Automatic starting parameters for saem.mmkin

For the case of mkin transformations. This gives faster convergence,
and appears to avoid problems with numeric ODE solutions

14 files changed, 1407 insertions, 1362 deletions

diff --git a/GNUmakefile b/GNUmakefile
index 114f7eef..6e75d666 100644
--- a/GNUmakefile
+++ b/GNUmakefile
@@ -103,7 +103,7 @@ vignettes/%.html: vignettes/mkin_vignettes.css vignettes/references.bib vignette
 vignettes: vignettes/mkin.html vignettes/FOCUS_D.html vignettes/FOCUS_L.html vignettes/twa.html
 
 vignettes/web_only/%.html: vignettes/references.bib vignettes/web_only/%.rmd
-	"$(RBIN)/Rscript" -e "tools::buildVignette(file = 'vignettes/web_only/$*.rmd', dir = 'vignettes/web_only', keep='mkin_benchmarks.rda')"
+	"$(RBIN)/Rscript" -e "tools::buildVignette(file = 'vignettes/web_only/$*.rmd', dir = 'vignettes/web_only', keep=c('mkin_benchmarks.rda', 'saem_benchmarks.rda'))"
 
 articles: vignettes/web_only/FOCUS_Z.html vignettes/web_only/compiled_models.html vignettes/web_only/benchmarks.html vignettes/web_only/dimethenamid_2018.html vignettes/web_only/multistart.html
 
diff --git a/NEWS.md b/NEWS.md
index ebd9a9f5..846c7c50 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -10,6 +10,8 @@
 
 - 'R/saem.R': 'logLik', 'update' and 'anova' methods for 'saem.mmkin' objects.
 
+- 'R/saem.R': Automatic estimation of start parameters for random effects for the case of mkin transformations, nicely improving convergence and reducing problems with iterative ODE solutions.
+
 - 'R/status.R': New generic to show status information for fit array objects with methods for 'mmkin', 'mhmkin' and 'multistart' objects.
 
 - 'R/summary.mmkin.R': Summary method for mmkin objects.
diff --git a/R/saem.R b/R/saem.R
index 87718603..e980ed1f 100644
--- a/R/saem.R
+++ b/R/saem.R
@@ -37,14 +37,22 @@ utils::globalVariables(c("predicted", "std"))
 #' @param no_random_effect Character vector of degradation parameters for
 #' which there should be no variability over the groups. Only used
 #' if the covariance model is not explicitly specified.
-#' @param covariance.model Will be passed to [saemix::SaemixModel()]. Per
+#' @param covariance.model Will be passed to [saemix::saemixModel()]. Per
 #' default, uncorrelated random effects are specified for all degradation
 #' parameters.
+#' @param 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.
 #' @param covariates A data frame with covariate data for use in
 #' 'covariate_models', with dataset names as row names.
 #' @param covariate_models A list containing linear model formulas with one explanatory
 #' variable, i.e. of the type 'parameter ~ covariate'. Covariates must be available
 #' in the 'covariates' data frame.
+#' @param error.init Will be passed to [saemix::saemixModel()].
 #' @param quiet Should we suppress the messages saemix prints at the beginning
 #' and the end of the optimisation process?
 #' @param nbiter.saemix Convenience option to increase the number of
@@ -136,9 +144,11 @@ saem.mmkin <- function(object,
   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,
@@ -154,8 +164,10 @@ saem.mmkin <- function(object,
     solution_type = solution_type,
     transformations = transformations,
     covariance.model = covariance.model,
+    omega.init = omega.init,
     covariates = covariates,
     covariate_models = covariate_models,
+    error.init = error.init,
     no_random_effect = no_random_effect,
     ...)
   d_saemix <- saemix_data(object, covariates = covariates, verbose = verbose)
@@ -283,7 +295,9 @@ saemix_model <- function(object, solution_type = "auto",
   transformations = c("mkin", "saemix"), error_model = "auto",
   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, ...)
 {
   if (nrow(object) > 1) stop("Only row objects allowed")
@@ -637,6 +651,18 @@ saemix_model <- function(object, solution_type = "auto",
     covariance.model = diag(covariance_diagonal)
   }
 
+  if (omega.init[1] == "auto") {
+    if (transformations == "mkin") {
+      degparms_eta_ini <- as.numeric( # remove names
+        mean_degparms(object,
+          random = TRUE, test_log_parms = TRUE)$eta)
+
+      omega.init <- 2 * diag(degparms_eta_ini^2)
+    } else {
+      omega.init <- matrix(nrow = 0, ncol = 0)
+    }
+  }
+
   if (is.null(covariate_models)) {
     covariate.model <- matrix(nrow = 0, ncol = 0) # default in saemixModel()
   } else {
@@ -680,6 +706,7 @@ saemix_model <- function(object, solution_type = "auto",
     verbose = verbose,
     covariance.model = covariance.model,
     covariate.model = covariate.model,
+    omega.init = omega.init,
     ...
   )
   attr(res, "mean_dp_start") <- degparms_optim
diff --git a/log/check.log b/log/check.log
index d8225158..3fea2ec6 100644
--- a/log/check.log
+++ b/log/check.log
@@ -57,12 +57,12 @@ Maintainer: ‘Johannes Ranke <johannes.ranke@jrwb.de>’
 * checking data for ASCII and uncompressed saves ... OK
 * checking installed files from ‘inst/doc’ ... OK
 * checking files in ‘vignettes’ ... OK
-* checking examples ... [36s/46s] OK
+* checking examples ... [15s/15s] OK
 * checking for unstated dependencies in ‘tests’ ... OK
 * checking tests ... SKIPPED
 * checking for unstated dependencies in vignettes ... OK
 * checking package vignettes in ‘inst/doc’ ... OK
-* checking re-building of vignette outputs ... [26s/41s] OK
+* checking re-building of vignette outputs ... OK
 * checking PDF version of manual ... OK
 * checking HTML version of manual ... OK
 * checking for non-standard things in the check directory ... OK
diff --git a/log/test.log b/log/test.log
index 874d6e24..f20a7f18 100644
--- a/log/test.log
+++ b/log/test.log
@@ -1,45 +1,45 @@
 ℹ Testing mkin
 ✔ | F W S  OK | Context
 ✔ |         5 | AIC calculation
-✔ |         5 | Analytical solutions for coupled models [3.3s]
+✔ |         5 | Analytical solutions for coupled models [3.2s]
 ✔ |         5 | Calculation of Akaike weights
 ✔ |         3 | Export dataset for reading into CAKE
 ✔ |        12 | Confidence intervals and p-values [1.0s]
-✔ |     1  12 | Dimethenamid data from 2018 [31.5s]
+✔ |     1  12 | Dimethenamid data from 2018 [32.1s]
 ────────────────────────────────────────────────────────────────────────────────
-Skip (test_dmta.R:98:3): Different backends get consistent results for SFO-SFO3+, dimethenamid data
+Skip ('test_dmta.R:98'): Different backends get consistent results for SFO-SFO3+, dimethenamid data
 Reason: Fitting this ODE model with saemix takes about 15 minutes on my system
 ────────────────────────────────────────────────────────────────────────────────
-✔ |        14 | Error model fitting [5.0s]
+✔ |        14 | Error model fitting [4.9s]
 ✔ |         5 | Time step normalisation
 ✔ |         4 | Calculation of FOCUS chi2 error levels [0.6s]
 ✔ |        14 | Results for FOCUS D established in expertise for UBA (Ranke 2014) [0.8s]
-✔ |         4 | Test fitting the decline of metabolites from their maximum [0.4s]
+✔ |         4 | Test fitting the decline of metabolites from their maximum [0.3s]
 ✔ |         1 | Fitting the logistic model [0.2s]
 ✔ |        10 | Batch fitting and diagnosing hierarchical kinetic models [24.0s]
 ✔ |     1  12 | Nonlinear mixed-effects models [0.3s]
 ────────────────────────────────────────────────────────────────────────────────
-Skip (test_mixed.R:74:3): saemix results are reproducible for biphasic fits
+Skip ('test_mixed.R:74'): saemix results are reproducible for biphasic fits
 Reason: Fitting with saemix takes around 10 minutes when using deSolve
 ────────────────────────────────────────────────────────────────────────────────
 ✔ |         3 | Test dataset classes mkinds and mkindsg
 ✔ |        10 | Special cases of mkinfit calls [0.5s]
 ✔ |         3 | mkinfit features [0.7s]
 ✔ |         8 | mkinmod model generation and printing [0.2s]
-✔ |         3 | Model predictions with mkinpredict [0.3s]
-✔ |         7 | Multistart method for saem.mmkin models [36.3s]
-✔ |        16 | Evaluations according to 2015 NAFTA guidance [2.4s]
-✔ |         9 | Nonlinear mixed-effects models with nlme [8.8s]
-✔ |        16 | Plotting [10.1s]
+✔ |         3 | Model predictions with mkinpredict [0.4s]
+✔ |         7 | Multistart method for saem.mmkin models [36.7s]
+✔ |        16 | Evaluations according to 2015 NAFTA guidance [2.3s]
+✔ |         9 | Nonlinear mixed-effects models with nlme [8.5s]
+✔ |        16 | Plotting [9.8s]
 ✔ |         4 | Residuals extracted from mkinfit models
-✔ |     1  37 | saemix parent models [71.5s]
+✔ |     1  36 | saemix parent models [66.4s]
 ────────────────────────────────────────────────────────────────────────────────
-Skip (test_saemix_parent.R:153:3): We can also use mkin solution methods for saem
+Skip ('test_saemix_parent.R:143'): We can also use mkin solution methods for saem
 Reason: This still takes almost 2.5 minutes although we do not solve ODEs
 ────────────────────────────────────────────────────────────────────────────────
 ✔ |         2 | Complex test case from Schaefer et al. (2007) Piacenza paper [1.4s]
 ✔ |        11 | Processing of residue series
-✔ |        10 | Fitting the SFORB model [3.8s]
+✔ |        10 | Fitting the SFORB model [3.7s]
 ✔ |         1 | Summaries of old mkinfit objects
 ✔ |         5 | Summary [0.2s]
 ✔ |         4 | Results for synthetic data established in expertise for UBA (Ranke 2014) [2.2s]
@@ -47,11 +47,11 @@ Reason: This still takes almost 2.5 minutes although we do not solve ODEs
 ✔ |         4 | Calculation of maximum time weighted average concentrations (TWAs) [2.2s]
 
 ══ Results ═════════════════════════════════════════════════════════════════════
-Duration: 216.0 s
+Duration: 211.1 s
 
 ── Skipped tests  ──────────────────────────────────────────────────────────────
 • Fitting this ODE model with saemix takes about 15 minutes on my system (1)
 • Fitting with saemix takes around 10 minutes when using deSolve (1)
 • This still takes almost 2.5 minutes although we do not solve ODEs (1)
 
-[ FAIL 0 | WARN 0 | SKIP 3 | PASS 268 ]
+[ FAIL 0 | WARN 0 | SKIP 3 | PASS 267 ]
diff --git a/man/saem.Rd b/man/saem.Rd
index 3dc8001a..11463351 100644
--- a/man/saem.Rd
+++ b/man/saem.Rd
@@ -20,9 +20,11 @@ saem(object, ...)
   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),
@@ -41,8 +43,10 @@ saemix_model(
   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,
@@ -81,10 +85,18 @@ for parameter that are tested if requested by 'test_log_parms'.}
 \item{solution_type}{Possibility to specify the solution type in case the
 automatic choice is not desired}
 
-\item{covariance.model}{Will be passed to \code{\link[saemix:SaemixModel-class]{saemix::SaemixModel()}}. Per
+\item{covariance.model}{Will be passed to \code{\link[saemix:saemixModel]{saemix::saemixModel()}}. Per
 default, uncorrelated random effects are specified for all degradation
 parameters.}
 
+\item{omega.init}{Will be passed to \code{\link[saemix:saemixModel]{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 \link{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 \link[saemix:saemixModel]{saemix::saemixModel} is used for omega.init.}
+
 \item{covariates}{A data frame with covariate data for use in
 'covariate_models', with dataset names as row names.}
 
@@ -96,6 +108,8 @@ in the 'covariates' data frame.}
 which there should be no variability over the groups. Only used
 if the covariance model is not explicitly specified.}
 
+\item{error.init}{Will be passed to \code{\link[saemix:saemixModel]{saemix::saemixModel()}}.}
+
 \item{nbiter.saemix}{Convenience option to increase the number of
 iterations}
 
diff --git a/tests/testthat/_snaps/multistart/llhist-for-biphasic-saemix-fit.svg b/tests/testthat/_snaps/multistart/llhist-for-biphasic-saemix-fit.svg
index fe38865d..6015aed8 100644
--- a/tests/testthat/_snaps/multistart/llhist-for-biphasic-saemix-fit.svg
+++ b/tests/testthat/_snaps/multistart/llhist-for-biphasic-saemix-fit.svg
@@ -21,24 +21,28 @@
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diff --git a/tests/testthat/_snaps/multistart/parplot-for-biphasic-saemix-fit.svg b/tests/testthat/_snaps/multistart/parplot-for-biphasic-saemix-fit.svg
index 75519b07..c0332fd5 100644
--- a/tests/testthat/_snaps/multistart/parplot-for-biphasic-saemix-fit.svg
+++ b/tests/testthat/_snaps/multistart/parplot-for-biphasic-saemix-fit.svg
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diff --git a/tests/testthat/anova_sfo_saem.txt b/tests/testthat/anova_sfo_saem.txt
index 4a21e81f..9e4bf71f 100644
--- a/tests/testthat/anova_sfo_saem.txt
+++ b/tests/testthat/anova_sfo_saem.txt
@@ -4,4 +4,4 @@ Data: 262 observations of 1 variable(s) grouped in 15 datasets
 sfo_saem_1_reduced         5 1310 1313 -650                    
 sfo_saem_1_reduced_mkin    5 1310 1313 -650     0  0           
 sfo_saem_1                 6 1312 1316 -650     0  1          1
-sfo_saem_1_mkin            6 1310 1315 -649     1  0           
+sfo_saem_1_mkin            6 1312 1316 -650     0  0           
diff --git a/tests/testthat/print_dfop_saemix_1.txt b/tests/testthat/print_dfop_saemix_1.txt
index f427b3e6..f6fda37c 100644
--- a/tests/testthat/print_dfop_saemix_1.txt
+++ b/tests/testthat/print_dfop_saemix_1.txt
@@ -13,12 +13,12 @@ Likelihood computed by importance sampling
 
 Fitted parameters:
             estimate lower  upper
-parent_0      100.04 98.89 101.20
-log_k1         -4.12 -4.24  -4.00
-log_k2         -2.67 -2.90  -2.44
-g_qlogis        0.43  0.22   0.64
-a.1             0.92  0.67   1.16
+parent_0      100.09 98.94 101.25
+log_k1         -2.68 -2.91  -2.45
+log_k2         -4.12 -4.24  -4.00
+g_qlogis       -0.41 -0.63  -0.20
+a.1             0.91  0.67   1.15
 b.1             0.05  0.04   0.06
-SD.log_k1       0.22  0.14   0.30
-SD.log_k2       0.36  0.21   0.51
-SD.g_qlogis     0.14 -0.11   0.39
+SD.log_k1       0.36  0.21   0.50
+SD.log_k2       0.22  0.13   0.30
+SD.g_qlogis     0.15 -0.09   0.40
diff --git a/tests/testthat/summary_hfit_sfo_tc.txt b/tests/testthat/summary_hfit_sfo_tc.txt
index 49765187..41743091 100644
--- a/tests/testthat/summary_hfit_sfo_tc.txt
+++ b/tests/testthat/summary_hfit_sfo_tc.txt
@@ -32,9 +32,9 @@ Likelihood computed by importance sampling
 
 Optimised parameters:
                   est.  lower  upper
-parent_0        101.01  99.57 102.45
+parent_0        101.02  99.58 102.46
 log_k_parent     -3.32  -3.53  -3.11
-a.1               0.90   0.64   1.17
+a.1               0.91   0.64   1.17
 b.1               0.05   0.04   0.06
 SD.log_k_parent   0.27   0.11   0.42
 
@@ -48,7 +48,7 @@ SD.log_k_parent  0.3   0.1   0.4
 
 Variance model:
     est. lower upper
-a.1 0.90  0.64  1.17
+a.1 0.91  0.64  1.17
 b.1 0.05  0.04  0.06
 
 Backtransformed parameters:
diff --git a/tests/testthat/test_multistart.R b/tests/testthat/test_multistart.R
index 56eb140c..c1a10d10 100644
--- a/tests/testthat/test_multistart.R
+++ b/tests/testthat/test_multistart.R
@@ -21,7 +21,10 @@ test_that("multistart works for saem.mmkin models", {
   anova_biphasic <- anova(saem_biphasic_m,
     best(saem_biphasic_m_multi))
 
-  expect_true(anova_biphasic[2, "AIC"] < anova_biphasic[1, "AIC"])
+  # With the new starting parameters we do not improve
+  # with multistart any more
+  expect_equal(anova_biphasic[2, "AIC"], anova_biphasic[1, "AIC"],
+    tolerance = 1e-4)
   skip_on_travis() # Plots are platform dependent
 
   llhist_sfo <- function() llhist(saem_sfo_s_multi)
diff --git a/tests/testthat/test_saemix_parent.R b/tests/testthat/test_saemix_parent.R
index 79c5fa69..20889c6c 100644
--- a/tests/testthat/test_saemix_parent.R
+++ b/tests/testthat/test_saemix_parent.R
@@ -73,40 +73,36 @@ test_that("Parent fits using saemix are correctly implemented", {
   # FOMC
   mmkin_fomc_1 <- mmkin("FOMC", ds_fomc, quiet = TRUE, error_model = "tc", cores = n_cores)
   fomc_saem_1 <- saem(mmkin_fomc_1, quiet = TRUE, transformations = "saemix", no_random_effect = "parent_0")
-  fomc_saem_2 <- update(fomc_saem_1, transformations = "mkin")
-  ci_fomc_s1 <- summary(fomc_saem_1)$confint_back
 
   fomc_pop <- as.numeric(fomc_pop)
+  ci_fomc_s1 <- summary(fomc_saem_1)$confint_back
   expect_true(all(ci_fomc_s1[, "lower"] < fomc_pop))
   expect_true(all(ci_fomc_s1[, "upper"] > fomc_pop))
-  expect_equal(endpoints(fomc_saem_1), endpoints(fomc_saem_2), tol = 0.01)
 
-  mmkin_fomc_2 <- update(mmkin_fomc_1, state.ini = 100, fixed_initials = "parent")
-  fomc_saem_2 <- saem(mmkin_fomc_2, quiet = TRUE, transformations = "mkin")
+  fomc_saem_2 <- update(fomc_saem_1, transformations = "mkin")
   ci_fomc_s2 <- summary(fomc_saem_2)$confint_back
+  expect_true(all(ci_fomc_s2[, "lower"] < fomc_pop))
+  expect_true(all(ci_fomc_s2[, "upper"] > fomc_pop))
 
-  expect_true(all(ci_fomc_s2[, "lower"] < fomc_pop[2:3]))
-  expect_true(all(ci_fomc_s2[, "upper"] > fomc_pop[2:3]))
+  expect_equal(endpoints(fomc_saem_1), endpoints(fomc_saem_2), tol = 0.01)
 
   # DFOP
   dfop_saemix_2 <- saem(mmkin_dfop_1, quiet = TRUE, transformations = "saemix",
     no_random_effect = "parent_0")
 
-  s_dfop_s1 <- summary(dfop_saemix_1)
-  s_dfop_s2 <- summary(dfop_saemix_2)
+  s_dfop_s1 <- summary(dfop_saemix_1) # mkin transformations
+  s_dfop_s2 <- summary(dfop_saemix_2) # saemix transformations
   s_dfop_n <- summary(dfop_nlme_1)
 
   dfop_pop <- as.numeric(dfop_pop)
 
-  # When using DFOP with mkin transformations, k1 and k2 are sometimes swapped
-  swap_k1_k2 <- function(p) c(p[1], p[3], p[2], 1 - p[4])
-  expect_true(all(s_dfop_s1$confint_back[, "lower"] < swap_k1_k2(dfop_pop)))
-  expect_true(all(s_dfop_s1$confint_back[, "upper"] > swap_k1_k2(dfop_pop)))
+  expect_true(all(s_dfop_s1$confint_back[, "lower"] < dfop_pop))
+  expect_true(all(s_dfop_s1$confint_back[, "upper"] > dfop_pop))
   expect_true(all(s_dfop_s2$confint_back[, "lower"] < dfop_pop))
   expect_true(all(s_dfop_s2$confint_back[, "upper"] > dfop_pop))
 
-  # We get < 20% deviations with transformations made in mkin (need to swap k1 and k2)
-  rel_diff_1 <- (swap_k1_k2(s_dfop_s1$confint_back[, "est."]) - dfop_pop) / dfop_pop
+  # We get < 20% deviations with transformations made in mkin
+  rel_diff_1 <- (s_dfop_s1$confint_back[, "est."] - dfop_pop) / dfop_pop
   expect_true(all(rel_diff_1 < 0.20))
 
   # We get < 20% deviations with transformations made in saemix
@@ -123,27 +119,21 @@ test_that("Parent fits using saemix are correctly implemented", {
     transformations = "saemix")
   expect_equal(
     log(endpoints(dfop_saemix_1)$distimes[1:2]),
-    log(endpoints(sforb_saemix_1)$distimes[1:2]), tolerance = 0.03)
+    log(endpoints(sforb_saemix_1)$distimes[1:2]), tolerance = 0.01)
   expect_equal(
     log(endpoints(sforb_saemix_1)$distimes[1:2]),
     log(endpoints(sforb_saemix_2)$distimes[1:2]), tolerance = 0.01)
 
   mmkin_hs_1 <- mmkin("HS", ds_hs, quiet = TRUE, error_model = "const", cores = n_cores)
-  hs_saem_1 <- saem(mmkin_hs_1, quiet = TRUE)
-  hs_saem_2 <- saem(mmkin_hs_1, quiet = TRUE, transformations = "mkin")
+  hs_saem_1 <- saem(mmkin_hs_1, quiet = TRUE, no_random_effect = "parent_0")
+  hs_saem_2 <- saem(mmkin_hs_1, quiet = TRUE, transformations = "mkin",
+    no_random_effect = "parent_0")
   expect_equal(endpoints(hs_saem_1), endpoints(hs_saem_2), tol = 0.01)
   ci_hs_s1 <- summary(hs_saem_1)$confint_back
 
   hs_pop <- as.numeric(hs_pop)
   #expect_true(all(ci_hs_s1[, "lower"] < hs_pop)) # k1 is overestimated
   expect_true(all(ci_hs_s1[, "upper"] > hs_pop))
-
-  mmkin_hs_2 <- update(mmkin_hs_1, state.ini = 100, fixed_initials = "parent")
-  hs_saem_3 <- saem(mmkin_hs_2, quiet = TRUE)
-  ci_hs_s3 <- summary(hs_saem_3)$confint_back
-
-  #expect_true(all(ci_hs_s3[, "lower"] < hs_pop[2:4])) # k1 again overestimated
-  expect_true(all(ci_hs_s3[, "upper"] > hs_pop[2:4]))
 })
 
 test_that("We can also use mkin solution methods for saem", {