] bslib_0.4.2       purrr_1.0.0       lattice_0.20-45   colorspace_2.0-3 
+ [9] vctrs_0.5.1       generics_0.1.3    htmltools_0.5.4   yaml_2.3.6       
+[13] pkgbuild_1.4.0    utf8_1.2.2        rlang_1.0.6       pkgdown_2.0.7    
+[17] jquerylib_0.1.4   pillar_1.8.1      glue_1.6.2        DBI_1.1.3        
+[21] lifecycle_1.0.3   stringr_1.5.0     munsell_0.5.0     gtable_0.3.1     
+[25] ragg_1.2.4        codetools_0.2-18  memoise_2.0.1     evaluate_0.19    
+[29] inline_0.3.19     callr_3.7.3       fastmap_1.1.0     ps_1.7.2         
+[33] lmtest_0.9-40     fansi_1.0.3       highr_0.9         scales_1.2.1     
+[37] cachem_1.0.6      desc_1.4.2        jsonlite_1.8.4    systemfonts_1.0.4
+[41] fs_1.5.2          textshaping_0.3.6 gridExtra_2.3     ggplot2_3.4.0    
+[45] digest_0.6.31     stringi_1.7.8     processx_3.8.0    dplyr_1.0.10     
+[49] grid_4.2.2        rprojroot_2.0.3   cli_3.5.0         tools_4.2.2      
+[53] magrittr_2.0.3    sass_0.4.4        tibble_3.1.8      crayon_1.5.2     
+[57] pkgconfig_2.0.3   prettyunits_1.1.1 assertthat_0.2.1  rmarkdown_2.19   
+[61] R6_2.5.1          mclust_6.0.0      nlme_3.1-161      compiler_4.2.2

Hardware info +

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

MemTotal:       64940452 kB

+ + + +

+ + + + +

+ + + + + + + + diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png new file mode 100644 index 00000000..206c424d Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/saem-sforb-path-1-tc-reduced-convergence-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png new file mode 100644 index 00000000..0fe084d3 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-2-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png new file mode 100644 index 00000000..1c81601e Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-3-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png new file mode 100644 index 00000000..e0961dce Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-4-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-5-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-5-1.png new file mode 100644 index 00000000..00db0c76 Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-5-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png new file mode 100644 index 00000000..ac5271ec Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png new file mode 100644 index 00000000..1c81601e Binary files /dev/null and b/docs/dev/articles/prebuilt/2022_dmta_pathway_files/figure-html/unnamed-chunk-7-1.png differ diff --git a/docs/dev/authors.html b/docs/dev/authors.html index 165e2400..4146fdf2 100644 --- a/docs/dev/authors.html +++ b/docs/dev/authors.html @@ -23,7 +23,7 @@

Thanks to everyone involved for collaboration and support!

Thanks are due also to Emmanuelle Comets, maintainer of the saemix package, for her interest and support for using the SAEM algorithm and its implementation in saemix for the evaluation of chemical degradation data.

diff --git a/docs/dev/news/index.html b/docs/dev/news/index.html index 060135bf..d8fcbfe9 100644 --- a/docs/dev/news/index.html +++ b/docs/dev/news/index.html @@ -23,7 +23,7 @@

- Functions and data + Reference
@@ -34,6 +34,8 @@
- Introduction to mkin
- +
- Example evaluations with (generalised) nonlinear least squares
- Example evaluation of FOCUS Example Dataset D
- - Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models + Example evaluation of FOCUS Example Dataset Z
- +
- Example evaluations with hierarchical models (nonlinear mixed-effects models)
- - Short demo of the multistart method + Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P
- - Performance benefit by using compiled model definitions in mkin + Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P
- - Example evaluation of FOCUS Example Dataset Z + Testing hierarchical pathway kinetics with residue data on cyantraniliprole
- - Calculation of time weighted average concentrations with mkin + Comparison of saemix and nlme evaluations of dimethenamid data from 2018
- - Example evaluation of NAFTA SOP Attachment examples + Short demo of the multistart method +
- +
- Performance
- + Performance benefit by using compiled model definitions in mkin
- Benchmark timings for mkin @@ -64,6 +73,14 @@
- Benchmark timings for saem.mmkin
- +
- Miscellaneous
- + Calculation of time weighted average concentrations with mkin +
- + Example evaluation of NAFTA SOP Attachment examples +
News diff --git a/docs/dev/pkgdown.yml b/docs/dev/pkgdown.yml index 760148d3..ca999f47 100644 --- a/docs/dev/pkgdown.yml +++ b/docs/dev/pkgdown.yml @@ -2,10 +2,12 @@ pandoc: 2.17.1.1 pkgdown: 2.0.7 pkgdown_sha: ~ articles: - 2022_wp_1.1_dmta_parent: 2022_wp_1.1_dmta_parent.html FOCUS_D: FOCUS_D.html FOCUS_L: FOCUS_L.html mkin: mkin.html + 2022_cyan_pathway: prebuilt/2022_cyan_pathway.html + 2022_dmta_parent: prebuilt/2022_dmta_parent.html + 2022_dmta_pathway: prebuilt/2022_dmta_pathway.html twa: twa.html FOCUS_Z: web_only/FOCUS_Z.html NAFTA_examples: web_only/NAFTA_examples.html @@ -14,7 +16,7 @@ articles: dimethenamid_2018: web_only/dimethenamid_2018.html multistart: web_only/multistart.html saem_benchmarks: web_only/saem_benchmarks.html -last_built: 2023-01-05T07:18Z +last_built: 2023-01-28T16:38Z urls: reference: https://pkgdown.jrwb.de/mkin/reference article: https://pkgdown.jrwb.de/mkin/articles diff --git a/docs/dev/reference/index.html b/docs/dev/reference/index.html index 525551fd..b6d2db20 100644 --- a/docs/dev/reference/index.html +++ b/docs/dev/reference/index.html @@ -23,7 +23,7 @@
- - Functions and data + Reference
- @@ -34,6 +34,8 @@
  - Introduction to mkin
  - +
  - Example evaluations with (generalised) nonlinear least squares
  - Example evaluation of FOCUS Example Dataset D
  - - Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models + Example evaluation of FOCUS Example Dataset Z
  - +
  - Example evaluations with hierarchical models (nonlinear mixed-effects models)
  - - Short demo of the multistart method + Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P
  - - Performance benefit by using compiled model definitions in mkin + Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P
  - - Example evaluation of FOCUS Example Dataset Z + Testing hierarchical pathway kinetics with residue data on cyantraniliprole
  - - Calculation of time weighted average concentrations with mkin + Comparison of saemix and nlme evaluations of dimethenamid data from 2018
  - - Example evaluation of NAFTA SOP Attachment examples + Short demo of the multistart method +
  - +
  - Performance
  - + Performance benefit by using compiled model definitions in mkin
  - Benchmark timings for mkin @@ -64,6 +73,14 @@
  - Benchmark timings for saem.mmkin
  - +
  - Miscellaneous
  - + Calculation of time weighted average concentrations with mkin +
  - + Example evaluation of NAFTA SOP Attachment examples +
- News diff --git a/docs/dev/sitemap.xml b/docs/dev/sitemap.xml index 6e51371c..b3542d0b 100644 --- a/docs/dev/sitemap.xml +++ b/docs/dev/sitemap.xml @@ -18,6 +18,15 @@ https://pkgdown.jrwb.de/mkin/articles/mkin.html + + https://pkgdown.jrwb.de/mkin/articles/prebuilt/2022_cyan_pathway.html + + + https://pkgdown.jrwb.de/mkin/articles/prebuilt/2022_dmta_parent.html + + + https://pkgdown.jrwb.de/mkin/articles/prebuilt/2022_dmta_pathway.html + https://pkgdown.jrwb.de/mkin/articles/twa.html -- cgit v1.2.3 From 0eefc969529af58a2e9f046c4a73a10cb20c27a5 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Sat, 28 Jan 2023 17:57:34 +0100 Subject: Some improvements to the README --- README.html | 236 +++++++++++++++++++++++++++++++++++++++++---------- README.md | 13 ++- docs/dev/index.html | 4 +- docs/dev/pkgdown.yml | 2 +- 4 files changed, 202 insertions(+), 53 deletions(-) (limited to 'docs/dev/index.html') diff --git a/README.html b/README.html index 46dcea8b..bf0b1160 100644 --- a/README.html +++ b/README.html @@ -30,7 +30,7 @@ document.addEventListener('DOMContentLoaded', function(e) { !function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],r=Object.getPrototypeOf,s=t.slice,g=t.flat?function(e){return t.flat.call(e)}:function(e){return t.concat.apply([],e)},u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType&&"function"!=typeof e.item},x=function(e){return null!=e&&e===e.window},E=C.document,c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof e?n[o.call(e)]||"object":typeof e}var f="3.6.0",S=function(e,t){return new S.fn.init(e,t)};function p(e){var t=!!e&&"length"in e&&e.length,n=w(e);return!m(e)&&!x(e)&&("array"===n||0===t||"number"==typeof t&&0+~]|"+M+")"+M+"*"),U=new RegExp(M+"|>"),X=new RegExp(F),V=new RegExp("^"+I+"$"),G={ID:new RegExp("^#("+I+")"),CLASS:new RegExp("^\\.("+I+")"),TAG:new RegExp("^("+I+"|[*])"),ATTR:new RegExp("^"+W),PSEUDO:new RegExp("^"+F),CHILD:new RegExp("^:(only|first|last|nth|nth-last)-(child|of-type)(?:\$"+M+"*(even|odd|(([+-]|)(\\d*)n|)"+M+"*(?:([+-]|)"+M+"*(\\d+)|))"+M+"*\$|)","i"),bool:new RegExp("^(?:"+R+")$","i"),needsContext:new RegExp("^"+M+"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\$"+M+"*((?:-\\d)?\\d*)"+M+"*\$|)(?=[^-]|$)","i")},Y=/HTML$/i,Q=/^(?:input|select|textarea|button)$/i,J=/^h\d$/i,K=/^[^{]+\{\s*\[native \w/,Z=/^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,ee=/[+~]/,te=new RegExp("\\\\[\\da-fA-F]{1,6}"+M+"?|\\\\([^\\r\\n\\f])","g"),ne=function(e,t){var n="0x"+e.slice(1)-65536;return t||(n<0?String.fromCharCode(n+65536):String.fromCharCode(n>>10|55296,1023&n|56320))},re=/([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,ie=function(e,t){return t?"\0"===e?"\ufffd":e.slice(0,-1)+"\\"+e.charCodeAt(e.length-1).toString(16)+" ":"\\"+e},oe=function(){T()},ae=be(function(e){return!0===e.disabled&&"fieldset"===e.nodeName.toLowerCase()},{dir:"parentNode",next:"legend"});try{H.apply(t=O.call(p.childNodes),p.childNodes),t[p.childNodes.length].nodeType}catch(e){H={apply:t.length?function(e,t){L.apply(e,O.call(t))}:function(e,t){var n=e.length,r=0;while(e[n++]=t[r++]);e.length=n-1}}}function se(t,e,n,r){var i,o,a,s,u,l,c,f=e&&e.ownerDocument,p=e?e.nodeType:9;if(n=n||[],"string"!=typeof t||!t||1!==p&&9!==p&&11!==p)return n;if(!r&&(T(e),e=e||C,E)){if(11!==p&&(u=Z.exec(t)))if(i=u[1]){if(9===p){if(!(a=e.getElementById(i)))return n;if(a.id===i)return n.push(a),n}else if(f&&(a=f.getElementById(i))&&y(e,a)&&a.id===i)return n.push(a),n}else{if(u[2])return H.apply(n,e.getElementsByTagName(t)),n;if((i=u[3])&&d.getElementsByClassName&&e.getElementsByClassName)return H.apply(n,e.getElementsByClassName(i)),n}if(d.qsa&&!N[t+" "]&&(!v||!v.test(t))&&(1!==p||"object"!==e.nodeName.toLowerCase())){if(c=t,f=e,1===p&&(U.test(t)||z.test(t))){(f=ee.test(t)&&ye(e.parentNode)||e)===e&&d.scope||((s=e.getAttribute("id"))?s=s.replace(re,ie):e.setAttribute("id",s=S)),o=(l=h(t)).length;while(o--)l[o]=(s?"#"+s:":scope")+" "+xe(l[o]);c=l.join(",")}try{return H.apply(n,f.querySelectorAll(c)),n}catch(e){N(t,!0)}finally{s===S&&e.removeAttribute("id")}}}return g(t.replace($,"$1"),e,n,r)}function ue(){var r=[];return function e(t,n){return r.push(t+" ")>b.cacheLength&&delete e[r.shift()],e[t+" "]=n}}function le(e){return e[S]=!0,e}function ce(e){var t=C.createElement("fieldset");try{return!!e(t)}catch(e){return!1}finally{t.parentNode&&t.parentNode.removeChild(t),t=null}}function fe(e,t){var n=e.split("|"),r=n.length;while(r--)b.attrHandle[n[r]]=t}function pe(e,t){var n=t&&e,r=n&&1===e.nodeType&&1===t.nodeType&&e.sourceIndex-t.sourceIndex;if(r)return r;if(n)while(n=n.nextSibling)if(n===t)return-1;return e?1:-1}function de(t){return function(e){return"input"===e.nodeName.toLowerCase()&&e.type===t}}function he(n){return function(e){var t=e.nodeName.toLowerCase();return("input"===t||"button"===t)&&e.type===n}}function ge(t){return function(e){return"form"in e?e.parentNode&&!1===e.disabled?"label"in e?"label"in e.parentNode?e.parentNode.disabled===t:e.disabled===t:e.isDisabled===t||e.isDisabled!==!t&&ae(e)===t:e.disabled===t:"label"in e&&e.disabled===t}}function ve(a){return le(function(o){return o=+o,le(function(e,t){var n,r=a([],e.length,o),i=r.length;while(i--)e[n=r[i]]&&(e[n]=!(t[n]=e[n]))})})}function ye(e){return e&&"undefined"!=typeof e.getElementsByTagName&&e}for(e in d=se.support={},i=se.isXML=function(e){var t=e&&e.namespaceURI,n=e&&(e.ownerDocument||e).documentElement;return!Y.test(t||n&&n.nodeName||"HTML")},T=se.setDocument=function(e){var t,n,r=e?e.ownerDocument||e:p;return r!=C&&9===r.nodeType&&r.documentElement&&(a=(C=r).documentElement,E=!i(C),p!=C&&(n=C.defaultView)&&n.top!==n&&(n.addEventListener?n.addEventListener("unload",oe,!1):n.attachEvent&&n.attachEvent("onunload",oe)),d.scope=ce(function(e){return a.appendChild(e).appendChild(C.createElement("div")),"undefined"!=typeof e.querySelectorAll&&!e.querySelectorAll(":scope fieldset div").length}),d.attributes=ce(function(e){return e.className="i",!e.getAttribute("className")}),d.getElementsByTagName=ce(function(e){return e.appendChild(C.createComment("")),!e.getElementsByTagName("*").length}),d.getElementsByClassName=K.test(C.getElementsByClassName),d.getById=ce(function(e){return a.appendChild(e).id=S,!C.getElementsByName||!C.getElementsByName(S).length}),d.getById?(b.filter.ID=function(e){var t=e.replace(te,ne);return function(e){return e.getAttribute("id")===t}},b.find.ID=function(e,t){if("undefined"!=typeof t.getElementById&&E){var n=t.getElementById(e);return n?[n]:[]}}):(b.filter.ID=function(e){var n=e.replace(te,ne);return function(e){var t="undefined"!=typeof e.getAttributeNode&&e.getAttributeNode("id");return t&&t.value===n}},b.find.ID=function(e,t){if("undefined"!=typeof t.getElementById&&E){var n,r,i,o=t.getElementById(e);if(o){if((n=o.getAttributeNode("id"))&&n.value===e)return[o];i=t.getElementsByName(e),r=0;while(o=i[r++])if((n=o.getAttributeNode("id"))&&n.value===e)return[o]}return[]}}),b.find.TAG=d.getElementsByTagName?function(e,t){return"undefined"!=typeof t.getElementsByTagName?t.getElementsByTagName(e):d.qsa?t.querySelectorAll(e):void 0}:function(e,t){var n,r=[],i=0,o=t.getElementsByTagName(e);if("*"===e){while(n=o[i++])1===n.nodeType&&r.push(n);return r}return o},b.find.CLASS=d.getElementsByClassName&&function(e,t){if("undefined"!=typeof t.getElementsByClassName&&E)return t.getElementsByClassName(e)},s=[],v=[],(d.qsa=K.test(C.querySelectorAll))&&(ce(function(e){var t;a.appendChild(e).innerHTML="",e.querySelectorAll("[msallowcapture^='']").length&&v.push("[*^$]="+M+"*(?:''|\"\")"),e.querySelectorAll("[selected]").length||v.push("\\["+M+"*(?:value|"+R+")"),e.querySelectorAll("[id~="+S+"-]").length||v.push("~="),(t=C.createElement("input")).setAttribute("name",""),e.appendChild(t),e.querySelectorAll("[name='']").length||v.push("\\["+M+"*name"+M+"*="+M+"*(?:''|\"\")"),e.querySelectorAll(":checked").length||v.push(":checked"),e.querySelectorAll("a#"+S+"+*").length||v.push(".#.+[+~]"),e.querySelectorAll("\\\f"),v.push("[\\r\\n\\f]")}),ce(function(e){e.innerHTML="";var t=C.createElement("input");t.setAttribute("type","hidden"),e.appendChild(t).setAttribute("name","D"),e.querySelectorAll("[name=d]").length&&v.push("name"+M+"*[*^$|!~]?="),2!==e.querySelectorAll(":enabled").length&&v.push(":enabled",":disabled"),a.appendChild(e).disabled=!0,2!==e.querySelectorAll(":disabled").length&&v.push(":enabled",":disabled"),e.querySelectorAll("*,:x"),v.push(",.*:")})),(d.matchesSelector=K.test(c=a.matches||a.webkitMatchesSelector||a.mozMatchesSelector||a.oMatchesSelector||a.msMatchesSelector))&&ce(function(e){d.disconnectedMatch=c.call(e,"*"),c.call(e,"[s!='']:x"),s.push("!=",F)}),v=v.length&&new RegExp(v.join("|")),s=s.length&&new RegExp(s.join("|")),t=K.test(a.compareDocumentPosition),y=t||K.test(a.contains)?function(e,t){var n=9===e.nodeType?e.documentElement:e,r=t&&t.parentNode;return e===r||!(!r||1!==r.nodeType||!(n.contains?n.contains(r):e.compareDocumentPosition&&16&e.compareDocumentPosition(r)))}:function(e,t){if(t)while(t=t.parentNode)if(t===e)return!0;return!1},j=t?function(e,t){if(e===t)return l=!0,0;var n=!e.compareDocumentPosition-!t.compareDocumentPosition;return n||(1&(n=(e.ownerDocument||e)==(t.ownerDocument||t)?e.compareDocumentPosition(t):1)||!d.sortDetached&&t.compareDocumentPosition(e)===n?e==C||e.ownerDocument==p&&y(p,e)?-1:t==C||t.ownerDocument==p&&y(p,t)?1:u?P(u,e)-P(u,t):0:4&n?-1:1)}:function(e,t){if(e===t)return l=!0,0;var n,r=0,i=e.parentNode,o=t.parentNode,a=[e],s=[t];if(!i||!o)return e==C?-1:t==C?1:i?-1:o?1:u?P(u,e)-P(u,t):0;if(i===o)return pe(e,t);n=e;while(n=n.parentNode)a.unshift(n);n=t;while(n=n.parentNode)s.unshift(n);while(a[r]===s[r])r++;return r?pe(a[r],s[r]):a[r]==p?-1:s[r]==p?1:0}),C},se.matches=function(e,t){return se(e,null,null,t)},se.matchesSelector=function(e,t){if(T(e),d.matchesSelector&&E&&!N[t+" "]&&(!s||!s.test(t))&&(!v||!v.test(t)))try{var n=c.call(e,t);if(n||d.disconnectedMatch||e.document&&11!==e.document.nodeType)return n}catch(e){N(t,!0)}return 0":{dir:"parentNode",first:!0}," ":{dir:"parentNode"},"+":{dir:"previousSibling",first:!0},"~":{dir:"previousSibling"}},preFilter:{ATTR:function(e){return e[1]=e[1].replace(te,ne),e[3]=(e[3]||e[4]||e[5]||"").replace(te,ne),"~="===e[2]&&(e[3]=" "+e[3]+" "),e.slice(0,4)},CHILD:function(e){return e[1]=e[1].toLowerCase(),"nth"===e[1].slice(0,3)?(e[3]||se.error(e[0]),e[4]=+(e[4]?e[5]+(e[6]||1):2*("even"===e[3]||"odd"===e[3])),e[5]=+(e[7]+e[8]||"odd"===e[3])):e[3]&&se.error(e[0]),e},PSEUDO:function(e){var t,n=!e[6]&&e[2];return G.CHILD.test(e[0])?null:(e[3]?e[2]=e[4]||e[5]||"":n&&X.test(n)&&(t=h(n,!0))&&(t=n.indexOf(")",n.length-t)-n.length)&&(e[0]=e[0].slice(0,t),e[2]=n.slice(0,t)),e.slice(0,3))}},filter:{TAG:function(e){var t=e.replace(te,ne).toLowerCase();return"*"===e?function(){return!0}:function(e){return e.nodeName&&e.nodeName.toLowerCase()===t}},CLASS:function(e){var t=m[e+" "];return t||(t=new RegExp("(^|"+M+")"+e+"("+M+"|$)"))&&m(e,function(e){return t.test("string"==typeof e.className&&e.className||"undefined"!=typeof e.getAttribute&&e.getAttribute("class")||"")})},ATTR:function(n,r,i){return function(e){var t=se.attr(e,n);return null==t?"!="===r:!r||(t+="","="===r?t===i:"!="===r?t!==i:"^="===r?i&&0===t.indexOf(i):"*="===r?i&&-1:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i;function j(e,n,r){return m(n)?S.grep(e,function(e,t){return!!n.call(e,t,e)!==r}):n.nodeType?S.grep(e,function(e){return e===n!==r}):"string"!=typeof n?S.grep(e,function(e){return-1)[^>]*|#([\w-]+))$/;(S.fn.init=function(e,t,n){var r,i;if(!e)return this;if(n=n||D,"string"==typeof e){if(!(r="<"===e[0]&&">"===e[e.length-1]&&3<=e.length?[null,e,null]:q.exec(e))||!r[1]&&t)return!t||t.jquery?(t||n).find(e):this.constructor(t).find(e);if(r[1]){if(t=t instanceof S?t[0]:t,S.merge(this,S.parseHTML(r[1],t&&t.nodeType?t.ownerDocument||t:E,!0)),N.test(r[1])&&S.isPlainObject(t))for(r in t)m(this[r])?this[r](t[r]):this.attr(r,t[r]);return this}return(i=E.getElementById(r[2]))&&(this[0]=i,this.length=1),this}return e.nodeType?(this[0]=e,this.length=1,this):m(e)?void 0!==n.ready?n.ready(e):e(S):S.makeArray(e,this)}).prototype=S.fn,D=S(E);var L=/^(?:parents|prev(?:Until|All))/,H={children:!0,contents:!0,next:!0,prev:!0};function O(e,t){while((e=e[t])&&1!==e.nodeType);return e}S.fn.extend({has:function(e){var t=S(e,this),n=t.length;return this.filter(function(){for(var e=0;e\x20\t\r\n\f]*)/i,he=/^$|^module$|\/(?:java|ecma)script/i;ce=E.createDocumentFragment().appendChild(E.createElement("div")),(fe=E.createElement("input")).setAttribute("type","radio"),fe.setAttribute("checked","checked"),fe.setAttribute("name","t"),ce.appendChild(fe),y.checkClone=ce.cloneNode(!0).cloneNode(!0).lastChild.checked,ce.innerHTML="x",y.noCloneChecked=!!ce.cloneNode(!0).lastChild.defaultValue,ce.innerHTML="",y.option=!!ce.lastChild;var ge={thead:[1,"","
  "],col:[2,"","
  "],tr:[2,"","
  "],td:[3,"","
  "],_default:[0,"",""]};function ve(e,t){var n;return n="undefined"!=typeof e.getElementsByTagName?e.getElementsByTagName(t||"*"):"undefined"!=typeof e.querySelectorAll?e.querySelectorAll(t||"*"):[],void 0===t||t&&A(e,t)?S.merge([e],n):n}function ye(e,t){for(var n=0,r=e.length;n",""]);var me=/<|&#?\w+;/;function xe(e,t,n,r,i){for(var o,a,s,u,l,c,f=t.createDocumentFragment(),p=[],d=0,h=e.length;d\s*$/g;function je(e,t){return A(e,"table")&&A(11!==t.nodeType?t:t.firstChild,"tr")&&S(e).children("tbody")[0]||e}function De(e){return e.type=(null!==e.getAttribute("type"))+"/"+e.type,e}function qe(e){return"true/"===(e.type||"").slice(0,5)?e.type=e.type.slice(5):e.removeAttribute("type"),e}function Le(e,t){var n,r,i,o,a,s;if(1===t.nodeType){if(Y.hasData(e)&&(s=Y.get(e).events))for(i in Y.remove(t,"handle events"),s)for(n=0,r=s[i].length;n").attr(n.scriptAttrs||{}).prop({charset:n.scriptCharset,src:n.url}).on("load error",i=function(e){r.remove(),i=null,e&&t("error"===e.type?404:200,e.type)}),E.head.appendChild(r[0])},abort:function(){i&&i()}}});var _t,zt=[],Ut=/(=)\?(?=&|$)|\?\?/;S.ajaxSetup({jsonp:"callback",jsonpCallback:function(){var e=zt.pop()||S.expando+"_"+wt.guid++;return this[e]=!0,e}}),S.ajaxPrefilter("json jsonp",function(e,t,n){var r,i,o,a=!1!==e.jsonp&&(Ut.test(e.url)?"url":"string"==typeof e.data&&0===(e.contentType||"").indexOf("application/x-www-form-urlencoded")&&Ut.test(e.data)&&"data");if(a||"jsonp"===e.dataTypes[0])return r=e.jsonpCallback=m(e.jsonpCallback)?e.jsonpCallback():e.jsonpCallback,a?e[a]=e[a].replace(Ut,"$1"+r):!1!==e.jsonp&&(e.url+=(Tt.test(e.url)?"&":"?")+e.jsonp+"="+r),e.converters["script json"]=function(){return o||S.error(r+" was not called"),o[0]},e.dataTypes[0]="json",i=C[r],C[r]=function(){o=arguments},n.always(function(){void 0===i?S(C).removeProp(r):C[r]=i,e[r]&&(e.jsonpCallback=t.jsonpCallback,zt.push(r)),o&&m(i)&&i(o[0]),o=i=void 0}),"script"}),y.createHTMLDocument=((_t=E.implementation.createHTMLDocument("").body).innerHTML="
  ",2===_t.childNodes.length),S.parseHTML=function(e,t,n){return"string"!=typeof e?[]:("boolean"==typeof t&&(n=t,t=!1),t||(y.createHTMLDocument?((r=(t=E.implementation.createHTMLDocument("")).createElement("base")).href=E.location.href,t.head.appendChild(r)):t=E),o=!n&&[],(i=N.exec(e))?[t.createElement(i[1])]:(i=xe([e],t,o),o&&o.length&&S(o).remove(),S.merge([],i.childNodes)));var r,i,o},S.fn.load=function(e,t,n){var r,i,o,a=this,s=e.indexOf(" ");return-1").append(S.parseHTML(e)).find(r):e)}).always(n&&function(e,t){a.each(function(){n.apply(this,o||[e.responseText,t,e])})}),this},S.expr.pseudos.animated=function(t){return S.grep(S.timers,function(e){return t===e.elem}).length},S.offset={setOffset:function(e,t,n){var r,i,o,a,s,u,l=S.css(e,"position"),c=S(e),f={};"static"===l&&(e.style.position="relative"),s=c.offset(),o=S.css(e,"top"),u=S.css(e,"left"),("absolute"===l||"fixed"===l)&&-1<(o+u).indexOf("auto")?(a=(r=c.position()).top,i=r.left):(a=parseFloat(o)||0,i=parseFloat(u)||0),m(t)&&(t=t.call(e,n,S.extend({},s))),null!=t.top&&(f.top=t.top-s.top+a),null!=t.left&&(f.left=t.left-s.left+i),"using"in t?t.using.call(e,f):c.css(f)}},S.fn.extend({offset:function(t){if(arguments.length)return void 0===t?this:this.each(function(e){S.offset.setOffset(this,t,e)});var e,n,r=this[0];return r?r.getClientRects().length?(e=r.getBoundingClientRect(),n=r.ownerDocument.defaultView,{top:e.top+n.pageYOffset,left:e.left+n.pageXOffset}):{top:0,left:0}:void 0},position:function(){if(this[0]){var e,t,n,r=this[0],i={top:0,left:0};if("fixed"===S.css(r,"position"))t=r.getBoundingClientRect();else{t=this.offset(),n=r.ownerDocument,e=r.offsetParent||n.documentElement;while(e&&(e===n.body||e===n.documentElement)&&"static"===S.css(e,"position"))e=e.parentNode;e&&e!==r&&1===e.nodeType&&((i=S(e).offset()).top+=S.css(e,"borderTopWidth",!0),i.left+=S.css(e,"borderLeftWidth",!0))}return{top:t.top-i.top-S.css(r,"marginTop",!0),left:t.left-i.left-S.css(r,"marginLeft",!0)}}},offsetParent:function(){return this.map(function(){var e=this.offsetParent;while(e&&"static"===S.css(e,"position"))e=e.offsetParent;return e||re})}}),S.each({scrollLeft:"pageXOffset",scrollTop:"pageYOffset"},function(t,i){var o="pageYOffset"===i;S.fn[t]=function(e){return $(this,function(e,t,n){var r;if(x(e)?r=e:9===e.nodeType&&(r=e.defaultView),void 0===n)return r?r[i]:e[t];r?r.scrollTo(o?r.pageXOffset:n,o?n:r.pageYOffset):e[t]=n},t,e,arguments.length)}}),S.each(["top","left"],function(e,n){S.cssHooks[n]=Fe(y.pixelPosition,function(e,t){if(t)return t=We(e,n),Pe.test(t)?S(e).position()[n]+"px":t})}),S.each({Height:"height",Width:"width"},function(a,s){S.each({padding:"inner"+a,content:s,"":"outer"+a},function(r,o){S.fn[o]=function(e,t){var n=arguments.length&&(r||"boolean"!=typeof e),i=r||(!0===e||!0===t?"margin":"border");return $(this,function(e,t,n){var r;return x(e)?0===o.indexOf("outer")?e["inner"+a]:e.document.documentElement["client"+a]:9===e.nodeType?(r=e.documentElement,Math.max(e.body["scroll"+a],r["scroll"+a],e.body["offset"+a],r["offset"+a],r["client"+a])):void 0===n?S.css(e,t,i):S.style(e,t,n,i)},s,n?e:void 0,n)}})}),S.each(["ajaxStart","ajaxStop","ajaxComplete","ajaxError","ajaxSuccess","ajaxSend"],function(e,t){S.fn[t]=function(e){return this.on(t,e)}}),S.fn.extend({bind:function(e,t,n){return this.on(e,null,t,n)},unbind:function(e,t){return this.off(e,null,t)},delegate:function(e,t,n,r){return this.on(t,e,n,r)},undelegate:function(e,t,n){return 1===arguments.length?this.off(e,"**"):this.off(t,e||"**",n)},hover:function(e,t){return this.mouseenter(e).mouseleave(t||e)}}),S.each("blur focus focusin focusout resize scroll click dblclick mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave change select submit keydown keypress keyup contextmenu".split(" "),function(e,n){S.fn[n]=function(e,t){return 0 -

General

GUI

References

mkin 1.2.2

mkin 1.2.1 (2022-11-19)

mkin 1.0.5 (2021-09-15)

mkin 1.0.4 (2021-04-20)

mkin 1.0.3 (2021-02-15)

mkin 1.0.2 (Unreleased)

mkin 1.0.1 (2021-02-10)

mkin 0.9.49.11 (2020-04-20)

mkin 0.9.49.10 (2020-04-18)

mkin 0.9.46 (2017-07-24)

mkin 0.9.45.2 (2017-07-24)

mkin 0.9.45.1 (2016-12-20)

New features

mkin 0.9.45 (2016-12-08)

mkin 0.9.44 (2016-06-29)

Bug fixes

mkin 0.9.43 (2016-06-28)

mkin 0.9.42 (2016-03-25)

Major changes

Minor changes

Bug fixes

mkin 0.9-40 (2015-07-21)

Bug fixes

Internal changes

mkin 0.9-39 (2015-06-26)

Bug fixes

mkin 0.9-38 (2015-06-24)

Bug fixes

mkin 0.9-36 (2015-06-21)

Minor changes

mkin 0.9-35 (2015-05-15)

Major changes

Bug fixes

mkin 0.9-31 (2014-07-14)

Bug fixes

mkin 0.9-30 (2014-07-11)

New features

Major changes

Value

Work package 1.1: Testing hierarchical parent +degradation kinetics with residue data on dimethenamid and +dimethenamid-P

Johannes +Ranke

Last change on 5 January +2022, last compiled on 5 Januar 2023

Introduction +

Preprocessing of test data +

Separate evaluations +

Hierarchichal model fits +

Parameter identifiability based on the Fisher Information +Matrix +

Alternative check of parameter identifiability +

Conclusions +

Appendix +

Hierarchical model fit listings +

Hierarchical model convergence plots +

Session info +

All vignettes

Hierarchical kinetics template

Arguments

Value

Examples

Display the output of a summary function according to the output format

Arguments

Testing hierarchical pathway kinetics with +residue data on cyantraniliprole

Johannes +Ranke

Last change on 6 January +2023, last compiled on 28 Januar 2023

Introduction +

Test data +

Parent only evaluations +

Pathway fits +

Evaluations with pathway established previously +

Alternative pathway fits +

Refinement of alternative pathway fits +

Conclusion +

Acknowledgements +

Appendix +

Plots of fits that were not refined further +

Hierarchical fit listings +

Pathway 1 +

Pathway 2 +