Benchmark timings for saem.mmkin

+ + + + +

Each system is characterized by operating system type, CPU type, mkin version, saemix version and R version. A compiler was available, so if no analytical solution was available, compiled ODE models are used.

Every fit is only performed once, so the accuracy of the benchmarks is limited.

For the initial mmkin fits, we use all available cores.

+n_cores <- parallel::detectCores()

Test data +

Please refer to the vignette dimethenamid_2018 for an explanation of the following preprocessing.

+dmta_ds <- lapply(1:7, function(i) {
+  ds_i <- dimethenamid_2018$ds[[i]]$data
+  ds_i[ds_i$name == "DMTAP", "name"] <-  "DMTA"
+  ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i]
+  ds_i
+})
+names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title)
+dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])
+dmta_ds[["Elliot 1"]] <- NULL
+dmta_ds[["Elliot 2"]] <- NULL

Test cases +

Parent only +

+parent_mods <- c("SFO", "DFOP", "SFORB", "HS")
+parent_sep_const <- mmkin(parent_mods, dmta_ds, quiet = TRUE, cores = n_cores)
+parent_sep_tc <- update(parent_sep_const, error_model = "tc")
+
+t1 <- system.time(sfo_const <- saem(parent_sep_const["SFO", ]))[["elapsed"]]
+t2 <- system.time(dfop_const <- saem(parent_sep_const["DFOP", ]))[["elapsed"]]
+t3 <- system.time(sforb_const <- saem(parent_sep_const["SFORB", ]))[["elapsed"]]
+t4 <- system.time(hs_const <- saem(parent_sep_const["HS", ]))[["elapsed"]]
+t5 <- system.time(sfo_tc <- saem(parent_sep_tc["SFO", ]))[["elapsed"]]
+t6 <- system.time(dfop_tc <- saem(parent_sep_tc["DFOP", ]))[["elapsed"]]
+t7 <- system.time(sforb_tc <- saem(parent_sep_tc["SFORB", ]))[["elapsed"]]
+t8 <- system.time(hs_tc <- saem(parent_sep_tc["HS", ]))[["elapsed"]]

+anova(
+  sfo_const, dfop_const, sforb_const, hs_const,
+  sfo_tc, dfop_tc, sforb_tc, hs_tc) |> 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
dfop_const	9	709.4	707.5	-345.7
sforb_const	9	710.0	708.1	-346.0
hs_const	9	713.7	711.8	-347.8
dfop_tc	10	669.8	667.7	-324.9
sforb_tc	10	662.8	660.7	-321.4
hs_tc	10	667.3	665.2	-323.6

The above model comparison suggests to use the SFORB model with two-component error. For comparison, we keep the DFOP model with two-component error, as it competes with SFORB for biphasic curves.

+illparms(dfop_tc)

## [1] "sd(log_k2)"

+illparms(sforb_tc)

## [1] "sd(log_k_DMTA_bound_free)"

For these two models, random effects for the transformed parameters k2 and k_DMTA_bound_free could not be quantified.

One metabolite +

We remove parameters that were found to be ill-defined in the parent only fits.

+one_met_mods <- list(
+  DFOP_SFO = mkinmod(
+    DMTA = mkinsub("DFOP", "M23"),
+    M23 = mkinsub("SFO")),
+  SFORB_SFO = mkinmod(
+    DMTA = mkinsub("SFORB", "M23"),
+    M23 = mkinsub("SFO")))
+
+one_met_sep_const <- mmkin(one_met_mods, dmta_ds, error_model = "const",
+  cores = n_cores, quiet = TRUE)
+one_met_sep_tc <- mmkin(one_met_mods, dmta_ds, error_model = "tc",
+  cores = n_cores, quiet = TRUE)
+
+t9 <- system.time(dfop_sfo_tc <- saem(one_met_sep_tc["DFOP_SFO", ],
+    no_random_effect = "log_k2"))[["elapsed"]]
+t10 <- system.time(sforb_sfo_tc <- saem(one_met_sep_tc["SFORB_SFO", ],
+    no_random_effect = "log_k_DMTA_bound_free"))[["elapsed"]]

Three metabolites +

For the case of three metabolites, we only keep the SFORB model in order to limit the time for compiling this vignette, and as fitting in parallel may disturb the benchmark. Again, we do not include random effects that were ill-defined in previous fits of subsets of the degradation model.

+illparms(sforb_sfo_tc)

+three_met_mods <- list(
+  SFORB_SFO3_plus = mkinmod(
+    DMTA = mkinsub("SFORB", c("M23", "M27", "M31")),
+    M23 = mkinsub("SFO"),
+    M27 = mkinsub("SFO"),
+    M31 = mkinsub("SFO", "M27", sink = FALSE)))
+
+three_met_sep_tc <- mmkin(three_met_mods, dmta_ds, error_model = "tc",
+  cores = n_cores, quiet = TRUE)
+
+t11 <- system.time(sforb_sfo3_plus_const <- saem(three_met_sep_tc["SFORB_SFO3_plus", ],
+    no_random_effect = "log_k_DMTA_bound_free"))[["elapsed"]]

Results +

Benchmarks for all available error models are shown. They are intended for improving mkin, not for comparing CPUs or operating systems. All trademarks belong to their respective owners.

Parent only +

Constant variance for SFO, DFOP, SFORB and HS.

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

CPU	OS	mkin	saemix	t1	t2	t3	t4
Ryzen 7 1700	Linux	1.2.0	3.2	2.589	4.945	4.786	4.484

Two-component error fits for SFO, DFOP, SFORB and HS.

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

CPU	OS	mkin	saemix	t5	t6	t7	t8
Ryzen 7 1700	Linux	1.2.0	3.2	5.645	8.115	7.737	7.782

One metabolite +

Two-component error for DFOP-SFO and SFORB-SFO.

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

CPU	OS	mkin	saemix	t9	t10
Ryzen 7 1700	Linux	1.2.0	3.2	25.921	766.034

Three metabolites +

Two-component error for SFORB-SFO3-plus

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

CPU	OS	mkin	saemix	t11
Ryzen 7 1700	Linux	1.2.0	3.2	1269.799

+ + + +

Details

@@ -158,8 +160,8 @@ HS and DFOP, as well as from Eigenvalues b1 and b2 of any SFORB models

#> 1 #> #> $SFORB -#> parent_b1 parent_b2 -#> 0.4595574 0.0178488 +#> parent_b1 parent_b2 parent_g +#> 0.4595574 0.0178488 0.8539454 #> #> $distimes #> DT50 DT90 DT50back DT50_parent_b1 DT50_parent_b2 diff --git a/docs/dev/reference/logistic.solution-1.png b/docs/dev/reference/logistic.solution-1.png index 84d8e722..73dad0a4 100644 Binary files a/docs/dev/reference/logistic.solution-1.png and b/docs/dev/reference/logistic.solution-1.png differ diff --git a/docs/dev/reference/logistic.solution-2.png b/docs/dev/reference/logistic.solution-2.png index 73e6436d..8d2514a3 100644 Binary files a/docs/dev/reference/logistic.solution-2.png and b/docs/dev/reference/logistic.solution-2.png differ diff --git a/docs/dev/reference/logistic.solution.html b/docs/dev/reference/logistic.solution.html index ab68c99e..1d1880fd 100644 --- a/docs/dev/reference/logistic.solution.html +++ b/docs/dev/reference/logistic.solution.html @@ -1,68 +1,13 @@ - - - - - - - -Logistic kinetics — logistic.solution • mkin - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Logistic kinetics — logistic.solution • mkin - + + - - - -

- -

@@ -149,136 +91,143 @@ an increasing rate constant, supposedly caused by microbial growth" /> an increasing rate constant, supposedly caused by microbial growth

logistic.solution(t, parent_0, kmax, k0, r)

logistic.solution(t, parent_0, kmax, k0, r)

Arguments

- - - - - - - - - - - - - - - - - - - - - - -

t	Time.
parent_0	Starting value for the response variable at time zero.
kmax	Maximum rate constant.
k0	Minimum rate constant effective at time zero.
r	Growth rate of the increase in the rate constant.

Arguments

t: Time.
parent_0: Starting value for the response variable at time zero.
kmax: Maximum rate constant.
k0: Minimum rate constant effective at time zero.
r: Growth rate of the increase in the rate constant.

Value

+ + +

The value of the response variable at time t.

Note

The solution of the logistic model reduces to the +SFO.solution if k0 is equal to kmax.

References

FOCUS (2006) “Guidance Document on Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in -EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, +EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, EC Document Reference Sanco/10058/2005 version 2.0, 434 pp, -http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics -FOCUS (2014) “Generic guidance for Estimating Persistence +http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics +FOCUS (2014) “Generic guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in -EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, +EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, Version 1.1, 18 December 2014 -http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics

Examples


-  # Reproduce the plot on page 57 of FOCUS (2014)
-  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2),
-       from = 0, to = 100, ylim = c(0, 100),
-       xlab = "Time", ylab = "Residue")
-
  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4),
-       from = 0, to = 100, add = TRUE, lty = 2, col = 2)
-
  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8),
-       from = 0, to = 100, add = TRUE, lty = 3, col = 3)
-
  plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2),
-       from = 0, to = 100, add = TRUE, lty = 4, col = 4)
-
  plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2),
-       from = 0, to = 100, add = TRUE, lty = 5, col = 5)
-
  legend("topright", inset = 0.05,
-         legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08),
-                         ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)),
-         lty = 1:5, col = 1:5)
-

-  # Fit with synthetic data
-  logistic <- mkinmod(parent = mkinsub("logistic"))
-
-  sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-  parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2)
-  d_logistic <- mkinpredict(logistic,
-    parms_logistic, c(parent = 100),
-    sampling_times)
-  d_2_1 <- add_err(d_logistic,
-    sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07),
-    n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]]
+http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics
+    
+    
+    See also
+    Other parent solutions: 
+DFOP.solution(),
+FOMC.solution(),
+HS.solution(),
+IORE.solution(),
+SFO.solution(),
+SFORB.solution()
+    
 
-  m <- mkinfit("logistic", d_2_1, quiet = TRUE)
-  plot_sep(m)
-

summary(m)$bpar -

#> Estimate se_notrans t value Pr(>t) Lower -#> parent_0 1.057896e+02 1.9023449590 55.610120 3.768360e-16 1.016451e+02 -#> kmax 6.398190e-02 0.0143201029 4.467978 3.841828e-04 3.929235e-02 -#> k0 1.612775e-04 0.0005866813 0.274898 3.940351e-01 5.846688e-08 -#> r 2.263946e-01 0.1718110662 1.317695 1.061043e-01 4.335843e-02 -#> sigma 5.332935e+00 0.9145907310 5.830952 4.036926e-05 3.340213e+00 -#> Upper -#> parent_0 109.9341588 -#> kmax 0.1041853 -#> k0 0.4448749 -#> r 1.1821120 -#> sigma 7.3256566

endpoints(m)$distimes -

#> DT50 DT90 DT50_k0 DT50_kmax -#> parent 36.86533 62.41511 4297.853 10.83349

Examples


+  # Reproduce the plot on page 57 of FOCUS (2014)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2),
+       from = 0, to = 100, ylim = c(0, 100),
+       xlab = "Time", ylab = "Residue")
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4),
+       from = 0, to = 100, add = TRUE, lty = 2, col = 2)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8),
+       from = 0, to = 100, add = TRUE, lty = 3, col = 3)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 4, col = 4)
+  plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2),
+       from = 0, to = 100, add = TRUE, lty = 5, col = 5)
+  legend("topright", inset = 0.05,
+         legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08),
+                         ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)),
+         lty = 1:5, col = 1:5)
+
+
+  # Fit with synthetic data
+  logistic <- mkinmod(parent = mkinsub("logistic"))
+
+  sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+  parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2)
+  d_logistic <- mkinpredict(logistic,
+    parms_logistic, c(parent = 100),
+    sampling_times)
+  d_2_1 <- add_err(d_logistic,
+    sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07),
+    n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]]
+
+  m <- mkinfit("logistic", d_2_1, quiet = TRUE)
+  plot_sep(m)
+
+  summary(m)$bpar
+#>              Estimate   se_notrans   t value       Pr(>t)        Lower
+#> parent_0 1.057896e+02 1.9023449590 55.610120 3.768360e-16 1.016451e+02
+#> kmax     6.398190e-02 0.0143201029  4.467978 3.841828e-04 3.929235e-02
+#> k0       1.612775e-04 0.0005866813  0.274898 3.940351e-01 5.846688e-08
+#> r        2.263946e-01 0.1718110662  1.317695 1.061043e-01 4.335843e-02
+#> sigma    5.332935e+00 0.9145907310  5.830952 4.036926e-05 3.340213e+00
+#>                Upper
+#> parent_0 109.9341588
+#> kmax       0.1041853
+#> k0         0.4448749
+#> r          1.1821120
+#> sigma      7.3256566
+  endpoints(m)$distimes
+#>            DT50     DT90  DT50_k0 DT50_kmax
+#> parent 36.86533 62.41511 4297.853  10.83349
+
+

mhmkin(objects, backend = "saemix", algorithm = "saem", ...)
+    mhmkin(objects, ...)
 
 # S3 method for mmkin
 mhmkin(objects, ...)
@@ -108,6 +108,9 @@ mhmkin(objects, ...)
 mhmkin(
   objects,
   backend = "saemix",
+  algorithm = "saem",
+  no_random_effect = NULL,
+  auto_ranef_threshold = 3,
   ...,
   cores = if (Sys.info()["sysname"] == "Windows") 1 else parallel::detectCores(),
   cluster = NULL
@@ -129,6 +132,11 @@ Alternatively, a single mmkin object containing fits of
 degradation models to the same data
 
 
+...
+Further arguments that will be passed to the nonlinear mixed-effects
+model fitting function.
+
+
 backend
 The backend to be used for fitting. Currently, only saemix is
 supported
@@ -138,9 +146,17 @@ supported
 The algorithm to be used for fitting (currently not used)
 
 
-...
-Further arguments that will be passed to the nonlinear mixed-effects
-model fitting function.
+no_random_effect
+Default is NULL and will be passed to saem. If
+you specify "auto", random effects are only included if the number
+of datasets in which the parameter passed the t-test is at least 'auto_ranef_threshold'.
+Beware that while this may make for convenient model reduction or even
+numerical stability of the algorithm, it will likely lead to
+underparameterised models.
+
+
+auto_ranef_threshold
+See 'no_random_effect.
 
 
 cores
diff --git a/docs/dev/reference/mkinpredict.html b/docs/dev/reference/mkinpredict.html
index 1ebaecb5..14f2b75b 100644
--- a/docs/dev/reference/mkinpredict.html
+++ b/docs/dev/reference/mkinpredict.html
@@ -1,69 +1,14 @@
-
 
-
-  
-  
-
-
-
-Produce predictions from a kinetic model using specific parameters — mkinpredict • mkin
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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-
-Produce predictions from a kinetic model using specific parameters — mkinpredict • mkin
-
-
-
-
-
-
-
-
-
-
-
+
+    
 
-  
-
-  
     
-      
-      
+      
   
     
       
       
         mkin
-        1.0.3.9000
+        1.2.0
       
     
 
     
-      
-        
+      
   Functions and data
 
 
-  
+  
     Articles
      
     
   
-  
-    
+  
       Introduction to mkin
     
     
@@ -100,11 +43,17 @@ kinetic parameters and initial values for the state variables." />
       Example evaluation of FOCUS Laboratory Data L1 to L3
     
     
-      Example evaluation of FOCUS Example Dataset Z
+      Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models
+    
+    
+      Short demo of the multistart method
     
     
       Performance benefit by using compiled model definitions in mkin
     
+    
+      Example evaluation of FOCUS Example Dataset Z
+    
     
       Calculation of time weighted average concentrations with mkin
     
@@ -114,343 +63,358 @@ kinetic parameters and initial values for the state variables." />
     
       Some benchmark timings
     
-  
-
+  
 
   News
 
-      
-      
-        
-  
+      

+  
     
      
   
 
-      
-      
-    

+      

   

 

 
       
 
-      
-
-
+      
   
     
     Produce predictions from a kinetic model using specific parameters
-    Source: R/mkinpredict.R
+    Source: R/mkinpredict.R
     mkinpredict.Rd
     
 
     
     This function produces a time series for all the observed variables in a
-kinetic model as specified by mkinmod, using a specific set of
+kinetic model as specified by mkinmod, using a specific set of
 kinetic parameters and initial values for the state variables.
     
 
-    mkinpredict(x, odeparms, odeini, outtimes, ...)
-
-# S3 method for mkinmod
-mkinpredict(
-  x,
-  odeparms = c(k_parent_sink = 0.1),
-  odeini = c(parent = 100),
-  outtimes = seq(0, 120, by = 0.1),
-  solution_type = "deSolve",
-  use_compiled = "auto",
-  method.ode = "lsoda",
-  atol = 1e-08,
-  rtol = 1e-10,
-  map_output = TRUE,
-  na_stop = TRUE,
-  ...
-)
-
-# S3 method for mkinfit
-mkinpredict(
-  x,
-  odeparms = x$bparms.ode,
-  odeini = x$bparms.state,
-  outtimes = seq(0, 120, by = 0.1),
-  solution_type = "deSolve",
-  use_compiled = "auto",
-  method.ode = "lsoda",
-  atol = 1e-08,
-  rtol = 1e-10,
-  map_output = TRUE,
-  ...
-)
-
-    Arguments
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    x A kinetic model as produced by mkinmod, or a kinetic
-fit as fitted by mkinfit. In the latter case, the fitted
-parameters are used for the prediction.
odeparms A numeric vector specifying the parameters used in the
-kinetic model, which is generally defined as a set of ordinary
-differential equations.
odeini A numeric vector containing the initial values of the state
+    

+    mkinpredict(x, odeparms, odeini, outtimes, ...)
+
+# S3 method for mkinmod
+mkinpredict(
+  x,
+  odeparms = c(k_parent_sink = 0.1),
+  odeini = c(parent = 100),
+  outtimes = seq(0, 120, by = 0.1),
+  solution_type = "deSolve",
+  use_compiled = "auto",
+  method.ode = "lsoda",
+  atol = 1e-08,
+  rtol = 1e-10,
+  maxsteps = 20000,
+  map_output = TRUE,
+  na_stop = TRUE,
+  ...
+)
+
+# S3 method for mkinfit
+mkinpredict(
+  x,
+  odeparms = x$bparms.ode,
+  odeini = x$bparms.state,
+  outtimes = seq(0, 120, by = 0.1),
+  solution_type = "deSolve",
+  use_compiled = "auto",
+  method.ode = "lsoda",
+  atol = 1e-08,
+  rtol = 1e-10,
+  map_output = TRUE,
+  ...
+)
+    
+
+    
+    Arguments
+    x
+A kinetic model as produced by mkinmod, or a kinetic fit as
+fitted by mkinfit. In the latter case, the fitted parameters are used for
+the prediction.
+
+
+odeparms
+A numeric vector specifying the parameters used in the
+kinetic model, which is generally defined as a set of ordinary differential
+equations.
+
+
+odeini
+A numeric vector containing the initial values of the state
 variables of the model. Note that the state variables can differ from the
-observed variables, for example in the case of the SFORB model.
outtimes A numeric vector specifying the time points for which model
-predictions should be generated.
... Further arguments passed to the ode solver in case such a
-solver is used.
solution_type The method that should be used for producing the
+observed variables, for example in the case of the SFORB model.
+
+
+outtimes
+A numeric vector specifying the time points for which model
+predictions should be generated.
+
+
+...
+Further arguments passed to the ode solver in case such a
+solver is used.
+
+
+solution_type
+The method that should be used for producing the
 predictions. This should generally be "analytical" if there is only one
 observed variable, and usually "deSolve" in the case of several observed
 variables. The third possibility "eigen" is faster but not applicable to
-some models e.g.  using FOMC for the parent compound.
use_compiled If set to FALSE, no compiled version of the
-mkinmod model is used, even if is present.
method.ode The solution method passed via mkinpredict
-to ode in case the solution type is "deSolve". The default
-"lsoda" is performant, but sometimes fails to converge.
atol Absolute error tolerance, passed to ode. Default
-is 1e-8, lower than in lsoda.
rtol Absolute error tolerance, passed to ode. Default
-is 1e-10, much lower than in lsoda.
map_output Boolean to specify if the output should list values for
+some models e.g.  using FOMC for the parent compound.
+
+
+use_compiled
+If set to FALSE, no compiled version of the
+mkinmod model is used, even if is present.
+
+
+method.ode
+The solution method passed via mkinpredict to ode] in
+case the solution type is "deSolve". The default "lsoda" is performant, but
+sometimes fails to converge.
+
+
+atol
+Absolute error tolerance, passed to ode. Default is 1e-8,
+lower than in lsoda.
+
+
+rtol
+Absolute error tolerance, passed to ode. Default is 1e-10,
+much lower than in lsoda.
+
+
+maxsteps
+Maximum number of steps, passed to ode.
+
+
+map_output
+Boolean to specify if the output should list values for
 the observed variables (default) or for all state variables (if set to
 FALSE). Setting this to FALSE has no effect for analytical solutions,
-as these always return mapped output.
na_stop Should it be an error if deSolve::ode returns NaN values
+as these always return mapped output.
+
 
-    Value
+na_stop
+Should it be an error if ode returns NaN values
 
-    A matrix with the numeric solution in wide format
-    Author
+
+    
+    Value
+    
 
+A matrix with the numeric solution in wide format
+    
+    
+    Author
     Johannes Ranke
+    
 
-    Examples
-    
-SFO <- mkinmod(degradinol = mkinsub("SFO"))
-# Compare solution types
-mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      solution_type = "analytical")
-
#>    time  degradinol
-#> 0     0 100.0000000
-#> 1     1  74.0818221
-#> 2     2  54.8811636
-#> 3     3  40.6569660
-#> 4     4  30.1194212
-#> 5     5  22.3130160
-#> 6     6  16.5298888
-#> 7     7  12.2456428
-#> 8     8   9.0717953
-#> 9     9   6.7205513
-#> 10   10   4.9787068
-#> 11   11   3.6883167
-#> 12   12   2.7323722
-#> 13   13   2.0241911
-#> 14   14   1.4995577
-#> 15   15   1.1108997
-#> 16   16   0.8229747
-#> 17   17   0.6096747
-#> 18   18   0.4516581
-#> 19   19   0.3345965
-#> 20   20   0.2478752
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      solution_type = "deSolve")
-
#>    time  degradinol
-#> 0     0 100.0000000
-#> 1     1  74.0818221
-#> 2     2  54.8811636
-#> 3     3  40.6569660
-#> 4     4  30.1194212
-#> 5     5  22.3130160
-#> 6     6  16.5298888
-#> 7     7  12.2456428
-#> 8     8   9.0717953
-#> 9     9   6.7205513
-#> 10   10   4.9787068
-#> 11   11   3.6883167
-#> 12   12   2.7323722
-#> 13   13   2.0241911
-#> 14   14   1.4995577
-#> 15   15   1.1108996
-#> 16   16   0.8229747
-#> 17   17   0.6096747
-#> 18   18   0.4516581
-#> 19   19   0.3345965
-#> 20   20   0.2478752
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      solution_type = "deSolve", use_compiled = FALSE)
-
#>    time  degradinol
-#> 0     0 100.0000000
-#> 1     1  74.0818221
-#> 2     2  54.8811636
-#> 3     3  40.6569660
-#> 4     4  30.1194212
-#> 5     5  22.3130160
-#> 6     6  16.5298888
-#> 7     7  12.2456428
-#> 8     8   9.0717953
-#> 9     9   6.7205513
-#> 10   10   4.9787068
-#> 11   11   3.6883167
-#> 12   12   2.7323722
-#> 13   13   2.0241911
-#> 14   14   1.4995577
-#> 15   15   1.1108996
-#> 16   16   0.8229747
-#> 17   17   0.6096747
-#> 18   18   0.4516581
-#> 19   19   0.3345965
-#> 20   20   0.2478752
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      solution_type = "eigen")
-
#>    time  degradinol
-#> 0     0 100.0000000
-#> 1     1  74.0818221
-#> 2     2  54.8811636
-#> 3     3  40.6569660
-#> 4     4  30.1194212
-#> 5     5  22.3130160
-#> 6     6  16.5298888
-#> 7     7  12.2456428
-#> 8     8   9.0717953
-#> 9     9   6.7205513
-#> 10   10   4.9787068
-#> 11   11   3.6883167
-#> 12   12   2.7323722
-#> 13   13   2.0241911
-#> 14   14   1.4995577
-#> 15   15   1.1108997
-#> 16   16   0.8229747
-#> 17   17   0.6096747
-#> 18   18   0.4516581
-#> 19   19   0.3345965
-#> 20   20   0.2478752

-# Compare integration methods to analytical solution
-mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      solution_type = "analytical")[21,]
-
#>       time degradinol 
-#> 20.0000000  0.2478752 
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      method = "lsoda")[21,]
-
#>       time degradinol 
-#> 20.0000000  0.2478752 
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      method = "ode45")[21,]
-
#>       time degradinol 
-#> 20.0000000  0.2478752 
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
-      method = "rk4")[21,]
-
#>       time degradinol 
-#> 20.0000000  0.2480043 
# rk4 is not as precise here
-
-# The number of output times used to make a lot of difference until the
-# default for atol was adjusted
-mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100),
-      seq(0, 20, by = 0.1))[201,]
-
#>       time degradinol 
-#> 20.0000000  0.2478752 
mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100),
-      seq(0, 20, by = 0.01))[2001,]
-
#>       time degradinol 
-#> 20.0000000  0.2478752 

-# Comparison of the performance of solution types
-SFO_SFO = mkinmod(parent = list(type = "SFO", to = "m1"),
-                  m1 = list(type = "SFO"), use_of_ff = "max")
-
#> Temporary DLL for differentials generated and loaded
if(require(rbenchmark)) {
-  benchmark(replications = 10, order = "relative", columns = c("test", "relative", "elapsed"),
-    eigen = mkinpredict(SFO_SFO,
-      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
-      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
-      solution_type = "eigen")[201,],
-    deSolve_compiled = mkinpredict(SFO_SFO,
-      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
-      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
-      solution_type = "deSolve")[201,],
-    deSolve = mkinpredict(SFO_SFO,
-      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
-      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
-      solution_type = "deSolve", use_compiled = FALSE)[201,],
-    analytical = mkinpredict(SFO_SFO,
-      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
-      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
-      solution_type = "analytical", use_compiled = FALSE)[201,])
-}
-
#>               test relative elapsed
-#> 2 deSolve_compiled      1.0   0.005
-#> 4       analytical      1.0   0.005
-#> 1            eigen      4.4   0.022
-#> 3          deSolve     46.8   0.234

-# \dontrun{
-  # Predict from a fitted model
-  f <- mkinfit(SFO_SFO, FOCUS_2006_C, quiet = TRUE)
-  f <- mkinfit(SFO_SFO, FOCUS_2006_C, quiet = TRUE, solution_type = "deSolve")
-  head(mkinpredict(f))
-
#>     time   parent       m1
-#> 0    0.0 82.49216 0.000000
-#> 0.1  0.1 80.00562 1.236394
-#> 0.2  0.2 77.59404 2.423201
-#> 0.3  0.3 75.25514 3.562040
-#> 0.4  0.4 72.98675 4.654478
-#> 0.5  0.5 70.78673 5.702033
# }
-
-
+    
+    Examples
+    
+SFO <- mkinmod(degradinol = mkinsub("SFO"))
+# Compare solution types
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      solution_type = "analytical")
+#>    time  degradinol
+#> 0     0 100.0000000
+#> 1     1  74.0818221
+#> 2     2  54.8811636
+#> 3     3  40.6569660
+#> 4     4  30.1194212
+#> 5     5  22.3130160
+#> 6     6  16.5298888
+#> 7     7  12.2456428
+#> 8     8   9.0717953
+#> 9     9   6.7205513
+#> 10   10   4.9787068
+#> 11   11   3.6883167
+#> 12   12   2.7323722
+#> 13   13   2.0241911
+#> 14   14   1.4995577
+#> 15   15   1.1108997
+#> 16   16   0.8229747
+#> 17   17   0.6096747
+#> 18   18   0.4516581
+#> 19   19   0.3345965
+#> 20   20   0.2478752
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      solution_type = "deSolve")
+#>    time  degradinol
+#> 0     0 100.0000000
+#> 1     1  74.0818221
+#> 2     2  54.8811636
+#> 3     3  40.6569660
+#> 4     4  30.1194212
+#> 5     5  22.3130160
+#> 6     6  16.5298888
+#> 7     7  12.2456428
+#> 8     8   9.0717953
+#> 9     9   6.7205513
+#> 10   10   4.9787068
+#> 11   11   3.6883167
+#> 12   12   2.7323722
+#> 13   13   2.0241911
+#> 14   14   1.4995577
+#> 15   15   1.1108996
+#> 16   16   0.8229747
+#> 17   17   0.6096747
+#> 18   18   0.4516581
+#> 19   19   0.3345965
+#> 20   20   0.2478752
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      solution_type = "deSolve", use_compiled = FALSE)
+#>    time  degradinol
+#> 0     0 100.0000000
+#> 1     1  74.0818221
+#> 2     2  54.8811636
+#> 3     3  40.6569660
+#> 4     4  30.1194212
+#> 5     5  22.3130160
+#> 6     6  16.5298888
+#> 7     7  12.2456428
+#> 8     8   9.0717953
+#> 9     9   6.7205513
+#> 10   10   4.9787068
+#> 11   11   3.6883167
+#> 12   12   2.7323722
+#> 13   13   2.0241911
+#> 14   14   1.4995577
+#> 15   15   1.1108996
+#> 16   16   0.8229747
+#> 17   17   0.6096747
+#> 18   18   0.4516581
+#> 19   19   0.3345965
+#> 20   20   0.2478752
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      solution_type = "eigen")
+#>    time  degradinol
+#> 0     0 100.0000000
+#> 1     1  74.0818221
+#> 2     2  54.8811636
+#> 3     3  40.6569660
+#> 4     4  30.1194212
+#> 5     5  22.3130160
+#> 6     6  16.5298888
+#> 7     7  12.2456428
+#> 8     8   9.0717953
+#> 9     9   6.7205513
+#> 10   10   4.9787068
+#> 11   11   3.6883167
+#> 12   12   2.7323722
+#> 13   13   2.0241911
+#> 14   14   1.4995577
+#> 15   15   1.1108997
+#> 16   16   0.8229747
+#> 17   17   0.6096747
+#> 18   18   0.4516581
+#> 19   19   0.3345965
+#> 20   20   0.2478752
+
+# Compare integration methods to analytical solution
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      solution_type = "analytical")[21,]
+#>       time degradinol 
+#> 20.0000000  0.2478752 
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      method = "lsoda")[21,]
+#>       time degradinol 
+#> 20.0000000  0.2478752 
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      method = "ode45")[21,]
+#>       time degradinol 
+#> 20.0000000  0.2478752 
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100), 0:20,
+      method = "rk4")[21,]
+#>       time degradinol 
+#> 20.0000000  0.2480043 
+# rk4 is not as precise here
+
+# The number of output times used to make a lot of difference until the
+# default for atol was adjusted
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100),
+      seq(0, 20, by = 0.1))[201,]
+#>       time degradinol 
+#> 20.0000000  0.2478752 
+mkinpredict(SFO, c(k_degradinol = 0.3), c(degradinol = 100),
+      seq(0, 20, by = 0.01))[2001,]
+#>       time degradinol 
+#> 20.0000000  0.2478752 
+
+# Comparison of the performance of solution types
+SFO_SFO = mkinmod(parent = list(type = "SFO", to = "m1"),
+                  m1 = list(type = "SFO"), use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+if(require(rbenchmark)) {
+  benchmark(replications = 10, order = "relative", columns = c("test", "relative", "elapsed"),
+    eigen = mkinpredict(SFO_SFO,
+      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
+      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
+      solution_type = "eigen")[201,],
+    deSolve_compiled = mkinpredict(SFO_SFO,
+      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
+      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
+      solution_type = "deSolve")[201,],
+    deSolve = mkinpredict(SFO_SFO,
+      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
+      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
+      solution_type = "deSolve", use_compiled = FALSE)[201,],
+    analytical = mkinpredict(SFO_SFO,
+      c(k_parent = 0.15, f_parent_to_m1 = 0.5, k_m1 = 0.01),
+      c(parent = 100, m1 = 0), seq(0, 20, by = 0.1),
+      solution_type = "analytical", use_compiled = FALSE)[201,])
+}
+#> Loading required package: rbenchmark
+#>               test relative elapsed
+#> 2 deSolve_compiled     1.00   0.004
+#> 4       analytical     5.25   0.021
+#> 1            eigen     6.00   0.024
+#> 3          deSolve    52.50   0.210
+
+# \dontrun{
+  # Predict from a fitted model
+  f <- mkinfit(SFO_SFO, FOCUS_2006_C, quiet = TRUE)
+  f <- mkinfit(SFO_SFO, FOCUS_2006_C, quiet = TRUE, solution_type = "deSolve")
+  head(mkinpredict(f))
+#> DLSODA-  At current T (=R1), MXSTEP (=I1) steps   
+#>       taken on this call before reaching TOUT     
+#> In above message, I1 = 1
+#>  
+#> In above message, R1 = 9.99904e-07
+#>  
+#> Warning: an excessive amount of work (> maxsteps ) was done, but integration was not successful - increase maxsteps
+#> Warning: Returning early. Results are accurate, as far as they go
+#> Error in out[available, var]: (subscript) logical subscript too long
+# }
+
+
+    
   
   
-    
-      Contents
-    
-  
+    Contents
+    
 
 
 
-      
-      
-  Developed by Johannes Ranke.
+      
+  
Developed by Johannes Ranke.
 
 
 
-  Site built with pkgdown 1.6.1.
+  
Site built with pkgdown 2.0.6.
 
 
-      
-   
+      

 
   
 
 
-  
-
+  
 
+  
 
diff --git a/docs/dev/reference/saem-1.png b/docs/dev/reference/saem-1.png
index 08939d4f..9e310252 100644
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diff --git a/docs/dev/reference/saem-2.png b/docs/dev/reference/saem-2.png
index b737db03..de1bcf57 100644
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diff --git a/docs/dev/reference/saem-3.png b/docs/dev/reference/saem-3.png
index 08e0f544..de569ce0 100644
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diff --git a/docs/dev/reference/saem-4.png b/docs/dev/reference/saem-4.png
index bb775c25..0f2ee3e7 100644
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diff --git a/docs/dev/reference/saem.html b/docs/dev/reference/saem.html
index 8ea0ef6e..968dc68c 100644
--- a/docs/dev/reference/saem.html
+++ b/docs/dev/reference/saem.html
@@ -106,13 +106,14 @@ Expectation Maximisation algorithm (SAEM).
   conf.level = 0.6,
   solution_type = "auto",
   covariance.model = "auto",
+  omega.init = "auto",
   covariates = NULL,
   covariate_models = NULL,
   no_random_effect = NULL,
+  error.init = c(3, 0.1),
   nbiter.saemix = c(300, 100),
   control = list(displayProgress = FALSE, print = FALSE, nbiter.saemix = nbiter.saemix,
     save = FALSE, save.graphs = FALSE),
-  fail_with_errors = TRUE,
   verbose = FALSE,
   quiet = FALSE,
   ...
@@ -129,8 +130,10 @@ Expectation Maximisation algorithm (SAEM).
   degparms_start = numeric(),
   covariance.model = "auto",
   no_random_effect = NULL,
+  omega.init = "auto",
   covariates = NULL,
   covariate_models = NULL,
+  error.init = numeric(),
   test_log_parms = FALSE,
   conf.level = 0.6,
   verbose = FALSE,
@@ -189,11 +192,21 @@ automatic choice is not desired
 
 
 covariance.model
-Will be passed to saemix::SaemixModel(). Per
+
Will be passed to saemix::saemixModel(). Per
 default, uncorrelated random effects are specified for all degradation
 parameters.
 
 
+omega.init
+Will be passed to saemix::saemixModel(). If using
+mkin transformations and the default covariance model with optionally
+excluded random effects, the variances of the degradation parameters
+are estimated using mean_degparms, with testing of untransformed
+log parameters for significant difference from zero. If not using
+mkin transformations or a custom covariance model, the default
+initialisation of saemix::saemixModel is used for omega.init.
+
+
 covariates
 A data frame with covariate data for use in
 'covariate_models', with dataset names as row names.
@@ -211,6 +224,10 @@ which there should be no variability over the groups. Only used
 if the covariance model is not explicitly specified.
 
 
+error.init
+Will be passed to saemix::saemixModel().
+
+
 nbiter.saemix
 Convenience option to increase the number of
 iterations
@@ -220,11 +237,6 @@ iterations
 Passed to saemix::saemix.
 
 
-fail_with_errors
-Should a failure to compute standard errors
-from the inverse of the Fisher Information Matrix be a failure?
-
-
 verbose
 Should we print information about created objects of
 type saemix::SaemixModel and saemix::SaemixData?
@@ -293,15 +305,15 @@ using mmkin.
 #> Data: 90 observations of 1 variable(s) grouped in 5 datasets
 #> 
 #>             npar    AIC    BIC     Lik
-#> f_saem_sfo     5 624.26 622.31 -307.13
-#> f_saem_fomc    7 467.87 465.13 -226.93
-#> f_saem_dfop    9 493.98 490.47 -237.99
+#> f_saem_sfo     5 624.33 622.38 -307.17
+#> f_saem_fomc    7 467.85 465.11 -226.92
+#> f_saem_dfop    9 493.76 490.24 -237.88
 anova(f_saem_sfo, f_saem_dfop, test = TRUE)
 #> Data: 90 observations of 1 variable(s) grouped in 5 datasets
 #> 
 #>             npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)    
-#> f_saem_sfo     5 624.26 622.31 -307.13                         
-#> f_saem_dfop    9 493.98 490.47 -237.99 138.28  4  < 2.2e-16 ***
+#> f_saem_sfo     5 624.33 622.38 -307.17                         
+#> f_saem_dfop    9 493.76 490.24 -237.88 138.57  4  < 2.2e-16 ***
 #> ---
 #> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 illparms(f_saem_dfop)
@@ -311,16 +323,16 @@ using mmkin.
 #> Data: 90 observations of 1 variable(s) grouped in 5 datasets
 #> 
 #>                 npar    AIC    BIC     Lik Chisq Df Pr(>Chisq)
-#> f_saem_dfop_red    8 490.64 487.52 -237.32                    
-#> f_saem_dfop        9 493.98 490.47 -237.99     0  1          1
+#> f_saem_dfop_red    8 488.68 485.55 -236.34                    
+#> f_saem_dfop        9 493.76 490.24 -237.88     0  1          1
 
 anova(f_saem_sfo, f_saem_fomc, f_saem_dfop)
 #> Data: 90 observations of 1 variable(s) grouped in 5 datasets
 #> 
 #>             npar    AIC    BIC     Lik
-#> f_saem_sfo     5 624.26 622.31 -307.13
-#> f_saem_fomc    7 467.87 465.13 -226.93
-#> f_saem_dfop    9 493.98 490.47 -237.99
+#> f_saem_sfo     5 624.33 622.38 -307.17
+#> f_saem_fomc    7 467.85 465.11 -226.92
+#> f_saem_dfop    9 493.76 490.24 -237.88
 # The returned saem.mmkin object contains an SaemixObject, therefore we can use
 # functions from saemix
 library(saemix)
@@ -335,9 +347,9 @@ using mmkin.
 compare.saemix(f_saem_sfo$so, f_saem_fomc$so, f_saem_dfop$so)
 #> Likelihoods calculated by importance sampling
 #>        AIC      BIC
-#> 1 624.2598 622.3070
-#> 2 467.8664 465.1324
-#> 3 493.9811 490.4660
+#> 1 624.3316 622.3788
+#> 2 467.8472 465.1132
+#> 3 493.7592 490.2441
 plot(f_saem_fomc$so, plot.type = "convergence")
 
 plot(f_saem_fomc$so, plot.type = "individual.fit")
@@ -354,9 +366,9 @@ using mmkin.
 anova(f_saem_fomc, f_saem_fomc_tc, test = TRUE)
 #> Data: 90 observations of 1 variable(s) grouped in 5 datasets
 #> 
-#>                npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)
-#> f_saem_fomc       7 467.87 465.13 -226.93                     
-#> f_saem_fomc_tc    8 469.80 466.68 -226.90 0.0645  1     0.7995
+#>                npar    AIC    BIC     Lik Chisq Df Pr(>Chisq)
+#> f_saem_fomc       7 467.85 465.11 -226.92                    
+#> f_saem_fomc_tc    8 469.83 466.71 -226.92 0.015  1     0.9027
 
 sfo_sfo <- mkinmod(parent = mkinsub("SFO", "A1"),
   A1 = mkinsub("SFO"))
@@ -393,32 +405,32 @@ using mmkin.
 #> 170 observations of 2 variable(s) grouped in 5 datasets
 #> 
 #> Likelihood computed by importance sampling
-#>   AIC   BIC logLik
-#>   842 836.9   -408
+#>     AIC   BIC logLik
+#>   839.2 834.1 -406.6
 #> 
 #> Fitted parameters:
-#>                    estimate   lower   upper
-#> parent_0            93.7701 91.1458 96.3945
-#> log_k_A1            -5.8116 -7.5998 -4.0234
-#> f_parent_qlogis     -0.9608 -1.3654 -0.5562
-#> log_k1              -2.5841 -3.6876 -1.4805
-#> log_k2              -3.5228 -5.3254 -1.7203
-#> g_qlogis            -0.1027 -0.8719  0.6665
-#> a.1                  1.8856  1.6676  2.1037
-#> SD.parent_0          2.7682  0.7668  4.7695
-#> SD.log_k_A1          1.7447  0.4047  3.0848
-#> SD.f_parent_qlogis   0.4525  0.1620  0.7431
-#> SD.log_k1            1.2423  0.4560  2.0285
-#> SD.log_k2            2.0390  0.7601  3.3180
-#> SD.g_qlogis          0.4439 -0.3069  1.1947
+#>                    estimate    lower   upper
+#> parent_0           93.70402 91.04104 96.3670
+#> log_k_A1           -5.83760 -7.66452 -4.0107
+#> f_parent_qlogis    -0.95718 -1.35955 -0.5548
+#> log_k1             -2.35514 -3.39402 -1.3163
+#> log_k2             -3.79634 -5.64009 -1.9526
+#> g_qlogis           -0.02108 -0.66463  0.6225
+#> a.1                 1.88191  1.66491  2.0989
+#> SD.parent_0         2.81628  0.78922  4.8433
+#> SD.log_k_A1         1.78751  0.42105  3.1540
+#> SD.f_parent_qlogis  0.45016  0.16116  0.7391
+#> SD.log_k1           1.06923  0.31676  1.8217
+#> SD.log_k2           2.03768  0.70938  3.3660
+#> SD.g_qlogis         0.44024 -0.09262  0.9731
 plot(f_saem_dfop_sfo)
 
 summary(f_saem_dfop_sfo, data = TRUE)
 #> saemix version used for fitting:      3.2 
 #> mkin version used for pre-fitting:  1.2.0 
 #> R version used for fitting:         4.2.2 
-#> Date of fit:     Tue Nov  1 14:12:07 2022 
-#> Date of summary: Tue Nov  1 14:12:07 2022 
+#> Date of fit:     Mon Nov 14 21:06:30 2022 
+#> Date of summary: Mon Nov 14 21:06:30 2022 
 #> 
 #> Equations:
 #> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -433,7 +445,7 @@ using mmkin.
 #> 
 #> Model predictions using solution type analytical 
 #> 
-#> Fitted in 8.45 s
+#> Fitted in 9.625 s
 #> Using 300, 100 iterations and 10 chains
 #> 
 #> Variance model: Constant variance 
@@ -450,237 +462,237 @@ using mmkin.
 #> Results:
 #> 
 #> Likelihood computed by importance sampling
-#>   AIC   BIC logLik
-#>   842 836.9   -408
+#>     AIC   BIC logLik
+#>   839.2 834.1 -406.6
 #> 
 #> Optimised parameters:
-#>                       est.   lower   upper
-#> parent_0           93.7701 91.1458 96.3945
-#> log_k_A1           -5.8116 -7.5998 -4.0234
-#> f_parent_qlogis    -0.9608 -1.3654 -0.5562
-#> log_k1             -2.5841 -3.6876 -1.4805
-#> log_k2             -3.5228 -5.3254 -1.7203
-#> g_qlogis           -0.1027 -0.8719  0.6665
-#> a.1                 1.8856  1.6676  2.1037
-#> SD.parent_0         2.7682  0.7668  4.7695
-#> SD.log_k_A1         1.7447  0.4047  3.0848
-#> SD.f_parent_qlogis  0.4525  0.1620  0.7431
-#> SD.log_k1           1.2423  0.4560  2.0285
-#> SD.log_k2           2.0390  0.7601  3.3180
-#> SD.g_qlogis         0.4439 -0.3069  1.1947
+#>                        est.    lower   upper
+#> parent_0           93.70402 91.04104 96.3670
+#> log_k_A1           -5.83760 -7.66452 -4.0107
+#> f_parent_qlogis    -0.95718 -1.35955 -0.5548
+#> log_k1             -2.35514 -3.39402 -1.3163
+#> log_k2             -3.79634 -5.64009 -1.9526
+#> g_qlogis           -0.02108 -0.66463  0.6225
+#> a.1                 1.88191  1.66491  2.0989
+#> SD.parent_0         2.81628  0.78922  4.8433
+#> SD.log_k_A1         1.78751  0.42105  3.1540
+#> SD.f_parent_qlogis  0.45016  0.16116  0.7391
+#> SD.log_k1           1.06923  0.31676  1.8217
+#> SD.log_k2           2.03768  0.70938  3.3660
+#> SD.g_qlogis         0.44024 -0.09262  0.9731
 #> 
 #> Correlation: 
 #>                 parnt_0 lg_k_A1 f_prnt_ log_k1  log_k2 
-#> log_k_A1        -0.0160                                
-#> f_parent_qlogis -0.0263  0.0612                        
-#> log_k1           0.0100 -0.0014 -0.0033                
-#> log_k2           0.0131  0.0050 -0.0011  0.0071        
-#> g_qlogis        -0.0419 -0.0199  0.0026 -0.0765 -0.0707
+#> log_k_A1        -0.0147                                
+#> f_parent_qlogis -0.0269  0.0573                        
+#> log_k1           0.0263 -0.0011 -0.0040                
+#> log_k2           0.0020  0.0065 -0.0002 -0.0776        
+#> g_qlogis        -0.0248 -0.0180 -0.0004 -0.0903 -0.0603
 #> 
 #> Random effects:
-#>                      est.   lower  upper
-#> SD.parent_0        2.7682  0.7668 4.7695
-#> SD.log_k_A1        1.7447  0.4047 3.0848
-#> SD.f_parent_qlogis 0.4525  0.1620 0.7431
-#> SD.log_k1          1.2423  0.4560 2.0285
-#> SD.log_k2          2.0390  0.7601 3.3180
-#> SD.g_qlogis        0.4439 -0.3069 1.1947
+#>                      est.    lower  upper
+#> SD.parent_0        2.8163  0.78922 4.8433
+#> SD.log_k_A1        1.7875  0.42105 3.1540
+#> SD.f_parent_qlogis 0.4502  0.16116 0.7391
+#> SD.log_k1          1.0692  0.31676 1.8217
+#> SD.log_k2          2.0377  0.70938 3.3660
+#> SD.g_qlogis        0.4402 -0.09262 0.9731
 #> 
 #> Variance model:
 #>      est. lower upper
-#> a.1 1.886 1.668 2.104
+#> a.1 1.882 1.665 2.099
 #> 
 #> Backtransformed parameters:
 #>                     est.     lower    upper
-#> parent_0       93.770115 9.115e+01 96.39447
-#> k_A1            0.002993 5.005e-04  0.01789
-#> f_parent_to_A1  0.276720 2.034e-01  0.36443
-#> k1              0.075467 2.503e-02  0.22753
-#> k2              0.029516 4.867e-03  0.17902
-#> g               0.474353 2.949e-01  0.66073
+#> parent_0       93.704015 9.104e+01 96.36699
+#> k_A1            0.002916 4.692e-04  0.01812
+#> f_parent_to_A1  0.277443 2.043e-01  0.36475
+#> k1              0.094880 3.357e-02  0.26813
+#> k2              0.022453 3.553e-03  0.14191
+#> g               0.494731 3.397e-01  0.65078
 #> 
 #> Resulting formation fractions:
 #>                 ff
-#> parent_A1   0.2767
-#> parent_sink 0.7233
+#> parent_A1   0.2774
+#> parent_sink 0.7226
 #> 
 #> Estimated disappearance times:
-#>          DT50   DT90 DT50back DT50_k1 DT50_k2
-#> parent  14.56  58.26    17.54   9.185   23.48
-#> A1     231.62 769.41       NA      NA      NA
+#>         DT50   DT90 DT50back DT50_k1 DT50_k2
+#> parent  14.0  72.38    21.79   7.306   30.87
+#> A1     237.7 789.68       NA      NA      NA
 #> 
 #> Data:
 #>          ds   name time observed predicted residual   std standardized
-#>   Dataset 6 parent    0     97.2  95.78623  1.41377 1.886     0.749758
-#>   Dataset 6 parent    0     96.4  95.78623  0.61377 1.886     0.325498
-#>   Dataset 6 parent    3     71.1  71.34666 -0.24666 1.886    -0.130812
-#>   Dataset 6 parent    3     69.2  71.34666 -2.14666 1.886    -1.138429
-#>   Dataset 6 parent    6     58.1  56.49768  1.60232 1.886     0.849749
-#>   Dataset 6 parent    6     56.6  56.49768  0.10232 1.886     0.054262
-#>   Dataset 6 parent   10     44.4  44.53511 -0.13511 1.886    -0.071650
-#>   Dataset 6 parent   10     43.4  44.53511 -1.13511 1.886    -0.601974
-#>   Dataset 6 parent   20     33.3  29.77451  3.52549 1.886     1.869656
-#>   Dataset 6 parent   20     29.2  29.77451 -0.57451 1.886    -0.304675
-#>   Dataset 6 parent   34     17.6  19.32540 -1.72540 1.886    -0.915023
-#>   Dataset 6 parent   34     18.0  19.32540 -1.32540 1.886    -0.702894
-#>   Dataset 6 parent   55     10.5  10.42781  0.07219 1.886     0.038282
-#>   Dataset 6 parent   55      9.3  10.42781 -1.12781 1.886    -0.598107
-#>   Dataset 6 parent   90      4.5   3.74190  0.75810 1.886     0.402037
-#>   Dataset 6 parent   90      4.7   3.74190  0.95810 1.886     0.508102
-#>   Dataset 6 parent  112      3.0   1.96485  1.03515 1.886     0.548966
-#>   Dataset 6 parent  112      3.4   1.96485  1.43515 1.886     0.761096
-#>   Dataset 6 parent  132      2.3   1.09395  1.20605 1.886     0.639596
-#>   Dataset 6 parent  132      2.7   1.09395  1.60605 1.886     0.851726
-#>   Dataset 6     A1    3      4.3   4.72702 -0.42702 1.886    -0.226458
-#>   Dataset 6     A1    3      4.6   4.72702 -0.12702 1.886    -0.067361
-#>   Dataset 6     A1    6      7.0   7.51314 -0.51314 1.886    -0.272128
-#>   Dataset 6     A1    6      7.2   7.51314 -0.31314 1.886    -0.166063
-#>   Dataset 6     A1   10      8.2   9.63719 -1.43719 1.886    -0.762179
-#>   Dataset 6     A1   10      8.0   9.63719 -1.63719 1.886    -0.868244
-#>   Dataset 6     A1   20     11.0  11.84931 -0.84931 1.886    -0.450409
-#>   Dataset 6     A1   20     13.7  11.84931  1.85069 1.886     0.981468
-#>   Dataset 6     A1   34     11.5  12.82336 -1.32336 1.886    -0.701808
-#>   Dataset 6     A1   34     12.7  12.82336 -0.12336 1.886    -0.065418
-#>   Dataset 6     A1   55     14.9  12.89456  2.00544 1.886     1.063533
-#>   Dataset 6     A1   55     14.5  12.89456  1.60544 1.886     0.851403
-#>   Dataset 6     A1   90     12.1  11.55919  0.54081 1.886     0.286806
-#>   Dataset 6     A1   90     12.3  11.55919  0.74081 1.886     0.392871
-#>   Dataset 6     A1  112      9.9  10.42334 -0.52334 1.886    -0.277539
-#>   Dataset 6     A1  112     10.2  10.42334 -0.22334 1.886    -0.118442
-#>   Dataset 6     A1  132      8.8   9.37987 -0.57987 1.886    -0.307519
-#>   Dataset 6     A1  132      7.8   9.37987 -1.57987 1.886    -0.837844
-#>   Dataset 7 parent    0     93.6  90.95702  2.64298 1.886     1.401639
-#>   Dataset 7 parent    0     92.3  90.95702  1.34298 1.886     0.712217
-#>   Dataset 7 parent    3     87.0  84.77506  2.22494 1.886     1.179942
-#>   Dataset 7 parent    3     82.2  84.77506 -2.57506 1.886    -1.365616
-#>   Dataset 7 parent    7     74.0  77.60962 -3.60962 1.886    -1.914268
-#>   Dataset 7 parent    7     73.9  77.60962 -3.70962 1.886    -1.967301
-#>   Dataset 7 parent   14     64.2  67.50646 -3.30646 1.886    -1.753499
-#>   Dataset 7 parent   14     69.5  67.50646  1.99354 1.886     1.057221
-#>   Dataset 7 parent   30     54.0  52.48909  1.51091 1.886     0.801271
-#>   Dataset 7 parent   30     54.6  52.48909  2.11091 1.886     1.119465
-#>   Dataset 7 parent   60     41.1  39.54372  1.55628 1.886     0.825335
-#>   Dataset 7 parent   60     38.4  39.54372 -1.14372 1.886    -0.606542
-#>   Dataset 7 parent   90     32.5  33.87968 -1.37968 1.886    -0.731676
-#>   Dataset 7 parent   90     35.5  33.87968  1.62032 1.886     0.859298
-#>   Dataset 7 parent  120     28.1  30.41071 -2.31071 1.886    -1.225427
-#>   Dataset 7 parent  120     29.0  30.41071 -1.41071 1.886    -0.748135
-#>   Dataset 7 parent  180     26.5  25.36386  1.13614 1.886     0.602524
-#>   Dataset 7 parent  180     27.6  25.36386  2.23614 1.886     1.185881
-#>   Dataset 7     A1    3      3.9   2.74863  1.15137 1.886     0.610600
-#>   Dataset 7     A1    3      3.1   2.74863  0.35137 1.886     0.186341
-#>   Dataset 7     A1    7      6.9   5.92686  0.97314 1.886     0.516081
-#>   Dataset 7     A1    7      6.6   5.92686  0.67314 1.886     0.356983
-#>   Dataset 7     A1   14     10.4  10.38800  0.01200 1.886     0.006362
-#>   Dataset 7     A1   14      8.3  10.38800 -2.08800 1.886    -1.107320
-#>   Dataset 7     A1   30     14.4  16.93529 -2.53529 1.886    -1.344524
-#>   Dataset 7     A1   30     13.7  16.93529 -3.23529 1.886    -1.715751
-#>   Dataset 7     A1   60     22.1  22.33044 -0.23044 1.886    -0.122209
-#>   Dataset 7     A1   60     22.3  22.33044 -0.03044 1.886    -0.016144
-#>   Dataset 7     A1   90     27.5  24.42300  3.07700 1.886     1.631809
-#>   Dataset 7     A1   90     25.4  24.42300  0.97700 1.886     0.518127
-#>   Dataset 7     A1  120     28.0  25.51140  2.48860 1.886     1.319768
-#>   Dataset 7     A1  120     26.6  25.51140  1.08860 1.886     0.577313
-#>   Dataset 7     A1  180     25.8  26.80282 -1.00282 1.886    -0.531818
-#>   Dataset 7     A1  180     25.3  26.80282 -1.50282 1.886    -0.796981
-#>   Dataset 8 parent    0     91.9  91.08733  0.81267 1.886     0.430980
-#>   Dataset 8 parent    0     90.8  91.08733 -0.28733 1.886    -0.152377
-#>   Dataset 8 parent    1     64.9  67.55332 -2.65332 1.886    -1.407123
-#>   Dataset 8 parent    1     66.2  67.55332 -1.35332 1.886    -0.717701
-#>   Dataset 8 parent    3     43.5  41.65811  1.84189 1.886     0.976800
-#>   Dataset 8 parent    3     44.1  41.65811  2.44189 1.886     1.294994
-#>   Dataset 8 parent    8     18.3  19.65773 -1.35773 1.886    -0.720038
-#>   Dataset 8 parent    8     18.1  19.65773 -1.55773 1.886    -0.826103
-#>   Dataset 8 parent   14     10.2  10.65118 -0.45118 1.886    -0.239269
-#>   Dataset 8 parent   14     10.8  10.65118  0.14882 1.886     0.078925
-#>   Dataset 8 parent   27      4.9   3.11694  1.78306 1.886     0.945601
-#>   Dataset 8 parent   27      3.3   3.11694  0.18306 1.886     0.097082
-#>   Dataset 8 parent   48      1.6   0.43165  1.16835 1.886     0.619603
-#>   Dataset 8 parent   48      1.5   0.43165  1.06835 1.886     0.566570
-#>   Dataset 8 parent   70      1.1   0.05441  1.04559 1.886     0.554503
-#>   Dataset 8 parent   70      0.9   0.05441  0.84559 1.886     0.448438
-#>   Dataset 8     A1    1      9.6   7.66431  1.93569 1.886     1.026546
-#>   Dataset 8     A1    1      7.7   7.66431  0.03569 1.886     0.018930
-#>   Dataset 8     A1    3     15.0  15.57948 -0.57948 1.886    -0.307311
-#>   Dataset 8     A1    3     15.1  15.57948 -0.47948 1.886    -0.254279
-#>   Dataset 8     A1    8     21.2  20.38988  0.81012 1.886     0.429625
-#>   Dataset 8     A1    8     21.1  20.38988  0.71012 1.886     0.376593
-#>   Dataset 8     A1   14     19.7  20.16439 -0.46439 1.886    -0.246276
-#>   Dataset 8     A1   14     18.9  20.16439 -1.26439 1.886    -0.670535
-#>   Dataset 8     A1   27     17.5  16.40918  1.09082 1.886     0.578489
-#>   Dataset 8     A1   27     15.9  16.40918 -0.50918 1.886    -0.270030
-#>   Dataset 8     A1   48      9.5  10.12011 -0.62011 1.886    -0.328861
-#>   Dataset 8     A1   48      9.8  10.12011 -0.32011 1.886    -0.169764
-#>   Dataset 8     A1   70      6.2   5.79080  0.40920 1.886     0.217011
-#>   Dataset 8     A1   70      6.1   5.79080  0.30920 1.886     0.163979
-#>   Dataset 9 parent    0     99.8  97.38786  2.41214 1.886     1.279218
-#>   Dataset 9 parent    0     98.3  97.38786  0.91214 1.886     0.483731
-#>   Dataset 9 parent    1     77.1  79.25431 -2.15431 1.886    -1.142481
-#>   Dataset 9 parent    1     77.2  79.25431 -2.05431 1.886    -1.089449
-#>   Dataset 9 parent    3     59.0  55.69866  3.30134 1.886     1.750781
-#>   Dataset 9 parent    3     58.1  55.69866  2.40134 1.886     1.273489
-#>   Dataset 9 parent    8     27.4  31.64893 -4.24893 1.886    -2.253314
-#>   Dataset 9 parent    8     29.2  31.64893 -2.44893 1.886    -1.298729
-#>   Dataset 9 parent   14     19.1  22.57316 -3.47316 1.886    -1.841901
-#>   Dataset 9 parent   14     29.6  22.57316  7.02684 1.886     3.726507
-#>   Dataset 9 parent   27     10.1  14.11345 -4.01345 1.886    -2.128430
-#>   Dataset 9 parent   27     18.2  14.11345  4.08655 1.886     2.167199
-#>   Dataset 9 parent   48      4.5   6.95586 -2.45586 1.886    -1.302400
-#>   Dataset 9 parent   48      9.1   6.95586  2.14414 1.886     1.137093
-#>   Dataset 9 parent   70      2.3   3.31753 -1.01753 1.886    -0.539619
-#>   Dataset 9 parent   70      2.9   3.31753 -0.41753 1.886    -0.221424
-#>   Dataset 9 parent   91      2.0   1.63642  0.36358 1.886     0.192816
-#>   Dataset 9 parent   91      1.8   1.63642  0.16358 1.886     0.086751
-#>   Dataset 9 parent  120      2.0   0.61667  1.38333 1.886     0.733614
-#>   Dataset 9 parent  120      2.2   0.61667  1.58333 1.886     0.839679
-#>   Dataset 9     A1    1      4.2   3.67247  0.52753 1.886     0.279763
-#>   Dataset 9     A1    1      3.9   3.67247  0.22753 1.886     0.120666
-#>   Dataset 9     A1    3      7.4   8.36240 -0.96240 1.886    -0.510385
-#>   Dataset 9     A1    3      7.9   8.36240 -0.46240 1.886    -0.245223
-#>   Dataset 9     A1    8     14.5  12.80590  1.69410 1.886     0.898422
-#>   Dataset 9     A1    8     13.7  12.80590  0.89410 1.886     0.474162
-#>   Dataset 9     A1   14     14.2  13.99625  0.20375 1.886     0.108053
-#>   Dataset 9     A1   14     12.2  13.99625 -1.79625 1.886    -0.952596
-#>   Dataset 9     A1   27     13.7  14.22730 -0.52730 1.886    -0.279641
-#>   Dataset 9     A1   27     13.2  14.22730 -1.02730 1.886    -0.544803
-#>   Dataset 9     A1   48     13.6  13.33713  0.26287 1.886     0.139406
-#>   Dataset 9     A1   48     15.4  13.33713  2.06287 1.886     1.093991
-#>   Dataset 9     A1   70     10.4  11.84008 -1.44008 1.886    -0.763708
-#>   Dataset 9     A1   70     11.6  11.84008 -0.24008 1.886    -0.127318
-#>   Dataset 9     A1   91     10.0  10.30732 -0.30732 1.886    -0.162980
-#>   Dataset 9     A1   91      9.5  10.30732 -0.80732 1.886    -0.428142
-#>   Dataset 9     A1  120      9.1   8.33981  0.76019 1.886     0.403149
-#>   Dataset 9     A1  120      9.0   8.33981  0.66019 1.886     0.350117
-#>  Dataset 10 parent    0     96.1  93.70349  2.39651 1.886     1.270926
-#>  Dataset 10 parent    0     94.3  93.70349  0.59651 1.886     0.316342
-#>  Dataset 10 parent    8     73.9  77.86253 -3.96253 1.886    -2.101429
-#>  Dataset 10 parent    8     73.9  77.86253 -3.96253 1.886    -2.101429
-#>  Dataset 10 parent   14     69.4  70.18665 -0.78665 1.886    -0.417182
-#>  Dataset 10 parent   14     73.1  70.18665  2.91335 1.886     1.545019
-#>  Dataset 10 parent   21     65.6  64.03245  1.56755 1.886     0.831308
-#>  Dataset 10 parent   21     65.3  64.03245  1.26755 1.886     0.672210
-#>  Dataset 10 parent   41     55.9  54.71491  1.18509 1.886     0.628480
-#>  Dataset 10 parent   41     54.4  54.71491 -0.31491 1.886    -0.167007
-#>  Dataset 10 parent   63     47.0  49.63436 -2.63436 1.886    -1.397065
-#>  Dataset 10 parent   63     49.3  49.63436 -0.33436 1.886    -0.177319
-#>  Dataset 10 parent   91     44.7  45.08853 -0.38853 1.886    -0.206049
-#>  Dataset 10 parent   91     46.7  45.08853  1.61147 1.886     0.854600
-#>  Dataset 10 parent  120     42.1  41.07653  1.02347 1.886     0.542772
-#>  Dataset 10 parent  120     41.3  41.07653  0.22347 1.886     0.118513
-#>  Dataset 10     A1    8      3.3   4.08295 -0.78295 1.886    -0.415218
-#>  Dataset 10     A1    8      3.4   4.08295 -0.68295 1.886    -0.362186
-#>  Dataset 10     A1   14      3.9   6.04367 -2.14367 1.886    -1.136841
-#>  Dataset 10     A1   14      2.9   6.04367 -3.14367 1.886    -1.667165
-#>  Dataset 10     A1   21      6.4   7.59693 -1.19693 1.886    -0.634761
-#>  Dataset 10     A1   21      7.2   7.59693 -0.39693 1.886    -0.210502
-#>  Dataset 10     A1   41      9.1   9.86436 -0.76436 1.886    -0.405361
-#>  Dataset 10     A1   41      8.5   9.86436 -1.36436 1.886    -0.723555
-#>  Dataset 10     A1   63     11.7  10.99397  0.70603 1.886     0.374425
-#>  Dataset 10     A1   63     12.0  10.99397  1.00603 1.886     0.533522
-#>  Dataset 10     A1   91     13.3  11.91274  1.38726 1.886     0.735696
-#>  Dataset 10     A1   91     13.2  11.91274  1.28726 1.886     0.682663
-#>  Dataset 10     A1  120     14.3  12.66519  1.63481 1.886     0.866981
-#>  Dataset 10     A1  120     12.1  12.66519 -0.56519 1.886    -0.299733
+#>   Dataset 6 parent    0     97.2  95.70025  1.49975 1.882      0.79693
+#>   Dataset 6 parent    0     96.4  95.70025  0.69975 1.882      0.37183
+#>   Dataset 6 parent    3     71.1  71.44670 -0.34670 1.882     -0.18423
+#>   Dataset 6 parent    3     69.2  71.44670 -2.24670 1.882     -1.19384
+#>   Dataset 6 parent    6     58.1  56.59283  1.50717 1.882      0.80087
+#>   Dataset 6 parent    6     56.6  56.59283  0.00717 1.882      0.00381
+#>   Dataset 6 parent   10     44.4  44.56648 -0.16648 1.882     -0.08847
+#>   Dataset 6 parent   10     43.4  44.56648 -1.16648 1.882     -0.61984
+#>   Dataset 6 parent   20     33.3  29.76020  3.53980 1.882      1.88096
+#>   Dataset 6 parent   20     29.2  29.76020 -0.56020 1.882     -0.29767
+#>   Dataset 6 parent   34     17.6  19.39208 -1.79208 1.882     -0.95226
+#>   Dataset 6 parent   34     18.0  19.39208 -1.39208 1.882     -0.73971
+#>   Dataset 6 parent   55     10.5  10.55761 -0.05761 1.882     -0.03061
+#>   Dataset 6 parent   55      9.3  10.55761 -1.25761 1.882     -0.66826
+#>   Dataset 6 parent   90      4.5   3.84742  0.65258 1.882      0.34676
+#>   Dataset 6 parent   90      4.7   3.84742  0.85258 1.882      0.45304
+#>   Dataset 6 parent  112      3.0   2.03997  0.96003 1.882      0.51013
+#>   Dataset 6 parent  112      3.4   2.03997  1.36003 1.882      0.72268
+#>   Dataset 6 parent  132      2.3   1.14585  1.15415 1.882      0.61328
+#>   Dataset 6 parent  132      2.7   1.14585  1.55415 1.882      0.82583
+#>   Dataset 6     A1    3      4.3   4.86054 -0.56054 1.882     -0.29786
+#>   Dataset 6     A1    3      4.6   4.86054 -0.26054 1.882     -0.13844
+#>   Dataset 6     A1    6      7.0   7.74179 -0.74179 1.882     -0.39417
+#>   Dataset 6     A1    6      7.2   7.74179 -0.54179 1.882     -0.28789
+#>   Dataset 6     A1   10      8.2   9.94048 -1.74048 1.882     -0.92485
+#>   Dataset 6     A1   10      8.0   9.94048 -1.94048 1.882     -1.03112
+#>   Dataset 6     A1   20     11.0  12.19109 -1.19109 1.882     -0.63291
+#>   Dataset 6     A1   20     13.7  12.19109  1.50891 1.882      0.80180
+#>   Dataset 6     A1   34     11.5  13.10706 -1.60706 1.882     -0.85395
+#>   Dataset 6     A1   34     12.7  13.10706 -0.40706 1.882     -0.21630
+#>   Dataset 6     A1   55     14.9  13.06131  1.83869 1.882      0.97703
+#>   Dataset 6     A1   55     14.5  13.06131  1.43869 1.882      0.76448
+#>   Dataset 6     A1   90     12.1  11.54495  0.55505 1.882      0.29494
+#>   Dataset 6     A1   90     12.3  11.54495  0.75505 1.882      0.40122
+#>   Dataset 6     A1  112      9.9  10.31533 -0.41533 1.882     -0.22070
+#>   Dataset 6     A1  112     10.2  10.31533 -0.11533 1.882     -0.06128
+#>   Dataset 6     A1  132      8.8   9.20222 -0.40222 1.882     -0.21373
+#>   Dataset 6     A1  132      7.8   9.20222 -1.40222 1.882     -0.74510
+#>   Dataset 7 parent    0     93.6  90.82357  2.77643 1.882      1.47532
+#>   Dataset 7 parent    0     92.3  90.82357  1.47643 1.882      0.78453
+#>   Dataset 7 parent    3     87.0  84.73448  2.26552 1.882      1.20384
+#>   Dataset 7 parent    3     82.2  84.73448 -2.53448 1.882     -1.34675
+#>   Dataset 7 parent    7     74.0  77.65013 -3.65013 1.882     -1.93958
+#>   Dataset 7 parent    7     73.9  77.65013 -3.75013 1.882     -1.99272
+#>   Dataset 7 parent   14     64.2  67.60639 -3.40639 1.882     -1.81007
+#>   Dataset 7 parent   14     69.5  67.60639  1.89361 1.882      1.00621
+#>   Dataset 7 parent   30     54.0  52.53663  1.46337 1.882      0.77760
+#>   Dataset 7 parent   30     54.6  52.53663  2.06337 1.882      1.09642
+#>   Dataset 7 parent   60     41.1  39.42728  1.67272 1.882      0.88884
+#>   Dataset 7 parent   60     38.4  39.42728 -1.02728 1.882     -0.54587
+#>   Dataset 7 parent   90     32.5  33.76360 -1.26360 1.882     -0.67144
+#>   Dataset 7 parent   90     35.5  33.76360  1.73640 1.882      0.92268
+#>   Dataset 7 parent  120     28.1  30.39975 -2.29975 1.882     -1.22203
+#>   Dataset 7 parent  120     29.0  30.39975 -1.39975 1.882     -0.74379
+#>   Dataset 7 parent  180     26.5  25.62379  0.87621 1.882      0.46559
+#>   Dataset 7 parent  180     27.6  25.62379  1.97621 1.882      1.05010
+#>   Dataset 7     A1    3      3.9   2.70005  1.19995 1.882      0.63762
+#>   Dataset 7     A1    3      3.1   2.70005  0.39995 1.882      0.21252
+#>   Dataset 7     A1    7      6.9   5.83475  1.06525 1.882      0.56605
+#>   Dataset 7     A1    7      6.6   5.83475  0.76525 1.882      0.40663
+#>   Dataset 7     A1   14     10.4  10.26142  0.13858 1.882      0.07364
+#>   Dataset 7     A1   14      8.3  10.26142 -1.96142 1.882     -1.04225
+#>   Dataset 7     A1   30     14.4  16.82999 -2.42999 1.882     -1.29123
+#>   Dataset 7     A1   30     13.7  16.82999 -3.12999 1.882     -1.66319
+#>   Dataset 7     A1   60     22.1  22.32486 -0.22486 1.882     -0.11949
+#>   Dataset 7     A1   60     22.3  22.32486 -0.02486 1.882     -0.01321
+#>   Dataset 7     A1   90     27.5  24.45927  3.04073 1.882      1.61576
+#>   Dataset 7     A1   90     25.4  24.45927  0.94073 1.882      0.49988
+#>   Dataset 7     A1  120     28.0  25.54862  2.45138 1.882      1.30260
+#>   Dataset 7     A1  120     26.6  25.54862  1.05138 1.882      0.55868
+#>   Dataset 7     A1  180     25.8  26.82277 -1.02277 1.882     -0.54347
+#>   Dataset 7     A1  180     25.3  26.82277 -1.52277 1.882     -0.80916
+#>   Dataset 8 parent    0     91.9  91.16791  0.73209 1.882      0.38901
+#>   Dataset 8 parent    0     90.8  91.16791 -0.36791 1.882     -0.19550
+#>   Dataset 8 parent    1     64.9  67.58358 -2.68358 1.882     -1.42598
+#>   Dataset 8 parent    1     66.2  67.58358 -1.38358 1.882     -0.73520
+#>   Dataset 8 parent    3     43.5  41.62086  1.87914 1.882      0.99853
+#>   Dataset 8 parent    3     44.1  41.62086  2.47914 1.882      1.31735
+#>   Dataset 8 parent    8     18.3  19.60116 -1.30116 1.882     -0.69140
+#>   Dataset 8 parent    8     18.1  19.60116 -1.50116 1.882     -0.79768
+#>   Dataset 8 parent   14     10.2  10.63101 -0.43101 1.882     -0.22903
+#>   Dataset 8 parent   14     10.8  10.63101  0.16899 1.882      0.08980
+#>   Dataset 8 parent   27      4.9   3.12435  1.77565 1.882      0.94354
+#>   Dataset 8 parent   27      3.3   3.12435  0.17565 1.882      0.09334
+#>   Dataset 8 parent   48      1.6   0.43578  1.16422 1.882      0.61864
+#>   Dataset 8 parent   48      1.5   0.43578  1.06422 1.882      0.56550
+#>   Dataset 8 parent   70      1.1   0.05534  1.04466 1.882      0.55510
+#>   Dataset 8 parent   70      0.9   0.05534  0.84466 1.882      0.44883
+#>   Dataset 8     A1    1      9.6   7.63450  1.96550 1.882      1.04442
+#>   Dataset 8     A1    1      7.7   7.63450  0.06550 1.882      0.03481
+#>   Dataset 8     A1    3     15.0  15.52593 -0.52593 1.882     -0.27947
+#>   Dataset 8     A1    3     15.1  15.52593 -0.42593 1.882     -0.22633
+#>   Dataset 8     A1    8     21.2  20.32192  0.87808 1.882      0.46659
+#>   Dataset 8     A1    8     21.1  20.32192  0.77808 1.882      0.41345
+#>   Dataset 8     A1   14     19.7  20.09721 -0.39721 1.882     -0.21107
+#>   Dataset 8     A1   14     18.9  20.09721 -1.19721 1.882     -0.63617
+#>   Dataset 8     A1   27     17.5  16.37477  1.12523 1.882      0.59792
+#>   Dataset 8     A1   27     15.9  16.37477 -0.47477 1.882     -0.25228
+#>   Dataset 8     A1   48      9.5  10.13141 -0.63141 1.882     -0.33551
+#>   Dataset 8     A1   48      9.8  10.13141 -0.33141 1.882     -0.17610
+#>   Dataset 8     A1   70      6.2   5.81827  0.38173 1.882      0.20284
+#>   Dataset 8     A1   70      6.1   5.81827  0.28173 1.882      0.14970
+#>   Dataset 9 parent    0     99.8  97.48728  2.31272 1.882      1.22892
+#>   Dataset 9 parent    0     98.3  97.48728  0.81272 1.882      0.43186
+#>   Dataset 9 parent    1     77.1  79.29476 -2.19476 1.882     -1.16624
+#>   Dataset 9 parent    1     77.2  79.29476 -2.09476 1.882     -1.11310
+#>   Dataset 9 parent    3     59.0  55.67060  3.32940 1.882      1.76915
+#>   Dataset 9 parent    3     58.1  55.67060  2.42940 1.882      1.29092
+#>   Dataset 9 parent    8     27.4  31.57871 -4.17871 1.882     -2.22046
+#>   Dataset 9 parent    8     29.2  31.57871 -2.37871 1.882     -1.26398
+#>   Dataset 9 parent   14     19.1  22.51546 -3.41546 1.882     -1.81489
+#>   Dataset 9 parent   14     29.6  22.51546  7.08454 1.882      3.76454
+#>   Dataset 9 parent   27     10.1  14.09074 -3.99074 1.882     -2.12057
+#>   Dataset 9 parent   27     18.2  14.09074  4.10926 1.882      2.18355
+#>   Dataset 9 parent   48      4.5   6.95747 -2.45747 1.882     -1.30584
+#>   Dataset 9 parent   48      9.1   6.95747  2.14253 1.882      1.13848
+#>   Dataset 9 parent   70      2.3   3.32472 -1.02472 1.882     -0.54451
+#>   Dataset 9 parent   70      2.9   3.32472 -0.42472 1.882     -0.22569
+#>   Dataset 9 parent   91      2.0   1.64300  0.35700 1.882      0.18970
+#>   Dataset 9 parent   91      1.8   1.64300  0.15700 1.882      0.08343
+#>   Dataset 9 parent  120      2.0   0.62073  1.37927 1.882      0.73291
+#>   Dataset 9 parent  120      2.2   0.62073  1.57927 1.882      0.83918
+#>   Dataset 9     A1    1      4.2   3.64568  0.55432 1.882      0.29455
+#>   Dataset 9     A1    1      3.9   3.64568  0.25432 1.882      0.13514
+#>   Dataset 9     A1    3      7.4   8.30173 -0.90173 1.882     -0.47916
+#>   Dataset 9     A1    3      7.9   8.30173 -0.40173 1.882     -0.21347
+#>   Dataset 9     A1    8     14.5  12.71589  1.78411 1.882      0.94803
+#>   Dataset 9     A1    8     13.7  12.71589  0.98411 1.882      0.52293
+#>   Dataset 9     A1   14     14.2  13.90452  0.29548 1.882      0.15701
+#>   Dataset 9     A1   14     12.2  13.90452 -1.70452 1.882     -0.90574
+#>   Dataset 9     A1   27     13.7  14.15523 -0.45523 1.882     -0.24190
+#>   Dataset 9     A1   27     13.2  14.15523 -0.95523 1.882     -0.50759
+#>   Dataset 9     A1   48     13.6  13.31038  0.28962 1.882      0.15389
+#>   Dataset 9     A1   48     15.4  13.31038  2.08962 1.882      1.11037
+#>   Dataset 9     A1   70     10.4  11.85965 -1.45965 1.882     -0.77562
+#>   Dataset 9     A1   70     11.6  11.85965 -0.25965 1.882     -0.13797
+#>   Dataset 9     A1   91     10.0  10.36294 -0.36294 1.882     -0.19286
+#>   Dataset 9     A1   91      9.5  10.36294 -0.86294 1.882     -0.45855
+#>   Dataset 9     A1  120      9.1   8.43003  0.66997 1.882      0.35601
+#>   Dataset 9     A1  120      9.0   8.43003  0.56997 1.882      0.30287
+#>  Dataset 10 parent    0     96.1  93.95603  2.14397 1.882      1.13925
+#>  Dataset 10 parent    0     94.3  93.95603  0.34397 1.882      0.18278
+#>  Dataset 10 parent    8     73.9  77.70592 -3.80592 1.882     -2.02237
+#>  Dataset 10 parent    8     73.9  77.70592 -3.80592 1.882     -2.02237
+#>  Dataset 10 parent   14     69.4  70.04570 -0.64570 1.882     -0.34311
+#>  Dataset 10 parent   14     73.1  70.04570  3.05430 1.882      1.62298
+#>  Dataset 10 parent   21     65.6  64.01710  1.58290 1.882      0.84111
+#>  Dataset 10 parent   21     65.3  64.01710  1.28290 1.882      0.68170
+#>  Dataset 10 parent   41     55.9  54.98434  0.91566 1.882      0.48656
+#>  Dataset 10 parent   41     54.4  54.98434 -0.58434 1.882     -0.31050
+#>  Dataset 10 parent   63     47.0  49.87137 -2.87137 1.882     -1.52577
+#>  Dataset 10 parent   63     49.3  49.87137 -0.57137 1.882     -0.30361
+#>  Dataset 10 parent   91     44.7  45.06727 -0.36727 1.882     -0.19516
+#>  Dataset 10 parent   91     46.7  45.06727  1.63273 1.882      0.86759
+#>  Dataset 10 parent  120     42.1  40.76402  1.33598 1.882      0.70991
+#>  Dataset 10 parent  120     41.3  40.76402  0.53598 1.882      0.28481
+#>  Dataset 10     A1    8      3.3   4.14599 -0.84599 1.882     -0.44954
+#>  Dataset 10     A1    8      3.4   4.14599 -0.74599 1.882     -0.39640
+#>  Dataset 10     A1   14      3.9   6.08478 -2.18478 1.882     -1.16093
+#>  Dataset 10     A1   14      2.9   6.08478 -3.18478 1.882     -1.69231
+#>  Dataset 10     A1   21      6.4   7.59411 -1.19411 1.882     -0.63452
+#>  Dataset 10     A1   21      7.2   7.59411 -0.39411 1.882     -0.20942
+#>  Dataset 10     A1   41      9.1   9.78292 -0.68292 1.882     -0.36289
+#>  Dataset 10     A1   41      8.5   9.78292 -1.28292 1.882     -0.68171
+#>  Dataset 10     A1   63     11.7  10.93274  0.76726 1.882      0.40770
+#>  Dataset 10     A1   63     12.0  10.93274  1.06726 1.882      0.56711
+#>  Dataset 10     A1   91     13.3  11.93986  1.36014 1.882      0.72274
+#>  Dataset 10     A1   91     13.2  11.93986  1.26014 1.882      0.66961
+#>  Dataset 10     A1  120     14.3  12.79238  1.50762 1.882      0.80111
+#>  Dataset 10     A1  120     12.1  12.79238 -0.69238 1.882     -0.36791
 
 # The following takes about 6 minutes
 #f_saem_dfop_sfo_deSolve <- saem(f_mmkin["DFOP-SFO", ], solution_type = "deSolve",
diff --git a/docs/dev/reference/summary.mkinfit.html b/docs/dev/reference/summary.mkinfit.html
index 993544c7..3994a424 100644
--- a/docs/dev/reference/summary.mkinfit.html
+++ b/docs/dev/reference/summary.mkinfit.html
@@ -108,7 +108,7 @@ values.
     
     Arguments
     object
-an object of class mkinfit.
+an object of class mkinfit.
 
 
 data
@@ -189,7 +189,8 @@ model.
 The DT50 and DT90 values for each observed variable.
 
 SFORB
-If applicable, eigenvalues of SFORB components of the model.
+If applicable, eigenvalues and fractional eigenvector component
+g of SFORB systems in the model.
 
 
The print method is called for its side effect, i.e. printing the summary.
     
@@ -212,8 +213,8 @@ EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
   summary(mkinfit("SFO", FOCUS_2006_A, quiet = TRUE))
 #> mkin version used for fitting:    1.2.0 
 #> R version used for fitting:       4.2.2 
-#> Date of fit:     Tue Nov  1 14:12:09 2022 
-#> Date of summary: Tue Nov  1 14:12:09 2022 
+#> Date of fit:     Mon Nov 14 21:06:31 2022 
+#> Date of summary: Mon Nov 14 21:06:31 2022 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent * parent
diff --git a/docs/dev/sitemap.xml b/docs/dev/sitemap.xml
index 17f86f6c..04cf230e 100644
--- a/docs/dev/sitemap.xml
+++ b/docs/dev/sitemap.xml
@@ -36,6 +36,9 @@
   
     https://pkgdown.jrwb.de/mkin/articles/web_only/multistart.html
   
+  
+    https://pkgdown.jrwb.de/mkin/articles/web_only/saem_benchmarks.html
+  
   
     https://pkgdown.jrwb.de/mkin/authors.html
   
diff --git a/vignettes/web_only/mkin_benchmarks.rda b/vignettes/web_only/mkin_benchmarks.rda
index ea9abf65..a0d4c72c 100644
Binary files a/vignettes/web_only/mkin_benchmarks.rda and b/vignettes/web_only/mkin_benchmarks.rda differ
diff --git a/vignettes/web_only/saem_benchmarks.rda b/vignettes/web_only/saem_benchmarks.rda
index 506d7591..1e75b20d 100644
Binary files a/vignettes/web_only/saem_benchmarks.rda and b/vignettes/web_only/saem_benchmarks.rda differ
-- 
cgit v1.2.1

t	Time.
parent_0	Starting value for the response variable at time zero.
alpha	Shape parameter determined by coefficient of variation of rate -constant values.
beta	Location parameter.

t	Time.
parent_0	Starting value for the response variable at time zero.
k_12	Kinetic constant describing transfer from free to bound.
k_21	Kinetic constant describing transfer from bound to free.
k_1output	Kinetic constant describing degradation of the free -fraction.

x	A kinetic model as produced by `mkinmod`, or a kinetic -fit as fitted by `mkinfit`. In the latter case, the fitted -parameters are used for the prediction.
odeparms	A numeric vector specifying the parameters used in the -kinetic model, which is generally defined as a set of ordinary -differential equations.
odeini	A numeric vector containing the initial values of the state + + mkinpredict(x, odeparms, odeini, outtimes, ...) + +# S3 method for mkinmod +mkinpredict( + x, + odeparms = c(k_parent_sink = 0.1), + odeini = c(parent = 100), + outtimes = seq(0, 120, by = 0.1), + solution_type = "deSolve", + use_compiled = "auto", + method.ode = "lsoda", + atol = 1e-08, + rtol = 1e-10, + maxsteps = 20000, + map_output = TRUE, + na_stop = TRUE, + ... +) + +# S3 method for mkinfit +mkinpredict( + x, + odeparms = x$bparms.ode, + odeini = x$bparms.state, + outtimes = seq(0, 120, by = 0.1), + solution_type = "deSolve", + use_compiled = "auto", + method.ode = "lsoda", + atol = 1e-08, + rtol = 1e-10, + map_output = TRUE, + ... +) + + + + Arguments + x + A kinetic model as produced by mkinmod, or a kinetic fit as +fitted by mkinfit. In the latter case, the fitted parameters are used for +the prediction. + + + odeparms + A numeric vector specifying the parameters used in the +kinetic model, which is generally defined as a set of ordinary differential +equations. + + + odeini + A numeric vector containing the initial values of the state variables of the model. Note that the state variables can differ from the -observed variables, for example in the case of the SFORB model.
outtimes	A numeric vector specifying the time points for which model -predictions should be generated.
...	Further arguments passed to the ode solver in case such a -solver is used.
solution_type	The method that should be used for producing the +observed variables, for example in the case of the SFORB model. + + + outtimes + A numeric vector specifying the time points for which model +predictions should be generated. + + + ... + Further arguments passed to the ode solver in case such a +solver is used. + + + solution_type + The method that should be used for producing the predictions. This should generally be "analytical" if there is only one observed variable, and usually "deSolve" in the case of several observed variables. The third possibility "eigen" is faster but not applicable to -some models e.g. using FOMC for the parent compound.
use_compiled	If set to `FALSE`, no compiled version of the -`mkinmod` model is used, even if is present.
method.ode	The solution method passed via `mkinpredict` -to `ode` in case the solution type is "deSolve". The default -"lsoda" is performant, but sometimes fails to converge.
atol	Absolute error tolerance, passed to `ode`. Default -is 1e-8, lower than in `lsoda`.
rtol	Absolute error tolerance, passed to `ode`. Default -is 1e-10, much lower than in `lsoda`.
map_output	Boolean to specify if the output should list values for +some models e.g. using FOMC for the parent compound. + + + use_compiled + If set to `FALSE`, no compiled version of the +mkinmod model is used, even if is present. + + + method.ode + The solution method passed via mkinpredict to ode] in +case the solution type is "deSolve". The default "lsoda" is performant, but +sometimes fails to converge. + + + atol + Absolute error tolerance, passed to ode. Default is 1e-8, +lower than in lsoda. + + + rtol + Absolute error tolerance, passed to ode. Default is 1e-10, +much lower than in lsoda. + + + maxsteps + Maximum number of steps, passed to ode. + + + map_output + Boolean to specify if the output should list values for the observed variables (default) or for all state variables (if set to FALSE). Setting this to FALSE has no effect for analytical solutions, -as these always return mapped output.
na_stop	Should it be an error if deSolve::ode returns NaN values

t	Time.
parent_0	Starting value for the response variable at time zero.
k1	First kinetic constant.
k2	Second kinetic constant.
tb	Break point. Before this time, exponential decline according to -`k1` is calculated, after this time, exponential decline proceeds -according to `k2`.

Benchmark timings for mkin

Johannes Ranke

Last change 14 July 2022 (rebuilt 2022-11-01)

Last change 14 July 2022 (rebuilt 2022-11-14)

Johannes Ranke

Last change 14 November 2022 (rebuilt 2022-11-14)

Test data +

Test cases +

Parent only +

One metabolite +

Three metabolites +

Results +

Parent only +

One metabolite +

Three metabolites +

Double First-Order in Parallel kinetics

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First-Order Multi-Compartment kinetics

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Hockey-Stick kinetics

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Indeterminate order rate equation kinetics

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Single First-Order kinetics

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Single First-Order Reversible Binding kinetics

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