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+---
+title: "Hierarchical kinetic modelling of degradation data"
+author:
+date:
+output: mkin::hierarchical_kinetics
+geometry: margin=2cm
+---
+
+\clearpage
+
+# Setup
+
+```{r packages, cache = FALSE, message = FALSE}
+library(mkin)
+library(knitr)
+library(saemix)
+library(parallel)
+library(readxl)
+```
+
+```{r n_cores, cache = FALSE}
+n_cores <- detectCores()
+
+if (Sys.info()["sysname"] == "Windows") {
+  cl <- makePSOCKcluster(n_cores)
+} else {
+  cl <- makeForkCluster(n_cores)
+}
+```
+
+\clearpage
+
+# Introduction
+
+This report shows hierarchical kinetic modelling for ...
+The data were obtained from ...
+
+```{r ds}
+data_path <- system.file(
+  "testdata", "lambda-cyhalothrin_soil_efsa_2014.xlsx",
+  package = "mkin")
+ds <- read_spreadsheet(data_path, valid_datasets = c(1:4, 7:13))
+covariates <- attr(ds, "covariates")
+```
+
+The covariate data are shown below.
+
+```{r results = "asis", dependson = "ds", echo = FALSE}
+kable(covariates, caption = "Covariate data for all datasets")
+```
+
+\clearpage
+
+The datasets with the residue time series are shown in the tables below. Please
+refer to the spreadsheet for details like data sources, treatment of values
+below reporting limits and time step normalisation factors.
+
+```{r results = "asis", dependson = "ds", echo = FALSE}
+for (ds_name in names(ds)) {
+  print(
+    kable(mkin_long_to_wide(ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+  cat("\n\\clearpage\n")
+}
+```
+
+# Parent only evaluations
+
+The following code performs separate fits of the candidate degradation models
+to all datasets using constant variance and the two-component error model.
+
+```{r parent-sep, dependson = "ds"}
+parent_deg_mods <- c("SFO", "FOMC", "DFOP", "SFORB")
+errmods <- c(const = "constant variance", tc = "two-component error")
+parent_sep_const <- mmkin(
+  parent_deg_mods, ds,
+  error_model = "const",
+  cluster = cl, quiet = TRUE)
+parent_sep_tc <- update(parent_sep_const, error_model = "tc")
+```
+
+To select the parent model, the corresponding hierarchical fits are performed below.
+
+```{r parent-mhmkin, dependson = "parent-sep"}
+parent_mhmkin <- mhmkin(list(parent_sep_const, parent_sep_tc), cluster = cl)
+status(parent_mhmkin) |> kable()
+```
+
+All fits terminate without errors (status OK). The check for ill-defined
+parameters shows that not all random effect parameters can be robustly
+quantified.
+
+```{r dependson = "parent_mhmkin"}
+illparms(parent_mhmkin) |> kable()
+```
+
+Therefore, the fits are updated, excluding random effects that were
+ill-defined according to the `illparms` function. The status of the fits
+is checked.
+
+```{r parent-mhmkin-refined}
+parent_mhmkin_refined <- update(parent_mhmkin,
+  no_random_effect = illparms(parent_mhmkin))
+status(parent_mhmkin_refined) |> kable()
+```
+
+Also, it is checked if the AIC values of the refined fits are actually smaller
+than the AIC values of the original fits.
+
+```{r dependson = "parent-mhmkin-refined"}
+(AIC(parent_mhmkin_refined) < AIC(parent_mhmkin)) |> kable()
+```
+
+From the refined fits, the most suitable model is selected using the AIC.
+
+```{r parent-best, dependson = "parent-mhmkin"}
+aic_parent <- AIC(parent_mhmkin_refined)
+min_aic <- which(aic_parent == min(aic_parent), arr.ind = TRUE)
+best_degmod_parent <- rownames(aic_parent)[min_aic[1]]
+best_errmod_parent <- colnames(aic_parent)[min_aic[2]]
+anova(parent_mhmkin_refined) |> kable(digits = 1)
+parent_best <- parent_mhmkin_refined[[best_degmod_parent, best_errmod_parent]]
+```
+
+Based on the AIC, the combination of the `r best_degmod_parent` degradation
+model with the error model `r errmods[best_errmod_parent]` is identified to
+be most suitable for the degradation of the parent. The check below
+confirms that no ill-defined parameters remain for this combined model.
+
+```{r dependson = "parent-best"}
+illparms(parent_best)
+```
+
+The corresponding fit is plotted below.
+
+```{r dependson = "parent-best"}
+plot(parent_best)
+```
+The fitted parameters, together with approximate confidence
+intervals are listed below.
+
+```{r dependson = "parent-best"}
+parms(parent_best, ci = TRUE) |> kable(digits = 3)
+```
+
+To investigate a potential covariate influence on degradation parameters, a
+covariate model is added to the hierarchical model for each of the degradation
+parameters with well-defined random effects. Also, a version with covariate
+models for both of them is fitted.
+
+```{r parent-best-pH}
+parent_best_pH_1 <- update(parent_best, covariates = covariates,
+  covariate_models = list(log_k_lambda_free ~ pH))
+parent_best_pH_2 <- update(parent_best, covariates = covariates,
+  covariate_models = list(log_k_lambda_bound_free ~ pH))
+parent_best_pH_3 <- update(parent_best, covariates = covariates,
+  covariate_models = list(log_k_lambda_free ~ pH, log_k_lambda_bound_free ~ pH))
+```
+
+The resulting models are compared.
+
+```{r dependson = "parent-best-pH"}
+anova(parent_best, parent_best_pH_1, parent_best_pH_2, parent_best_pH_3) |>
+  kable(digits = 1)
+```
+
+The model fit with the lowest AIC is the one with a pH correlation of the
+desorption rate constant `k_lambda_bound_free`. Plot and parameter listing
+of this fit are shown below. Also, it is confirmed that no ill-defined
+variance parameters are found.
+
+```{r dependson = "parent-best-pH"}
+plot(parent_best_pH_2)
+```
+
+```{r dependson = "parent-best-pH"}
+illparms(parent_best_pH_2)
+parms(parent_best_pH_2, ci = TRUE) |> kable(digits = 3)
+```
+
+\clearpage
+
+# Pathway fits
+
+As an example of a pathway fit, a model with SFORB for the parent compound and
+parallel formation of two metabolites is set up.
+
+```{r path-1-degmod}
+if (!dir.exists("dlls")) dir.create("dlls")
+
+m_sforb_sfo2 = mkinmod(
+  lambda = mkinsub("SFORB", to = c("c_V", "c_XV")),
+  c_V = mkinsub("SFO"),
+  c_XV = mkinsub("SFO"),
+  name = "sforb_sfo2",
+  dll_dir = "dlls",
+  overwrite = TRUE, quiet = TRUE
+)
+```
+
+Separate evaluations of all datasets are performed with constant variance
+and using two-component error.
+
+```{r path-1-sep, dependson = c("path-1-degmod", "ds")}
+sforb_sep_const <- mmkin(list(sforb_path = m_sforb_sfo2), ds,
+  cluster = cl, quiet = TRUE)
+sforb_sep_tc <- update(sforb_sep_const, error_model = "tc")
+```
+
+The separate fits with constant variance are plotted.
+
+```{r dependson = "path-1-sep", fig.height = 9}
+plot(mixed(sforb_sep_const))
+```
+
+The two corresponding hierarchical fits, with the random effects for the parent
+degradation parameters excluded as discussed above, and including the covariate
+model that was identified for the parent degradation, are attempted below.
+
+```{r path-1, dependson = "path-1-sep"}
+path_1 <- mhmkin(list(sforb_sep_const, sforb_sep_tc),
+  no_random_effect = c("lambda_free_0", "log_k_lambda_free_bound"),
+  covariates = covariates, covariate_models = list(log_k_lambda_bound_free ~ pH),
+  cluster = cl)
+```
+
+```{r dependson = "path-1"}
+status(path_1) |> kable()
+```
+
+The status information shows that both fits were successfully completed.
+
+```{r dependson = "path-1"}
+anova(path_1) |> kable(digits = 1)
+```
+Model comparison shows that the two-component error model provides a much
+better fit.
+
+```{r dependson = "path-1"}
+illparms(path_1[["sforb_path", "tc"]])
+```
+
+Two ill-defined variance components are found. Therefore, the fit is
+repeated with the corresponding random effects removed.
+
+```{r path-1-refined, dependson = "path-1"}
+path_1_refined <- update(path_1[["sforb_path", "tc"]],
+  no_random_effect = c("lambda_free_0", "log_k_lambda_free_bound",
+    "log_k_c_XV", "f_lambda_ilr_2"))
+```
+
+The empty output of the illparms function indicates that there are no
+ill-defined parameters remaining in the refined fit.
+
+```{r dependson = "path-1-refined"}
+illparms(path_1_refined)
+```
+
+Below, the refined fit is plotted and the fitted parameters are shown together
+with their 95% confidence intervals.
+
+```{r dependson = "path-1-refined", fig.height = 9}
+plot(path_1_refined)
+```
+
+```{r dependson = "path-1-refined", fig.height = 9}
+parms(path_1_refined, ci = TRUE) |> kable(digits = 3)
+```
+
+\clearpage
+
+# Appendix
+
+## Listings of initial parent fits
+
+```{r listings-parent, results = "asis", echo = FALSE, dependson = "parent_mhmkin"}
+for (deg_mod in parent_deg_mods) {
+  for (err_mod in c("const", "tc")) {
+    caption <- paste("Hierarchical", deg_mod, "fit with", errmods[err_mod])
+    tex_listing(parent_mhmkin[[deg_mod, err_mod]], caption)
+  }
+}
+```
+
+## Listings of refined parent fits
+
+```{r listings-parent-refined, results = "asis", echo = FALSE, dependson = "parent_mhmkin_refined"}
+for (deg_mod in parent_deg_mods) {
+  for (err_mod in c("const", "tc")) {
+    caption <- paste("Refined hierarchical", deg_mod, "fit with", errmods[err_mod])
+    tex_listing(parent_mhmkin_refined[[deg_mod, err_mod]], caption)
+  }
+}
+```
+
+## Listings of pathway fits
+
+```{r listings-path-1, results = "asis", echo = FALSE, dependson = "path-1-refined"}
+tex_listing(path_1[["sforb_path", "const"]],
+  caption = "Hierarchical fit of SFORB-SFO2 with constant variance")
+tex_listing(path_1[["sforb_path", "tc"]],
+  caption = "Hierarchical fit of SFORB-SFO2 with two-component error")
+tex_listing(path_1_refined,
+  caption = "Refined hierarchical fit of SFORB-SFO2 with two-component error")
+```
+
+## Session info
+
+```{r echo = FALSE, cache = FALSE}
+parallel::stopCluster(cl)
+sessionInfo()
+```
+