From 886c9ef013124aa954d960c655b349b5340ff154 Mon Sep 17 00:00:00 2001
From: Johannes Ranke  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  This document is processed with the  The test data are available in the mkin package as an object of class
+ The following commented R code performs this preprocessing. The following tables show the 6 datasets. 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  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. 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. 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  Convergence plots and summaries for these fits are shown in the
+appendix. The output of the  The AIC and BIC values show that the biphasic models DFOP and HS give
+the best fits. 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. Using the  According to the  The thus identified overparameterisation is addressed by removing the
+random effect for  For the resulting fit, it is checked whether there are still
+ill-defined parameters, which is not the case. Below, the refined model is compared with the
+previous best model. The model without random effect for  The AIC and BIC criteria are lower after removal of the ill-defined
+random effect for  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 of the final NLHM DFOP fit
+ Finally, a summary report of the fit is produced. The parameter check used in the  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. 
+Scaled parameters from the multistart runs, full model
+ The graph clearly confirms the lack of identifiability of the
+variance of  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. 
+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. 
+Scaled parameters from the multistart runs, reduced model, fits with the
+top 25% likelihood values
+ 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. 
+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
+ Ranke J (2022).
+     Ranke J (2023).
 mkin: Kinetic Evaluation of Chemical Degradation Data.
 R package version 1.2.2, https://pkgdown.jrwb.de/mkin/. 
  R markdown format for setting up hierarchical kinetics based on a template
+provided with the mkin package. Arguments to  Keep the intermediate tex file used in the conversion to PDF R Markdown output format to pass to
+
\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 @@
+
+
+
+
+
+
+
+\n")
+  cat(capture.output(suppressWarnings(summary(object))), sep = "\n")
+  cat("\n")
+  cat("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
+      
+      Source: vignettes/2022_wp_1.1_dmta_parent.rmd
+      2022_wp_1.1_dmta_parent.rmdIntroduction
+
+saemix
+package is used as a backend for fitting the NLHM, but is also loaded to
+make the convergence plot function available.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
+
+mkindsg (mkin dataset group) under the identifier
+dimethenamid_2018. The following preprocessing steps are
+still necessary:
+
+Elliot 1
+and Elliot 2) are combined, resulting in dimethenamid
+(DMTA) data from six soils.
+
# 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
+
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")
+}
+
+
+ 
+
+time 
+DMTA 
+
+ 
+0 
+95.8 
+
+ 
+0 
+98.7 
+
+ 
+14 
+60.5 
+
+ 
+30 
+39.1 
+
+ 
+59 
+15.2 
+
+ 
+120 
+4.8 
+
+ 
+
+120 
+4.6 
+
+
+
+ 
+
+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 
+
+
+
+ 
+
+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 
+
+
+
+ 
+
+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 
+
+
+
+ 
+
+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 
+
+
+
+ 
+
+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
+
+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 
+
+
+
+ 
+
+
+ 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 
+Hierarchichal model fits
+
+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.status function shows that all fits
+terminated successfully.
+
+
+ 
+
+
+ const 
+tc 
+
+ 
+SFO 
+OK 
+OK 
+
+ 
+FOMC 
+OK 
+OK 
+
+ 
+DFOP 
+OK 
+OK 
+
+ 
+
+HS 
+OK 
+OK 
+
+
+
+ 
+
+
+ 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
+
+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.
+
+
+ 
+
+
+ const 
+tc 
+
+ 
+SFO 
+
+ b.1 
+
+ 
+FOMC 
+
+ sd(DMTA_0) 
+
+ 
+DFOP 
+sd(k2) 
+sd(k2) 
+
+ 
+
+HS 
+
+ sd(tb) 
+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.k2 from the parameter model.
+
f_saem_dfop_tc_no_ranef_k2 <- update(f_saem[["DFOP", "tc"]],
+  no_random_effect = "k2")
+
illparms(f_saem_dfop_tc_no_ranef_k2)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 
+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).
+
plot(f_saem_dfop_tc_no_ranef_k2)
+
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   83.54Alternative check of parameter identifiability
+
+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.
+
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)
k2 in the full model. The overparameterisation
+of the model also indicates a lack of identifiability of the variance of
+parameter g.
+
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")
+
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")
Conclusions
+
+Appendix
+
+Hierarchical model fit listings
+
+
+
+
+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
+
+
+
+
+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
+
+
+
+
+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
+
+
+
+
+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
+
+
+
+
+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
+
+
+
+
+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
+
+
+
+
+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
+
+
+
+
+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
+
+







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   All vignettes
       
 
-      @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
 
 
 
 
       
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(..., keep_tex = FALSE)Arguments
+    rmarkdown::pdf_documentValue
+    
+
+render
Create and work with nonlinear hierarchical models
Hierarchical kinetics template
Read datasets and relevant meta information from a spreadsheet file
Wrap the output of a summary function in tex listing environment
Display the output of a summary function according to the output format
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.
R/summary_listing.R
+    summary_listing.RdThis 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)The object for which the summary is to be listed
An optional caption
An optional label, ignored in html output
Should a new page be started after the listing? Ignored in html output