Date: Thu, 13 Feb 2025 16:30:31 +0100 Subject: Axis legend formatting, update vignettes --- vignettes/prebuilt/2022_cyan_pathway.html | 5697 ++++++++++++++++++++ vignettes/prebuilt/2022_cyan_pathway.pdf | Bin 680647 -> 677584 bytes vignettes/prebuilt/2022_cyan_pathway.rmd | 23 +- vignettes/prebuilt/2022_dmta_parent.html | 2489 +++++++++ vignettes/prebuilt/2022_dmta_parent.pdf | Bin 544763 -> 545250 bytes vignettes/prebuilt/2022_dmta_pathway.html | 2314 ++++++++ vignettes/prebuilt/2022_dmta_pathway.pdf | Bin 607671 -> 608651 bytes vignettes/prebuilt/2023_mesotrione_parent.html | 2790 ++++++++++ vignettes/web_only/dimethenamid_2018.html | 115 +- .../figure-html/f_parent_mkin_dfop_const-1.png | Bin 57786 -> 57786 bytes .../f_parent_mkin_dfop_const_test-1.png | Bin 57786 -> 57786 bytes .../figure-html/f_parent_mkin_dfop_tc_test-1.png | Bin 59396 -> 59146 bytes .../figure-html/f_parent_saemix_dfop_tc-1.png | Bin 29299 -> 29343 bytes .../figure-html/plot_parent_nlme-1.png | Bin 59192 -> 59209 bytes vignettes/web_only/mkin_benchmarks.rda | Bin 2149 -> 2200 bytes vignettes/web_only/saem_benchmarks.rda | Bin 1049 -> 1106 bytes 16 files changed, 13360 insertions(+), 68 deletions(-) create mode 100644 vignettes/prebuilt/2022_cyan_pathway.html create mode 100644 vignettes/prebuilt/2022_dmta_parent.html create mode 100644 vignettes/prebuilt/2022_dmta_pathway.html create mode 100644 vignettes/prebuilt/2023_mesotrione_parent.html (limited to 'vignettes') diff --git a/vignettes/prebuilt/2022_cyan_pathway.html b/vignettes/prebuilt/2022_cyan_pathway.html new file mode 100644 index 00000000..ea4dd035 --- /dev/null +++ b/vignettes/prebuilt/2022_cyan_pathway.html @@ -0,0 +1,5697 @@ + + + + + + + + + + + + + + +Testing hierarchical pathway kinetics with residue data on cyantraniliprole + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + + + +

+true +

+ +

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 1.2.9 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.

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

Test data

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

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

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	700.0	696.1	-340.0
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.

stopCluster(cl)

Pathway fits

Evaluations with pathway established previously

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

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

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

f_sep_1_const <- mmkin(
+  cyan_path_1,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_1,
+  quiet = TRUE)
+status(f_sep_1_const) |> kable()

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

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

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_path_1)

status(f_saem_1) |> kable()

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

	const	tc
sfo_path_1	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	FO	E

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	E

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

anova(f_saem_1[, "const"]) |> kable(digits = 1)

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

	npar	AIC	BIC	Lik
sfo_path_1 const	16	2693.0	2686.8	-1330.5
fomc_path_1 const	18	2427.9	2420.9	-1196.0
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	2427.2	2419.4	-1193.6

anova(f_saem_1[1:4, ]) |> kable(digits = 1)

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

	npar	AIC	BIC	Lik
sfo_path_1 const	16	2693.0	2686.8	-1330.5
sfo_path_1 tc	17	2657.6	2651.0	-1311.8
fomc_path_1 const	18	2427.9	2420.9	-1196.0
fomc_path_1 tc	19	2423.6	2416.2	-1192.8
dfop_path_1 const	20	2403.2	2395.4	-1181.6
sforb_path_1 const	20	2401.4	2393.6	-1180.7
dfop_path_1 tc	20	2398.0	2390.1	-1179.0
sforb_path_1 tc	20	2399.9	2392.1	-1180.0

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.

stopCluster(cl_path_1)

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
+  )
+)
+
+cl_path_2 <- start_cluster(n_cores)
+f_sep_2_const <- mmkin(
+  cyan_path_2,
+  cyan_ds,
+  error_model = "const",
+  cluster = cl_path_2,
+  quiet = TRUE)
+
+status(f_sep_2_const) |> kable()

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

	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	OK	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	OK	OK	C	OK
dfop_path_2	OK	C	OK	C	OK
sforb_path_2	OK	OK	OK	C	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_path_2)

status(f_saem_2) |> kable()

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

	const	tc
fomc_path_2	E	OK
dfop_path_2	OK	OK
sforb_path_2	OK	OK

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

illparms(f_saem_2) |> kable()

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

	const	tc
fomc_path_2	E	sd(f_JSE76_qlogis)
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 all biphasic fits (DFOP or SFORB for the parent compound), 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[, "tc"]) |> kable(digits = 1)

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

	npar	AIC	BIC	Lik
fomc_path_2 tc	21	2249.0	2240.8	-1103.5
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2239.7	2231.1	-1097.9

anova(f_saem_2[2:3,]) |> kable(digits = 1)

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

	npar	AIC	BIC	Lik
dfop_path_2 const	22	2288.4	2279.8	-1122.2
sforb_path_2 const	22	2283.3	2274.7	-1119.7
dfop_path_2 tc	22	2234.4	2225.8	-1095.2
sforb_path_2 tc	22	2239.7	2231.1	-1097.9

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 +

Refinement of alternative pathway fits

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

no_ranef <- matrix(list(), nrow = 3, ncol = 2, dimnames = dimnames(f_saem_2))
+no_ranef[["fomc_path_2", "const"]] <- c("log_beta", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["fomc_path_2", "tc"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "const"]] <- c("cyan_0", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["dfop_path_2", "tc"]] <- c("cyan_0", "log_k1", "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "const"]] <- c("cyan_free_0",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+no_ranef[["sforb_path_2", "tc"]] <- c("cyan_free_0", "log_k_cyan_free_bound",
+  "f_JCZ38_qlogis", "f_JSE76_qlogis")
+clusterExport(cl_path_2, "no_ranef")
+
+f_saem_3 <- update(f_saem_2,
+  no_random_effect = no_ranef,
+  cluster = cl_path_2)

status(f_saem_3) |> kable()

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

	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[, "tc"]) |> kable(digits = 1)

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

	npar	AIC	BIC	Lik
fomc_path_2 tc	19	2249.1	2241.6	-1105.5
dfop_path_2 tc	20	2237.3	2229.5	-1098.6
sforb_path_2 tc	20	2241.3	2233.5	-1100.7

anova(f_saem_3[2:3,]) |> kable(digits = 1)

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

	npar	AIC	BIC	Lik
dfop_path_2 const	20	2282.2	2274.4	-1121.1
sforb_path_2 const	20	2279.7	2271.9	-1119.9
dfop_path_2 tc	20	2237.3	2229.5	-1098.6
sforb_path_2 tc	20	2241.3	2233.5	-1100.7

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.

stopCluster(cl_path_2)

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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:31:33 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 480.873 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        23.5335        11.8774 
+
+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        9.247           0.00
+f_JCZ38_qlogis       0.0000        0.000          16.61
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2693 2687  -1331
+
+Optimised parameters:
+                     est.      lower      upper
+cyan_0            95.1279  9.354e+01  9.671e+01
+log_k_cyan        -3.8527 -4.367e+00 -3.338e+00
+log_k_JCZ38       -3.0381 -4.187e+00 -1.889e+00
+log_k_J9Z38       -5.0095 -5.623e+00 -4.396e+00
+log_k_JSE76       -5.3357 -6.025e+00 -4.646e+00
+f_cyan_ilr_1       0.8050  5.174e-01  1.093e+00
+f_cyan_ilr_2      12.4820 -1.050e+06  1.051e+06
+f_JCZ38_qlogis     1.2912  3.561e-01  2.226e+00
+a.1                4.8393         NA         NA
+SD.log_k_cyan      0.5840         NA         NA
+SD.log_k_JCZ38     1.2740         NA         NA
+SD.log_k_J9Z38     0.3172         NA         NA
+SD.log_k_JSE76     0.5677         NA         NA
+SD.f_cyan_ilr_1    0.2623         NA         NA
+SD.f_cyan_ilr_2    1.3724         NA         NA
+SD.f_JCZ38_qlogis  0.1464         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5840    NA    NA
+SD.log_k_JCZ38    1.2740    NA    NA
+SD.log_k_J9Z38    0.3172    NA    NA
+SD.log_k_JSE76    0.5677    NA    NA
+SD.f_cyan_ilr_1   0.2623    NA    NA
+SD.f_cyan_ilr_2   1.3724    NA    NA
+SD.f_JCZ38_qlogis 0.1464    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 4.839    NA    NA
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           95.127935 93.542456 96.713413
+k_cyan            0.021221  0.012687  0.035497
+k_JCZ38           0.047924  0.015189  0.151213
+k_J9Z38           0.006674  0.003612  0.012332
+k_JSE76           0.004817  0.002417  0.009601
+f_cyan_to_JCZ38   0.757402        NA        NA
+f_cyan_to_J9Z38   0.242597        NA        NA
+f_JCZ38_to_JSE76  0.784347  0.588098  0.902582
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  7.574e-01
+cyan_J9Z38  2.426e-01
+cyan_sink   9.839e-08
+JCZ38_JSE76 7.843e-01
+JCZ38_sink  2.157e-01
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   32.66 108.50
+JCZ38  14.46  48.05
+J9Z38 103.86 345.00
+JSE76 143.91 478.04
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:32:28 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 534.75 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        22.3422        17.8932 
+
+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        8.939           0.00
+f_JCZ38_qlogis       0.0000        0.000          14.49
+
+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            94.81681    NA    NA
+log_k_cyan        -3.91558    NA    NA
+log_k_JCZ38       -3.12715    NA    NA
+log_k_J9Z38       -5.04840    NA    NA
+log_k_JSE76       -5.10443    NA    NA
+f_cyan_ilr_1       0.80760    NA    NA
+f_cyan_ilr_2      48.66960    NA    NA
+f_JCZ38_qlogis     3.03397    NA    NA
+a.1                3.93879    NA    NA
+b.1                0.08057    NA    NA
+SD.log_k_cyan      0.58921    NA    NA
+SD.log_k_JCZ38     1.29813    NA    NA
+SD.log_k_J9Z38     0.68372    NA    NA
+SD.log_k_JSE76     0.35128    NA    NA
+SD.f_cyan_ilr_1    0.38352    NA    NA
+SD.f_cyan_ilr_2    4.98884    NA    NA
+SD.f_JCZ38_qlogis  1.75636    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_cyan     0.5892    NA    NA
+SD.log_k_JCZ38    1.2981    NA    NA
+SD.log_k_J9Z38    0.6837    NA    NA
+SD.log_k_JSE76    0.3513    NA    NA
+SD.f_cyan_ilr_1   0.3835    NA    NA
+SD.f_cyan_ilr_2   4.9888    NA    NA
+SD.f_JCZ38_qlogis 1.7564    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.93879    NA    NA
+b.1 0.08057    NA    NA
+
+Backtransformed parameters:
+                     est. lower upper
+cyan_0           94.81681    NA    NA
+k_cyan            0.01993    NA    NA
+k_JCZ38           0.04384    NA    NA
+k_J9Z38           0.00642    NA    NA
+k_JSE76           0.00607    NA    NA
+f_cyan_to_JCZ38   0.75807    NA    NA
+f_cyan_to_J9Z38   0.24193    NA    NA
+f_JCZ38_to_JSE76  0.95409    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.75807
+cyan_J9Z38  0.24193
+cyan_sink   0.00000
+JCZ38_JSE76 0.95409
+JCZ38_sink  0.04591
+
+Estimated disappearance times:
+        DT50   DT90
+cyan   34.78 115.54
+JCZ38  15.81  52.52
+J9Z38 107.97 358.68
+JSE76 114.20 379.35
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:33:51 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 618.676 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 
+        7.0229        14.9234        -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          11.57           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          18.81    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            101.1664 98.51265 103.8202
+log_k_JCZ38        -3.3883 -4.78250  -1.9941
+log_k_J9Z38        -5.3087 -5.91564  -4.7017
+log_k_JSE76        -6.1313 -7.30061  -4.9619
+f_cyan_ilr_1        0.7456  0.43782   1.0534
+f_cyan_ilr_2        0.8181  0.24956   1.3866
+f_JCZ38_qlogis      2.0467  0.61165   3.4817
+log_alpha          -0.2391 -0.62806   0.1499
+log_beta            2.8739  2.67664   3.0711
+a.1                 3.4160  3.17960   3.6525
+SD.cyan_0           2.4355  0.40399   4.4671
+SD.log_k_JCZ38      1.5654  0.57311   2.5576
+SD.log_k_J9Z38      0.4645 -0.06533   0.9943
+SD.log_k_JSE76      0.9841  0.10738   1.8609
+SD.f_cyan_ilr_1     0.3285  0.10546   0.5515
+SD.f_cyan_ilr_2     0.2276 -0.38711   0.8424
+SD.f_JCZ38_qlogis   0.8340 -0.20970   1.8777
+SD.log_alpha        0.4250  0.16017   0.6898
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 log_lph
+log_k_JCZ38    -0.0159                                                        
+log_k_J9Z38    -0.0546  0.0080                                                
+log_k_JSE76    -0.0337  0.0016  0.0074                                        
+f_cyan_ilr_1   -0.0095  0.0194 -0.1573  0.0003                                
+f_cyan_ilr_2   -0.2733  0.0799  0.3059  0.0263  0.0125                        
+f_JCZ38_qlogis  0.0755 -0.0783 -0.0516  0.1222 -0.1155 -0.5231                
+log_alpha      -0.0567  0.0120  0.0351  0.0189  0.0040  0.0829 -0.0502        
+log_beta       -0.2980  0.0461  0.1382  0.0758  0.0209  0.4079 -0.2053  0.2759
+
+Random effects:
+                    est.    lower  upper
+SD.cyan_0         2.4355  0.40399 4.4671
+SD.log_k_JCZ38    1.5654  0.57311 2.5576
+SD.log_k_J9Z38    0.4645 -0.06533 0.9943
+SD.log_k_JSE76    0.9841  0.10738 1.8609
+SD.f_cyan_ilr_1   0.3285  0.10546 0.5515
+SD.f_cyan_ilr_2   0.2276 -0.38711 0.8424
+SD.f_JCZ38_qlogis 0.8340 -0.20970 1.8777
+SD.log_alpha      0.4250  0.16017 0.6898
+
+Variance model:
+     est. lower upper
+a.1 3.416  3.18 3.652
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.012e+02 9.851e+01 103.82023
+k_JCZ38          3.377e-02 8.375e-03   0.13614
+k_J9Z38          4.948e-03 2.697e-03   0.00908
+k_JSE76          2.174e-03 6.751e-04   0.00700
+f_cyan_to_JCZ38  6.389e-01        NA        NA
+f_cyan_to_J9Z38  2.226e-01        NA        NA
+f_JCZ38_to_JSE76 8.856e-01 6.483e-01   0.97016
+alpha            7.873e-01 5.336e-01   1.16166
+beta             1.771e+01 1.454e+01  21.56509
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6389
+cyan_J9Z38  0.2226
+cyan_sink   0.1385
+JCZ38_JSE76 0.8856
+JCZ38_sink  0.1144
+
+Estimated disappearance times:
+        DT50    DT90 DT50back
+cyan   25.00  312.06    93.94
+JCZ38  20.53   68.19       NA
+J9Z38 140.07  465.32       NA
+JSE76 318.86 1059.22       NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:34:01 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 627.822 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 
+     101.13294       -3.32499       -5.09097       -5.93566        0.71359 
+  f_cyan_ilr_2 f_JCZ38_qlogis      log_alpha       log_beta 
+      10.30315       14.62272       -0.09633        3.10634 
+
+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          5.649       0.000        0.00        0.00       0.0000
+log_k_JCZ38     0.000       2.319        0.00        0.00       0.0000
+log_k_J9Z38     0.000       0.000        1.73        0.00       0.0000
+log_k_JSE76     0.000       0.000        0.00        1.86       0.0000
+f_cyan_ilr_1    0.000       0.000        0.00        0.00       0.7183
+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
+log_alpha       0.000       0.000        0.00        0.00       0.0000
+log_beta        0.000       0.000        0.00        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          12.85           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          18.54    0.0000   0.0000
+log_alpha              0.00           0.00    0.3142   0.0000
+log_beta               0.00           0.00    0.0000   0.7333
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2424 2416  -1193
+
+Optimised parameters:
+                       est. lower upper
+cyan_0            100.65667    NA    NA
+log_k_JCZ38        -3.45782    NA    NA
+log_k_J9Z38        -5.23476    NA    NA
+log_k_JSE76        -5.71827    NA    NA
+f_cyan_ilr_1        0.68389    NA    NA
+f_cyan_ilr_2        0.61027    NA    NA
+f_JCZ38_qlogis    116.27482    NA    NA
+log_alpha          -0.14484    NA    NA
+log_beta            3.03220    NA    NA
+a.1                 3.11051    NA    NA
+b.1                 0.04508    NA    NA
+SD.log_k_JCZ38      1.39961    NA    NA
+SD.log_k_J9Z38      0.57920    NA    NA
+SD.log_k_JSE76      0.68364    NA    NA
+SD.f_cyan_ilr_1     0.31477    NA    NA
+SD.f_cyan_ilr_2     0.37716    NA    NA
+SD.f_JCZ38_qlogis   5.52695    NA    NA
+SD.log_alpha        0.22823    NA    NA
+SD.log_beta         0.39161    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3996    NA    NA
+SD.log_k_J9Z38    0.5792    NA    NA
+SD.log_k_JSE76    0.6836    NA    NA
+SD.f_cyan_ilr_1   0.3148    NA    NA
+SD.f_cyan_ilr_2   0.3772    NA    NA
+SD.f_JCZ38_qlogis 5.5270    NA    NA
+SD.log_alpha      0.2282    NA    NA
+SD.log_beta       0.3916    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 3.11051    NA    NA
+b.1 0.04508    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.007e+02    NA    NA
+k_JCZ38          3.150e-02    NA    NA
+k_J9Z38          5.328e-03    NA    NA
+k_JSE76          3.285e-03    NA    NA
+f_cyan_to_JCZ38  5.980e-01    NA    NA
+f_cyan_to_J9Z38  2.273e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+alpha            8.652e-01    NA    NA
+beta             2.074e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5980
+cyan_J9Z38  0.2273
+cyan_sink   0.1746
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50  DT90 DT50back
+cyan   25.48 276.2    83.15
+JCZ38  22.01  73.1       NA
+J9Z38 130.09 432.2       NA
+JSE76 210.98 700.9       NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:33:18 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 584.724 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 
+      102.0643        -3.4008        -5.0024        -5.8612         0.6855 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2       g_qlogis 
+        1.2366        13.6901        -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          16.08 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            102.5565    NA    NA
+log_k_JCZ38        -3.4729    NA    NA
+log_k_J9Z38        -5.1533    NA    NA
+log_k_JSE76        -5.6669    NA    NA
+f_cyan_ilr_1        0.6665    NA    NA
+f_cyan_ilr_2        0.5191    NA    NA
+f_JCZ38_qlogis     37.0113    NA    NA
+log_k1             -1.8497    NA    NA
+log_k2             -4.4931    NA    NA
+g_qlogis           -0.6383    NA    NA
+a.1                 3.2397    NA    NA
+SD.log_k_JCZ38      1.4286    NA    NA
+SD.log_k_J9Z38      0.5312    NA    NA
+SD.log_k_JSE76      0.6627    NA    NA
+SD.f_cyan_ilr_1     0.3013    NA    NA
+SD.f_cyan_ilr_2     0.2980    NA    NA
+SD.f_JCZ38_qlogis   0.1637    NA    NA
+SD.log_k1           0.5069    NA    NA
+SD.log_k2           0.3828    NA    NA
+SD.g_qlogis         0.8641    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4286    NA    NA
+SD.log_k_J9Z38    0.5312    NA    NA
+SD.log_k_JSE76    0.6627    NA    NA
+SD.f_cyan_ilr_1   0.3013    NA    NA
+SD.f_cyan_ilr_2   0.2980    NA    NA
+SD.f_JCZ38_qlogis 0.1637    NA    NA
+SD.log_k1         0.5069    NA    NA
+SD.log_k2         0.3828    NA    NA
+SD.g_qlogis       0.8641    NA    NA
+
+Variance model:
+    est. lower upper
+a.1 3.24    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          3.103e-02    NA    NA
+k_J9Z38          5.780e-03    NA    NA
+k_JSE76          3.459e-03    NA    NA
+f_cyan_to_JCZ38  5.813e-01    NA    NA
+f_cyan_to_J9Z38  2.265e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.573e-01    NA    NA
+k2               1.119e-02    NA    NA
+g                3.456e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.5813
+cyan_J9Z38  0.2265
+cyan_sink   0.1922
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.23 167.94    50.55   4.407   61.97
+JCZ38  22.34  74.22       NA      NA      NA
+J9Z38 119.92 398.36       NA      NA      NA
+JSE76 200.41 665.76       NA      NA      NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:35:43 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 729.575 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 
+        6.8713        13.6901        -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       0.6839
+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          11.95           0.00 0.0000 0.0000    0.000
+f_JCZ38_qlogis         0.00          16.08 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            100.69709    NA    NA
+log_k_JCZ38        -3.46669    NA    NA
+log_k_J9Z38        -5.05076    NA    NA
+log_k_JSE76        -5.55558    NA    NA
+f_cyan_ilr_1        0.66045    NA    NA
+f_cyan_ilr_2        0.84275    NA    NA
+f_JCZ38_qlogis     64.22404    NA    NA
+log_k1             -2.17715    NA    NA
+log_k2             -4.55002    NA    NA
+g_qlogis           -0.55920    NA    NA
+a.1                 2.95785    NA    NA
+b.1                 0.04456    NA    NA
+SD.log_k_JCZ38      1.39881    NA    NA
+SD.log_k_J9Z38      0.67788    NA    NA
+SD.log_k_JSE76      0.52603    NA    NA
+SD.f_cyan_ilr_1     0.32490    NA    NA
+SD.f_cyan_ilr_2     0.53923    NA    NA
+SD.f_JCZ38_qlogis   2.75576    NA    NA
+SD.log_k2           0.30694    NA    NA
+SD.g_qlogis         0.83619    NA    NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.3988    NA    NA
+SD.log_k_J9Z38    0.6779    NA    NA
+SD.log_k_JSE76    0.5260    NA    NA
+SD.f_cyan_ilr_1   0.3249    NA    NA
+SD.f_cyan_ilr_2   0.5392    NA    NA
+SD.f_JCZ38_qlogis 2.7558    NA    NA
+SD.log_k2         0.3069    NA    NA
+SD.g_qlogis       0.8362    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.95785    NA    NA
+b.1 0.04456    NA    NA
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.007e+02    NA    NA
+k_JCZ38          3.122e-02    NA    NA
+k_J9Z38          6.404e-03    NA    NA
+k_JSE76          3.866e-03    NA    NA
+f_cyan_to_JCZ38  6.187e-01    NA    NA
+f_cyan_to_J9Z38  2.431e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+k1               1.134e-01    NA    NA
+k2               1.057e-02    NA    NA
+g                3.637e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6187
+cyan_J9Z38  0.2431
+cyan_sink   0.1382
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   26.35 175.12    52.72   6.114    65.6
+JCZ38  22.20  73.75       NA      NA      NA
+J9Z38 108.23 359.53       NA      NA      NA
+JSE76 179.30 595.62       NA      NA      NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:34:05 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 632.71 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 
+              13.7395 
+
+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          16.13
+
+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              102.8136    NA    NA
+log_k_cyan_free           -2.7935    NA    NA
+log_k_cyan_free_bound     -2.5440    NA    NA
+log_k_cyan_bound_free     -3.4303    NA    NA
+log_k_JCZ38               -3.5010    NA    NA
+log_k_J9Z38               -5.1226    NA    NA
+log_k_JSE76               -5.6314    NA    NA
+f_cyan_ilr_1               0.6609    NA    NA
+f_cyan_ilr_2               0.5085    NA    NA
+f_JCZ38_qlogis            44.0153    NA    NA
+a.1                        3.2318    NA    NA
+SD.log_k_cyan_free         0.3211    NA    NA
+SD.log_k_cyan_free_bound   0.8408    NA    NA
+SD.log_k_cyan_bound_free   0.5724    NA    NA
+SD.log_k_JCZ38             1.4925    NA    NA
+SD.log_k_J9Z38             0.5816    NA    NA
+SD.log_k_JSE76             0.6037    NA    NA
+SD.f_cyan_ilr_1            0.3115    NA    NA
+SD.f_cyan_ilr_2            0.3436    NA    NA
+SD.f_JCZ38_qlogis          4.8937    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.3211    NA    NA
+SD.log_k_cyan_free_bound 0.8408    NA    NA
+SD.log_k_cyan_bound_free 0.5724    NA    NA
+SD.log_k_JCZ38           1.4925    NA    NA
+SD.log_k_J9Z38           0.5816    NA    NA
+SD.log_k_JSE76           0.6037    NA    NA
+SD.f_cyan_ilr_1          0.3115    NA    NA
+SD.f_cyan_ilr_2          0.3436    NA    NA
+SD.f_JCZ38_qlogis        4.8937    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.232    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.028e+02    NA    NA
+k_cyan_free          6.120e-02    NA    NA
+k_cyan_free_bound    7.855e-02    NA    NA
+k_cyan_bound_free    3.238e-02    NA    NA
+k_JCZ38              3.017e-02    NA    NA
+k_J9Z38              5.961e-03    NA    NA
+k_JSE76              3.584e-03    NA    NA
+f_cyan_free_to_JCZ38 5.784e-01    NA    NA
+f_cyan_free_to_J9Z38 2.271e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.15973 0.01241 0.33124 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.5784
+cyan_free_J9Z38 0.2271
+cyan_free_sink  0.1945
+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   24.51 153.18    46.11         4.34        55.87
+JCZ38  22.98  76.33       NA           NA           NA
+J9Z38 116.28 386.29       NA           NA           NA
+JSE76 193.42 642.53       NA           NA           NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:37:01 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 807.852 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                6.7399 
+       f_JCZ38_qlogis 
+              13.7395 
+
+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        11.69           0.00
+f_JCZ38_qlogis              0.0000         0.00          16.13
+
+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              100.56004    NA    NA
+log_k_cyan_free           -3.12657    NA    NA
+log_k_cyan_free_bound     -3.16825    NA    NA
+log_k_cyan_bound_free     -3.66003    NA    NA
+log_k_JCZ38               -3.47278    NA    NA
+log_k_J9Z38               -5.06823    NA    NA
+log_k_JSE76               -5.54327    NA    NA
+f_cyan_ilr_1               0.66631    NA    NA
+f_cyan_ilr_2               0.82898    NA    NA
+f_JCZ38_qlogis            38.31115    NA    NA
+a.1                        2.98352    NA    NA
+b.1                        0.04388    NA    NA
+SD.log_k_cyan_free         0.49145    NA    NA
+SD.log_k_cyan_bound_free   0.27347    NA    NA
+SD.log_k_JCZ38             1.41193    NA    NA
+SD.log_k_J9Z38             0.66073    NA    NA
+SD.log_k_JSE76             0.55885    NA    NA
+SD.f_cyan_ilr_1            0.33020    NA    NA
+SD.f_cyan_ilr_2            0.51367    NA    NA
+SD.f_JCZ38_qlogis          5.52122    NA    NA
+
+Correlation is not available
+
+Random effects:
+                           est. lower upper
+SD.log_k_cyan_free       0.4914    NA    NA
+SD.log_k_cyan_bound_free 0.2735    NA    NA
+SD.log_k_JCZ38           1.4119    NA    NA
+SD.log_k_J9Z38           0.6607    NA    NA
+SD.log_k_JSE76           0.5589    NA    NA
+SD.f_cyan_ilr_1          0.3302    NA    NA
+SD.f_cyan_ilr_2          0.5137    NA    NA
+SD.f_JCZ38_qlogis        5.5212    NA    NA
+
+Variance model:
+       est. lower upper
+a.1 2.98352    NA    NA
+b.1 0.04388    NA    NA
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.006e+02    NA    NA
+k_cyan_free          4.387e-02    NA    NA
+k_cyan_free_bound    4.208e-02    NA    NA
+k_cyan_bound_free    2.573e-02    NA    NA
+k_JCZ38              3.103e-02    NA    NA
+k_J9Z38              6.294e-03    NA    NA
+k_JSE76              3.914e-03    NA    NA
+f_cyan_free_to_JCZ38 6.188e-01    NA    NA
+f_cyan_free_to_J9Z38 2.412e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.10044 0.01124 0.36580 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6188
+cyan_free_J9Z38 0.2412
+cyan_free_sink  0.1400
+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   26.05 164.4    49.48        6.901        61.67
+JCZ38  22.34  74.2       NA           NA           NA
+J9Z38 110.14 365.9       NA           NA           NA
+JSE76 177.11 588.3       NA           NA           NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:33:29 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 596.235 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 
+      102.8845        -3.4495        -4.9355        -5.6040         0.6468 
+  f_cyan_ilr_2 f_JCZ38_qlogis         log_k1         log_k2         log_tb 
+        1.2396         9.7220        -2.9079        -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          5.406        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       1.013       0.0000
+f_cyan_ilr_1    0.000        0.00        0.00       0.000       0.6367
+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          2.038           0.00 0.0000 0.0000 0.0000
+f_JCZ38_qlogis        0.000          10.33 0.0000 0.0000 0.0000
+log_k1                0.000           0.00 0.7006 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 0.6773
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2427 2419  -1194
+
+Optimised parameters:
+                      est.      lower      upper
+cyan_0            101.9660  1.005e+02  1.035e+02
+log_k_JCZ38        -3.4698 -4.716e+00 -2.224e+00
+log_k_J9Z38        -5.0947 -5.740e+00 -4.450e+00
+log_k_JSE76        -5.5977 -6.321e+00 -4.875e+00
+f_cyan_ilr_1        0.6595  3.734e-01  9.456e-01
+f_cyan_ilr_2        0.5905  1.664e-01  1.015e+00
+f_JCZ38_qlogis     25.8627 -4.224e+05  4.225e+05
+log_k1             -3.0884 -3.453e+00 -2.723e+00
+log_k2             -4.3877 -4.778e+00 -3.998e+00
+log_tb              2.3057  1.715e+00  2.896e+00
+a.1                 3.3228         NA         NA
+SD.log_k_JCZ38      1.4071         NA         NA
+SD.log_k_J9Z38      0.5774         NA         NA
+SD.log_k_JSE76      0.6214         NA         NA
+SD.f_cyan_ilr_1     0.3058         NA         NA
+SD.f_cyan_ilr_2     0.3470         NA         NA
+SD.f_JCZ38_qlogis   0.0644         NA         NA
+SD.log_k1           0.3994         NA         NA
+SD.log_k2           0.4373         NA         NA
+SD.log_tb           0.6419         NA         NA
+
+Correlation is not available
+
+Random effects:
+                    est. lower upper
+SD.log_k_JCZ38    1.4071    NA    NA
+SD.log_k_J9Z38    0.5774    NA    NA
+SD.log_k_JSE76    0.6214    NA    NA
+SD.f_cyan_ilr_1   0.3058    NA    NA
+SD.f_cyan_ilr_2   0.3470    NA    NA
+SD.f_JCZ38_qlogis 0.0644    NA    NA
+SD.log_k1         0.3994    NA    NA
+SD.log_k2         0.4373    NA    NA
+SD.log_tb         0.6419    NA    NA
+
+Variance model:
+     est. lower upper
+a.1 3.323    NA    NA
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.020e+02 1.005e+02 1.035e+02
+k_JCZ38          3.112e-02 8.951e-03 1.082e-01
+k_J9Z38          6.129e-03 3.216e-03 1.168e-02
+k_JSE76          3.706e-03 1.798e-03 7.639e-03
+f_cyan_to_JCZ38  5.890e-01        NA        NA
+f_cyan_to_J9Z38  2.318e-01        NA        NA
+f_JCZ38_to_JSE76 1.000e+00 0.000e+00 1.000e+00
+k1               4.558e-02 3.164e-02 6.565e-02
+k2               1.243e-02 8.417e-03 1.835e-02
+tb               1.003e+01 5.557e+00 1.811e+01
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  5.890e-01
+cyan_J9Z38  2.318e-01
+cyan_sink   1.793e-01
+JCZ38_JSE76 1.000e+00
+JCZ38_sink  5.861e-12
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   29.02 158.51    47.72   15.21   55.77
+JCZ38  22.27  73.98       NA      NA      NA
+J9Z38 113.09 375.69       NA      NA      NA
+JSE76 187.01 621.23       NA      NA      NA
+
+

Pathway 2

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:46:08 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 536.687 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 
+      102.4477        -1.8631        -5.1087        -2.5114         0.6826 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.7944        15.9616        13.1566        -0.1564         2.9781 
+
+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          7.701       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.448       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.724       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.659       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6356
+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          10.32           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.23           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          14.99    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3924   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5639
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2249 2241  -1104
+
+Optimised parameters:
+                       est.      lower     upper
+cyan_0            101.55265  9.920e+01  103.9059
+log_k_JCZ38        -2.32302 -2.832e+00   -1.8142
+log_k_J9Z38        -5.13082 -5.942e+00   -4.3199
+log_k_JSE76        -3.01756 -4.262e+00   -1.7736
+f_cyan_ilr_1        0.70850  3.657e-01    1.0513
+f_cyan_ilr_2        0.95775  2.612e-01    1.6543
+f_JCZ38_qlogis      3.86105  9.248e-01    6.7973
+f_JSE76_qlogis      7.51583 -1.120e+02  127.0392
+log_alpha          -0.15308 -4.508e-01    0.1446
+log_beta            2.99165  2.711e+00    3.2720
+a.1                 2.04034  1.843e+00    2.2382
+b.1                 0.06924  5.749e-02    0.0810
+SD.log_k_JCZ38      0.50818  1.390e-01    0.8774
+SD.log_k_J9Z38      0.86597  2.652e-01    1.4667
+SD.log_k_JSE76      1.38092  4.864e-01    2.2754
+SD.f_cyan_ilr_1     0.38204  1.354e-01    0.6286
+SD.f_cyan_ilr_2     0.55129  7.198e-02    1.0306
+SD.f_JCZ38_qlogis   1.88457  1.711e-02    3.7520
+SD.f_JSE76_qlogis   2.64018 -2.450e+03 2454.9447
+SD.log_alpha        0.31860  1.047e-01    0.5325
+SD.log_beta         0.24195  1.273e-02    0.4712
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0235                                                        
+log_k_J9Z38    -0.0442  0.0047                                                
+log_k_JSE76    -0.0023  0.0966  0.0006                                        
+f_cyan_ilr_1   -0.0032  0.0070 -0.0536 -0.0001                                
+f_cyan_ilr_2   -0.5189  0.0452  0.1152  0.0013 -0.0304                        
+f_JCZ38_qlogis  0.1088 -0.0848 -0.0240  0.0040 -0.0384 -0.2303                
+f_JSE76_qlogis -0.0545  0.1315  0.0195  0.0020  0.0252  0.1737 -0.5939        
+log_alpha      -0.0445  0.0056  0.0261  0.0019 -0.0055  0.0586 -0.0239 -0.0284
+log_beta       -0.2388  0.0163  0.0566  0.0040 -0.0078  0.2183 -0.0714 -0.0332
+               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        0.2135
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    0.5082  1.390e-01    0.8774
+SD.log_k_J9Z38    0.8660  2.652e-01    1.4667
+SD.log_k_JSE76    1.3809  4.864e-01    2.2754
+SD.f_cyan_ilr_1   0.3820  1.354e-01    0.6286
+SD.f_cyan_ilr_2   0.5513  7.198e-02    1.0306
+SD.f_JCZ38_qlogis 1.8846  1.711e-02    3.7520
+SD.f_JSE76_qlogis 2.6402 -2.450e+03 2454.9447
+SD.log_alpha      0.3186  1.047e-01    0.5325
+SD.log_beta       0.2420  1.273e-02    0.4712
+
+Variance model:
+       est.   lower upper
+a.1 2.04034 1.84252 2.238
+b.1 0.06924 0.05749 0.081
+
+Backtransformed parameters:
+                      est.     lower    upper
+cyan_0           1.016e+02 9.920e+01 103.9059
+k_JCZ38          9.798e-02 5.890e-02   0.1630
+k_J9Z38          5.912e-03 2.627e-03   0.0133
+k_JSE76          4.892e-02 1.410e-02   0.1697
+f_cyan_to_JCZ38  6.432e-01        NA       NA
+f_cyan_to_J9Z38  2.362e-01        NA       NA
+f_JCZ38_to_JSE76 9.794e-01 7.160e-01   0.9989
+f_JSE76_to_JCZ38 9.995e-01 2.268e-49   1.0000
+alpha            8.581e-01 6.371e-01   1.1556
+beta             1.992e+01 1.505e+01  26.3646
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  0.6432301
+cyan_J9Z38  0.2361657
+cyan_sink   0.1206042
+JCZ38_JSE76 0.9793879
+JCZ38_sink  0.0206121
+JSE76_JCZ38 0.9994559
+JSE76_sink  0.0005441
+
+Estimated disappearance times:
+         DT50   DT90 DT50back
+cyan   24.759 271.61    81.76
+JCZ38   7.075  23.50       NA
+J9Z38 117.249 389.49       NA
+JSE76  14.169  47.07       NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:47:06 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 594.209 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 
+      102.4380        -2.3107        -5.3123        -3.7120         0.6757 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1439        13.1194        12.3492        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5644 
+
+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          4.591      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           0.00  0.000 0.0000
+log_k_JCZ38           0.000           0.00           0.00  0.000 0.0000
+log_k_J9Z38           0.000           0.00           0.00  0.000 0.0000
+log_k_JSE76           0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00           0.00  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.86           0.00  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00          13.91  0.000 0.0000
+log_k1                0.000           0.00           0.00  1.106 0.0000
+log_k2                0.000           0.00           0.00  0.000 0.6141
+g_qlogis              0.000           0.00           0.00  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
+  2288 2280  -1122
+
+Optimised parameters:
+                      est.      lower      upper
+cyan_0            102.7204  1.014e+02  1.040e+02
+log_k_JCZ38        -2.8925 -4.044e+00 -1.741e+00
+log_k_J9Z38        -5.1430 -5.828e+00 -4.457e+00
+log_k_JSE76        -3.5577 -4.174e+00 -2.941e+00
+f_cyan_ilr_1        0.6929  3.788e-01  1.007e+00
+f_cyan_ilr_2        0.6066  5.342e-02  1.160e+00
+f_JCZ38_qlogis      9.8071 -2.819e+03  2.838e+03
+f_JSE76_qlogis      2.2229  5.684e-01  3.877e+00
+log_k1             -1.9339 -2.609e+00 -1.258e+00
+log_k2             -4.4709 -4.935e+00 -4.007e+00
+g_qlogis           -0.4987 -1.373e+00  3.757e-01
+a.1                 2.7368  2.545e+00  2.928e+00
+SD.log_k_JCZ38      1.2747  4.577e-01  2.092e+00
+SD.log_k_J9Z38      0.6758  1.418e-01  1.210e+00
+SD.log_k_JSE76      0.5869  1.169e-01  1.057e+00
+SD.f_cyan_ilr_1     0.3392  1.161e-01  5.622e-01
+SD.f_cyan_ilr_2     0.4200  8.501e-02  7.550e-01
+SD.f_JCZ38_qlogis   0.8511 -1.137e+06  1.137e+06
+SD.f_JSE76_qlogis   0.3767 -5.238e-01  1.277e+00
+SD.log_k1           0.7475  2.601e-01  1.235e+00
+SD.log_k2           0.5179  1.837e-01  8.521e-01
+SD.g_qlogis         0.9817  3.553e-01  1.608e+00
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0351                                                        
+log_k_J9Z38    -0.0541  0.0043                                                
+log_k_JSE76    -0.0078  0.0900 -0.0014                                        
+f_cyan_ilr_1   -0.0249  0.0268 -0.0962  0.0000                                
+f_cyan_ilr_2   -0.3560  0.0848  0.1545 -0.0022  0.0463                        
+f_JCZ38_qlogis  0.2005 -0.1226 -0.0347  0.0514 -0.1840 -0.5906                
+f_JSE76_qlogis -0.1638  0.1307  0.0266  0.0001  0.1645  0.5181 -0.9297        
+log_k1          0.0881 -0.0071  0.0005 -0.0070 -0.0064 -0.0346  0.0316 -0.0341
+log_k2          0.0238 -0.0003  0.0082 -0.0022 -0.0017 -0.0017 -0.0002 -0.0076
+g_qlogis        0.0198 -0.0002 -0.0109  0.0034  0.0017 -0.0176  0.0044  0.0051
+               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          0.0276        
+g_qlogis       -0.0283 -0.0309
+
+Random effects:
+                    est.      lower     upper
+SD.log_k_JCZ38    1.2747  4.577e-01 2.092e+00
+SD.log_k_J9Z38    0.6758  1.418e-01 1.210e+00
+SD.log_k_JSE76    0.5869  1.169e-01 1.057e+00
+SD.f_cyan_ilr_1   0.3392  1.161e-01 5.622e-01
+SD.f_cyan_ilr_2   0.4200  8.501e-02 7.550e-01
+SD.f_JCZ38_qlogis 0.8511 -1.137e+06 1.137e+06
+SD.f_JSE76_qlogis 0.3767 -5.238e-01 1.277e+00
+SD.log_k1         0.7475  2.601e-01 1.235e+00
+SD.log_k2         0.5179  1.837e-01 8.521e-01
+SD.g_qlogis       0.9817  3.553e-01 1.608e+00
+
+Variance model:
+     est. lower upper
+a.1 2.737 2.545 2.928
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           102.72037 1.014e+02 104.00464
+k_JCZ38            0.05544 1.752e-02   0.17539
+k_J9Z38            0.00584 2.942e-03   0.01159
+k_JSE76            0.02850 1.539e-02   0.05279
+f_cyan_to_JCZ38    0.59995        NA        NA
+f_cyan_to_J9Z38    0.22519        NA        NA
+f_JCZ38_to_JSE76   0.99994 0.000e+00   1.00000
+f_JSE76_to_JCZ38   0.90229 6.384e-01   0.97971
+k1                 0.14459 7.357e-02   0.28414
+k2                 0.01144 7.192e-03   0.01819
+g                  0.37784 2.021e-01   0.59284
+
+Resulting formation fractions:
+                   ff
+cyan_JCZ38  5.999e-01
+cyan_J9Z38  2.252e-01
+cyan_sink   1.749e-01
+JCZ38_JSE76 9.999e-01
+JCZ38_sink  5.506e-05
+JSE76_JCZ38 9.023e-01
+JSE76_sink  9.771e-02
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   21.93 159.83    48.11   4.794    60.6
+JCZ38  12.50  41.53       NA      NA      NA
+J9Z38 118.69 394.27       NA      NA      NA
+JSE76  24.32  80.78       NA      NA      NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:49:43 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 751.883 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 
+      101.7393        -1.4493        -5.0118        -2.1269         0.6720 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        7.3362        13.4423        13.2659        -2.0061        -4.5527 
+      g_qlogis 
+       -0.5806 
+
+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          5.604        0.00       0.000       0.000       0.0000
+log_k_JCZ38     0.000        2.77       0.000       0.000       0.0000
+log_k_J9Z38     0.000        0.00       1.662       0.000       0.0000
+log_k_JSE76     0.000        0.00       0.000       5.021       0.0000
+f_cyan_ilr_1    0.000        0.00       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000        0.00       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000        0.00       0.000       0.000       0.0000
+log_k1          0.000        0.00       0.000       0.000       0.0000
+log_k2          0.000        0.00       0.000       0.000       0.0000
+g_qlogis        0.000        0.00       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+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          13.37           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis         0.00          14.21           0.00 0.0000 0.0000
+f_JSE76_qlogis         0.00           0.00          14.58 0.0000 0.0000
+log_k1                 0.00           0.00           0.00 0.8453 0.0000
+log_k2                 0.00           0.00           0.00 0.0000 0.5969
+g_qlogis               0.00           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0             0.00
+log_k_JCZ38        0.00
+log_k_J9Z38        0.00
+log_k_JSE76        0.00
+f_cyan_ilr_1       0.00
+f_cyan_ilr_2       0.00
+f_JCZ38_qlogis     0.00
+f_JSE76_qlogis     0.00
+log_k1             0.00
+log_k2             0.00
+g_qlogis           1.69
+
+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            101.25496  99.14662 103.36331
+log_k_JCZ38        -2.55593  -3.32972  -1.78215
+log_k_J9Z38        -5.07103  -5.85423  -4.28783
+log_k_JSE76        -3.25468  -4.17577  -2.33360
+f_cyan_ilr_1        0.70139   0.35924   1.04355
+f_cyan_ilr_2        1.07712   0.17789   1.97636
+f_JCZ38_qlogis      3.57483   0.05990   7.08976
+f_JSE76_qlogis      4.54884  -7.25628  16.35395
+log_k1             -2.38201  -2.51639  -2.24763
+log_k2             -4.66741  -4.91865  -4.41617
+g_qlogis           -0.28446  -1.14192   0.57300
+a.1                 2.05925   1.86481   2.25369
+b.1                 0.06172   0.05062   0.07282
+SD.log_k_JCZ38      0.81137   0.25296   1.36977
+SD.log_k_J9Z38      0.83542   0.25395   1.41689
+SD.log_k_JSE76      0.97903   0.30100   1.65707
+SD.f_cyan_ilr_1     0.37878   0.13374   0.62382
+SD.f_cyan_ilr_2     0.67274   0.10102   1.24446
+SD.f_JCZ38_qlogis   1.35327  -0.42359   3.13012
+SD.f_JSE76_qlogis   1.43956 -19.14972  22.02884
+SD.log_k2           0.25329   0.07521   0.43138
+SD.g_qlogis         0.95167   0.35149   1.55184
+
+Correlation: 
+               cyan_0  l__JCZ3 l__J9Z3 l__JSE7 f_cy__1 f_cy__2 f_JCZ38 f_JSE76
+log_k_JCZ38    -0.0265                                                        
+log_k_J9Z38    -0.0392  0.0024                                                
+log_k_JSE76     0.0011  0.1220 -0.0016                                        
+f_cyan_ilr_1   -0.0161  0.0217 -0.0552  0.0034                                
+f_cyan_ilr_2   -0.4718  0.0829  0.1102  0.0042  0.0095                        
+f_JCZ38_qlogis  0.1609 -0.1318 -0.0277  0.0081 -0.1040 -0.4559                
+f_JSE76_qlogis -0.1289  0.1494  0.0219  0.0012  0.1004  0.4309 -0.8543        
+log_k1          0.2618 -0.0739 -0.0167 -0.0148 -0.0444 -0.2768  0.3518 -0.3818
+log_k2          0.0603 -0.0217  0.0174 -0.0058 -0.0197 -0.0533  0.0923 -0.1281
+g_qlogis        0.0362  0.0115 -0.0111  0.0040  0.0095 -0.0116 -0.0439  0.0651
+               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          0.3269        
+g_qlogis       -0.1656 -0.0928
+
+Random effects:
+                    est.     lower   upper
+SD.log_k_JCZ38    0.8114   0.25296  1.3698
+SD.log_k_J9Z38    0.8354   0.25395  1.4169
+SD.log_k_JSE76    0.9790   0.30100  1.6571
+SD.f_cyan_ilr_1   0.3788   0.13374  0.6238
+SD.f_cyan_ilr_2   0.6727   0.10102  1.2445
+SD.f_JCZ38_qlogis 1.3533  -0.42359  3.1301
+SD.f_JSE76_qlogis 1.4396 -19.14972 22.0288
+SD.log_k2         0.2533   0.07521  0.4314
+SD.g_qlogis       0.9517   0.35149  1.5518
+
+Variance model:
+       est.   lower   upper
+a.1 2.05925 1.86481 2.25369
+b.1 0.06172 0.05062 0.07282
+
+Backtransformed parameters:
+                      est.     lower     upper
+cyan_0           1.013e+02 9.915e+01 103.36331
+k_JCZ38          7.762e-02 3.580e-02   0.16828
+k_J9Z38          6.276e-03 2.868e-03   0.01373
+k_JSE76          3.859e-02 1.536e-02   0.09695
+f_cyan_to_JCZ38  6.520e-01        NA        NA
+f_cyan_to_J9Z38  2.418e-01        NA        NA
+f_JCZ38_to_JSE76 9.727e-01 5.150e-01   0.99917
+f_JSE76_to_JCZ38 9.895e-01 7.052e-04   1.00000
+k1               9.236e-02 8.075e-02   0.10565
+k2               9.397e-03 7.309e-03   0.01208
+g                4.294e-01 2.420e-01   0.63945
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.65203
+cyan_J9Z38  0.24181
+cyan_sink   0.10616
+JCZ38_JSE76 0.97274
+JCZ38_sink  0.02726
+JSE76_JCZ38 0.98953
+JSE76_sink  0.01047
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   24.26 185.34    55.79   7.504   73.77
+JCZ38   8.93  29.66       NA      NA      NA
+J9Z38 110.45 366.89       NA      NA      NA
+JSE76  17.96  59.66       NA      NA      NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:46:57 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 585.771 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 
+             102.4395               -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 
+              14.8408               15.4734 
+
+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            0.0           0.00
+log_k_cyan_free             0.0000        0.000            0.0           0.00
+log_k_cyan_free_bound       0.0000        0.000            0.0           0.00
+log_k_cyan_bound_free       0.0000        0.000            0.0           0.00
+log_k_JCZ38                 0.0000        0.000            0.0           0.00
+log_k_J9Z38                 0.0000        0.000            0.0           0.00
+log_k_JSE76                 0.0000        0.000            0.0           0.00
+f_cyan_ilr_1                0.6349        0.000            0.0           0.00
+f_cyan_ilr_2                0.0000        1.797            0.0           0.00
+f_JCZ38_qlogis              0.0000        0.000           15.6           0.00
+f_JSE76_qlogis              0.0000        0.000            0.0          17.52
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2283 2275  -1120
+
+Optimised parameters:
+                             est.     lower    upper
+cyan_free_0              102.6517 101.40815 103.8952
+log_k_cyan_free           -2.8729  -3.18649  -2.5593
+log_k_cyan_free_bound     -2.7803  -3.60525  -1.9552
+log_k_cyan_bound_free     -3.5845  -4.16644  -3.0026
+log_k_JCZ38               -2.3411  -2.89698  -1.7852
+log_k_J9Z38               -5.2487  -6.01271  -4.4847
+log_k_JSE76               -3.0259  -4.28274  -1.7690
+f_cyan_ilr_1               0.7289   0.38214   1.0756
+f_cyan_ilr_2               0.6891   0.18277   1.1954
+f_JCZ38_qlogis             4.2162   0.47015   7.9622
+f_JSE76_qlogis             5.8911 -20.19088  31.9730
+a.1                        2.7159   2.52587   2.9060
+SD.log_k_cyan_free         0.3354   0.10979   0.5610
+SD.log_k_cyan_free_bound   0.9061   0.30969   1.5025
+SD.log_k_cyan_bound_free   0.6376   0.21229   1.0628
+SD.log_k_JCZ38             0.5499   0.14533   0.9545
+SD.log_k_J9Z38             0.7457   0.15106   1.3404
+SD.log_k_JSE76             1.3822   0.47329   2.2912
+SD.f_cyan_ilr_1            0.3820   0.13280   0.6313
+SD.f_cyan_ilr_2            0.4317   0.06803   0.7953
+SD.f_JCZ38_qlogis          1.8258  -0.25423   3.9059
+SD.f_JSE76_qlogis          2.2348 -83.33679  87.8065
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.1944                                                
+log_k_cyan_free_bound  0.0815  0.0814                                        
+log_k_cyan_bound_free  0.0106  0.0426  0.0585                                
+log_k_JCZ38           -0.0231 -0.0106 -0.0089     -0.0051                    
+log_k_J9Z38           -0.0457 -0.0108  0.0019      0.0129      0.0032        
+log_k_JSE76           -0.0054 -0.0024 -0.0017     -0.0005      0.1108  0.0009
+f_cyan_ilr_1           0.0051 -0.0005 -0.0035     -0.0056      0.0131 -0.0967
+f_cyan_ilr_2          -0.3182 -0.0771 -0.0309     -0.0038      0.0680  0.1643
+f_JCZ38_qlogis         0.0834  0.0369  0.0302      0.0172     -0.1145 -0.0204
+f_JSE76_qlogis        -0.0553 -0.0365 -0.0441     -0.0414      0.1579  0.0175
+                      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          -0.0002                        
+f_cyan_ilr_2           0.0020 -0.0415                
+f_JCZ38_qlogis         0.0052 -0.0665 -0.3437        
+f_JSE76_qlogis         0.0066  0.0635  0.3491 -0.7487
+
+Random effects:
+                           est.     lower   upper
+SD.log_k_cyan_free       0.3354   0.10979  0.5610
+SD.log_k_cyan_free_bound 0.9061   0.30969  1.5025
+SD.log_k_cyan_bound_free 0.6376   0.21229  1.0628
+SD.log_k_JCZ38           0.5499   0.14533  0.9545
+SD.log_k_J9Z38           0.7457   0.15106  1.3404
+SD.log_k_JSE76           1.3822   0.47329  2.2912
+SD.f_cyan_ilr_1          0.3820   0.13280  0.6313
+SD.f_cyan_ilr_2          0.4317   0.06803  0.7953
+SD.f_JCZ38_qlogis        1.8258  -0.25423  3.9059
+SD.f_JSE76_qlogis        2.2348 -83.33679 87.8065
+
+Variance model:
+     est. lower upper
+a.1 2.716 2.526 2.906
+
+Backtransformed parameters:
+                          est.     lower     upper
+cyan_free_0          1.027e+02 1.014e+02 103.89517
+k_cyan_free          5.654e-02 4.132e-02   0.07736
+k_cyan_free_bound    6.202e-02 2.718e-02   0.14153
+k_cyan_bound_free    2.775e-02 1.551e-02   0.04966
+k_JCZ38              9.622e-02 5.519e-02   0.16777
+k_J9Z38              5.254e-03 2.447e-03   0.01128
+k_JSE76              4.852e-02 1.380e-02   0.17051
+f_cyan_free_to_JCZ38 6.197e-01 5.643e-01   0.84429
+f_cyan_free_to_J9Z38 2.211e-01 5.643e-01   0.84429
+f_JCZ38_to_JSE76     9.855e-01 6.154e-01   0.99965
+f_JSE76_to_JCZ38     9.972e-01 1.703e-09   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.13466 0.01165 0.36490 
+
+Resulting formation fractions:
+                      ff
+cyan_free_JCZ38 0.619745
+cyan_free_J9Z38 0.221083
+cyan_free_sink  0.159172
+cyan_free       1.000000
+JCZ38_JSE76     0.985460
+JCZ38_sink      0.014540
+JSE76_JCZ38     0.997244
+JSE76_sink      0.002756
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.293 158.67    47.77        5.147         59.5
+JCZ38   7.203  23.93       NA           NA           NA
+J9Z38 131.918 438.22       NA           NA           NA
+JSE76  14.287  47.46       NA           NA           NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 18:50:00 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 767.874 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 
+             101.7511               -2.8370               -3.0162 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6600               -2.2988               -5.3129 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.6991                0.6722                4.8596 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.4678               14.2149 
+
+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        0.000           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                0.6518        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        9.981           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          14.26           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          16.17
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2240 2231  -1098
+
+Optimised parameters:
+                              est.      lower      upper
+cyan_free_0              100.73014  9.873e+01  1.027e+02
+log_k_cyan_free           -3.19634 -3.641e+00 -2.752e+00
+log_k_cyan_free_bound     -3.43533 -3.674e+00 -3.197e+00
+log_k_cyan_bound_free     -3.83282 -4.163e+00 -3.503e+00
+log_k_JCZ38               -2.51065 -3.225e+00 -1.796e+00
+log_k_J9Z38               -5.02539 -5.825e+00 -4.226e+00
+log_k_JSE76               -3.24777 -4.163e+00 -2.333e+00
+f_cyan_ilr_1               0.70640  3.562e-01  1.057e+00
+f_cyan_ilr_2               1.42704  3.170e-01  2.537e+00
+f_JCZ38_qlogis             2.84779  1.042e+00  4.654e+00
+f_JSE76_qlogis             8.63674 -6.407e+02  6.580e+02
+a.1                        2.07082  1.877e+00  2.265e+00
+b.1                        0.06227  5.098e-02  7.355e-02
+SD.log_k_cyan_free         0.49674  1.865e-01  8.069e-01
+SD.log_k_cyan_bound_free   0.28537  6.809e-02  5.027e-01
+SD.log_k_JCZ38             0.74846  2.305e-01  1.266e+00
+SD.log_k_J9Z38             0.86077  2.713e-01  1.450e+00
+SD.log_k_JSE76             0.97613  3.030e-01  1.649e+00
+SD.f_cyan_ilr_1            0.38994  1.382e-01  6.417e-01
+SD.f_cyan_ilr_2            0.82869  3.917e-02  1.618e+00
+SD.f_JCZ38_qlogis          1.05000 -2.808e-02  2.128e+00
+SD.f_JSE76_qlogis          0.44681 -3.985e+05  3.985e+05
+
+Correlation: 
+                      cyn_f_0 lg_k_c_ lg_k_cyn_f_ lg_k_cyn_b_ l__JCZ3 l__J9Z3
+log_k_cyan_free        0.0936                                                
+log_k_cyan_free_bound  0.1302  0.1627                                        
+log_k_cyan_bound_free  0.0029  0.0525  0.5181                                
+log_k_JCZ38           -0.0116 -0.0077 -0.0430     -0.0236                    
+log_k_J9Z38           -0.0192 -0.0077 -0.0048      0.0229     -0.0005        
+log_k_JSE76            0.0007 -0.0020 -0.0134     -0.0072      0.1225 -0.0016
+f_cyan_ilr_1          -0.0118 -0.0027 -0.0132     -0.0118      0.0127 -0.0505
+f_cyan_ilr_2          -0.4643 -0.0762 -0.1245      0.0137      0.0497  0.1003
+f_JCZ38_qlogis         0.0710  0.0371  0.1826      0.0925     -0.0869 -0.0130
+f_JSE76_qlogis        -0.0367 -0.0270 -0.2274     -0.1865      0.1244  0.0098
+                      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           0.0036                        
+f_cyan_ilr_2           0.0050 -0.0201                
+f_JCZ38_qlogis         0.0142 -0.0529 -0.2698        
+f_JSE76_qlogis         0.0064  0.0345  0.2015 -0.7058
+
+Random effects:
+                           est.      lower     upper
+SD.log_k_cyan_free       0.4967  1.865e-01 8.069e-01
+SD.log_k_cyan_bound_free 0.2854  6.809e-02 5.027e-01
+SD.log_k_JCZ38           0.7485  2.305e-01 1.266e+00
+SD.log_k_J9Z38           0.8608  2.713e-01 1.450e+00
+SD.log_k_JSE76           0.9761  3.030e-01 1.649e+00
+SD.f_cyan_ilr_1          0.3899  1.382e-01 6.417e-01
+SD.f_cyan_ilr_2          0.8287  3.917e-02 1.618e+00
+SD.f_JCZ38_qlogis        1.0500 -2.808e-02 2.128e+00
+SD.f_JSE76_qlogis        0.4468 -3.985e+05 3.985e+05
+
+Variance model:
+       est.   lower   upper
+a.1 2.07082 1.87680 2.26483
+b.1 0.06227 0.05098 0.07355
+
+Backtransformed parameters:
+                          est.      lower     upper
+cyan_free_0          1.007e+02  9.873e+01 102.72898
+k_cyan_free          4.091e-02  2.623e-02   0.06382
+k_cyan_free_bound    3.221e-02  2.537e-02   0.04090
+k_cyan_bound_free    2.165e-02  1.557e-02   0.03011
+k_JCZ38              8.122e-02  3.975e-02   0.16594
+k_J9Z38              6.569e-03  2.954e-03   0.01461
+k_JSE76              3.886e-02  1.556e-02   0.09703
+f_cyan_free_to_JCZ38 6.785e-01  6.102e-01   0.97309
+f_cyan_free_to_J9Z38 2.498e-01  6.102e-01   0.97309
+f_JCZ38_to_JSE76     9.452e-01  7.392e-01   0.99056
+f_JSE76_to_JCZ38     9.998e-01 5.580e-279   1.00000
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08426 0.01051 0.41220 
+
+Resulting formation fractions:
+                       ff
+cyan_free_JCZ38 0.6784541
+cyan_free_J9Z38 0.2498405
+cyan_free_sink  0.0717054
+cyan_free       1.0000000
+JCZ38_JSE76     0.9452043
+JCZ38_sink      0.0547957
+JSE76_JCZ38     0.9998226
+JSE76_sink      0.0001774
+
+Estimated disappearance times:
+         DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.237 168.51    50.73        8.226        65.95
+JCZ38   8.535  28.35       NA           NA           NA
+J9Z38 105.517 350.52       NA           NA           NA
+JSE76  17.837  59.25       NA           NA           NA
+
+

Pathway 2, refined fits

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:03:52 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 830.375 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 
+      102.4477        -1.8631        -5.1087        -2.5114         0.6826 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis      log_alpha       log_beta 
+        4.7944        15.9616        13.1566        -0.1564         2.9781 
+
+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          7.701       0.000       0.000       0.000       0.0000
+log_k_JCZ38     0.000       1.448       0.000       0.000       0.0000
+log_k_J9Z38     0.000       0.000       1.724       0.000       0.0000
+log_k_JSE76     0.000       0.000       0.000       3.659       0.0000
+f_cyan_ilr_1    0.000       0.000       0.000       0.000       0.6356
+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          10.32           0.00           0.00    0.0000   0.0000
+f_JCZ38_qlogis         0.00          12.23           0.00    0.0000   0.0000
+f_JSE76_qlogis         0.00           0.00          14.99    0.0000   0.0000
+log_alpha              0.00           0.00           0.00    0.3924   0.0000
+log_beta               0.00           0.00           0.00    0.0000   0.5639
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2249 2242  -1106
+
+Optimised parameters:
+                     est.   lower  upper
+cyan_0          101.24524      NA     NA
+log_k_JCZ38      -2.85375      NA     NA
+log_k_J9Z38      -5.07729      NA     NA
+log_k_JSE76      -3.53511      NA     NA
+f_cyan_ilr_1      0.67478      NA     NA
+f_cyan_ilr_2      0.97152      NA     NA
+f_JCZ38_qlogis  213.48001      NA     NA
+f_JSE76_qlogis    2.02040      NA     NA
+log_alpha        -0.11041      NA     NA
+log_beta          3.06575      NA     NA
+a.1               2.05279 1.85495 2.2506
+b.1               0.07116 0.05912 0.0832
+SD.log_k_JCZ38    1.21713 0.44160 1.9927
+SD.log_k_J9Z38    0.88268 0.27541 1.4900
+SD.log_k_JSE76    0.59452 0.15005 1.0390
+SD.f_cyan_ilr_1   0.35370 0.12409 0.5833
+SD.f_cyan_ilr_2   0.78186 0.18547 1.3782
+SD.log_alpha      0.27781 0.08168 0.4739
+SD.log_beta       0.32608 0.06490 0.5873
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.2171 0.44160 1.9927
+SD.log_k_J9Z38  0.8827 0.27541 1.4900
+SD.log_k_JSE76  0.5945 0.15005 1.0390
+SD.f_cyan_ilr_1 0.3537 0.12409 0.5833
+SD.f_cyan_ilr_2 0.7819 0.18547 1.3782
+SD.log_alpha    0.2778 0.08168 0.4739
+SD.log_beta     0.3261 0.06490 0.5873
+
+Variance model:
+       est.   lower  upper
+a.1 2.05279 1.85495 2.2506
+b.1 0.07116 0.05912 0.0832
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.012e+02    NA    NA
+k_JCZ38          5.763e-02    NA    NA
+k_J9Z38          6.237e-03    NA    NA
+k_JSE76          2.916e-02    NA    NA
+f_cyan_to_JCZ38  6.354e-01    NA    NA
+f_cyan_to_J9Z38  2.447e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.829e-01    NA    NA
+alpha            8.955e-01    NA    NA
+beta             2.145e+01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6354
+cyan_J9Z38  0.2447
+cyan_sink   0.1200
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8829
+JSE76_sink  0.1171
+
+Estimated disappearance times:
+        DT50   DT90 DT50back
+cyan   25.07 259.21    78.03
+JCZ38  12.03  39.96       NA
+J9Z38 111.14 369.19       NA
+JSE76  23.77  78.98       NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:47 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 945.728 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 
+      102.4380        -2.3107        -5.3123        -3.7120         0.6757 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        1.1439        13.1194        12.3492        -1.9317        -4.4557 
+      g_qlogis 
+       -0.5644 
+
+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          4.591      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           0.00  0.000 0.0000
+log_k_JCZ38           0.000           0.00           0.00  0.000 0.0000
+log_k_J9Z38           0.000           0.00           0.00  0.000 0.0000
+log_k_JSE76           0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_1          0.000           0.00           0.00  0.000 0.0000
+f_cyan_ilr_2          1.797           0.00           0.00  0.000 0.0000
+f_JCZ38_qlogis        0.000          13.86           0.00  0.000 0.0000
+f_JSE76_qlogis        0.000           0.00          13.91  0.000 0.0000
+log_k1                0.000           0.00           0.00  1.106 0.0000
+log_k2                0.000           0.00           0.00  0.000 0.6141
+g_qlogis              0.000           0.00           0.00  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           102.6036      NA     NA
+log_k_JCZ38       -2.9348      NA     NA
+log_k_J9Z38       -5.1617      NA     NA
+log_k_JSE76       -3.6396      NA     NA
+f_cyan_ilr_1       0.6991      NA     NA
+f_cyan_ilr_2       0.6341      NA     NA
+f_JCZ38_qlogis  4232.3011      NA     NA
+f_JSE76_qlogis     1.9658      NA     NA
+log_k1            -1.9503      NA     NA
+log_k2            -4.4745      NA     NA
+g_qlogis          -0.4967      NA     NA
+a.1                2.7461 2.59274 2.8994
+SD.log_k_JCZ38     1.3178 0.47602 2.1596
+SD.log_k_J9Z38     0.7022 0.15061 1.2538
+SD.log_k_JSE76     0.6566 0.15613 1.1570
+SD.f_cyan_ilr_1    0.3409 0.11666 0.5652
+SD.f_cyan_ilr_2    0.4385 0.09482 0.7821
+SD.log_k1          0.7381 0.25599 1.2202
+SD.log_k2          0.5133 0.18152 0.8450
+SD.g_qlogis        0.9866 0.35681 1.6164
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3178 0.47602 2.1596
+SD.log_k_J9Z38  0.7022 0.15061 1.2538
+SD.log_k_JSE76  0.6566 0.15613 1.1570
+SD.f_cyan_ilr_1 0.3409 0.11666 0.5652
+SD.f_cyan_ilr_2 0.4385 0.09482 0.7821
+SD.log_k1       0.7381 0.25599 1.2202
+SD.log_k2       0.5133 0.18152 0.8450
+SD.g_qlogis     0.9866 0.35681 1.6164
+
+Variance model:
+     est. lower upper
+a.1 2.746 2.593 2.899
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.026e+02    NA    NA
+k_JCZ38          5.314e-02    NA    NA
+k_J9Z38          5.732e-03    NA    NA
+k_JSE76          2.626e-02    NA    NA
+f_cyan_to_JCZ38  6.051e-01    NA    NA
+f_cyan_to_J9Z38  2.251e-01    NA    NA
+f_JCZ38_to_JSE76 1.000e+00    NA    NA
+f_JSE76_to_JCZ38 8.772e-01    NA    NA
+k1               1.422e-01    NA    NA
+k2               1.140e-02    NA    NA
+g                3.783e-01    NA    NA
+
+Resulting formation fractions:
+                ff
+cyan_JCZ38  0.6051
+cyan_J9Z38  0.2251
+cyan_sink   0.1698
+JCZ38_JSE76 1.0000
+JCZ38_sink  0.0000
+JSE76_JCZ38 0.8772
+JSE76_sink  0.1228
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   22.05 160.35    48.27   4.873   60.83
+JCZ38  13.04  43.33       NA      NA      NA
+J9Z38 120.93 401.73       NA      NA      NA
+JSE76  26.39  87.68       NA      NA      NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:49 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 947.743 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 
+      101.7393        -1.4493        -5.0118        -2.1269         0.6720 
+  f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis         log_k1         log_k2 
+        7.3362        13.4423        13.2659        -2.0061        -4.5527 
+      g_qlogis 
+       -0.5806 
+
+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          5.604        0.00       0.000       0.000       0.0000
+log_k_JCZ38     0.000        2.77       0.000       0.000       0.0000
+log_k_J9Z38     0.000        0.00       1.662       0.000       0.0000
+log_k_JSE76     0.000        0.00       0.000       5.021       0.0000
+f_cyan_ilr_1    0.000        0.00       0.000       0.000       0.6519
+f_cyan_ilr_2    0.000        0.00       0.000       0.000       0.0000
+f_JCZ38_qlogis  0.000        0.00       0.000       0.000       0.0000
+f_JSE76_qlogis  0.000        0.00       0.000       0.000       0.0000
+log_k1          0.000        0.00       0.000       0.000       0.0000
+log_k2          0.000        0.00       0.000       0.000       0.0000
+g_qlogis        0.000        0.00       0.000       0.000       0.0000
+               f_cyan_ilr_2 f_JCZ38_qlogis f_JSE76_qlogis log_k1 log_k2
+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          13.37           0.00           0.00 0.0000 0.0000
+f_JCZ38_qlogis         0.00          14.21           0.00 0.0000 0.0000
+f_JSE76_qlogis         0.00           0.00          14.58 0.0000 0.0000
+log_k1                 0.00           0.00           0.00 0.8453 0.0000
+log_k2                 0.00           0.00           0.00 0.0000 0.5969
+g_qlogis               0.00           0.00           0.00 0.0000 0.0000
+               g_qlogis
+cyan_0             0.00
+log_k_JCZ38        0.00
+log_k_J9Z38        0.00
+log_k_JSE76        0.00
+f_cyan_ilr_1       0.00
+f_cyan_ilr_2       0.00
+f_JCZ38_qlogis     0.00
+f_JSE76_qlogis     0.00
+log_k1             0.00
+log_k2             0.00
+g_qlogis           1.69
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2237 2229  -1099
+
+Optimised parameters:
+                     est.   lower   upper
+cyan_0          101.00243      NA      NA
+log_k_JCZ38      -2.80828      NA      NA
+log_k_J9Z38      -5.04449      NA      NA
+log_k_JSE76      -3.66981      NA      NA
+f_cyan_ilr_1      0.72564      NA      NA
+f_cyan_ilr_2      1.37978      NA      NA
+f_JCZ38_qlogis    1.98726      NA      NA
+f_JSE76_qlogis  414.80884      NA      NA
+log_k1           -2.38601      NA      NA
+log_k2           -4.63632      NA      NA
+g_qlogis         -0.33920      NA      NA
+a.1               2.10837 1.91261 2.30413
+b.1               0.06223 0.05085 0.07361
+SD.log_k_JCZ38    1.30902 0.48128 2.13675
+SD.log_k_J9Z38    0.83882 0.25790 1.41974
+SD.log_k_JSE76    0.58104 0.14201 1.02008
+SD.f_cyan_ilr_1   0.35421 0.12398 0.58443
+SD.f_cyan_ilr_2   0.79373 0.12007 1.46739
+SD.log_k2         0.27476 0.08557 0.46394
+SD.g_qlogis       0.96170 0.35463 1.56878
+
+Correlation is not available
+
+Random effects:
+                  est.   lower  upper
+SD.log_k_JCZ38  1.3090 0.48128 2.1367
+SD.log_k_J9Z38  0.8388 0.25790 1.4197
+SD.log_k_JSE76  0.5810 0.14201 1.0201
+SD.f_cyan_ilr_1 0.3542 0.12398 0.5844
+SD.f_cyan_ilr_2 0.7937 0.12007 1.4674
+SD.log_k2       0.2748 0.08557 0.4639
+SD.g_qlogis     0.9617 0.35463 1.5688
+
+Variance model:
+       est.   lower   upper
+a.1 2.10837 1.91261 2.30413
+b.1 0.06223 0.05085 0.07361
+
+Backtransformed parameters:
+                      est. lower upper
+cyan_0           1.010e+02    NA    NA
+k_JCZ38          6.031e-02    NA    NA
+k_J9Z38          6.445e-03    NA    NA
+k_JSE76          2.548e-02    NA    NA
+f_cyan_to_JCZ38  6.808e-01    NA    NA
+f_cyan_to_J9Z38  2.440e-01    NA    NA
+f_JCZ38_to_JSE76 8.795e-01    NA    NA
+f_JSE76_to_JCZ38 1.000e+00    NA    NA
+k1               9.200e-02    NA    NA
+k2               9.693e-03    NA    NA
+g                4.160e-01    NA    NA
+
+Resulting formation fractions:
+                 ff
+cyan_JCZ38  0.68081
+cyan_J9Z38  0.24398
+cyan_sink   0.07521
+JCZ38_JSE76 0.87945
+JCZ38_sink  0.12055
+JSE76_JCZ38 1.00000
+JSE76_sink  0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_k1 DT50_k2
+cyan   25.00 182.05     54.8   7.535   71.51
+JCZ38  11.49  38.18       NA      NA      NA
+J9Z38 107.55 357.28       NA      NA      NA
+JSE76  27.20  90.36       NA      NA      NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:38 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 936.368 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 
+             102.4395               -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 
+              14.8408               15.4734 
+
+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            0.0           0.00
+log_k_cyan_free             0.0000        0.000            0.0           0.00
+log_k_cyan_free_bound       0.0000        0.000            0.0           0.00
+log_k_cyan_bound_free       0.0000        0.000            0.0           0.00
+log_k_JCZ38                 0.0000        0.000            0.0           0.00
+log_k_J9Z38                 0.0000        0.000            0.0           0.00
+log_k_JSE76                 0.0000        0.000            0.0           0.00
+f_cyan_ilr_1                0.6349        0.000            0.0           0.00
+f_cyan_ilr_2                0.0000        1.797            0.0           0.00
+f_JCZ38_qlogis              0.0000        0.000           15.6           0.00
+f_JSE76_qlogis              0.0000        0.000            0.0          17.52
+
+Starting values for error model parameters:
+a.1 
+  1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2280 2272  -1120
+
+Optimised parameters:
+                              est.   lower  upper
+cyan_free_0               102.6532      NA     NA
+log_k_cyan_free            -2.8547      NA     NA
+log_k_cyan_free_bound      -2.7004      NA     NA
+log_k_cyan_bound_free      -3.5078      NA     NA
+log_k_JCZ38                -2.9255      NA     NA
+log_k_J9Z38                -5.1089      NA     NA
+log_k_JSE76                -3.6263      NA     NA
+f_cyan_ilr_1                0.6873      NA     NA
+f_cyan_ilr_2                0.6498      NA     NA
+f_JCZ38_qlogis           3624.2149      NA     NA
+f_JSE76_qlogis              1.9991      NA     NA
+a.1                         2.7472 2.55559 2.9388
+SD.log_k_cyan_free          0.3227 0.10296 0.5423
+SD.log_k_cyan_free_bound    0.8757 0.29525 1.4562
+SD.log_k_cyan_bound_free    0.6128 0.20220 1.0233
+SD.log_k_JCZ38              1.3431 0.48474 2.2014
+SD.log_k_J9Z38              0.6881 0.14714 1.2291
+SD.log_k_JSE76              0.6461 0.15321 1.1390
+SD.f_cyan_ilr_1             0.3361 0.11376 0.5585
+SD.f_cyan_ilr_2             0.4286 0.08419 0.7730
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.3227 0.10296 0.5423
+SD.log_k_cyan_free_bound 0.8757 0.29525 1.4562
+SD.log_k_cyan_bound_free 0.6128 0.20220 1.0233
+SD.log_k_JCZ38           1.3431 0.48474 2.2014
+SD.log_k_J9Z38           0.6881 0.14714 1.2291
+SD.log_k_JSE76           0.6461 0.15321 1.1390
+SD.f_cyan_ilr_1          0.3361 0.11376 0.5585
+SD.f_cyan_ilr_2          0.4286 0.08419 0.7730
+
+Variance model:
+     est. lower upper
+a.1 2.747 2.556 2.939
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.027e+02    NA    NA
+k_cyan_free          5.758e-02    NA    NA
+k_cyan_free_bound    6.718e-02    NA    NA
+k_cyan_bound_free    2.996e-02    NA    NA
+k_JCZ38              5.364e-02    NA    NA
+k_J9Z38              6.042e-03    NA    NA
+k_JSE76              2.662e-02    NA    NA
+f_cyan_free_to_JCZ38 6.039e-01    NA    NA
+f_cyan_free_to_J9Z38 2.285e-01    NA    NA
+f_JCZ38_to_JSE76     1.000e+00    NA    NA
+f_JSE76_to_JCZ38     8.807e-01    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+ 0.1426  0.0121  0.3484 
+
+Resulting formation fractions:
+                    ff
+cyan_free_JCZ38 0.6039
+cyan_free_J9Z38 0.2285
+cyan_free_sink  0.1676
+cyan_free       1.0000
+JCZ38_JSE76     1.0000
+JCZ38_sink      0.0000
+JSE76_JCZ38     0.8807
+JSE76_sink      0.1193
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   23.84 154.95    46.65         4.86        57.31
+JCZ38  12.92  42.93       NA           NA           NA
+J9Z38 114.71 381.07       NA           NA           NA
+JSE76  26.04  86.51       NA           NA           NA
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 19:05:52 2025 
+Date of summary: Thu Feb 13 19:05:53 2025 
+
+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 950.661 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 
+             101.7511               -2.8370               -3.0162 
+log_k_cyan_bound_free           log_k_JCZ38           log_k_J9Z38 
+              -3.6600               -2.2988               -5.3129 
+          log_k_JSE76          f_cyan_ilr_1          f_cyan_ilr_2 
+              -3.6991                0.6722                4.8596 
+       f_JCZ38_qlogis        f_JSE76_qlogis 
+              13.4678               14.2149 
+
+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        0.000           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                0.6518        0.000           0.00           0.00
+f_cyan_ilr_2                0.0000        9.981           0.00           0.00
+f_JCZ38_qlogis              0.0000        0.000          14.26           0.00
+f_JSE76_qlogis              0.0000        0.000           0.00          16.17
+
+Starting values for error model parameters:
+a.1 b.1 
+  1   1 
+
+Results:
+
+Likelihood computed by importance sampling
+   AIC  BIC logLik
+  2241 2233  -1101
+
+Optimised parameters:
+                              est.   lower   upper
+cyan_free_0              100.95469      NA      NA
+log_k_cyan_free           -3.18706      NA      NA
+log_k_cyan_free_bound     -3.38455      NA      NA
+log_k_cyan_bound_free     -3.75788      NA      NA
+log_k_JCZ38               -2.77024      NA      NA
+log_k_J9Z38               -5.03665      NA      NA
+log_k_JSE76               -3.60289      NA      NA
+f_cyan_ilr_1               0.72263      NA      NA
+f_cyan_ilr_2               1.45352      NA      NA
+f_JCZ38_qlogis             2.00778      NA      NA
+f_JSE76_qlogis           941.58570      NA      NA
+a.1                        2.11130 1.91479 2.30780
+b.1                        0.06299 0.05152 0.07445
+SD.log_k_cyan_free         0.50098 0.18805 0.81390
+SD.log_k_cyan_bound_free   0.31671 0.08467 0.54875
+SD.log_k_JCZ38             1.25865 0.45932 2.05798
+SD.log_k_J9Z38             0.86833 0.27222 1.46444
+SD.log_k_JSE76             0.59325 0.14711 1.03940
+SD.f_cyan_ilr_1            0.35705 0.12521 0.58890
+SD.f_cyan_ilr_2            0.88541 0.13797 1.63286
+
+Correlation is not available
+
+Random effects:
+                           est.   lower  upper
+SD.log_k_cyan_free       0.5010 0.18805 0.8139
+SD.log_k_cyan_bound_free 0.3167 0.08467 0.5487
+SD.log_k_JCZ38           1.2587 0.45932 2.0580
+SD.log_k_J9Z38           0.8683 0.27222 1.4644
+SD.log_k_JSE76           0.5933 0.14711 1.0394
+SD.f_cyan_ilr_1          0.3571 0.12521 0.5889
+SD.f_cyan_ilr_2          0.8854 0.13797 1.6329
+
+Variance model:
+       est.   lower   upper
+a.1 2.11130 1.91479 2.30780
+b.1 0.06299 0.05152 0.07445
+
+Backtransformed parameters:
+                          est. lower upper
+cyan_free_0          1.010e+02    NA    NA
+k_cyan_free          4.129e-02    NA    NA
+k_cyan_free_bound    3.389e-02    NA    NA
+k_cyan_bound_free    2.333e-02    NA    NA
+k_JCZ38              6.265e-02    NA    NA
+k_J9Z38              6.495e-03    NA    NA
+k_JSE76              2.724e-02    NA    NA
+f_cyan_free_to_JCZ38 6.844e-01    NA    NA
+f_cyan_free_to_J9Z38 2.463e-01    NA    NA
+f_JCZ38_to_JSE76     8.816e-01    NA    NA
+f_JSE76_to_JCZ38     1.000e+00    NA    NA
+
+Estimated Eigenvalues of SFORB model(s):
+cyan_b1 cyan_b2  cyan_g 
+0.08751 0.01101 0.39586 
+
+Resulting formation fractions:
+                     ff
+cyan_free_JCZ38 0.68444
+cyan_free_J9Z38 0.24633
+cyan_free_sink  0.06923
+cyan_free       1.00000
+JCZ38_JSE76     0.88161
+JCZ38_sink      0.11839
+JSE76_JCZ38     1.00000
+JSE76_sink      0.00000
+
+Estimated disappearance times:
+        DT50   DT90 DT50back DT50_cyan_b1 DT50_cyan_b2
+cyan   25.36 163.36    49.18        7.921        62.95
+JCZ38  11.06  36.75       NA           NA           NA
+J9Z38 106.71 354.49       NA           NA           NA
+JSE76  25.44  84.51       NA           NA           NA
+
+

Session info

R version 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+
+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       
+
+time zone: Europe/Berlin
+tzcode source: system (glibc)
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
+[5] rmarkdown_2.29  nvimcom_0.9-167
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     cellranger_1.1.0  jsonlite_1.8.9    processx_3.8.4   
+[13] pkgbuild_1.4.5    deSolve_1.40      mclust_6.1.1      ps_1.8.1         
+[17] gridExtra_2.3     fansi_1.0.6       scales_1.3.0      codetools_0.2-20 
+[21] jquerylib_0.1.4   cli_3.6.3         rlang_1.1.4       munsell_0.5.1    
+[25] cachem_1.1.0      yaml_2.3.10       inline_0.3.20     tools_4.4.2      
+[29] colorout_1.3-2    dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1    
+[33] vctrs_0.6.5       R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4  
+[37] MASS_7.3-61       pkgconfig_2.0.3   callr_3.7.6       pillar_1.9.0     
+[41] bslib_0.8.0       gtable_0.3.6      glue_1.8.0        xfun_0.49        
+[45] tibble_3.2.1      lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1
+[49] nlme_3.1-166      compiler_4.4.2    readxl_1.4.3

Hardware info

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

MemTotal:       64927788 kB

+ + + + +

+ + + + + + + + + + + + + + + diff --git a/vignettes/prebuilt/2022_cyan_pathway.pdf b/vignettes/prebuilt/2022_cyan_pathway.pdf index ec37706f..78e1964c 100644 Binary files a/vignettes/prebuilt/2022_cyan_pathway.pdf and b/vignettes/prebuilt/2022_cyan_pathway.pdf differ diff --git a/vignettes/prebuilt/2022_cyan_pathway.rmd b/vignettes/prebuilt/2022_cyan_pathway.rmd index 8463c854..e7401f3e 100644 --- a/vignettes/prebuilt/2022_cyan_pathway.rmd +++ b/vignettes/prebuilt/2022_cyan_pathway.rmd @@ -1,7 +1,7 @@ --- title: "Testing hierarchical pathway kinetics with residue data on cyantraniliprole" author: Johannes Ranke -date: Last change on 20 April 2023, last compiled on `r format(Sys.time(), "%e +date: Last change on 13 February 2023, last compiled on `r format(Sys.time(), "%e %B %Y")` output: pdf_document: @@ -240,11 +240,12 @@ because it relies on the Fisher Information Matrix. illparms(f_saem_1) |> kable() ``` -The model comparison below suggests that the pathway fits using +The model comparisons below suggest that the pathway fits using DFOP or SFORB for the parent compound provide the best fit. ```{r, dependson = "f-saem-1"} -anova(f_saem_1) |> kable(digits = 1) +anova(f_saem_1[, "const"]) |> kable(digits = 1) +anova(f_saem_1[1:4, ]) |> kable(digits = 1) ``` For these two parent model, successful fits are shown below. Plots of the fits @@ -344,18 +345,21 @@ f_saem_2 <- mhmkin(list(f_sep_2_const, f_sep_2_tc), status(f_saem_2) |> kable() ``` -The hierarchical fits for the alternative pathway completed successfully. +The hierarchical fits for the alternative pathway completed successfully, with +the exception of the model using FOMC for the parent compound and constant +variance as the error model. ```{r dependson = "f-saem-2"} illparms(f_saem_2) |> kable() ``` -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. +In all biphasic fits (DFOP or SFORB for the parent compound), 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. ```{r dependson = "f-saem-2"} -anova(f_saem_2) |> kable(digits = 1) +anova(f_saem_2[, "tc"]) |> kable(digits = 1) +anova(f_saem_2[2:3,]) |> kable(digits = 1) ``` The variants using the biexponential models DFOP and SFORB for the parent @@ -423,7 +427,8 @@ illparms(f_saem_3) |> kable() ``` ```{r dependson = "f-saem-3"} -anova(f_saem_3) |> kable(digits = 1) +anova(f_saem_3[, "tc"]) |> kable(digits = 1) +anova(f_saem_3[2:3,]) |> kable(digits = 1) ``` While the AIC and BIC values of the best fit (DFOP pathway fit with diff --git a/vignettes/prebuilt/2022_dmta_parent.html b/vignettes/prebuilt/2022_dmta_parent.html new file mode 100644 index 00000000..14f12c0e --- /dev/null +++ b/vignettes/prebuilt/2022_dmta_parent.html @@ -0,0 +1,2489 @@ + + + + + + + + + + + + + + +Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + + + +

+true +

+ +

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.

The mkin package is used in version 1.2.9. 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 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	OK	OK	C	OK
HS	OK	OK	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	720.7	719.1	-352.4
DFOP const	9	711.8	710.0	-346.9
HS const	9	714.0	712.1	-348.0
DFOP tc	10	665.7	663.6	-322.9
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	663.7	661.8	-322.9	NA	NA	NA
f_saem[[“DFOP”, “tc”]]	10	665.7	663.6	-322.9	0	1	1

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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:33 2025 
+Date of summary: Thu Feb 13 16:33:34 2025 
+
+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 3.778 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.71186  0.08675  0.01374  0.93491 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.71  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
+  663.7 661.8 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.256267 96.286112 100.22642
+k1         0.064037  0.033281   0.09479
+k2         0.008469  0.006002   0.01094
+g          0.954167  0.914460   0.99387
+a.1        1.061795  0.878608   1.24498
+b.1        0.029550  0.022593   0.03651
+SD.DMTA_0  2.068581  0.427178   3.70998
+SD.k1      0.598285  0.258235   0.93833
+SD.g       1.016689  0.360061   1.67332
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0213                
+k2  0.0541  0.0344        
+g  -0.0521 -0.0286 -0.2744
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 2.0686 0.4272 3.7100
+SD.k1     0.5983 0.2582 0.9383
+SD.g      1.0167 0.3601 1.6733
+
+Variance model:
+       est.   lower   upper
+a.1 1.06180 0.87861 1.24498
+b.1 0.02955 0.02259 0.03651
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.32    12.44   10.82   81.85

Alternative check of parameter identifiability

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.

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.

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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:26 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 0.792 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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 2.245 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 95.70316 98.84049
+k_DMTA     0.056638  0.02911  0.08417
+a.1        2.660081  2.27492  3.04525
+b.1        0.001665 -0.14451  0.14784
+SD.DMTA_0  1.545520  0.14301  2.94803
+SD.k_DMTA  0.606422  0.26227  0.95057
+
+Correlation: 
+       DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+            est.  lower  upper
+SD.DMTA_0 1.5455 0.1430 2.9480
+SD.k_DMTA 0.6064 0.2623 0.9506
+
+Variance model:
+        est.   lower  upper
+a.1 2.660081  2.2749 3.0452
+b.1 0.001665 -0.1445 0.1478
+
+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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:27 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 1.409 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      112.8745 34.8816 190.867
+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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 2.811 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
+  720.7 719.1 -352.4
+
+Optimised parameters:
+              est.    lower     upper
+DMTA_0    99.10577 97.33296 100.87859
+alpha      5.46260  2.52199   8.40321
+beta      81.66080 30.46664 132.85497
+a.1        1.50219  1.25801   1.74636
+b.1        0.02893  0.02048   0.03739
+SD.DMTA_0  1.61887 -0.03843   3.27618
+SD.alpha   0.58145  0.17364   0.98925
+SD.beta    0.68205  0.21108   1.15302
+
+Correlation: 
+      DMTA_0  alpha  
+alpha -0.1321        
+beta  -0.1430  0.2467
+
+Random effects:
+            est.    lower  upper
+SD.DMTA_0 1.6189 -0.03843 3.2762
+SD.alpha  0.5814  0.17364 0.9892
+SD.beta   0.6821  0.21108 1.1530
+
+Variance model:
+       est.   lower   upper
+a.1 1.50219 1.25801 1.74636
+b.1 0.02893 0.02048 0.03739
+
+Estimated disappearance times:
+      DT50  DT90 DT50back
+DMTA 11.05 42.81    12.89
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:27 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 1.638 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 96.573899 99.61106
+k1         0.062499  0.030336  0.09466
+k2         0.009065 -0.005133  0.02326
+g          0.948967  0.862080  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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 3.024 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function 
+
+Starting values for degradation parameters:
+  DMTA_0       k1       k2        g 
+98.71186  0.08675  0.01374  0.93491 
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+       DMTA_0 k1 k2 g
+DMTA_0  98.71  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
+  665.7 663.6 -322.9
+
+Optimised parameters:
+               est.     lower     upper
+DMTA_0    98.347470 96.380815 100.31413
+k1         0.064524  0.034279   0.09477
+k2         0.008304  0.005843   0.01076
+g          0.952128  0.909578   0.99468
+a.1        1.068907  0.883665   1.25415
+b.1        0.029265  0.022318   0.03621
+SD.DMTA_0  2.065796  0.427951   3.70364
+SD.k1      0.583703  0.251796   0.91561
+SD.k2      0.004167 -7.831228   7.83956
+SD.g       1.064450  0.397479   1.73142
+
+Correlation: 
+   DMTA_0  k1      k2     
+k1  0.0223                
+k2  0.0568  0.0394        
+g  -0.0464 -0.0269 -0.2713
+
+Random effects:
+              est.   lower  upper
+SD.DMTA_0 2.065796  0.4280 3.7036
+SD.k1     0.583703  0.2518 0.9156
+SD.k2     0.004167 -7.8312 7.8396
+SD.g      1.064450  0.3975 1.7314
+
+Variance model:
+       est.   lower   upper
+a.1 1.06891 0.88367 1.25415
+b.1 0.02927 0.02232 0.03621
+
+Estimated disappearance times:
+      DT50  DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.39 41.36    12.45   10.74   83.48
+
+

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


+saemix version used for fitting:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:28 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 2.301 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:      3.3 
+mkin version used for pre-fitting:  1.2.9 
+R version used for fitting:         4.4.2 
+Date of fit:     Thu Feb 13 16:33:29 2025 
+Date of summary: Thu Feb 13 16:34:39 2025 
+
+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 3.264 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    97.76571 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  0.90059  1.27611
+b.1        0.02964  0.02261  0.03667
+SD.DMTA_0  2.04877  0.42553  3.67200
+SD.k1      0.59166  0.25621  0.92711
+SD.k2      0.30698  0.09561  0.51835
+SD.tb      0.01274 -0.10915  0.13464
+
+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  0.42553 3.6720
+SD.k1     0.59166  0.25621 0.9271
+SD.k2     0.30698  0.09561 0.5183
+SD.tb     0.01274 -0.10915 0.1346
+
+Variance model:
+       est.   lower   upper
+a.1 1.08835 0.90059 1.27611
+b.1 0.02964 0.02261 0.03667
+
+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 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+
+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       
+
+time zone: Europe/Berlin
+tzcode source: system (glibc)
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
+[5] rmarkdown_2.29  nvimcom_0.9-167
+
+loaded via a namespace (and not attached):
+ [1] jsonlite_1.8.9    gtable_0.3.6      dplyr_1.1.4       compiler_4.4.2   
+ [5] tidyselect_1.2.1  colorout_1.3-2    tinytex_0.54      gridExtra_2.3    
+ [9] jquerylib_0.1.4   scales_1.3.0      yaml_2.3.10       fastmap_1.2.0    
+[13] lattice_0.22-6    ggplot2_3.5.1     R6_2.5.1          generics_0.1.3   
+[17] lmtest_0.9-40     MASS_7.3-61       tibble_3.2.1      munsell_0.5.1    
+[21] bslib_0.8.0       pillar_1.9.0      rlang_1.1.4       utf8_1.2.4       
+[25] cachem_1.1.0      xfun_0.49         sass_0.4.9        cli_3.6.3        
+[29] magrittr_2.0.3    digest_0.6.37     grid_4.4.2        mclust_6.1.1     
+[33] lifecycle_1.0.4   nlme_3.1-166      vctrs_0.6.5       evaluate_1.0.1   
+[37] glue_1.8.0        codetools_0.2-20  zoo_1.8-12        fansi_1.0.6      
+[41] colorspace_2.1-1  tools_4.4.2       pkgconfig_2.0.3   htmltools_0.5.8.1

Hardware info

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

MemTotal:       64927788 kB

+ + + + +

+ + + + + + + + + + + + + + + diff --git a/vignettes/prebuilt/2022_dmta_parent.pdf b/vignettes/prebuilt/2022_dmta_parent.pdf index 6e05e6a6..a48626df 100644 Binary files a/vignettes/prebuilt/2022_dmta_parent.pdf and b/vignettes/prebuilt/2022_dmta_parent.pdf differ diff --git a/vignettes/prebuilt/2022_dmta_pathway.html b/vignettes/prebuilt/2022_dmta_pathway.html new file mode 100644 index 00000000..c9f87cd8 --- /dev/null +++ b/vignettes/prebuilt/2022_dmta_pathway.html @@ -0,0 +1,2314 @@ + + + + + + + + + + + + + + +Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + + + +

+true +

+ +

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 1.2.9, 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()
+
+# We need to start a new cluster after defining a compiled model that is
+# saved as a DLL to the user directory, therefore we define a function
+# This is used again after defining the pathway model
+start_cluster <- function(n_cores) {
+  if (Sys.info()["sysname"] == "Windows") {
+    ret <- makePSOCKcluster(n_cores)
+  } else {
+    ret <- makeForkCluster(n_cores)
+  }
+  return(ret)
+}

Data

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
+)
+cl <- start_cluster(n_cores)
+
+deg_mods_1 <- list(
+  sfo_path_1 = m_sfo_path_1,
+  fomc_path_1 = m_fomc_path_1,
+  dfop_path_1 = m_dfop_path_1,
+  sforb_path_1 = m_sforb_path_1,
+  hs_path_1 = m_hs_path_1)
+
+sep_1_const <- mmkin(
+  deg_mods_1,
+  dmta_ds,
+  error_model = "const",
+  quiet = TRUE)
+
+status(sep_1_const) |> kable()

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

	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	OK	OK	OK	OK
sforb_path_1	OK	OK	C	OK	OK	OK
hs_path_1	C	C	OK	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	OK	OK	OK	OK
dfop_path_1	OK	C	OK	C	OK	OK
sforb_path_1	OK	OK	OK	OK	OK	OK
hs_path_1	C	C	C	C	C	C

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)

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

	npar	AIC	BIC	Lik
sfo_path_1 const	17	2291.8	2288.3	-1128.9
sfo_path_1 tc	18	2276.4	2272.7	-1120.2
fomc_path_1 const	19	2095.9	2091.9	-1028.9
fomc_path_1 tc	20	1939.0	1934.8	-949.5
dfop_path_1 const	21	2039.7	2035.3	-998.8
sforb_path_1 const	21	2017.7	2013.4	-987.9
hs_path_1 const	21	2023.7	2019.3	-990.9
dfop_path_1 tc	22	1881.7	1877.1	-918.9
sforb_path_1 tc	22	1832.7	1828.1	-894.3
hs_path_1 tc	22	1831.6	1827.0	-893.8

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)	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	1830.4	1826.0	-894.2
saem_1[[“sforb_path_1”, “tc”]]	22	1832.7	1828.1	-894.3

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)

 
+  (subscript) logical subscript too long

print(saem_sforb_path_1_tc_reduced_multi)

<multistart> object with 32 fits:
+ E OK 
+ 7 25 
+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.

stopCluster(cl)

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

Plots of hierarchical fits not selected for refinement

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 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+
+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       
+
+time zone: Europe/Berlin
+tzcode source: system (glibc)
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
+[5] rmarkdown_2.29  nvimcom_0.9-167
+
+loaded via a namespace (and not attached):
+ [1] sass_0.4.9        utf8_1.2.4        generics_0.1.3    lattice_0.22-6   
+ [5] digest_0.6.37     magrittr_2.0.3    evaluate_1.0.1    grid_4.4.2       
+ [9] fastmap_1.2.0     jsonlite_1.8.9    processx_3.8.4    pkgbuild_1.4.5   
+[13] deSolve_1.40      mclust_6.1.1      ps_1.8.1          gridExtra_2.3    
+[17] fansi_1.0.6       scales_1.3.0      codetools_0.2-20  jquerylib_0.1.4  
+[21] cli_3.6.3         rlang_1.1.4       munsell_0.5.1     cachem_1.1.0     
+[25] yaml_2.3.10       tools_4.4.2       inline_0.3.20     colorout_1.3-2   
+[29] dplyr_1.1.4       colorspace_2.1-1  ggplot2_3.5.1     vctrs_0.6.5      
+[33] R6_2.5.1          zoo_1.8-12        lifecycle_1.0.4   MASS_7.3-61      
+[37] pkgconfig_2.0.3   callr_3.7.6       pillar_1.9.0      bslib_0.8.0      
+[41] gtable_0.3.6      glue_1.8.0        xfun_0.49         tibble_3.2.1     
+[45] lmtest_0.9-40     tidyselect_1.2.1  htmltools_0.5.8.1 nlme_3.1-166     
+[49] compiler_4.4.2

Hardware info

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

MemTotal:       64927788 kB

+ + + + +

+ + + + + + + + + + + + + + + diff --git a/vignettes/prebuilt/2022_dmta_pathway.pdf b/vignettes/prebuilt/2022_dmta_pathway.pdf index 95d0964d..def37fc7 100644 Binary files a/vignettes/prebuilt/2022_dmta_pathway.pdf and b/vignettes/prebuilt/2022_dmta_pathway.pdf differ diff --git a/vignettes/prebuilt/2023_mesotrione_parent.html b/vignettes/prebuilt/2023_mesotrione_parent.html new file mode 100644 index 00000000..8bb993dc --- /dev/null +++ b/vignettes/prebuilt/2023_mesotrione_parent.html @@ -0,0 +1,2790 @@ + + + + + + + + + + + + + + +Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + + + +

+true +

+ +

Introduction

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

The mkin package is used in version 1.2.9, which is contains the +functions that were used for the evaluations. The saemix +package is used as a backend for fitting the NLHM, but is also loaded to +make the convergence plot function available.

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

Test data

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

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

pH <- attr(meso_ds, "covariates")
+kable(pH, caption = "Covariate data")

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

Covariate data
	pH
Richmond	6.2
Richmond 2	6.2
ERTC	6.4
Toulouse	7.7
Picket Piece	7.1
721	5.6
722	5.7
723	5.4
724	4.8
725	5.8
727	5.1
728	5.9
729	5.6
730	5.3
731	6.1
732	5.0
741	5.7
742	7.2

for (ds_name in names(meso_ds)) {
+  print(
+    kable(mkin_long_to_wide(meso_ds[[ds_name]]),
+      caption = paste("Dataset", ds_name),
+      booktabs = TRUE, row.names = FALSE))
+}

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

Dataset Richmond
time	meso
0.000000	91.00
1.179050	86.70
3.537149	73.60
7.074299	61.50
10.611448	55.70
15.327647	47.70
17.685747	39.50
24.760046	29.80
35.371494	19.60
68.384889	5.67
0.000000	97.90
1.179050	96.40
3.537149	89.10
7.074299	74.40
10.611448	57.40
15.327647	46.30
18.864797	35.50
27.118146	27.20
35.371494	19.10
74.280138	6.50
108.472582	3.40
142.665027	2.20

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

Dataset Richmond 2
time	meso
0.000000	96.0
2.422004	82.4
5.651343	71.2
8.073348	53.1
11.302687	48.5
16.954030	33.4
22.605373	24.2
45.210746	11.9

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

Dataset ERTC
time	meso
0.000000	99.9
2.755193	80.0
6.428782	42.1
9.183975	50.1
12.857565	28.4
19.286347	39.8
25.715130	29.9
51.430259	2.5

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

Dataset Toulouse
time	meso
0.000000	96.8
2.897983	63.3
6.761960	22.3
9.659942	16.6
13.523919	16.1
20.285879	17.2
27.047838	1.8

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

Dataset Picket Piece
time	meso
0.000000	102.0
2.841195	73.7
6.629454	35.5
9.470649	31.8
13.258909	18.0
19.888364	3.7

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

Dataset 721
time	meso
0.00000	86.4
11.24366	61.4
22.48733	49.8
33.73099	41.0
44.97466	35.1

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

Dataset 722
time	meso
0.00000	90.3
11.24366	52.1
22.48733	37.4
33.73099	21.2
44.97466	14.3

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

Dataset 723
time	meso
0.00000	89.3
11.24366	70.8
22.48733	51.1
33.73099	42.7
44.97466	26.7

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

Dataset 724
time	meso
0.000000	89.4
9.008208	65.2
18.016415	55.8
27.024623	46.0
36.032831	41.7

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

Dataset 725
time	meso
0.00000	89.0
10.99058	35.4
21.98116	18.6
32.97174	11.6
43.96232	7.6

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

Dataset 727
time	meso
0.00000	91.3
10.96104	63.2
21.92209	51.1
32.88313	42.0
43.84417	40.8

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

Dataset 728
time	meso
0.00000	91.8
11.24366	43.6
22.48733	22.0
33.73099	15.9
44.97466	8.8

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

Dataset 729
time	meso
0.00000	91.6
11.24366	60.5
22.48733	43.5
33.73099	28.4
44.97466	20.5

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

Dataset 730
time	meso
0.00000	92.7
11.07446	58.9
22.14893	44.0
33.22339	46.0
44.29785	29.3

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

Dataset 731
time	meso
0.00000	92.1
11.24366	64.4
22.48733	45.3
33.73099	33.6
44.97466	23.5

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

Dataset 732
time	meso
0.00000	90.3
11.24366	58.2
22.48733	40.1
33.73099	33.1
44.97466	25.8

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

Dataset 741
time	meso
0.00000	90.3
10.84712	68.7
21.69424	58.0
32.54136	52.2
43.38848	48.0

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

Dataset 742
time	meso
0.00000	92.0
11.24366	60.9
22.48733	36.2
33.73099	18.3
44.97466	8.7

Separate evaluations

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

deg_mods <- c("SFO", "FOMC", "DFOP", "SFORB", "HS")
+f_sep_const <- mmkin(
+  deg_mods,
+  meso_ds,
+  error_model = "const",
+  cluster = cl,
+  quiet = TRUE)

status(f_sep_const[, 1:5]) |> kable()

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

	Richmond	Richmond 2	ERTC	Toulouse	Picket Piece
SFO	OK	OK	OK	OK	OK
FOMC	OK	OK	OK	OK	C
DFOP	OK	OK	OK	OK	OK
SFORB	OK	OK	OK	OK	OK
HS	OK	OK	C	OK	OK

status(f_sep_const[, 6:18]) |> kable()

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

	721	722	723	724	725	727	728	729	730	731	732	741	742
SFO	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK
FOMC	OK	OK	C	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK
DFOP	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK
SFORB	OK	OK	OK	OK	OK	OK	OK	C	OK	OK	OK	OK	OK
HS	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK

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

f_sep_tc <- update(f_sep_const, error_model = "tc")

status(f_sep_tc[, 1:5]) |> kable()

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

	Richmond	Richmond 2	ERTC	Toulouse	Picket Piece
SFO	OK	OK	OK	OK	OK
FOMC	OK	OK	OK	OK	OK
DFOP	C	OK	OK	OK	OK
SFORB	OK	OK	OK	OK	OK
HS	OK	OK	C	OK	OK

status(f_sep_tc[, 6:18]) |> kable()

	721	722	723	724	725	727	728	729	730	731	732	741	742
SFO	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK	OK
FOMC	OK	OK	C	OK	C	C	OK	C	OK	C	OK	C	OK
DFOP	C	OK	OK	OK	C	OK	OK	OK	OK	C	OK	C	OK
SFORB	C	OK	OK	OK	C	OK	OK	C	OK	OK	OK	C	OK
HS	OK	OK	OK	OK	OK	OK	OK	OK	OK	C	OK	OK	OK

With the two-component error model, the set of fits that did not +converge is larger, with convergence problems appearing for a number of +non-SFO fits.

Hierarchical model fits without covariate effect

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

f_saem_1 <- mhmkin(list(f_sep_const, f_sep_tc), cluster = cl)
+status(f_saem_1) |> kable()

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

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

All fits terminate without errors (status OK).

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

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

	npar	AIC	BIC	Lik
SFO const	5	800.0	804.5	-395.0
SFO tc	6	801.9	807.2	-394.9
FOMC const	7	787.4	793.6	-386.7
FOMC tc	8	788.9	796.1	-386.5
DFOP const	9	787.6	795.6	-384.8
SFORB const	9	787.4	795.4	-384.7
HS const	9	781.9	789.9	-382.0
DFOP tc	10	787.4	796.3	-383.7
SFORB tc	10	795.8	804.7	-387.9
HS tc	10	783.7	792.7	-381.9

The model comparisons show that the fits with constant variance are +consistently preferable to the corresponding fits with two-component +error for these data. This is confirmed by the fact that the parameter +b.1 (the relative standard deviation in the fits obtained +with the saemix package), is ill-defined in all fits.

illparms(f_saem_1) |> kable()

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

	const	tc
SFO	sd(meso_0)	sd(meso_0), b.1
FOMC	sd(meso_0), sd(log_beta)	sd(meso_0), sd(log_beta), b.1
DFOP	sd(meso_0), sd(log_k1)	sd(meso_0), sd(g_qlogis), b.1
SFORB	sd(meso_free_0), sd(log_k_meso_free_bound)	sd(meso_free_0), sd(log_k_meso_free_bound), b.1
HS	sd(meso_0)	sd(meso_0), b.1

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

f_saem_2 <- update(f_saem_1, no_random_effect = illparms(f_saem_1))
+status(f_saem_2) |> kable()

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

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

The updated fits terminate without errors.

illparms(f_saem_2) |> kable()

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

	const	tc
SFO		b.1
FOMC		b.1
DFOP		b.1
SFORB		b.1
HS		b.1

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

Hierarchical model fits with covariate effect

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

SFO

sfo_pH <- saem(f_sep_const["SFO", ], no_random_effect = "meso_0", covariates = pH,
+  covariate_models = list(log_k_meso ~ pH))

summary(sfo_pH)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	91.35	89.27	93.43
log_k_meso	-6.66	-7.97	-5.35
beta_pH(log_k_meso)	0.59	0.37	0.81
a.1	5.48	4.71	6.24
SD.log_k_meso	0.35	0.23	0.47

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

anova(f_saem_2[["SFO", "const"]], sfo_pH, test = TRUE)

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

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

plot(sfo_pH)

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

endpoints(sfo_pH)

$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90
+meso 18.52069 61.52441

endpoints(sfo_pH, covariate_quantile = 0.9)

$covariates
+      pH
+90% 7.13
+
+$distimes
+         DT50     DT90
+meso 8.237019 27.36278

endpoints(sfo_pH, covariates = c(pH = 7.0))

$covariates
+     pH
+User  7
+
+$distimes
+        DT50    DT90
+meso 8.89035 29.5331

FOMC

fomc_pH <- saem(f_sep_const["FOMC", ], no_random_effect = "meso_0", covariates = pH,
+  covariate_models = list(log_alpha ~ pH))

summary(fomc_pH)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	92.84	90.75	94.93
log_alpha	-2.21	-3.49	-0.92
beta_pH(log_alpha)	0.58	0.37	0.79
log_beta	4.21	3.44	4.99
a.1	5.03	4.32	5.73
SD.log_alpha	0.00	-23.77	23.78
SD.log_beta	0.37	0.01	0.74

As in the case of SFO, the confidence interval of the slope parameter +(here beta_pH(log_alpha)) quantifying the influence of soil +pH does not include zero, and the model comparison clearly indicates +that the model with covariate influence is preferable. However, the +random effect for alpha is not well-defined any more after +inclusion of the covariate effect (the confidence interval of +SD.log_alpha includes zero).

illparms(fomc_pH)

[1] "sd(log_alpha)"

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

fomc_pH_2 <- update(fomc_pH, no_random_effect = c("meso_0", "log_alpha"))
+illparms(fomc_pH_2)

anova(f_saem_2[["FOMC", "const"]], fomc_pH, fomc_pH_2, test = TRUE)

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

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

summary(fomc_pH_2)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	93.05	90.98	95.13
log_alpha	-2.91	-4.18	-1.63
beta_pH(log_alpha)	0.66	0.44	0.87
log_beta	3.95	3.29	4.62
a.1	4.98	4.28	5.68
SD.log_beta	0.40	0.26	0.54

plot(fomc_pH_2)

endpoints(fomc_pH_2)

$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back
+meso 17.30248 82.91343 24.95943

endpoints(fomc_pH_2, covariates = c(pH = 7))

$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back
+meso 6.986239 27.02927 8.136621

DFOP

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

summary(f_saem_2[["DFOP", "const"]])$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	93.61	91.58	95.63
log_k1	-1.53	-2.27	-0.79
log_k2	-3.42	-3.73	-3.11
g_qlogis	-1.67	-2.57	-0.77
a.1	4.74	4.02	5.45
SD.log_k2	0.60	0.38	0.81
SD.g_qlogis	0.94	0.33	1.54

A fit with pH dependent degradation parameters was obtained by +excluding the same random effects as in the refined DFOP fit without +covariate influence, and including covariate models for the two +identifiable parameters k2 and g.

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

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

summary(dfop_pH)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	92.84	90.85	94.84
log_k1	-2.82	-3.09	-2.54
log_k2	-11.48	-15.32	-7.64
beta_pH(log_k2)	1.31	0.69	1.92
g_qlogis	3.13	0.47	5.80
beta_pH(g_qlogis)	-0.57	-1.04	-0.09
a.1	4.96	4.26	5.65
SD.log_k2	0.76	0.47	1.05
SD.g_qlogis	0.01	-9.96	9.97

illparms(dfop_pH)

[1] "sd(g_qlogis)"

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

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

[1] "beta_pH(g_qlogis)"

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

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

[1] "sd(g_qlogis)"

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

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

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

anova(f_saem_2[["DFOP", "const"]], dfop_pH, dfop_pH_2, dfop_pH_3, dfop_pH_4)

Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                            npar    AIC    BIC     Lik
+f_saem_2[["DFOP", "const"]]    7 782.94 789.18 -384.47
+dfop_pH_4                      7 767.35 773.58 -376.68
+dfop_pH_2                      8 765.14 772.26 -374.57
+dfop_pH_3                      8 769.00 776.12 -376.50
+dfop_pH                        9 769.10 777.11 -375.55

anova(dfop_pH_2, dfop_pH_4, test = TRUE)

Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+          npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)  
+dfop_pH_4    7 767.35 773.58 -376.68                       
+dfop_pH_2    8 765.14 772.26 -374.57 4.2153  1    0.04006 *
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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

plot(dfop_pH_2)

endpoints(dfop_pH_2)

$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 18.36876 73.51841 22.13125 4.191901 23.98672

endpoints(dfop_pH_2, covariates = c(pH = 7))

$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.346428 28.34437 8.532507 4.191901 8.753618

SFORB

sforb_pH <- saem(f_sep_const["SFORB", ], no_random_effect = c("meso_free_0", "log_k_meso_free_bound"),
+  covariates = pH,
+  covariate_models = list(log_k_meso_free ~ pH, log_k_meso_bound_free ~ pH))

summary(sforb_pH)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_free_0	93.42	91.32	95.52
log_k_meso_free	-5.37	-6.94	-3.81
beta_pH(log_k_meso_free)	0.42	0.18	0.67
log_k_meso_free_bound	-3.49	-4.92	-2.05
log_k_meso_bound_free	-9.98	-19.22	-0.74
beta_pH(log_k_meso_bound_free)	1.23	-0.21	2.67
a.1	4.90	4.18	5.63
SD.log_k_meso_free	0.35	0.23	0.47
SD.log_k_meso_bound_free	0.13	-1.95	2.20

The confidence interval of +beta_pH(log_k_meso_bound_free) includes zero, indicating +that the influence of soil pH on k_meso_bound_free cannot +reliably be quantified. Also, the confidence interval for the random +effect on this parameter (SD.log_k_meso_bound_free) +includes zero.

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

illparms(sforb_pH)

[1] "sd(log_k_meso_bound_free)"      "beta_pH(log_k_meso_bound_free)"

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

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

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

anova(f_saem_2[["SFORB", "const"]], sforb_pH, sforb_pH_2, test = TRUE)

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

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

summary(sforb_pH_2)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_free_0	93.32	91.16	95.48
log_k_meso_free	-6.15	-7.43	-4.86
beta_pH(log_k_meso_free)	0.54	0.33	0.75
log_k_meso_free_bound	-3.80	-5.20	-2.40
log_k_meso_bound_free	-2.95	-4.26	-1.64
a.1	5.08	4.38	5.79
SD.log_k_meso_free	0.33	0.22	0.45

plot(sforb_pH_2)

endpoints(sforb_pH_2)

$covariates
+      pH
+50% 5.75
+
+$ff
+meso_free 
+        1 
+
+$SFORB
+   meso_b1    meso_b2     meso_g 
+0.09735824 0.02631699 0.31602120 
+
+$distimes
+         DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
+meso 16.86549 73.15824 22.02282     7.119554     26.33839

endpoints(sforb_pH_2, covariates = c(pH = 7))

$covariates
+     pH
+User  7
+
+$ff
+meso_free 
+        1 
+
+$SFORB
+   meso_b1    meso_b2     meso_g 
+0.13315233 0.03795988 0.61186191 
+
+$distimes
+         DT50     DT90 DT50back DT50_meso_b1 DT50_meso_b2
+meso 7.932495 36.93311 11.11797     5.205671        18.26

HS

hs_pH <- saem(f_sep_const["HS", ], no_random_effect = c("meso_0"),
+  covariates = pH,
+  covariate_models = list(log_k1 ~ pH, log_k2 ~ pH, log_tb ~ pH))

summary(hs_pH)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	93.33	91.47	95.19
log_k1	-5.81	-7.27	-4.36
beta_pH(log_k1)	0.47	0.23	0.72
log_k2	-6.80	-8.76	-4.83
beta_pH(log_k2)	0.54	0.21	0.87
log_tb	3.25	1.25	5.25
beta_pH(log_tb)	-0.10	-0.43	0.23
a.1	4.49	3.78	5.21
SD.log_k1	0.37	0.24	0.51
SD.log_k2	0.29	0.10	0.48
SD.log_tb	0.25	-0.07	0.57

illparms(hs_pH)

[1] "sd(log_tb)"      "beta_pH(log_tb)"

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

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

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

anova(f_saem_2[["HS", "const"]], hs_pH, hs_pH_2, test = TRUE)

Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+                          npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)    
+f_saem_2[["HS", "const"]]    8 780.08 787.20 -382.04                         
+hs_pH_2                     10 766.47 775.37 -373.23 17.606  2  0.0001503 ***
+hs_pH                       11 769.80 779.59 -373.90  0.000  1  1.0000000    
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(hs_pH_2)$confint_trans |> kable(digits = 2)

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

	est.	lower	upper
meso_0	93.33	91.50	95.15
log_k1	-5.68	-7.09	-4.27
beta_pH(log_k1)	0.46	0.22	0.69
log_k2	-6.61	-8.34	-4.88
beta_pH(log_k2)	0.50	0.21	0.79
log_tb	2.70	2.33	3.08
a.1	4.45	3.74	5.16
SD.log_k1	0.36	0.22	0.49
SD.log_k2	0.23	0.02	0.43
SD.log_tb	0.55	0.25	0.85

plot(hs_pH_2)

endpoints(hs_pH_2)

$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 14.68725 82.45287 24.82079 14.68725 29.29299

endpoints(hs_pH_2, covariates = c(pH = 7))

$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.298536 38.85371 11.69613 8.298536 15.71561

Comparison across parent models

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

anova(sfo_pH, fomc_pH_2, dfop_pH_2, dfop_pH_4, sforb_pH_2, hs_pH_2)

Data: 116 observations of 1 variable(s) grouped in 18 datasets
+
+           npar    AIC    BIC     Lik
+sfo_pH        5 783.09 787.54 -386.54
+fomc_pH_2     6 767.49 772.83 -377.75
+dfop_pH_4     7 767.35 773.58 -376.68
+sforb_pH_2    7 770.94 777.17 -378.47
+dfop_pH_2     8 765.14 772.26 -374.57
+hs_pH_2      10 766.47 775.37 -373.23

The DFOP model with pH influence on k2 and +g and a random effect only on k2 is finally +selected as the best fit.

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

endpoints(dfop_pH_2)

$covariates
+      pH
+50% 5.75
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 18.36876 73.51841 22.13125 4.191901 23.98672

endpoints(dfop_pH_2, covariates = c(pH = 7))

$covariates
+     pH
+User  7
+
+$distimes
+         DT50     DT90 DT50back  DT50_k1  DT50_k2
+meso 8.346428 28.34437 8.532507 4.191901 8.753618

Conclusions

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

Appendix

Hierarchical fit listings

Fits without covariate effects

+ +

Fits with covariate effects

+ +

Session info

R version 4.4.2 (2024-10-31)
+Platform: x86_64-pc-linux-gnu
+Running under: Debian GNU/Linux 12 (bookworm)
+
+Matrix products: default
+BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.11.0 
+LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.11.0
+
+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       
+
+time zone: Europe/Berlin
+tzcode source: system (glibc)
+
+attached base packages:
+[1] parallel  stats     graphics  grDevices utils     datasets  methods  
+[8] base     
+
+other attached packages:
+[1] saemix_3.3      npde_3.5        knitr_1.49      mkin_1.2.9     
+[5] rmarkdown_2.29  nvimcom_0.9-167
+
+loaded via a namespace (and not attached):
+ [1] gtable_0.3.6      jsonlite_1.8.9    dplyr_1.1.4       compiler_4.4.2   
+ [5] tidyselect_1.2.1  colorout_1.3-2    gridExtra_2.3     jquerylib_0.1.4  
+ [9] scales_1.3.0      readxl_1.4.3      yaml_2.3.10       fastmap_1.2.0    
+[13] lattice_0.22-6    ggplot2_3.5.1     R6_2.5.1          generics_0.1.3   
+[17] lmtest_0.9-40     MASS_7.3-61       tibble_3.2.1      munsell_0.5.1    
+[21] bslib_0.8.0       pillar_1.9.0      rlang_1.1.4       utf8_1.2.4       
+[25] cachem_1.1.0      xfun_0.49         sass_0.4.9        cli_3.6.3        
+[29] magrittr_2.0.3    digest_0.6.37     grid_4.4.2        mclust_6.1.1     
+[33] lifecycle_1.0.4   nlme_3.1-166      vctrs_0.6.5       evaluate_1.0.1   
+[37] glue_1.8.0        cellranger_1.1.0  codetools_0.2-20  zoo_1.8-12       
+[41] fansi_1.0.6       colorspace_2.1-1  tools_4.4.2       pkgconfig_2.0.3  
+[45] htmltools_0.5.8.1

Hardware info

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

MemTotal:       64927788 kB

+ + + + +

+ + + + + + + + + + + + + + + diff --git a/vignettes/web_only/dimethenamid_2018.html b/vignettes/web_only/dimethenamid_2018.html index daa0bb8f..18f9c9de 100644 --- a/vignettes/web_only/dimethenamid_2018.html +++ b/vignettes/web_only/dimethenamid_2018.html @@ -66,18 +66,12 @@ if (!!window.navigator.userAgent.match("MSIE 8")) { h6 {font-size: 12px;} code {color: inherit; background-color: rgba(0, 0, 0, 0.04);} pre:not([class]) { background-color: white } - +!function(t){"use strict";"function"==typeof define&&define.amd?define(["jquery"],t):t(jQuery)}(function(V){"use strict";V.ui=V.ui||{};V.ui.version="1.13.2";var n,i=0,a=Array.prototype.hasOwnProperty,r=Array.prototype.slice;V.cleanData=(n=V.cleanData,function(t){for(var e,i,s=0;null!=(i=t[s]);s++)(e=V._data(i,"events"))&&e.remove&&V(i).triggerHandler("remove");n(t)}),V.widget=function(t,i,e){var s,n,o,a={},r=t.split(".")[0],l=r+"-"+(t=t.split(".")[1]);return e||(e=i,i=V.Widget),Array.isArray(e)&&(e=V.extend.apply(null,[{}].concat(e))),V.expr.pseudos[l.toLowerCase()]=function(t){return!!V.data(t,l)},V[r]=V[r]||{},s=V[r][t],n=V[r][t]=function(t,e){if(!this||!this._createWidget)return new n(t,e);arguments.length&&this._createWidget(t,e)},V.extend(n,s,{version:e.version,_proto:V.extend({},e),_childConstructors:[]}),(o=new i).options=V.widget.extend({},o.options),V.each(e,function(e,s){function n(){return i.prototype[e].apply(this,arguments)}function o(t){return i.prototype[e].apply(this,t)}a[e]="function"==typeof s?function(){var t,e=this._super,i=this._superApply;return this._super=n,this._superApply=o,t=s.apply(this,arguments),this._super=e,this._superApply=i,t}:s}),n.prototype=V.widget.extend(o,{widgetEventPrefix:s&&o.widgetEventPrefix||t},a,{constructor:n,namespace:r,widgetName:t,widgetFullName:l}),s?(V.each(s._childConstructors,function(t,e){var i=e.prototype;V.widget(i.namespace+"."+i.widgetName,n,e._proto)}),delete s._childConstructors):i._childConstructors.push(n),V.widget.bridge(t,n),n},V.widget.extend=function(t){for(var e,i,s=r.call(arguments,1),n=0,o=s.length;n",options:{classes:{},disabled:!1,create:null},_createWidget:function(t,e){e=V(e||this.defaultElement||this)[0],this.element=V(e),this.uuid=i++,this.eventNamespace="."+this.widgetName+this.uuid,this.bindings=V(),this.hoverable=V(),this.focusable=V(),this.classesElementLookup={},e!==this&&(V.data(e,this.widgetFullName,this),this._on(!0,this.element,{remove:function(t){t.target===e&&this.destroy()}}),this.document=V(e.style?e.ownerDocument:e.document||e),this.window=V(this.document[0].defaultView||this.document[0].parentWindow)),this.options=V.widget.extend({},this.options,this._getCreateOptions(),t),this._create(),this.options.disabled&&this._setOptionDisabled(this.options.disabled),this._trigger("create",null,this._getCreateEventData()),this._init()},_getCreateOptions:function(){return{}},_getCreateEventData:V.noop,_create:V.noop,_init:V.noop,destroy:function(){var i=this;this._destroy(),V.each(this.classesElementLookup,function(t,e){i._removeClass(e,t)}),this.element.off(this.eventNamespace).removeData(this.widgetFullName),this.widget().off(this.eventNamespace).removeAttr("aria-disabled"),this.bindings.off(this.eventNamespace)},_destroy:V.noop,widget:function(){return this.element},option:function(t,e){var i,s,n,o=t;if(0===arguments.length)return V.widget.extend({},this.options);if("string"==typeof t)if(o={},t=(i=t.split(".")).shift(),i.length){for(s=o[t]=V.widget.extend({},this.options[t]),n=0;n

"),i=e.children()[0];return V("body").append(e),t=i.offsetWidth,e.css("overflow","scroll"),t===(i=i.offsetWidth)&&(i=e[0].clientWidth),e.remove(),s=t-i},getScrollInfo:function(t){var e=t.isWindow||t.isDocument?"":t.element.css("overflow-x"),i=t.isWindow||t.isDocument?"":t.element.css("overflow-y"),e="scroll"===e||"auto"===e&&t.widthx(k(s),k(n))?o.important="horizontal":o.important="vertical",u.using.call(this,t,o)}),a.offset(V.extend(h,{using:t}))})},V.ui.position={fit:{left:function(t,e){var i=e.within,s=i.isWindow?i.scrollLeft:i.offset.left,n=i.width,o=t.left-e.collisionPosition.marginLeft,a=s-o,r=o+e.collisionWidth-n-s;e.collisionWidth>n?0n?0")[0],w=d.each;function P(t){return null==t?t+"":"object"==typeof t?p[e.call(t)]||"object":typeof t}function M(t,e,i){var s=v[e.type]||{};return null==t?i||!e.def?null:e.def:(t=s.floor?~~t:parseFloat(t),isNaN(t)?e.def:s.mod?(t+s.mod)%s.mod:Math.min(s.max,Math.max(0,t)))}function S(s){var n=m(),o=n._rgba=[];return s=s.toLowerCase(),w(g,function(t,e){var i=e.re.exec(s),i=i&&e.parse(i),e=e.space||"rgba";if(i)return i=n[e](i),n[_[e].cache]=i[_[e].cache],o=n._rgba=i._rgba,!1}),o.length?("0,0,0,0"===o.join()&&d.extend(o,B.transparent),n):B[s]}function H(t,e,i){return 6*(i=(i+1)%1)<1?t+(e-t)*i*6:2*i<1?e:3*i<2?t+(e-t)*(2/3-i)*6:t}y.style.cssText="background-color:rgba(1,1,1,.5)",b.rgba=-1o.mod/2?s+=o.mod:s-n>o.mod/2&&(s-=o.mod)),l[i]=M((n-s)*a+s,e)))}),this[e](l)},blend:function(t){if(1===this._rgba[3])return this;var e=this._rgba.slice(),i=e.pop(),s=m(t)._rgba;return m(d.map(e,function(t,e){return(1-i)*s[e]+i*t}))},toRgbaString:function(){var t="rgba(",e=d.map(this._rgba,function(t,e){return null!=t?t:2").addClass("ui-effects-wrapper").css({fontSize:"100%",background:"transparent",border:"none",margin:0,padding:0}),e={width:i.width(),height:i.height()},n=document.activeElement;try{n.id}catch(t){n=document.body}return i.wrap(t),i[0]!==n&&!V.contains(i[0],n)||V(n).trigger("focus"),t=i.parent(),"static"===i.css("position")?(t.css({position:"relative"}),i.css({position:"relative"})):(V.extend(s,{position:i.css("position"),zIndex:i.css("z-index")}),V.each(["top","left","bottom","right"],function(t,e){s[e]=i.css(e),isNaN(parseInt(s[e],10))&&(s[e]="auto")}),i.css({position:"relative",top:0,left:0,right:"auto",bottom:"auto"})),i.css(e),t.css(s).show()},removeWrapper:function(t){var e=document.activeElement;return t.parent().is(".ui-effects-wrapper")&&(t.parent().replaceWith(t),t[0]!==e&&!V.contains(t[0],e)||V(e).trigger("focus")),t}}),V.extend(V.effects,{version:"1.13.2",define:function(t,e,i){return i||(i=e,e="effect"),V.effects.effect[t]=i,V.effects.effect[t].mode=e,i},scaledDimensions:function(t,e,i){if(0===e)return{height:0,width:0,outerHeight:0,outerWidth:0};var s="horizontal"!==i?(e||100)/100:1,e="vertical"!==i?(e||100)/100:1;return{height:t.height()*e,width:t.width()*s,outerHeight:t.outerHeight()*e,outerWidth:t.outerWidth()*s}},clipToBox:function(t){return{width:t.clip.right-t.clip.left,height:t.clip.bottom-t.clip.top,left:t.clip.left,top:t.clip.top}},unshift:function(t,e,i){var s=t.queue();1").insertAfter(t).css({display:/^(inline|ruby)/.test(t.css("display"))?"inline-block":"block",visibility:"hidden",marginTop:t.css("marginTop"),marginBottom:t.css("marginBottom"),marginLeft:t.css("marginLeft"),marginRight:t.css("marginRight"),float:t.css("float")}).outerWidth(t.outerWidth()).outerHeight(t.outerHeight()).addClass("ui-effects-placeholder"),t.data(j+"placeholder",e)),t.css({position:i,left:s.left,top:s.top}),e},removePlaceholder:function(t){var e=j+"placeholder",i=t.data(e);i&&(i.remove(),t.removeData(e))},cleanUp:function(t){V.effects.restoreStyle(t),V.effects.removePlaceholder(t)},setTransition:function(s,t,n,o){return o=o||{},V.each(t,function(t,e){var i=s.cssUnit(e);0");l.appendTo("body").addClass(t.className).css({top:s.top-a,left:s.left-r,height:i.innerHeight(),width:i.innerWidth(),position:n?"fixed":"absolute"}).animate(o,t.duration,t.easing,function(){l.remove(),"function"==typeof e&&e()})}}),V.fx.step.clip=function(t){t.clipInit||(t.start=V(t.elem).cssClip(),"string"==typeof t.end&&(t.end=G(t.end,t.elem)),t.clipInit=!0),V(t.elem).cssClip({top:t.pos*(t.end.top-t.start.top)+t.start.top,right:t.pos*(t.end.right-t.start.right)+t.start.right,bottom:t.pos*(t.end.bottom-t.start.bottom)+t.start.bottom,left:t.pos*(t.end.left-t.start.left)+t.start.left})},Y={},V.each(["Quad","Cubic","Quart","Quint","Expo"],function(e,t){Y[t]=function(t){return Math.pow(t,e+2)}}),V.extend(Y,{Sine:function(t){return 1-Math.cos(t*Math.PI/2)},Circ:function(t){return 1-Math.sqrt(1-t*t)},Elastic:function(t){return 0===t||1===t?t:-Math.pow(2,8*(t-1))*Math.sin((80*(t-1)-7.5)*Math.PI/15)},Back:function(t){return t*t*(3*t-2)},Bounce:function(t){for(var e,i=4;t<((e=Math.pow(2,--i))-1)/11;);return 1/Math.pow(4,3-i)-7.5625*Math.pow((3*e-2)/22-t,2)}}),V.each(Y,function(t,e){V.easing["easeIn"+t]=e,V.easing["easeOut"+t]=function(t){return 1-e(1-t)},V.easing["easeInOut"+t]=function(t){return t<.5?e(2*t)/2:1-e(-2*t+2)/2}});y=V.effects,V.effects.define("blind","hide",function(t,e){var i={up:["bottom","top"],vertical:["bottom","top"],down:["top","bottom"],left:["right","left"],horizontal:["right","left"],right:["left","right"]},s=V(this),n=t.direction||"up",o=s.cssClip(),a={clip:V.extend({},o)},r=V.effects.createPlaceholder(s);a.clip[i[n][0]]=a.clip[i[n][1]],"show"===t.mode&&(s.cssClip(a.clip),r&&r.css(V.effects.clipToBox(a)),a.clip=o),r&&r.animate(V.effects.clipToBox(a),t.duration,t.easing),s.animate(a,{queue:!1,duration:t.duration,easing:t.easing,complete:e})}),V.effects.define("bounce",function(t,e){var i,s,n=V(this),o=t.mode,a="hide"===o,r="show"===o,l=t.direction||"up",h=t.distance,c=t.times||5,o=2*c+(r||a?1:0),u=t.duration/o,d=t.easing,p="up"===l||"down"===l?"top":"left",f="up"===l||"left"===l,g=0,t=n.queue().length;for(V.effects.createPlaceholder(n),l=n.css(p),h=h||n["top"==p?"outerHeight":"outerWidth"]()/3,r&&((s={opacity:1})[p]=l,n.css("opacity",0).css(p,f?2*-h:2*h).animate(s,u,d)),a&&(h/=Math.pow(2,c-1)),(s={})[p]=l;g").css({position:"absolute",visibility:"visible",left:-s*p,top:-i*f}).parent().addClass("ui-effects-explode").css({position:"absolute",overflow:"hidden",width:p,height:f,left:n+(u?a*p:0),top:o+(u?r*f:0),opacity:u?0:1}).animate({left:n+(u?0:a*p),top:o+(u?0:r*f),opacity:u?1:0},t.duration||500,t.easing,m)}),V.effects.define("fade","toggle",function(t,e){var i="show"===t.mode;V(this).css("opacity",i?0:1).animate({opacity:i?1:0},{queue:!1,duration:t.duration,easing:t.easing,complete:e})}),V.effects.define("fold","hide",function(e,t){var i=V(this),s=e.mode,n="show"===s,o="hide"===s,a=e.size||15,r=/([0-9]+)%/.exec(a),l=!!e.horizFirst?["right","bottom"]:["bottom","right"],h=e.duration/2,c=V.effects.createPlaceholder(i),u=i.cssClip(),d={clip:V.extend({},u)},p={clip:V.extend({},u)},f=[u[l[0]],u[l[1]]],s=i.queue().length;r&&(a=parseInt(r[1],10)/100*f[o?0:1]),d.clip[l[0]]=a,p.clip[l[0]]=a,p.clip[l[1]]=0,n&&(i.cssClip(p.clip),c&&c.css(V.effects.clipToBox(p)),p.clip=u),i.queue(function(t){c&&c.animate(V.effects.clipToBox(d),h,e.easing).animate(V.effects.clipToBox(p),h,e.easing),t()}).animate(d,h,e.easing).animate(p,h,e.easing).queue(t),V.effects.unshift(i,s,4)}),V.effects.define("highlight","show",function(t,e){var i=V(this),s={backgroundColor:i.css("backgroundColor")};"hide"===t.mode&&(s.opacity=0),V.effects.saveStyle(i),i.css({backgroundImage:"none",backgroundColor:t.color||"#ffff99"}).animate(s,{queue:!1,duration:t.duration,easing:t.easing,complete:e})}),V.effects.define("size",function(s,e){var n,i=V(this),t=["fontSize"],o=["borderTopWidth","borderBottomWidth","paddingTop","paddingBottom"],a=["borderLeftWidth","borderRightWidth","paddingLeft","paddingRight"],r=s.mode,l="effect"!==r,h=s.scale||"both",c=s.origin||["middle","center"],u=i.css("position"),d=i.position(),p=V.effects.scaledDimensions(i),f=s.from||p,g=s.to||V.effects.scaledDimensions(i,0);V.effects.createPlaceholder(i),"show"===r&&(r=f,f=g,g=r),n={from:{y:f.height/p.height,x:f.width/p.width},to:{y:g.height/p.height,x:g.width/p.width}},"box"!==h&&"both"!==h||(n.from.y!==n.to.y&&(f=V.effects.setTransition(i,o,n.from.y,f),g=V.effects.setTransition(i,o,n.to.y,g)),n.from.x!==n.to.x&&(f=V.effects.setTransition(i,a,n.from.x,f),g=V.effects.setTransition(i,a,n.to.x,g))),"content"!==h&&"both"!==h||n.from.y!==n.to.y&&(f=V.effects.setTransition(i,t,n.from.y,f),g=V.effects.setTransition(i,t,n.to.y,g)),c&&(c=V.effects.getBaseline(c,p),f.top=(p.outerHeight-f.outerHeight)*c.y+d.top,f.left=(p.outerWidth-f.outerWidth)*c.x+d.left,g.top=(p.outerHeight-g.outerHeight)*c.y+d.top,g.left=(p.outerWidth-g.outerWidth)*c.x+d.left),delete f.outerHeight,delete f.outerWidth,i.css(f),"content"!==h&&"both"!==h||(o=o.concat(["marginTop","marginBottom"]).concat(t),a=a.concat(["marginLeft","marginRight"]),i.find("*[width]").each(function(){var t=V(this),e=V.effects.scaledDimensions(t),i={height:e.height*n.from.y,width:e.width*n.from.x,outerHeight:e.outerHeight*n.from.y,outerWidth:e.outerWidth*n.from.x},e={height:e.height*n.to.y,width:e.width*n.to.x,outerHeight:e.height*n.to.y,outerWidth:e.width*n.to.x};n.from.y!==n.to.y&&(i=V.effects.setTransition(t,o,n.from.y,i),e=V.effects.setTransition(t,o,n.to.y,e)),n.from.x!==n.to.x&&(i=V.effects.setTransition(t,a,n.from.x,i),e=V.effects.setTransition(t,a,n.to.x,e)),l&&V.effects.saveStyle(t),t.css(i),t.animate(e,s.duration,s.easing,function(){l&&V.effects.restoreStyle(t)})})),i.animate(g,{queue:!1,duration:s.duration,easing:s.easing,complete:function(){var t=i.offset();0===g.opacity&&i.css("opacity",f.opacity),l||(i.css("position","static"===u?"relative":u).offset(t),V.effects.saveStyle(i)),e()}})}),V.effects.define("scale",function(t,e){var i=V(this),s=t.mode,s=parseInt(t.percent,10)||(0===parseInt(t.percent,10)||"effect"!==s?0:100),s=V.extend(!0,{from:V.effects.scaledDimensions(i),to:V.effects.scaledDimensions(i,s,t.direction||"both"),origin:t.origin||["middle","center"]},t);t.fade&&(s.from.opacity=1,s.to.opacity=0),V.effects.effect.size.call(this,s,e)}),V.effects.define("puff","hide",function(t,e){t=V.extend(!0,{},t,{fade:!0,percent:parseInt(t.percent,10)||150});V.effects.effect.scale.call(this,t,e)}),V.effects.define("pulsate","show",function(t,e){var i=V(this),s=t.mode,n="show"===s,o=2*(t.times||5)+(n||"hide"===s?1:0),a=t.duration/o,r=0,l=1,s=i.queue().length;for(!n&&i.is(":visible")||(i.css("opacity",0).show(),r=1);l li > :first-child").add(t.find("> :not(li)").even())},heightStyle:"auto",icons:{activeHeader:"ui-icon-triangle-1-s",header:"ui-icon-triangle-1-e"},activate:null,beforeActivate:null},hideProps:{borderTopWidth:"hide",borderBottomWidth:"hide",paddingTop:"hide",paddingBottom:"hide",height:"hide"},showProps:{borderTopWidth:"show",borderBottomWidth:"show",paddingTop:"show",paddingBottom:"show",height:"show"},_create:function(){var t=this.options;this.prevShow=this.prevHide=V(),this._addClass("ui-accordion","ui-widget ui-helper-reset"),this.element.attr("role","tablist"),t.collapsible||!1!==t.active&&null!=t.active||(t.active=0),this._processPanels(),t.active<0&&(t.active+=this.headers.length),this._refresh()},_getCreateEventData:function(){return{header:this.active,panel:this.active.length?this.active.next():V()}},_createIcons:function(){var t,e=this.options.icons;e&&(t=V(""),this._addClass(t,"ui-accordion-header-icon","ui-icon "+e.header),t.prependTo(this.headers),t=this.active.children(".ui-accordion-header-icon"),this._removeClass(t,e.header)._addClass(t,null,e.activeHeader)._addClass(this.headers,"ui-accordion-icons"))},_destroyIcons:function(){this._removeClass(this.headers,"ui-accordion-icons"),this.headers.children(".ui-accordion-header-icon").remove()},_destroy:function(){var t;this.element.removeAttr("role"),this.headers.removeAttr("role aria-expanded aria-selected aria-controls tabIndex").removeUniqueId(),this._destroyIcons(),t=this.headers.next().css("display","").removeAttr("role aria-hidden aria-labelledby").removeUniqueId(),"content"!==this.options.heightStyle&&t.css("height","")},_setOption:function(t,e){"active"!==t?("event"===t&&(this.options.event&&this._off(this.headers,this.options.event),this._setupEvents(e)),this._super(t,e),"collapsible"!==t||e||!1!==this.options.active||this._activate(0),"icons"===t&&(this._destroyIcons(),e&&this._createIcons())):this._activate(e)},_setOptionDisabled:function(t){this._super(t),this.element.attr("aria-disabled",t),this._toggleClass(null,"ui-state-disabled",!!t),this._toggleClass(this.headers.add(this.headers.next()),null,"ui-state-disabled",!!t)},_keydown:function(t){if(!t.altKey&&!t.ctrlKey){var e=V.ui.keyCode,i=this.headers.length,s=this.headers.index(t.target),n=!1;switch(t.keyCode){case e.RIGHT:case e.DOWN:n=this.headers[(s+1)%i];break;case e.LEFT:case e.UP:n=this.headers[(s-1+i)%i];break;case e.SPACE:case e.ENTER:this._eventHandler(t);break;case e.HOME:n=this.headers[0];break;case e.END:n=this.headers[i-1]}n&&(V(t.target).attr("tabIndex",-1),V(n).attr("tabIndex",0),V(n).trigger("focus"),t.preventDefault())}},_panelKeyDown:function(t){t.keyCode===V.ui.keyCode.UP&&t.ctrlKey&&V(t.currentTarget).prev().trigger("focus")},refresh:function(){var t=this.options;this._processPanels(),!1===t.active&&!0===t.collapsible||!this.headers.length?(t.active=!1,this.active=V()):!1===t.active?this._activate(0):this.active.length&&!V.contains(this.element[0],this.active[0])?this.headers.length===this.headers.find(".ui-state-disabled").length?(t.active=!1,this.active=V()):this._activate(Math.max(0,t.active-1)):t.active=this.headers.index(this.active),this._destroyIcons(),this._refresh()},_processPanels:function(){var t=this.headers,e=this.panels;"function"==typeof this.options.header?this.headers=this.options.header(this.element):this.headers=this.element.find(this.options.header),this._addClass(this.headers,"ui-accordion-header ui-accordion-header-collapsed","ui-state-default"),this.panels=this.headers.next().filter(":not(.ui-accordion-content-active)").hide(),this._addClass(this.panels,"ui-accordion-content","ui-helper-reset ui-widget-content"),e&&(this._off(t.not(this.headers)),this._off(e.not(this.panels)))},_refresh:function(){var i,t=this.options,e=t.heightStyle,s=this.element.parent();this.active=this._findActive(t.active),this._addClass(this.active,"ui-accordion-header-active","ui-state-active")._removeClass(this.active,"ui-accordion-header-collapsed"),this._addClass(this.active.next(),"ui-accordion-content-active"),this.active.next().show(),this.headers.attr("role","tab").each(function(){var t=V(this),e=t.uniqueId().attr("id"),i=t.next(),s=i.uniqueId().attr("id");t.attr("aria-controls",s),i.attr("aria-labelledby",e)}).next().attr("role","tabpanel"),this.headers.not(this.active).attr({"aria-selected":"false","aria-expanded":"false",tabIndex:-1}).next().attr({"aria-hidden":"true"}).hide(),this.active.length?this.active.attr({"aria-selected":"true","aria-expanded":"true",tabIndex:0}).next().attr({"aria-hidden":"false"}):this.headers.eq(0).attr("tabIndex",0),this._createIcons(),this._setupEvents(t.event),"fill"===e?(i=s.height(),this.element.siblings(":visible").each(function(){var t=V(this),e=t.css("position");"absolute"!==e&&"fixed"!==e&&(i-=t.outerHeight(!0))}),this.headers.each(function(){i-=V(this).outerHeight(!0)}),this.headers.next().each(function(){V(this).height(Math.max(0,i-V(this).innerHeight()+V(this).height()))}).css("overflow","auto")):"auto"===e&&(i=0,this.headers.next().each(function(){var t=V(this).is(":visible");t||V(this).show(),i=Math.max(i,V(this).css("height","").height()),t||V(this).hide()}).height(i))},_activate:function(t){t=this._findActive(t)[0];t!==this.active[0]&&(t=t||this.active[0],this._eventHandler({target:t,currentTarget:t,preventDefault:V.noop}))},_findActive:function(t){return"number"==typeof t?this.headers.eq(t):V()},_setupEvents:function(t){var i={keydown:"_keydown"};t&&V.each(t.split(" "),function(t,e){i[e]="_eventHandler"}),this._off(this.headers.add(this.headers.next())),this._on(this.headers,i),this._on(this.headers.next(),{keydown:"_panelKeyDown"}),this._hoverable(this.headers),this._focusable(this.headers)},_eventHandler:function(t){var e=this.options,i=this.active,s=V(t.currentTarget),n=s[0]===i[0],o=n&&e.collapsible,a=o?V():s.next(),r=i.next(),a={oldHeader:i,oldPanel:r,newHeader:o?V():s,newPanel:a};t.preventDefault(),n&&!e.collapsible||!1===this._trigger("beforeActivate",t,a)||(e.active=!o&&this.headers.index(s),this.active=n?V():s,this._toggle(a),this._removeClass(i,"ui-accordion-header-active","ui-state-active"),e.icons&&(i=i.children(".ui-accordion-header-icon"),this._removeClass(i,null,e.icons.activeHeader)._addClass(i,null,e.icons.header)),n||(this._removeClass(s,"ui-accordion-header-collapsed")._addClass(s,"ui-accordion-header-active","ui-state-active"),e.icons&&(n=s.children(".ui-accordion-header-icon"),this._removeClass(n,null,e.icons.header)._addClass(n,null,e.icons.activeHeader)),this._addClass(s.next(),"ui-accordion-content-active")))},_toggle:function(t){var e=t.newPanel,i=this.prevShow.length?this.prevShow:t.oldPanel;this.prevShow.add(this.prevHide).stop(!0,!0),this.prevShow=e,this.prevHide=i,this.options.animate?this._animate(e,i,t):(i.hide(),e.show(),this._toggleComplete(t)),i.attr({"aria-hidden":"true"}),i.prev().attr({"aria-selected":"false","aria-expanded":"false"}),e.length&&i.length?i.prev().attr({tabIndex:-1,"aria-expanded":"false"}):e.length&&this.headers.filter(function(){return 0===parseInt(V(this).attr("tabIndex"),10)}).attr("tabIndex",-1),e.attr("aria-hidden","false").prev().attr({"aria-selected":"true","aria-expanded":"true",tabIndex:0})},_animate:function(t,i,e){var s,n,o,a=this,r=0,l=t.css("box-sizing"),h=t.length&&(!i.length||t.index()",delay:300,options:{icons:{submenu:"ui-icon-caret-1-e"},items:"> *",menus:"ul",position:{my:"left top",at:"right top"},role:"menu",blur:null,focus:null,select:null},_create:function(){this.activeMenu=this.element,this.mouseHandled=!1,this.lastMousePosition={x:null,y:null},this.element.uniqueId().attr({role:this.options.role,tabIndex:0}),this._addClass("ui-menu","ui-widget ui-widget-content"),this._on({"mousedown .ui-menu-item":function(t){t.preventDefault(),this._activateItem(t)},"click .ui-menu-item":function(t){var e=V(t.target),i=V(V.ui.safeActiveElement(this.document[0]));!this.mouseHandled&&e.not(".ui-state-disabled").length&&(this.select(t),t.isPropagationStopped()||(this.mouseHandled=!0),e.has(".ui-menu").length?this.expand(t):!this.element.is(":focus")&&i.closest(".ui-menu").length&&(this.element.trigger("focus",[!0]),this.active&&1===this.active.parents(".ui-menu").length&&clearTimeout(this.timer)))},"mouseenter .ui-menu-item":"_activateItem","mousemove .ui-menu-item":"_activateItem",mouseleave:"collapseAll","mouseleave .ui-menu":"collapseAll",focus:function(t,e){var i=this.active||this._menuItems().first();e||this.focus(t,i)},blur:function(t){this._delay(function(){V.contains(this.element[0],V.ui.safeActiveElement(this.document[0]))||this.collapseAll(t)})},keydown:"_keydown"}),this.refresh(),this._on(this.document,{click:function(t){this._closeOnDocumentClick(t)&&this.collapseAll(t,!0),this.mouseHandled=!1}})},_activateItem:function(t){var e,i;this.previousFilter||t.clientX===this.lastMousePosition.x&&t.clientY===this.lastMousePosition.y||(this.lastMousePosition={x:t.clientX,y:t.clientY},e=V(t.target).closest(".ui-menu-item"),i=V(t.currentTarget),e[0]===i[0]&&(i.is(".ui-state-active")||(this._removeClass(i.siblings().children(".ui-state-active"),null,"ui-state-active"),this.focus(t,i))))},_destroy:function(){var t=this.element.find(".ui-menu-item").removeAttr("role aria-disabled").children(".ui-menu-item-wrapper").removeUniqueId().removeAttr("tabIndex role aria-haspopup");this.element.removeAttr("aria-activedescendant").find(".ui-menu").addBack().removeAttr("role aria-labelledby aria-expanded aria-hidden aria-disabled tabIndex").removeUniqueId().show(),t.children().each(function(){var t=V(this);t.data("ui-menu-submenu-caret")&&t.remove()})},_keydown:function(t){var e,i,s,n=!0;switch(t.keyCode){case V.ui.keyCode.PAGE_UP:this.previousPage(t);break;case V.ui.keyCode.PAGE_DOWN:this.nextPage(t);break;case V.ui.keyCode.HOME:this._move("first","first",t);break;case V.ui.keyCode.END:this._move("last","last",t);break;case V.ui.keyCode.UP:this.previous(t);break;case V.ui.keyCode.DOWN:this.next(t);break;case V.ui.keyCode.LEFT:this.collapse(t);break;case V.ui.keyCode.RIGHT:this.active&&!this.active.is(".ui-state-disabled")&&this.expand(t);break;case V.ui.keyCode.ENTER:case V.ui.keyCode.SPACE:this._activate(t);break;case V.ui.keyCode.ESCAPE:this.collapse(t);break;default:e=this.previousFilter||"",s=n=!1,i=96<=t.keyCode&&t.keyCode<=105?(t.keyCode-96).toString():String.fromCharCode(t.keyCode),clearTimeout(this.filterTimer),i===e?s=!0:i=e+i,e=this._filterMenuItems(i),(e=s&&-1!==e.index(this.active.next())?this.active.nextAll(".ui-menu-item"):e).length||(i=String.fromCharCode(t.keyCode),e=this._filterMenuItems(i)),e.length?(this.focus(t,e),this.previousFilter=i,this.filterTimer=this._delay(function(){delete this.previousFilter},1e3)):delete this.previousFilter}n&&t.preventDefault()},_activate:function(t){this.active&&!this.active.is(".ui-state-disabled")&&(this.active.children("[aria-haspopup='true']").length?this.expand(t):this.select(t))},refresh:function(){var t,e,s=this,n=this.options.icons.submenu,i=this.element.find(this.options.menus);this._toggleClass("ui-menu-icons",null,!!this.element.find(".ui-icon").length),e=i.filter(":not(.ui-menu)").hide().attr({role:this.options.role,"aria-hidden":"true","aria-expanded":"false"}).each(function(){var t=V(this),e=t.prev(),i=V("").data("ui-menu-submenu-caret",!0);s._addClass(i,"ui-menu-icon","ui-icon "+n),e.attr("aria-haspopup","true").prepend(i),t.attr("aria-labelledby",e.attr("id"))}),this._addClass(e,"ui-menu","ui-widget ui-widget-content ui-front"),(t=i.add(this.element).find(this.options.items)).not(".ui-menu-item").each(function(){var t=V(this);s._isDivider(t)&&s._addClass(t,"ui-menu-divider","ui-widget-content")}),i=(e=t.not(".ui-menu-item, .ui-menu-divider")).children().not(".ui-menu").uniqueId().attr({tabIndex:-1,role:this._itemRole()}),this._addClass(e,"ui-menu-item")._addClass(i,"ui-menu-item-wrapper"),t.filter(".ui-state-disabled").attr("aria-disabled","true"),this.active&&!V.contains(this.element[0],this.active[0])&&this.blur()},_itemRole:function(){return{menu:"menuitem",listbox:"option"}[this.options.role]},_setOption:function(t,e){var i;"icons"===t&&(i=this.element.find(".ui-menu-icon"),this._removeClass(i,null,this.options.icons.submenu)._addClass(i,null,e.submenu)),this._super(t,e)},_setOptionDisabled:function(t){this._super(t),this.element.attr("aria-disabled",String(t)),this._toggleClass(null,"ui-state-disabled",!!t)},focus:function(t,e){var i;this.blur(t,t&&"focus"===t.type),this._scrollIntoView(e),this.active=e.first(),i=this.active.children(".ui-menu-item-wrapper"),this._addClass(i,null,"ui-state-active"),this.options.role&&this.element.attr("aria-activedescendant",i.attr("id")),i=this.active.parent().closest(".ui-menu-item").children(".ui-menu-item-wrapper"),this._addClass(i,null,"ui-state-active"),t&&"keydown"===t.type?this._close():this.timer=this._delay(function(){this._close()},this.delay),(i=e.children(".ui-menu")).length&&t&&/^mouse/.test(t.type)&&this._startOpening(i),this.activeMenu=e.parent(),this._trigger("focus",t,{item:e})},_scrollIntoView:function(t){var e,i,s;this._hasScroll()&&(i=parseFloat(V.css(this.activeMenu[0],"borderTopWidth"))||0,s=parseFloat(V.css(this.activeMenu[0],"paddingTop"))||0,e=t.offset().top-this.activeMenu.offset().top-i-s,i=this.activeMenu.scrollTop(),s=this.activeMenu.height(),t=t.outerHeight(),e<0?this.activeMenu.scrollTop(i+e):s",options:{appendTo:null,autoFocus:!1,delay:300,minLength:1,position:{my:"left top",at:"left bottom",collision:"none"},source:null,change:null,close:null,focus:null,open:null,response:null,search:null,select:null},requestIndex:0,pending:0,liveRegionTimer:null,_create:function(){var i,s,n,t=this.element[0].nodeName.toLowerCase(),e="textarea"===t,t="input"===t;this.isMultiLine=e||!t&&this._isContentEditable(this.element),this.valueMethod=this.element[e||t?"val":"text"],this.isNewMenu=!0,this._addClass("ui-autocomplete-input"),this.element.attr("autocomplete","off"),this._on(this.element,{keydown:function(t){if(this.element.prop("readOnly"))s=n=i=!0;else{s=n=i=!1;var e=V.ui.keyCode;switch(t.keyCode){case e.PAGE_UP:i=!0,this._move("previousPage",t);break;case e.PAGE_DOWN:i=!0,this._move("nextPage",t);break;case e.UP:i=!0,this._keyEvent("previous",t);break;case e.DOWN:i=!0,this._keyEvent("next",t);break;case e.ENTER:this.menu.active&&(i=!0,t.preventDefault(),this.menu.select(t));break;case e.TAB:this.menu.active&&this.menu.select(t);break;case e.ESCAPE:this.menu.element.is(":visible")&&(this.isMultiLine||this._value(this.term),this.close(t),t.preventDefault());break;default:s=!0,this._searchTimeout(t)}}},keypress:function(t){if(i)return i=!1,void(this.isMultiLine&&!this.menu.element.is(":visible")||t.preventDefault());if(!s){var e=V.ui.keyCode;switch(t.keyCode){case e.PAGE_UP:this._move("previousPage",t);break;case e.PAGE_DOWN:this._move("nextPage",t);break;case e.UP:this._keyEvent("previous",t);break;case e.DOWN:this._keyEvent("next",t)}}},input:function(t){if(n)return n=!1,void t.preventDefault();this._searchTimeout(t)},focus:function(){this.selectedItem=null,this.previous=this._value()},blur:function(t){clearTimeout(this.searching),this.close(t),this._change(t)}}),this._initSource(),this.menu=V("

").text(i))},100))},menuselect:function(t,e){var i=e.item.data("ui-autocomplete-item"),s=this.previous;this.element[0]!==V.ui.safeActiveElement(this.document[0])&&(this.element.trigger("focus"),this.previous=s,this._delay(function(){this.previous=s,this.selectedItem=i})),!1!==this._trigger("select",t,{item:i})&&this._value(i.value),this.term=this._value(),this.close(t),this.selectedItem=i}}),this.liveRegion=V("

",{role:"status","aria-live":"assertive","aria-relevant":"additions"}).appendTo(this.document[0].body),this._addClass(this.liveRegion,null,"ui-helper-hidden-accessible"),this._on(this.window,{beforeunload:function(){this.element.removeAttr("autocomplete")}})},_destroy:function(){clearTimeout(this.searching),this.element.removeAttr("autocomplete"),this.menu.element.remove(),this.liveRegion.remove()},_setOption:function(t,e){this._super(t,e),"source"===t&&this._initSource(),"appendTo"===t&&this.menu.element.appendTo(this._appendTo()),"disabled"===t&&e&&this.xhr&&this.xhr.abort()},_isEventTargetInWidget:function(t){var e=this.menu.element[0];return t.target===this.element[0]||t.target===e||V.contains(e,t.target)},_closeOnClickOutside:function(t){this._isEventTargetInWidget(t)||this.close()},_appendTo:function(){var t=this.options.appendTo;return t=!(t=!(t=t&&(t.jquery||t.nodeType?V(t):this.document.find(t).eq(0)))||!t[0]?this.element.closest(".ui-front, dialog"):t).length?this.document[0].body:t},_initSource:function(){var i,s,n=this;Array.isArray(this.options.source)?(i=this.options.source,this.source=function(t,e){e(V.ui.autocomplete.filter(i,t.term))}):"string"==typeof this.options.source?(s=this.options.source,this.source=function(t,e){n.xhr&&n.xhr.abort(),n.xhr=V.ajax({url:s,data:t,dataType:"json",success:function(t){e(t)},error:function(){e([])}})}):this.source=this.options.source},_searchTimeout:function(s){clearTimeout(this.searching),this.searching=this._delay(function(){var t=this.term===this._value(),e=this.menu.element.is(":visible"),i=s.altKey||s.ctrlKey||s.metaKey||s.shiftKey;t&&(e||i)||(this.selectedItem=null,this.search(null,s))},this.options.delay)},search:function(t,e){return t=null!=t?t:this._value(),this.term=this._value(),t.length").append(V("

").text(e.label)).appendTo(t)},_move:function(t,e){if(this.menu.element.is(":visible"))return this.menu.isFirstItem()&&/^previous/.test(t)||this.menu.isLastItem()&&/^next/.test(t)?(this.isMultiLine||this._value(this.term),void this.menu.blur()):void this.menu[t](e);this.search(null,e)},widget:function(){return this.menu.element},_value:function(){return this.valueMethod.apply(this.element,arguments)},_keyEvent:function(t,e){this.isMultiLine&&!this.menu.element.is(":visible")||(this._move(t,e),e.preventDefault())},_isContentEditable:function(t){if(!t.length)return!1;var e=t.prop("contentEditable");return"inherit"===e?this._isContentEditable(t.parent()):"true"===e}}),V.extend(V.ui.autocomplete,{escapeRegex:function(t){return t.replace(/[\-\[\]{}()*+?.,\\\^$|#\s]/g,"\\$&")},filter:function(t,e){var i=new RegExp(V.ui.autocomplete.escapeRegex(e),"i");return V.grep(t,function(t){return i.test(t.label||t.value||t)})}}),V.widget("ui.autocomplete",V.ui.autocomplete,{options:{messages:{noResults:"No search results.",results:function(t){return t+(1").text(e))},100))}});V.ui.autocomplete;var tt=/ui-corner-([a-z]){2,6}/g;V.widget("ui.controlgroup",{version:"1.13.2",defaultElement:"

",options:{direction:"horizontal",disabled:null,onlyVisible:!0,items:{button:"input[type=button], input[type=submit], input[type=reset], button, a",controlgroupLabel:".ui-controlgroup-label",checkboxradio:"input[type='checkbox'], input[type='radio']",selectmenu:"select",spinner:".ui-spinner-input"}},_create:function(){this._enhance()},_enhance:function(){this.element.attr("role","toolbar"),this.refresh()},_destroy:function(){this._callChildMethod("destroy"),this.childWidgets.removeData("ui-controlgroup-data"),this.element.removeAttr("role"),this.options.items.controlgroupLabel&&this.element.find(this.options.items.controlgroupLabel).find(".ui-controlgroup-label-contents").contents().unwrap()},_initWidgets:function(){var o=this,a=[];V.each(this.options.items,function(s,t){var e,n={};if(t)return"controlgroupLabel"===s?((e=o.element.find(t)).each(function(){var t=V(this);t.children(".ui-controlgroup-label-contents").length||t.contents().wrapAll("")}),o._addClass(e,null,"ui-widget ui-widget-content ui-state-default"),void(a=a.concat(e.get()))):void(V.fn[s]&&(n=o["_"+s+"Options"]?o["_"+s+"Options"]("middle"):{classes:{}},o.element.find(t).each(function(){var t=V(this),e=t[s]("instance"),i=V.widget.extend({},n);"button"===s&&t.parent(".ui-spinner").length||((e=e||t[s]()[s]("instance"))&&(i.classes=o._resolveClassesValues(i.classes,e)),t[s](i),i=t[s]("widget"),V.data(i[0],"ui-controlgroup-data",e||t[s]("instance")),a.push(i[0]))})))}),this.childWidgets=V(V.uniqueSort(a)),this._addClass(this.childWidgets,"ui-controlgroup-item")},_callChildMethod:function(e){this.childWidgets.each(function(){var t=V(this).data("ui-controlgroup-data");t&&t[e]&&t[e]()})},_updateCornerClass:function(t,e){e=this._buildSimpleOptions(e,"label").classes.label;this._removeClass(t,null,"ui-corner-top ui-corner-bottom ui-corner-left ui-corner-right ui-corner-all"),this._addClass(t,null,e)},_buildSimpleOptions:function(t,e){var i="vertical"===this.options.direction,s={classes:{}};return s.classes[e]={middle:"",first:"ui-corner-"+(i?"top":"left"),last:"ui-corner-"+(i?"bottom":"right"),only:"ui-corner-all"}[t],s},_spinnerOptions:function(t){t=this._buildSimpleOptions(t,"ui-spinner");return t.classes["ui-spinner-up"]="",t.classes["ui-spinner-down"]="",t},_buttonOptions:function(t){return this._buildSimpleOptions(t,"ui-button")},_checkboxradioOptions:function(t){return this._buildSimpleOptions(t,"ui-checkboxradio-label")},_selectmenuOptions:function(t){var e="vertical"===this.options.direction;return{width:e&&"auto",classes:{middle:{"ui-selectmenu-button-open":"","ui-selectmenu-button-closed":""},first:{"ui-selectmenu-button-open":"ui-corner-"+(e?"top":"tl"),"ui-selectmenu-button-closed":"ui-corner-"+(e?"top":"left")},last:{"ui-selectmenu-button-open":e?"":"ui-corner-tr","ui-selectmenu-button-closed":"ui-corner-"+(e?"bottom":"right")},only:{"ui-selectmenu-button-open":"ui-corner-top","ui-selectmenu-button-closed":"ui-corner-all"}}[t]}},_resolveClassesValues:function(i,s){var n={};return V.each(i,function(t){var e=s.options.classes[t]||"",e=String.prototype.trim.call(e.replace(tt,""));n[t]=(e+" "+i[t]).replace(/\s+/g," ")}),n},_setOption:function(t,e){"direction"===t&&this._removeClass("ui-controlgroup-"+this.options.direction),this._super(t,e),"disabled"!==t?this.refresh():this._callChildMethod(e?"disable":"enable")},refresh:function(){var n,o=this;this._addClass("ui-controlgroup ui-controlgroup-"+this.options.direction),"horizontal"===this.options.direction&&this._addClass(null,"ui-helper-clearfix"),this._initWidgets(),n=this.childWidgets,(n=this.options.onlyVisible?n.filter(":visible"):n).length&&(V.each(["first","last"],function(t,e){var i,s=n[e]().data("ui-controlgroup-data");s&&o["_"+s.widgetName+"Options"]?((i=o["_"+s.widgetName+"Options"](1===n.length?"only":e)).classes=o._resolveClassesValues(i.classes,s),s.element[s.widgetName](i)):o._updateCornerClass(n[e](),e)}),this._callChildMethod("refresh"))}});V.widget("ui.checkboxradio",[V.ui.formResetMixin,{version:"1.13.2",options:{disabled:null,label:null,icon:!0,classes:{"ui-checkboxradio-label":"ui-corner-all","ui-checkboxradio-icon":"ui-corner-all"}},_getCreateOptions:function(){var t,e=this._super()||{};return this._readType(),t=this.element.labels(),this.label=V(t[t.length-1]),this.label.length||V.error("No label found for checkboxradio widget"),this.originalLabel="",(t=this.label.contents().not(this.element[0])).length&&(this.originalLabel+=t.clone().wrapAll("

").parent().html()),this.originalLabel&&(e.label=this.originalLabel),null!=(t=this.element[0].disabled)&&(e.disabled=t),e},_create:function(){var t=this.element[0].checked;this._bindFormResetHandler(),null==this.options.disabled&&(this.options.disabled=this.element[0].disabled),this._setOption("disabled",this.options.disabled),this._addClass("ui-checkboxradio","ui-helper-hidden-accessible"),this._addClass(this.label,"ui-checkboxradio-label","ui-button ui-widget"),"radio"===this.type&&this._addClass(this.label,"ui-checkboxradio-radio-label"),this.options.label&&this.options.label!==this.originalLabel?this._updateLabel():this.originalLabel&&(this.options.label=this.originalLabel),this._enhance(),t&&this._addClass(this.label,"ui-checkboxradio-checked","ui-state-active"),this._on({change:"_toggleClasses",focus:function(){this._addClass(this.label,null,"ui-state-focus ui-visual-focus")},blur:function(){this._removeClass(this.label,null,"ui-state-focus ui-visual-focus")}})},_readType:function(){var t=this.element[0].nodeName.toLowerCase();this.type=this.element[0].type,"input"===t&&/radio|checkbox/.test(this.type)||V.error("Can't create checkboxradio on element.nodeName="+t+" and element.type="+this.type)},_enhance:function(){this._updateIcon(this.element[0].checked)},widget:function(){return this.label},_getRadioGroup:function(){var t=this.element[0].name,e="input[name='"+V.escapeSelector(t)+"']";return t?(this.form.length?V(this.form[0].elements).filter(e):V(e).filter(function(){return 0===V(this)._form().length})).not(this.element):V([])},_toggleClasses:function(){var t=this.element[0].checked;this._toggleClass(this.label,"ui-checkboxradio-checked","ui-state-active",t),this.options.icon&&"checkbox"===this.type&&this._toggleClass(this.icon,null,"ui-icon-check ui-state-checked",t)._toggleClass(this.icon,null,"ui-icon-blank",!t),"radio"===this.type&&this._getRadioGroup().each(function(){var t=V(this).checkboxradio("instance");t&&t._removeClass(t.label,"ui-checkboxradio-checked","ui-state-active")})},_destroy:function(){this._unbindFormResetHandler(),this.icon&&(this.icon.remove(),this.iconSpace.remove())},_setOption:function(t,e){if("label"!==t||e){if(this._super(t,e),"disabled"===t)return this._toggleClass(this.label,null,"ui-state-disabled",e),void(this.element[0].disabled=e);this.refresh()}},_updateIcon:function(t){var e="ui-icon ui-icon-background ";this.options.icon?(this.icon||(this.icon=V(""),this.iconSpace=V(" "),this._addClass(this.iconSpace,"ui-checkboxradio-icon-space")),"checkbox"===this.type?(e+=t?"ui-icon-check ui-state-checked":"ui-icon-blank",this._removeClass(this.icon,null,t?"ui-icon-blank":"ui-icon-check")):e+="ui-icon-blank",this._addClass(this.icon,"ui-checkboxradio-icon",e),t||this._removeClass(this.icon,null,"ui-icon-check ui-state-checked"),this.icon.prependTo(this.label).after(this.iconSpace)):void 0!==this.icon&&(this.icon.remove(),this.iconSpace.remove(),delete this.icon)},_updateLabel:function(){var t=this.label.contents().not(this.element[0]);this.icon&&(t=t.not(this.icon[0])),(t=this.iconSpace?t.not(this.iconSpace[0]):t).remove(),this.label.append(this.options.label)},refresh:function(){var t=this.element[0].checked,e=this.element[0].disabled;this._updateIcon(t),this._toggleClass(this.label,"ui-checkboxradio-checked","ui-state-active",t),null!==this.options.label&&this._updateLabel(),e!==this.options.disabled&&this._setOptions({disabled:e})}}]);var et;V.ui.checkboxradio;V.widget("ui.button",{version:"1.13.2",defaultElement:"

"+(0

":""):"")}f+=_}return f+=F,t._keyEvent=!1,f},_generateMonthYearHeader:function(t,e,i,s,n,o,a,r){var l,h,c,u,d,p,f=this._get(t,"changeMonth"),g=this._get(t,"changeYear"),m=this._get(t,"showMonthAfterYear"),_=this._get(t,"selectMonthLabel"),v=this._get(t,"selectYearLabel"),b="

",y="";if(o||!f)y+=""+a[e]+"";else{for(l=s&&s.getFullYear()===i,h=n&&n.getFullYear()===i,y+=""}if(m||(b+=y+(!o&&f&&g?"":" ")),!t.yearshtml)if(t.yearshtml="",o||!g)b+=""+i+"";else{for(a=this._get(t,"yearRange").split(":"),u=(new Date).getFullYear(),d=(_=function(t){t=t.match(/c[+\-].*/)?i+parseInt(t.substring(1),10):t.match(/[+\-].*/)?u+parseInt(t,10):parseInt(t,10);return isNaN(t)?u:t})(a[0]),p=Math.max(d,_(a[1]||"")),d=s?Math.max(d,s.getFullYear()):d,p=n?Math.min(p,n.getFullYear()):p,t.yearshtml+="",b+=t.yearshtml,t.yearshtml=null}return b+=this._get(t,"yearSuffix"),m&&(b+=(!o&&f&&g?"":" ")+y),b+="

"},_adjustInstDate:function(t,e,i){var s=t.selectedYear+("Y"===i?e:0),n=t.selectedMonth+("M"===i?e:0),e=Math.min(t.selectedDay,this._getDaysInMonth(s,n))+("D"===i?e:0),e=this._restrictMinMax(t,this._daylightSavingAdjust(new Date(s,n,e)));t.selectedDay=e.getDate(),t.drawMonth=t.selectedMonth=e.getMonth(),t.drawYear=t.selectedYear=e.getFullYear(),"M"!==i&&"Y"!==i||this._notifyChange(t)},_restrictMinMax:function(t,e){var i=this._getMinMaxDate(t,"min"),t=this._getMinMaxDate(t,"max"),e=i&&e=i.getTime())&&(!s||e.getTime()<=s.getTime())&&(!n||e.getFullYear()>=n)&&(!o||e.getFullYear()<=o)},_getFormatConfig:function(t){var e=this._get(t,"shortYearCutoff");return{shortYearCutoff:e="string"!=typeof e?e:(new Date).getFullYear()%100+parseInt(e,10),dayNamesShort:this._get(t,"dayNamesShort"),dayNames:this._get(t,"dayNames"),monthNamesShort:this._get(t,"monthNamesShort"),monthNames:this._get(t,"monthNames")}},_formatDate:function(t,e,i,s){e||(t.currentDay=t.selectedDay,t.currentMonth=t.selectedMonth,t.currentYear=t.selectedYear);e=e?"object"==typeof e?e:this._daylightSavingAdjust(new Date(s,i,e)):this._daylightSavingAdjust(new Date(t.currentYear,t.currentMonth,t.currentDay));return this.formatDate(this._get(t,"dateFormat"),e,this._getFormatConfig(t))}}),V.fn.datepicker=function(t){if(!this.length)return this;V.datepicker.initialized||(V(document).on("mousedown",V.datepicker._checkExternalClick),V.datepicker.initialized=!0),0===V("#"+V.datepicker._mainDivId).length&&V("body").append(V.datepicker.dpDiv);var e=Array.prototype.slice.call(arguments,1);return"string"==typeof t&&("isDisabled"===t||"getDate"===t||"widget"===t)||"option"===t&&2===arguments.length&&"string"==typeof arguments[1]?V.datepicker["_"+t+"Datepicker"].apply(V.datepicker,[this[0]].concat(e)):this.each(function(){"string"==typeof t?V.datepicker["_"+t+"Datepicker"].apply(V.datepicker,[this].concat(e)):V.datepicker._attachDatepicker(this,t)})},V.datepicker=new st,V.datepicker.initialized=!1,V.datepicker.uuid=(new Date).getTime(),V.datepicker.version="1.13.2";V.datepicker,V.ui.ie=!!/msie [\w.]+/.exec(navigator.userAgent.toLowerCase());var rt=!1;V(document).on("mouseup",function(){rt=!1});V.widget("ui.mouse",{version:"1.13.2",options:{cancel:"input, textarea, button, select, option",distance:1,delay:0},_mouseInit:function(){var e=this;this.element.on("mousedown."+this.widgetName,function(t){return e._mouseDown(t)}).on("click."+this.widgetName,function(t){if(!0===V.data(t.target,e.widgetName+".preventClickEvent"))return V.removeData(t.target,e.widgetName+".preventClickEvent"),t.stopImmediatePropagation(),!1}),this.started=!1},_mouseDestroy:function(){this.element.off("."+this.widgetName),this._mouseMoveDelegate&&this.document.off("mousemove."+this.widgetName,this._mouseMoveDelegate).off("mouseup."+this.widgetName,this._mouseUpDelegate)},_mouseDown:function(t){if(!rt){this._mouseMoved=!1,this._mouseStarted&&this._mouseUp(t),this._mouseDownEvent=t;var e=this,i=1===t.which,s=!("string"!=typeof this.options.cancel||!t.target.nodeName)&&V(t.target).closest(this.options.cancel).length;return i&&!s&&this._mouseCapture(t)?(this.mouseDelayMet=!this.options.delay,this.mouseDelayMet||(this._mouseDelayTimer=setTimeout(function(){e.mouseDelayMet=!0},this.options.delay)),this._mouseDistanceMet(t)&&this._mouseDelayMet(t)&&(this._mouseStarted=!1!==this._mouseStart(t),!this._mouseStarted)?(t.preventDefault(),!0):(!0===V.data(t.target,this.widgetName+".preventClickEvent")&&V.removeData(t.target,this.widgetName+".preventClickEvent"),this._mouseMoveDelegate=function(t){return e._mouseMove(t)},this._mouseUpDelegate=function(t){return e._mouseUp(t)},this.document.on("mousemove."+this.widgetName,this._mouseMoveDelegate).on("mouseup."+this.widgetName,this._mouseUpDelegate),t.preventDefault(),rt=!0)):!0}},_mouseMove:function(t){if(this._mouseMoved){if(V.ui.ie&&(!document.documentMode||document.documentMode<9)&&!t.button)return this._mouseUp(t);if(!t.which)if(t.originalEvent.altKey||t.originalEvent.ctrlKey||t.originalEvent.metaKey||t.originalEvent.shiftKey)this.ignoreMissingWhich=!0;else if(!this.ignoreMissingWhich)return this._mouseUp(t)}return(t.which||t.button)&&(this._mouseMoved=!0),this._mouseStarted?(this._mouseDrag(t),t.preventDefault()):(this._mouseDistanceMet(t)&&this._mouseDelayMet(t)&&(this._mouseStarted=!1!==this._mouseStart(this._mouseDownEvent,t),this._mouseStarted?this._mouseDrag(t):this._mouseUp(t)),!this._mouseStarted)},_mouseUp:function(t){this.document.off("mousemove."+this.widgetName,this._mouseMoveDelegate).off("mouseup."+this.widgetName,this._mouseUpDelegate),this._mouseStarted&&(this._mouseStarted=!1,t.target===this._mouseDownEvent.target&&V.data(t.target,this.widgetName+".preventClickEvent",!0),this._mouseStop(t)),this._mouseDelayTimer&&(clearTimeout(this._mouseDelayTimer),delete this._mouseDelayTimer),this.ignoreMissingWhich=!1,rt=!1,t.preventDefault()},_mouseDistanceMet:function(t){return Math.max(Math.abs(this._mouseDownEvent.pageX-t.pageX),Math.abs(this._mouseDownEvent.pageY-t.pageY))>=this.options.distance},_mouseDelayMet:function(){return this.mouseDelayMet},_mouseStart:function(){},_mouseDrag:function(){},_mouseStop:function(){},_mouseCapture:function(){return!0}}),V.ui.plugin={add:function(t,e,i){var s,n=V.ui[t].prototype;for(s in i)n.plugins[s]=n.plugins[s]||[],n.plugins[s].push([e,i[s]])},call:function(t,e,i,s){var n,o=t.plugins[e];if(o&&(s||t.element[0].parentNode&&11!==t.element[0].parentNode.nodeType))for(n=0;n").css("position","absolute").appendTo(t.parent()).outerWidth(t.outerWidth()).outerHeight(t.outerHeight()).offset(t.offset())[0]})},_unblockFrames:function(){this.iframeBlocks&&(this.iframeBlocks.remove(),delete this.iframeBlocks)},_blurActiveElement:function(t){var e=V.ui.safeActiveElement(this.document[0]);V(t.target).closest(e).length||V.ui.safeBlur(e)},_mouseStart:function(t){var e=this.options;return this.helper=this._createHelper(t),this._addClass(this.helper,"ui-draggable-dragging"),this._cacheHelperProportions(),V.ui.ddmanager&&(V.ui.ddmanager.current=this),this._cacheMargins(),this.cssPosition=this.helper.css("position"),this.scrollParent=this.helper.scrollParent(!0),this.offsetParent=this.helper.offsetParent(),this.hasFixedAncestor=0i[2]&&(o=i[2]+this.offset.click.left),t.pageY-this.offset.click.top>i[3]&&(a=i[3]+this.offset.click.top)),s.grid&&(t=s.grid[1]?this.originalPageY+Math.round((a-this.originalPageY)/s.grid[1])*s.grid[1]:this.originalPageY,a=!i||t-this.offset.click.top>=i[1]||t-this.offset.click.top>i[3]?t:t-this.offset.click.top>=i[1]?t-s.grid[1]:t+s.grid[1],t=s.grid[0]?this.originalPageX+Math.round((o-this.originalPageX)/s.grid[0])*s.grid[0]:this.originalPageX,o=!i||t-this.offset.click.left>=i[0]||t-this.offset.click.left>i[2]?t:t-this.offset.click.left>=i[0]?t-s.grid[0]:t+s.grid[0]),"y"===s.axis&&(o=this.originalPageX),"x"===s.axis&&(a=this.originalPageY)),{top:a-this.offset.click.top-this.offset.relative.top-this.offset.parent.top+("fixed"===this.cssPosition?-this.offset.scroll.top:n?0:this.offset.scroll.top),left:o-this.offset.click.left-this.offset.relative.left-this.offset.parent.left+("fixed"===this.cssPosition?-this.offset.scroll.left:n?0:this.offset.scroll.left)}},_clear:function(){this._removeClass(this.helper,"ui-draggable-dragging"),this.helper[0]===this.element[0]||this.cancelHelperRemoval||this.helper.remove(),this.helper=null,this.cancelHelperRemoval=!1,this.destroyOnClear&&this.destroy()},_trigger:function(t,e,i){return i=i||this._uiHash(),V.ui.plugin.call(this,t,[e,i,this],!0),/^(drag|start|stop)/.test(t)&&(this.positionAbs=this._convertPositionTo("absolute"),i.offset=this.positionAbs),V.Widget.prototype._trigger.call(this,t,e,i)},plugins:{},_uiHash:function(){return{helper:this.helper,position:this.position,originalPosition:this.originalPosition,offset:this.positionAbs}}}),V.ui.plugin.add("draggable","connectToSortable",{start:function(e,t,i){var s=V.extend({},t,{item:i.element});i.sortables=[],V(i.options.connectToSortable).each(function(){var t=V(this).sortable("instance");t&&!t.options.disabled&&(i.sortables.push(t),t.refreshPositions(),t._trigger("activate",e,s))})},stop:function(e,t,i){var s=V.extend({},t,{item:i.element});i.cancelHelperRemoval=!1,V.each(i.sortables,function(){var t=this;t.isOver?(t.isOver=0,i.cancelHelperRemoval=!0,t.cancelHelperRemoval=!1,t._storedCSS={position:t.placeholder.css("position"),top:t.placeholder.css("top"),left:t.placeholder.css("left")},t._mouseStop(e),t.options.helper=t.options._helper):(t.cancelHelperRemoval=!0,t._trigger("deactivate",e,s))})},drag:function(i,s,n){V.each(n.sortables,function(){var t=!1,e=this;e.positionAbs=n.positionAbs,e.helperProportions=n.helperProportions,e.offset.click=n.offset.click,e._intersectsWith(e.containerCache)&&(t=!0,V.each(n.sortables,function(){return this.positionAbs=n.positionAbs,this.helperProportions=n.helperProportions,this.offset.click=n.offset.click,t=this!==e&&this._intersectsWith(this.containerCache)&&V.contains(e.element[0],this.element[0])?!1:t})),t?(e.isOver||(e.isOver=1,n._parent=s.helper.parent(),e.currentItem=s.helper.appendTo(e.element).data("ui-sortable-item",!0),e.options._helper=e.options.helper,e.options.helper=function(){return s.helper[0]},i.target=e.currentItem[0],e._mouseCapture(i,!0),e._mouseStart(i,!0,!0),e.offset.click.top=n.offset.click.top,e.offset.click.left=n.offset.click.left,e.offset.parent.left-=n.offset.parent.left-e.offset.parent.left,e.offset.parent.top-=n.offset.parent.top-e.offset.parent.top,n._trigger("toSortable",i),n.dropped=e.element,V.each(n.sortables,function(){this.refreshPositions()}),n.currentItem=n.element,e.fromOutside=n),e.currentItem&&(e._mouseDrag(i),s.position=e.position)):e.isOver&&(e.isOver=0,e.cancelHelperRemoval=!0,e.options._revert=e.options.revert,e.options.revert=!1,e._trigger("out",i,e._uiHash(e)),e._mouseStop(i,!0),e.options.revert=e.options._revert,e.options.helper=e.options._helper,e.placeholder&&e.placeholder.remove(),s.helper.appendTo(n._parent),n._refreshOffsets(i),s.position=n._generatePosition(i,!0),n._trigger("fromSortable",i),n.dropped=!1,V.each(n.sortables,function(){this.refreshPositions()}))})}}),V.ui.plugin.add("draggable","cursor",{start:function(t,e,i){var s=V("body"),i=i.options;s.css("cursor")&&(i._cursor=s.css("cursor")),s.css("cursor",i.cursor)},stop:function(t,e,i){i=i.options;i._cursor&&V("body").css("cursor",i._cursor)}}),V.ui.plugin.add("draggable","opacity",{start:function(t,e,i){e=V(e.helper),i=i.options;e.css("opacity")&&(i._opacity=e.css("opacity")),e.css("opacity",i.opacity)},stop:function(t,e,i){i=i.options;i._opacity&&V(e.helper).css("opacity",i._opacity)}}),V.ui.plugin.add("draggable","scroll",{start:function(t,e,i){i.scrollParentNotHidden||(i.scrollParentNotHidden=i.helper.scrollParent(!1)),i.scrollParentNotHidden[0]!==i.document[0]&&"HTML"!==i.scrollParentNotHidden[0].tagName&&(i.overflowOffset=i.scrollParentNotHidden.offset())},drag:function(t,e,i){var s=i.options,n=!1,o=i.scrollParentNotHidden[0],a=i.document[0];o!==a&&"HTML"!==o.tagName?(s.axis&&"x"===s.axis||(i.overflowOffset.top+o.offsetHeight-t.pageY

").css({overflow:"hidden",position:this.element.css("position"),width:this.element.outerWidth(),height:this.element.outerHeight(),top:this.element.css("top"),left:this.element.css("left")})),this.element=this.element.parent().data("ui-resizable",this.element.resizable("instance")),this.elementIsWrapper=!0,t={marginTop:this.originalElement.css("marginTop"),marginRight:this.originalElement.css("marginRight"),marginBottom:this.originalElement.css("marginBottom"),marginLeft:this.originalElement.css("marginLeft")},this.element.css(t),this.originalElement.css("margin",0),this.originalResizeStyle=this.originalElement.css("resize"),this.originalElement.css("resize","none"),this._proportionallyResizeElements.push(this.originalElement.css({position:"static",zoom:1,display:"block"})),this.originalElement.css(t),this._proportionallyResize()),this._setupHandles(),e.autoHide&&V(this.element).on("mouseenter",function(){e.disabled||(i._removeClass("ui-resizable-autohide"),i._handles.show())}).on("mouseleave",function(){e.disabled||i.resizing||(i._addClass("ui-resizable-autohide"),i._handles.hide())}),this._mouseInit()},_destroy:function(){this._mouseDestroy(),this._addedHandles.remove();function t(t){V(t).removeData("resizable").removeData("ui-resizable").off(".resizable")}var e;return this.elementIsWrapper&&(t(this.element),e=this.element,this.originalElement.css({position:e.css("position"),width:e.outerWidth(),height:e.outerHeight(),top:e.css("top"),left:e.css("left")}).insertAfter(e),e.remove()),this.originalElement.css("resize",this.originalResizeStyle),t(this.originalElement),this},_setOption:function(t,e){switch(this._super(t,e),t){case"handles":this._removeHandles(),this._setupHandles();break;case"aspectRatio":this._aspectRatio=!!e}},_setupHandles:function(){var t,e,i,s,n,o=this.options,a=this;if(this.handles=o.handles||(V(".ui-resizable-handle",this.element).length?{n:".ui-resizable-n",e:".ui-resizable-e",s:".ui-resizable-s",w:".ui-resizable-w",se:".ui-resizable-se",sw:".ui-resizable-sw",ne:".ui-resizable-ne",nw:".ui-resizable-nw"}:"e,s,se"),this._handles=V(),this._addedHandles=V(),this.handles.constructor===String)for("all"===this.handles&&(this.handles="n,e,s,w,se,sw,ne,nw"),i=this.handles.split(","),this.handles={},e=0;e"),this._addClass(n,"ui-resizable-handle "+s),n.css({zIndex:o.zIndex}),this.handles[t]=".ui-resizable-"+t,this.element.children(this.handles[t]).length||(this.element.append(n),this._addedHandles=this._addedHandles.add(n));this._renderAxis=function(t){var e,i,s;for(e in t=t||this.element,this.handles)this.handles[e].constructor===String?this.handles[e]=this.element.children(this.handles[e]).first().show():(this.handles[e].jquery||this.handles[e].nodeType)&&(this.handles[e]=V(this.handles[e]),this._on(this.handles[e],{mousedown:a._mouseDown})),this.elementIsWrapper&&this.originalElement[0].nodeName.match(/^(textarea|input|select|button)$/i)&&(i=V(this.handles[e],this.element),s=/sw|ne|nw|se|n|s/.test(e)?i.outerHeight():i.outerWidth(),i=["padding",/ne|nw|n/.test(e)?"Top":/se|sw|s/.test(e)?"Bottom":/^e$/.test(e)?"Right":"Left"].join(""),t.css(i,s),this._proportionallyResize()),this._handles=this._handles.add(this.handles[e])},this._renderAxis(this.element),this._handles=this._handles.add(this.element.find(".ui-resizable-handle")),this._handles.disableSelection(),this._handles.on("mouseover",function(){a.resizing||(this.className&&(n=this.className.match(/ui-resizable-(se|sw|ne|nw|n|e|s|w)/i)),a.axis=n&&n[1]?n[1]:"se")}),o.autoHide&&(this._handles.hide(),this._addClass("ui-resizable-autohide"))},_removeHandles:function(){this._addedHandles.remove()},_mouseCapture:function(t){var e,i,s=!1;for(e in this.handles)(i=V(this.handles[e])[0])!==t.target&&!V.contains(i,t.target)||(s=!0);return!this.options.disabled&&s},_mouseStart:function(t){var e,i,s=this.options,n=this.element;return this.resizing=!0,this._renderProxy(),e=this._num(this.helper.css("left")),i=this._num(this.helper.css("top")),s.containment&&(e+=V(s.containment).scrollLeft()||0,i+=V(s.containment).scrollTop()||0),this.offset=this.helper.offset(),this.position={left:e,top:i},this.size=this._helper?{width:this.helper.width(),height:this.helper.height()}:{width:n.width(),height:n.height()},this.originalSize=this._helper?{width:n.outerWidth(),height:n.outerHeight()}:{width:n.width(),height:n.height()},this.sizeDiff={width:n.outerWidth()-n.width(),height:n.outerHeight()-n.height()},this.originalPosition={left:e,top:i},this.originalMousePosition={left:t.pageX,top:t.pageY},this.aspectRatio="number"==typeof s.aspectRatio?s.aspectRatio:this.originalSize.width/this.originalSize.height||1,s=V(".ui-resizable-"+this.axis).css("cursor"),V("body").css("cursor","auto"===s?this.axis+"-resize":s),this._addClass("ui-resizable-resizing"),this._propagate("start",t),!0},_mouseDrag:function(t){var e=this.originalMousePosition,i=this.axis,s=t.pageX-e.left||0,e=t.pageY-e.top||0,i=this._change[i];return this._updatePrevProperties(),i&&(e=i.apply(this,[t,s,e]),this._updateVirtualBoundaries(t.shiftKey),(this._aspectRatio||t.shiftKey)&&(e=this._updateRatio(e,t)),e=this._respectSize(e,t),this._updateCache(e),this._propagate("resize",t),e=this._applyChanges(),!this._helper&&this._proportionallyResizeElements.length&&this._proportionallyResize(),V.isEmptyObject(e)||(this._updatePrevProperties(),this._trigger("resize",t,this.ui()),this._applyChanges())),!1},_mouseStop:function(t){this.resizing=!1;var e,i,s,n=this.options,o=this;return this._helper&&(s=(e=(i=this._proportionallyResizeElements).length&&/textarea/i.test(i[0].nodeName))&&this._hasScroll(i[0],"left")?0:o.sizeDiff.height,i=e?0:o.sizeDiff.width,e={width:o.helper.width()-i,height:o.helper.height()-s},i=parseFloat(o.element.css("left"))+(o.position.left-o.originalPosition.left)||null,s=parseFloat(o.element.css("top"))+(o.position.top-o.originalPosition.top)||null,n.animate||this.element.css(V.extend(e,{top:s,left:i})),o.helper.height(o.size.height),o.helper.width(o.size.width),this._helper&&!n.animate&&this._proportionallyResize()),V("body").css("cursor","auto"),this._removeClass("ui-resizable-resizing"),this._propagate("stop",t),this._helper&&this.helper.remove(),!1},_updatePrevProperties:function(){this.prevPosition={top:this.position.top,left:this.position.left},this.prevSize={width:this.size.width,height:this.size.height}},_applyChanges:function(){var t={};return this.position.top!==this.prevPosition.top&&(t.top=this.position.top+"px"),this.position.left!==this.prevPosition.left&&(t.left=this.position.left+"px"),this.size.width!==this.prevSize.width&&(t.width=this.size.width+"px"),this.size.height!==this.prevSize.height&&(t.height=this.size.height+"px"),this.helper.css(t),t},_updateVirtualBoundaries:function(t){var e,i,s=this.options,n={minWidth:this._isNumber(s.minWidth)?s.minWidth:0,maxWidth:this._isNumber(s.maxWidth)?s.maxWidth:1/0,minHeight:this._isNumber(s.minHeight)?s.minHeight:0,maxHeight:this._isNumber(s.maxHeight)?s.maxHeight:1/0};(this._aspectRatio||t)&&(e=n.minHeight*this.aspectRatio,i=n.minWidth/this.aspectRatio,s=n.maxHeight*this.aspectRatio,t=n.maxWidth/this.aspectRatio,e>n.minWidth&&(n.minWidth=e),i>n.minHeight&&(n.minHeight=i),st.width,a=this._isNumber(t.height)&&e.minHeight&&e.minHeight>t.height,r=this.originalPosition.left+this.originalSize.width,l=this.originalPosition.top+this.originalSize.height,h=/sw|nw|w/.test(i),i=/nw|ne|n/.test(i);return o&&(t.width=e.minWidth),a&&(t.height=e.minHeight),s&&(t.width=e.maxWidth),n&&(t.height=e.maxHeight),o&&h&&(t.left=r-e.minWidth),s&&h&&(t.left=r-e.maxWidth),a&&i&&(t.top=l-e.minHeight),n&&i&&(t.top=l-e.maxHeight),t.width||t.height||t.left||!t.top?t.width||t.height||t.top||!t.left||(t.left=null):t.top=null,t},_getPaddingPlusBorderDimensions:function(t){for(var e=0,i=[],s=[t.css("borderTopWidth"),t.css("borderRightWidth"),t.css("borderBottomWidth"),t.css("borderLeftWidth")],n=[t.css("paddingTop"),t.css("paddingRight"),t.css("paddingBottom"),t.css("paddingLeft")];e<4;e++)i[e]=parseFloat(s[e])||0,i[e]+=parseFloat(n[e])||0;return{height:i[0]+i[2],width:i[1]+i[3]}},_proportionallyResize:function(){if(this._proportionallyResizeElements.length)for(var t,e=0,i=this.helper||this.element;e

d,s=i.minHeight&&i.minHeight>p;i.grid=r,m&&(d+=l),s&&(p+=h),f&&(d-=l),g&&(p-=h),/^(se|s|e)$/.test(a)?(e.size.width=d,e.size.height=p):/^(ne)$/.test(a)?(e.size.width=d,e.size.height=p,e.position.top=o.top-u):/^(sw)$/.test(a)?(e.size.width=d,e.size.height=p,e.position.left=o.left-c):((p-h<=0||d-l<=0)&&(t=e._getPaddingPlusBorderDimensions(this)),0=+this.uiDialog.css("z-index")&&(this.uiDialog.css("z-index",s+1),i=!0),i&&!e&&this._trigger("focus",t),i},open:function(){var t=this;this._isOpen?this._moveToTop()&&this._focusTabbable():(this._isOpen=!0,this.opener=V(V.ui.safeActiveElement(this.document[0])),this._size(),this._position(),this._createOverlay(),this._moveToTop(null,!0),this.overlay&&this.overlay.css("z-index",this.uiDialog.css("z-index")-1),this._show(this.uiDialog,this.options.show,function(){t._focusTabbable(),t._trigger("focus")}),this._makeFocusTarget(),this._trigger("open"))},_focusTabbable:function(){var t=this._focusedElement;(t=!(t=!(t=!(t=!(t=t||this.element.find("[autofocus]")).length?this.element.find(":tabbable"):t).length?this.uiDialogButtonPane.find(":tabbable"):t).length?this.uiDialogTitlebarClose.filter(":tabbable"):t).length?this.uiDialog:t).eq(0).trigger("focus")},_restoreTabbableFocus:function(){var t=V.ui.safeActiveElement(this.document[0]);this.uiDialog[0]===t||V.contains(this.uiDialog[0],t)||this._focusTabbable()},_keepFocus:function(t){t.preventDefault(),this._restoreTabbableFocus(),this._delay(this._restoreTabbableFocus)},_createWrapper:function(){this.uiDialog=V("

").hide().attr({tabIndex:-1,role:"dialog"}).appendTo(this._appendTo()),this._addClass(this.uiDialog,"ui-dialog","ui-widget ui-widget-content ui-front"),this._on(this.uiDialog,{keydown:function(t){if(this.options.closeOnEscape&&!t.isDefaultPrevented()&&t.keyCode&&t.keyCode===V.ui.keyCode.ESCAPE)return t.preventDefault(),void this.close(t);var e,i,s;t.keyCode!==V.ui.keyCode.TAB||t.isDefaultPrevented()||(e=this.uiDialog.find(":tabbable"),i=e.first(),s=e.last(),t.target!==s[0]&&t.target!==this.uiDialog[0]||t.shiftKey?t.target!==i[0]&&t.target!==this.uiDialog[0]||!t.shiftKey||(this._delay(function(){s.trigger("focus")}),t.preventDefault()):(this._delay(function(){i.trigger("focus")}),t.preventDefault()))},mousedown:function(t){this._moveToTop(t)&&this._focusTabbable()}}),this.element.find("[aria-describedby]").length||this.uiDialog.attr({"aria-describedby":this.element.uniqueId().attr("id")})},_createTitlebar:function(){var t;this.uiDialogTitlebar=V("

"),this._addClass(this.uiDialogButtonPane,"ui-dialog-buttonpane","ui-widget-content ui-helper-clearfix"),this.uiButtonSet=V("

").appendTo(this.uiDialogButtonPane),this._addClass(this.uiButtonSet,"ui-dialog-buttonset"),this._createButtons()},_createButtons:function(){var s=this,t=this.options.buttons;this.uiDialogButtonPane.remove(),this.uiButtonSet.empty(),V.isEmptyObject(t)||Array.isArray(t)&&!t.length?this._removeClass(this.uiDialog,"ui-dialog-buttons"):(V.each(t,function(t,e){var i;e=V.extend({type:"button"},e="function"==typeof e?{click:e,text:t}:e),i=e.click,t={icon:e.icon,iconPosition:e.iconPosition,showLabel:e.showLabel,icons:e.icons,text:e.text},delete e.click,delete e.icon,delete e.iconPosition,delete e.showLabel,delete e.icons,"boolean"==typeof e.text&&delete e.text,V("",e).button(t).appendTo(s.uiButtonSet).on("click",function(){i.apply(s.element[0],arguments)})}),this._addClass(this.uiDialog,"ui-dialog-buttons"),this.uiDialogButtonPane.appendTo(this.uiDialog))},_makeDraggable:function(){var n=this,o=this.options;function a(t){return{position:t.position,offset:t.offset}}this.uiDialog.draggable({cancel:".ui-dialog-content, .ui-dialog-titlebar-close",handle:".ui-dialog-titlebar",containment:"document",start:function(t,e){n._addClass(V(this),"ui-dialog-dragging"),n._blockFrames(),n._trigger("dragStart",t,a(e))},drag:function(t,e){n._trigger("drag",t,a(e))},stop:function(t,e){var i=e.offset.left-n.document.scrollLeft(),s=e.offset.top-n.document.scrollTop();o.position={my:"left top",at:"left"+(0<=i?"+":"")+i+" top"+(0<=s?"+":"")+s,of:n.window},n._removeClass(V(this),"ui-dialog-dragging"),n._unblockFrames(),n._trigger("dragStop",t,a(e))}})},_makeResizable:function(){var n=this,o=this.options,t=o.resizable,e=this.uiDialog.css("position"),t="string"==typeof t?t:"n,e,s,w,se,sw,ne,nw";function a(t){return{originalPosition:t.originalPosition,originalSize:t.originalSize,position:t.position,size:t.size}}this.uiDialog.resizable({cancel:".ui-dialog-content",containment:"document",alsoResize:this.element,maxWidth:o.maxWidth,maxHeight:o.maxHeight,minWidth:o.minWidth,minHeight:this._minHeight(),handles:t,start:function(t,e){n._addClass(V(this),"ui-dialog-resizing"),n._blockFrames(),n._trigger("resizeStart",t,a(e))},resize:function(t,e){n._trigger("resize",t,a(e))},stop:function(t,e){var i=n.uiDialog.offset(),s=i.left-n.document.scrollLeft(),i=i.top-n.document.scrollTop();o.height=n.uiDialog.height(),o.width=n.uiDialog.width(),o.position={my:"left top",at:"left"+(0<=s?"+":"")+s+" top"+(0<=i?"+":"")+i,of:n.window},n._removeClass(V(this),"ui-dialog-resizing"),n._unblockFrames(),n._trigger("resizeStop",t,a(e))}}).css("position",e)},_trackFocus:function(){this._on(this.widget(),{focusin:function(t){this._makeFocusTarget(),this._focusedElement=V(t.target)}})},_makeFocusTarget:function(){this._untrackInstance(),this._trackingInstances().unshift(this)},_untrackInstance:function(){var t=this._trackingInstances(),e=V.inArray(this,t);-1!==e&&t.splice(e,1)},_trackingInstances:function(){var t=this.document.data("ui-dialog-instances");return t||this.document.data("ui-dialog-instances",t=[]),t},_minHeight:function(){var t=this.options;return"auto"===t.height?t.minHeight:Math.min(t.minHeight,t.height)},_position:function(){var t=this.uiDialog.is(":visible");t||this.uiDialog.show(),this.uiDialog.position(this.options.position),t||this.uiDialog.hide()},_setOptions:function(t){var i=this,s=!1,n={};V.each(t,function(t,e){i._setOption(t,e),t in i.sizeRelatedOptions&&(s=!0),t in i.resizableRelatedOptions&&(n[t]=e)}),s&&(this._size(),this._position()),this.uiDialog.is(":data(ui-resizable)")&&this.uiDialog.resizable("option",n)},_setOption:function(t,e){var i,s=this.uiDialog;"disabled"!==t&&(this._super(t,e),"appendTo"===t&&this.uiDialog.appendTo(this._appendTo()),"buttons"===t&&this._createButtons(),"closeText"===t&&this.uiDialogTitlebarClose.button({label:V("").text(""+this.options.closeText).html()}),"draggable"===t&&((i=s.is(":data(ui-draggable)"))&&!e&&s.draggable("destroy"),!i&&e&&this._makeDraggable()),"position"===t&&this._position(),"resizable"===t&&((i=s.is(":data(ui-resizable)"))&&!e&&s.resizable("destroy"),i&&"string"==typeof e&&s.resizable("option","handles",e),i||!1===e||this._makeResizable()),"title"===t&&this._title(this.uiDialogTitlebar.find(".ui-dialog-title")))},_size:function(){var t,e,i,s=this.options;this.element.show().css({width:"auto",minHeight:0,maxHeight:"none",height:0}),s.minWidth>s.width&&(s.width=s.minWidth),t=this.uiDialog.css({height:"auto",width:s.width}).outerHeight(),e=Math.max(0,s.minHeight-t),i="number"==typeof s.maxHeight?Math.max(0,s.maxHeight-t):"none","auto"===s.height?this.element.css({minHeight:e,maxHeight:i,height:"auto"}):this.element.height(Math.max(0,s.height-t)),this.uiDialog.is(":data(ui-resizable)")&&this.uiDialog.resizable("option","minHeight",this._minHeight())},_blockFrames:function(){this.iframeBlocks=this.document.find("iframe").map(function(){var t=V(this);return V("

").css({position:"absolute",width:t.outerWidth(),height:t.outerHeight()}).appendTo(t.parent()).offset(t.offset())[0]})},_unblockFrames:function(){this.iframeBlocks&&(this.iframeBlocks.remove(),delete this.iframeBlocks)},_allowInteraction:function(t){return!!V(t.target).closest(".ui-dialog").length||!!V(t.target).closest(".ui-datepicker").length},_createOverlay:function(){var i,s;this.options.modal&&(i=V.fn.jquery.substring(0,4),s=!0,this._delay(function(){s=!1}),this.document.data("ui-dialog-overlays")||this.document.on("focusin.ui-dialog",function(t){var e;s||((e=this._trackingInstances()[0])._allowInteraction(t)||(t.preventDefault(),e._focusTabbable(),"3.4."!==i&&"3.5."!==i||e._delay(e._restoreTabbableFocus)))}.bind(this)),this.overlay=V("

").appendTo(this._appendTo()),this._addClass(this.overlay,null,"ui-widget-overlay ui-front"),this._on(this.overlay,{mousedown:"_keepFocus"}),this.document.data("ui-dialog-overlays",(this.document.data("ui-dialog-overlays")||0)+1))},_destroyOverlay:function(){var t;this.options.modal&&this.overlay&&((t=this.document.data("ui-dialog-overlays")-1)?this.document.data("ui-dialog-overlays",t):(this.document.off("focusin.ui-dialog"),this.document.removeData("ui-dialog-overlays")),this.overlay.remove(),this.overlay=null)}}),!1!==V.uiBackCompat&&V.widget("ui.dialog",V.ui.dialog,{options:{dialogClass:""},_createWrapper:function(){this._super(),this.uiDialog.addClass(this.options.dialogClass)},_setOption:function(t,e){"dialogClass"===t&&this.uiDialog.removeClass(this.options.dialogClass).addClass(e),this._superApply(arguments)}});V.ui.dialog;function lt(t,e,i){return e<=t&&t").appendTo(this.element),this._addClass(this.valueDiv,"ui-progressbar-value","ui-widget-header"),this._refreshValue()},_destroy:function(){this.element.removeAttr("role aria-valuemin aria-valuemax aria-valuenow"),this.valueDiv.remove()},value:function(t){if(void 0===t)return this.options.value;this.options.value=this._constrainedValue(t),this._refreshValue()},_constrainedValue:function(t){return void 0===t&&(t=this.options.value),this.indeterminate=!1===t,"number"!=typeof t&&(t=0),!this.indeterminate&&Math.min(this.options.max,Math.max(this.min,t))},_setOptions:function(t){var e=t.value;delete t.value,this._super(t),this.options.value=this._constrainedValue(e),this._refreshValue()},_setOption:function(t,e){"max"===t&&(e=Math.max(this.min,e)),this._super(t,e)},_setOptionDisabled:function(t){this._super(t),this.element.attr("aria-disabled",t),this._toggleClass(null,"ui-state-disabled",!!t)},_percentage:function(){return this.indeterminate?100:100*(this.options.value-this.min)/(this.options.max-this.min)},_refreshValue:function(){var t=this.options.value,e=this._percentage();this.valueDiv.toggle(this.indeterminate||t>this.min).width(e.toFixed(0)+"%"),this._toggleClass(this.valueDiv,"ui-progressbar-complete",null,t===this.options.max)._toggleClass("ui-progressbar-indeterminate",null,this.indeterminate),this.indeterminate?(this.element.removeAttr("aria-valuenow"),this.overlayDiv||(this.overlayDiv=V("

").appendTo(this.valueDiv),this._addClass(this.overlayDiv,"ui-progressbar-overlay"))):(this.element.attr({"aria-valuemax":this.options.max,"aria-valuenow":t}),this.overlayDiv&&(this.overlayDiv.remove(),this.overlayDiv=null)),this.oldValue!==t&&(this.oldValue=t,this._trigger("change")),t===this.options.max&&this._trigger("complete")}}),V.widget("ui.selectable",V.ui.mouse,{version:"1.13.2",options:{appendTo:"body",autoRefresh:!0,distance:0,filter:"*",tolerance:"touch",selected:null,selecting:null,start:null,stop:null,unselected:null,unselecting:null},_create:function(){var i=this;this._addClass("ui-selectable"),this.dragged=!1,this.refresh=function(){i.elementPos=V(i.element[0]).offset(),i.selectees=V(i.options.filter,i.element[0]),i._addClass(i.selectees,"ui-selectee"),i.selectees.each(function(){var t=V(this),e=t.offset(),e={left:e.left-i.elementPos.left,top:e.top-i.elementPos.top};V.data(this,"selectable-item",{element:this,$element:t,left:e.left,top:e.top,right:e.left+t.outerWidth(),bottom:e.top+t.outerHeight(),startselected:!1,selected:t.hasClass("ui-selected"),selecting:t.hasClass("ui-selecting"),unselecting:t.hasClass("ui-unselecting")})})},this.refresh(),this._mouseInit(),this.helper=V("

"),this._addClass(this.helper,"ui-selectable-helper")},_destroy:function(){this.selectees.removeData("selectable-item"),this._mouseDestroy()},_mouseStart:function(i){var s=this,t=this.options;this.opos=[i.pageX,i.pageY],this.elementPos=V(this.element[0]).offset(),this.options.disabled||(this.selectees=V(t.filter,this.element[0]),this._trigger("start",i),V(t.appendTo).append(this.helper),this.helper.css({left:i.pageX,top:i.pageY,width:0,height:0}),t.autoRefresh&&this.refresh(),this.selectees.filter(".ui-selected").each(function(){var t=V.data(this,"selectable-item");t.startselected=!0,i.metaKey||i.ctrlKey||(s._removeClass(t.$element,"ui-selected"),t.selected=!1,s._addClass(t.$element,"ui-unselecting"),t.unselecting=!0,s._trigger("unselecting",i,{unselecting:t.element}))}),V(i.target).parents().addBack().each(function(){var t,e=V.data(this,"selectable-item");if(e)return t=!i.metaKey&&!i.ctrlKey||!e.$element.hasClass("ui-selected"),s._removeClass(e.$element,t?"ui-unselecting":"ui-selected")._addClass(e.$element,t?"ui-selecting":"ui-unselecting"),e.unselecting=!t,e.selecting=t,(e.selected=t)?s._trigger("selecting",i,{selecting:e.element}):s._trigger("unselecting",i,{unselecting:e.element}),!1}))},_mouseDrag:function(s){if(this.dragged=!0,!this.options.disabled){var t,n=this,o=this.options,a=this.opos[0],r=this.opos[1],l=s.pageX,h=s.pageY;return ll||i.righth||i.bottoma&&i.rightr&&i.bottom",options:{appendTo:null,classes:{"ui-selectmenu-button-open":"ui-corner-top","ui-selectmenu-button-closed":"ui-corner-all"},disabled:null,icons:{button:"ui-icon-triangle-1-s"},position:{my:"left top",at:"left bottom",collision:"none"},width:!1,change:null,close:null,focus:null,open:null,select:null},_create:function(){var t=this.element.uniqueId().attr("id");this.ids={element:t,button:t+"-button",menu:t+"-menu"},this._drawButton(),this._drawMenu(),this._bindFormResetHandler(),this._rendered=!1,this.menuItems=V()},_drawButton:function(){var t,e=this,i=this._parseOption(this.element.find("option:selected"),this.element[0].selectedIndex);this.labels=this.element.labels().attr("for",this.ids.button),this._on(this.labels,{click:function(t){this.button.trigger("focus"),t.preventDefault()}}),this.element.hide(),this.button=V("",{tabindex:this.options.disabled?-1:0,id:this.ids.button,role:"combobox","aria-expanded":"false","aria-autocomplete":"list","aria-owns":this.ids.menu,"aria-haspopup":"true",title:this.element.attr("title")}).insertAfter(this.element),this._addClass(this.button,"ui-selectmenu-button ui-selectmenu-button-closed","ui-button ui-widget"),t=V("").appendTo(this.button),this._addClass(t,"ui-selectmenu-icon","ui-icon "+this.options.icons.button),this.buttonItem=this._renderButtonItem(i).appendTo(this.button),!1!==this.options.width&&this._resizeButton(),this._on(this.button,this._buttonEvents),this.button.one("focusin",function(){e._rendered||e._refreshMenu()})},_drawMenu:function(){var i=this;this.menu=V("

",{"aria-hidden":"true","aria-labelledby":this.ids.button,id:this.ids.menu}),this.menuWrap=V("

").append(this.menu),this._addClass(this.menuWrap,"ui-selectmenu-menu","ui-front"),this.menuWrap.appendTo(this._appendTo()),this.menuInstance=this.menu.menu({classes:{"ui-menu":"ui-corner-bottom"},role:"listbox",select:function(t,e){t.preventDefault(),i._setSelection(),i._select(e.item.data("ui-selectmenu-item"),t)},focus:function(t,e){e=e.item.data("ui-selectmenu-item");null!=i.focusIndex&&e.index!==i.focusIndex&&(i._trigger("focus",t,{item:e}),i.isOpen||i._select(e,t)),i.focusIndex=e.index,i.button.attr("aria-activedescendant",i.menuItems.eq(e.index).attr("id"))}}).menu("instance"),this.menuInstance._off(this.menu,"mouseleave"),this.menuInstance._closeOnDocumentClick=function(){return!1},this.menuInstance._isDivider=function(){return!1}},refresh:function(){this._refreshMenu(),this.buttonItem.replaceWith(this.buttonItem=this._renderButtonItem(this._getSelectedItem().data("ui-selectmenu-item")||{})),null===this.options.width&&this._resizeButton()},_refreshMenu:function(){var t=this.element.find("option");this.menu.empty(),this._parseOptions(t),this._renderMenu(this.menu,this.items),this.menuInstance.refresh(),this.menuItems=this.menu.find("li").not(".ui-selectmenu-optgroup").find(".ui-menu-item-wrapper"),this._rendered=!0,t.length&&(t=this._getSelectedItem(),this.menuInstance.focus(null,t),this._setAria(t.data("ui-selectmenu-item")),this._setOption("disabled",this.element.prop("disabled")))},open:function(t){this.options.disabled||(this._rendered?(this._removeClass(this.menu.find(".ui-state-active"),null,"ui-state-active"),this.menuInstance.focus(null,this._getSelectedItem())):this._refreshMenu(),this.menuItems.length&&(this.isOpen=!0,this._toggleAttr(),this._resizeMenu(),this._position(),this._on(this.document,this._documentClick),this._trigger("open",t)))},_position:function(){this.menuWrap.position(V.extend({of:this.button},this.options.position))},close:function(t){this.isOpen&&(this.isOpen=!1,this._toggleAttr(),this.range=null,this._off(this.document),this._trigger("close",t))},widget:function(){return this.button},menuWidget:function(){return this.menu},_renderButtonItem:function(t){var e=V("");return this._setText(e,t.label),this._addClass(e,"ui-selectmenu-text"),e},_renderMenu:function(s,t){var n=this,o="";V.each(t,function(t,e){var i;e.optgroup!==o&&(i=V("

",{text:e.optgroup}),n._addClass(i,"ui-selectmenu-optgroup","ui-menu-divider"+(e.element.parent("optgroup").prop("disabled")?" ui-state-disabled":"")),i.appendTo(s),o=e.optgroup),n._renderItemData(s,e)})},_renderItemData:function(t,e){return this._renderItem(t,e).data("ui-selectmenu-item",e)},_renderItem:function(t,e){var i=V("

"),s=V("

").attr("id",t).data("ui-tabs-destroy",!0)},_setOptionDisabled:function(t){var e,i;for(Array.isArray(t)&&(t.length?t.length===this.anchors.length&&(t=!0):t=!1),i=0;e=this.tabs[i];i++)e=V(e),!0===t||-1!==V.inArray(i,t)?(e.attr("aria-disabled","true"),this._addClass(e,null,"ui-state-disabled")):(e.removeAttr("aria-disabled"),this._removeClass(e,null,"ui-state-disabled"));this.options.disabled=t,this._toggleClass(this.widget(),this.widgetFullName+"-disabled",null,!0===t)},_setupEvents:function(t){var i={};t&&V.each(t.split(" "),function(t,e){i[e]="_eventHandler"}),this._off(this.anchors.add(this.tabs).add(this.panels)),this._on(!0,this.anchors,{click:function(t){t.preventDefault()}}),this._on(this.anchors,i),this._on(this.tabs,{keydown:"_tabKeydown"}),this._on(this.panels,{keydown:"_panelKeydown"}),this._focusable(this.tabs),this._hoverable(this.tabs)},_setupHeightStyle:function(t){var i,e=this.element.parent();"fill"===t?(i=e.height(),i-=this.element.outerHeight()-this.element.height(),this.element.siblings(":visible").each(function(){var t=V(this),e=t.css("position");"absolute"!==e&&"fixed"!==e&&(i-=t.outerHeight(!0))}),this.element.children().not(this.panels).each(function(){i-=V(this).outerHeight(!0)}),this.panels.each(function(){V(this).height(Math.max(0,i-V(this).innerHeight()+V(this).height()))}).css("overflow","auto")):"auto"===t&&(i=0,this.panels.each(function(){i=Math.max(i,V(this).height("").height())}).height(i))},_eventHandler:function(t){var e=this.options,i=this.active,s=V(t.currentTarget).closest("li"),n=s[0]===i[0],o=n&&e.collapsible,a=o?V():this._getPanelForTab(s),r=i.length?this._getPanelForTab(i):V(),i={oldTab:i,oldPanel:r,newTab:o?V():s,newPanel:a};t.preventDefault(),s.hasClass("ui-state-disabled")||s.hasClass("ui-tabs-loading")||this.running||n&&!e.collapsible||!1===this._trigger("beforeActivate",t,i)||(e.active=!o&&this.tabs.index(s),this.active=n?V():s,this.xhr&&this.xhr.abort(),r.length||a.length||V.error("jQuery UI Tabs: Mismatching fragment identifier."),a.length&&this.load(this.tabs.index(s),t),this._toggle(t,i))},_toggle:function(t,e){var i=this,s=e.newPanel,n=e.oldPanel;function o(){i.running=!1,i._trigger("activate",t,e)}function a(){i._addClass(e.newTab.closest("li"),"ui-tabs-active","ui-state-active"),s.length&&i.options.show?i._show(s,i.options.show,o):(s.show(),o())}this.running=!0,n.length&&this.options.hide?this._hide(n,this.options.hide,function(){i._removeClass(e.oldTab.closest("li"),"ui-tabs-active","ui-state-active"),a()}):(this._removeClass(e.oldTab.closest("li"),"ui-tabs-active","ui-state-active"),n.hide(),a()),n.attr("aria-hidden","true"),e.oldTab.attr({"aria-selected":"false","aria-expanded":"false"}),s.length&&n.length?e.oldTab.attr("tabIndex",-1):s.length&&this.tabs.filter(function(){return 0===V(this).attr("tabIndex")}).attr("tabIndex",-1),s.attr("aria-hidden","false"),e.newTab.attr({"aria-selected":"true","aria-expanded":"true",tabIndex:0})},_activate:function(t){var t=this._findActive(t);t[0]!==this.active[0]&&(t=(t=!t.length?this.active:t).find(".ui-tabs-anchor")[0],this._eventHandler({target:t,currentTarget:t,preventDefault:V.noop}))},_findActive:function(t){return!1===t?V():this.tabs.eq(t)},_getIndex:function(t){return t="string"==typeof t?this.anchors.index(this.anchors.filter("[href$='"+V.escapeSelector(t)+"']")):t},_destroy:function(){this.xhr&&this.xhr.abort(),this.tablist.removeAttr("role").off(this.eventNamespace),this.anchors.removeAttr("role tabIndex").removeUniqueId(),this.tabs.add(this.panels).each(function(){V.data(this,"ui-tabs-destroy")?V(this).remove():V(this).removeAttr("role tabIndex aria-live aria-busy aria-selected aria-labelledby aria-hidden aria-expanded")}),this.tabs.each(function(){var t=V(this),e=t.data("ui-tabs-aria-controls");e?t.attr("aria-controls",e).removeData("ui-tabs-aria-controls"):t.removeAttr("aria-controls")}),this.panels.show(),"content"!==this.options.heightStyle&&this.panels.css("height","")},enable:function(i){var t=this.options.disabled;!1!==t&&(t=void 0!==i&&(i=this._getIndex(i),Array.isArray(t)?V.map(t,function(t){return t!==i?t:null}):V.map(this.tabs,function(t,e){return e!==i?e:null})),this._setOptionDisabled(t))},disable:function(t){var e=this.options.disabled;if(!0!==e){if(void 0===t)e=!0;else{if(t=this._getIndex(t),-1!==V.inArray(t,e))return;e=Array.isArray(e)?V.merge([t],e).sort():[t]}this._setOptionDisabled(e)}},load:function(t,s){t=this._getIndex(t);function n(t,e){"abort"===e&&o.panels.stop(!1,!0),o._removeClass(i,"ui-tabs-loading"),a.removeAttr("aria-busy"),t===o.xhr&&delete o.xhr}var o=this,i=this.tabs.eq(t),t=i.find(".ui-tabs-anchor"),a=this._getPanelForTab(i),r={tab:i,panel:a};this._isLocal(t[0])||(this.xhr=V.ajax(this._ajaxSettings(t,s,r)),this.xhr&&"canceled"!==this.xhr.statusText&&(this._addClass(i,"ui-tabs-loading"),a.attr("aria-busy","true"),this.xhr.done(function(t,e,i){setTimeout(function(){a.html(t),o._trigger("load",s,r),n(i,e)},1)}).fail(function(t,e){setTimeout(function(){n(t,e)},1)})))},_ajaxSettings:function(t,i,s){var n=this;return{url:t.attr("href").replace(/#.*$/,""),beforeSend:function(t,e){return n._trigger("beforeLoad",i,V.extend({jqXHR:t,ajaxSettings:e},s))}}},_getPanelForTab:function(t){t=V(t).attr("aria-controls");return this.element.find(this._sanitizeSelector("#"+t))}}),!1!==V.uiBackCompat&&V.widget("ui.tabs",V.ui.tabs,{_processTabs:function(){this._superApply(arguments),this._addClass(this.tabs,"ui-tab")}});V.ui.tabs;V.widget("ui.tooltip",{version:"1.13.2",options:{classes:{"ui-tooltip":"ui-corner-all ui-widget-shadow"},content:function(){var t=V(this).attr("title");return V("").text(t).html()},hide:!0,items:"[title]:not([disabled])",position:{my:"left top+15",at:"left bottom",collision:"flipfit flip"},show:!0,track:!1,close:null,open:null},_addDescribedBy:function(t,e){var i=(t.attr("aria-describedby")||"").split(/\s+/);i.push(e),t.data("ui-tooltip-id",e).attr("aria-describedby",String.prototype.trim.call(i.join(" ")))},_removeDescribedBy:function(t){var e=t.data("ui-tooltip-id"),i=(t.attr("aria-describedby")||"").split(/\s+/),e=V.inArray(e,i);-1!==e&&i.splice(e,1),t.removeData("ui-tooltip-id"),(i=String.prototype.trim.call(i.join(" ")))?t.attr("aria-describedby",i):t.removeAttr("aria-describedby")},_create:function(){this._on({mouseover:"open",focusin:"open"}),this.tooltips={},this.parents={},this.liveRegion=V("

").attr({role:"log","aria-live":"assertive","aria-relevant":"additions"}).appendTo(this.document[0].body),this._addClass(this.liveRegion,null,"ui-helper-hidden-accessible"),this.disabledTitles=V([])},_setOption:function(t,e){var i=this;this._super(t,e),"content"===t&&V.each(this.tooltips,function(t,e){i._updateContent(e.element)})},_setOptionDisabled:function(t){this[t?"_disable":"_enable"]()},_disable:function(){var s=this;V.each(this.tooltips,function(t,e){var i=V.Event("blur");i.target=i.currentTarget=e.element[0],s.close(i,!0)}),this.disabledTitles=this.disabledTitles.add(this.element.find(this.options.items).addBack().filter(function(){var t=V(this);if(t.is("[title]"))return t.data("ui-tooltip-title",t.attr("title")).removeAttr("title")}))},_enable:function(){this.disabledTitles.each(function(){var t=V(this);t.data("ui-tooltip-title")&&t.attr("title",t.data("ui-tooltip-title"))}),this.disabledTitles=V([])},open:function(t){var i=this,e=V(t?t.target:this.element).closest(this.options.items);e.length&&!e.data("ui-tooltip-id")&&(e.attr("title")&&e.data("ui-tooltip-title",e.attr("title")),e.data("ui-tooltip-open",!0),t&&"mouseover"===t.type&&e.parents().each(function(){var t,e=V(this);e.data("ui-tooltip-open")&&((t=V.Event("blur")).target=t.currentTarget=this,i.close(t,!0)),e.attr("title")&&(e.uniqueId(),i.parents[this.id]={element:this,title:e.attr("title")},e.attr("title",""))}),this._registerCloseHandlers(t,e),this._updateContent(e,t))},_updateContent:function(e,i){var t=this.options.content,s=this,n=i?i.type:null;if("string"==typeof t||t.nodeType||t.jquery)return this._open(i,e,t);(t=t.call(e[0],function(t){s._delay(function(){e.data("ui-tooltip-open")&&(i&&(i.type=n),this._open(i,e,t))})}))&&this._open(i,e,t)},_open:function(t,e,i){var s,n,o,a=V.extend({},this.options.position);function r(t){a.of=t,n.is(":hidden")||n.position(a)}i&&((s=this._find(e))?s.tooltip.find(".ui-tooltip-content").html(i):(e.is("[title]")&&(t&&"mouseover"===t.type?e.attr("title",""):e.removeAttr("title")),s=this._tooltip(e),n=s.tooltip,this._addDescribedBy(e,n.attr("id")),n.find(".ui-tooltip-content").html(i),this.liveRegion.children().hide(),(i=V("

").html(n.find(".ui-tooltip-content").html())).removeAttr("name").find("[name]").removeAttr("name"),i.removeAttr("id").find("[id]").removeAttr("id"),i.appendTo(this.liveRegion),this.options.track&&t&&/^mouse/.test(t.type)?(this._on(this.document,{mousemove:r}),r(t)):n.position(V.extend({of:e},this.options.position)),n.hide(),this._show(n,this.options.show),this.options.track&&this.options.show&&this.options.show.delay&&(o=this.delayedShow=setInterval(function(){n.is(":visible")&&(r(a.of),clearInterval(o))},13)),this._trigger("open",t,{tooltip:n})))},_registerCloseHandlers:function(t,e){var i={keyup:function(t){t.keyCode===V.ui.keyCode.ESCAPE&&((t=V.Event(t)).currentTarget=e[0],this.close(t,!0))}};e[0]!==this.element[0]&&(i.remove=function(){var t=this._find(e);t&&this._removeTooltip(t.tooltip)}),t&&"mouseover"!==t.type||(i.mouseleave="close"),t&&"focusin"!==t.type||(i.focusout="close"),this._on(!0,e,i)},close:function(t){var e,i=this,s=V(t?t.currentTarget:this.element),n=this._find(s);n?(e=n.tooltip,n.closing||(clearInterval(this.delayedShow),s.data("ui-tooltip-title")&&!s.attr("title")&&s.attr("title",s.data("ui-tooltip-title")),this._removeDescribedBy(s),n.hiding=!0,e.stop(!0),this._hide(e,this.options.hide,function(){i._removeTooltip(V(this))}),s.removeData("ui-tooltip-open"),this._off(s,"mouseleave focusout keyup"),s[0]!==this.element[0]&&this._off(s,"remove"),this._off(this.document,"mousemove"),t&&"mouseleave"===t.type&&V.each(this.parents,function(t,e){V(e.element).attr("title",e.title),delete i.parents[t]}),n.closing=!0,this._trigger("close",t,{tooltip:e}),n.hiding||(n.closing=!1))):s.removeData("ui-tooltip-open")},_tooltip:function(t){var e=V("

").attr("role","tooltip"),i=V("

").appendTo(e),s=e.uniqueId().attr("id");return this._addClass(i,"ui-tooltip-content"),this._addClass(e,"ui-tooltip","ui-widget ui-widget-content"),e.appendTo(this._appendTo(t)),this.tooltips[s]={element:t,tooltip:e}},_find:function(t){t=t.data("ui-tooltip-id");return t?this.tooltips[t]:null},_removeTooltip:function(t){clearInterval(this.delayedShow),t.remove(),delete this.tooltips[t.attr("id")]},_appendTo:function(t){t=t.closest(".ui-front, dialog");return t=!t.length?this.document[0].body:t},_destroy:function(){var s=this;V.each(this.tooltips,function(t,e){var i=V.Event("blur"),e=e.element;i.target=i.currentTarget=e[0],s.close(i,!0),V("#"+t).remove(),e.data("ui-tooltip-title")&&(e.attr("title")||e.attr("title",e.data("ui-tooltip-title")),e.removeData("ui-tooltip-title"))}),this.liveRegion.remove()}}),!1!==V.uiBackCompat&&V.widget("ui.tooltip",V.ui.tooltip,{options:{tooltipClass:null},_tooltip:function(){var t=this._superApply(arguments);return this.options.tooltipClass&&t.tooltip.addClass(this.options.tooltipClass),t}});V.ui.tooltip});

Testing hierarchical pathway kinetics with +residue data on cyantraniliprole

Johannes Ranke

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

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

Pathway 2, refined fits

Session info

Hardware info

Testing hierarchical parent degradation +kinetics with residue data on dimethenamid and dimethenamid-P

Johannes Ranke

Last change on 5 January 2023, last compiled on 13 +Februar 2025

Introduction

Data

Separate evaluations

Hierarchichal model fits

Parameter identifiability based on the Fisher Information +Matrix

Alternative check of parameter identifiability

Conclusions

Acknowledgements

References

Appendix

Hierarchical model fit listings

Hierarchical model convergence plots

Session info

Hardware info

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

Johannes Ranke

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

Introduction

Data

Separate evaluations

Hierarchichal model fits

Parameter identifiability based on the Fisher Information +Matrix

Alternative check of parameter identifiability

Plots of selected fits

Conclusions

Acknowledgements

References

Appendix

Plots of hierarchical fits not selected for refinement

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

Hardware info

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

Johannes Ranke

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

Introduction

Test data

Separate evaluations

Hierarchical model fits without covariate effect

Hierarchical model fits with covariate effect

SFO

FOMC

DFOP

SFORB

HS

Comparison across parent models

Conclusions

Appendix

Hierarchical fit listings

Fits without covariate effects

Fits with covariate effects

Session info

Hardware info