Warn if standardized residuals are unlikely normal

This revealed a bug in the data returned in mkinfit$data in the case
of the d_3 algorithm, which also affected the residual plot - the
data from the direct fitting was not returned even if this was
the better method.

14 files changed, 131 insertions, 152 deletions

diff --git a/NAMESPACE b/NAMESPACE
index f8be4fae..0330f88f 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -115,6 +115,7 @@ importFrom(stats,qnorm)
 importFrom(stats,qt)
 importFrom(stats,residuals)
 importFrom(stats,rnorm)
+importFrom(stats,shapiro.test)
 importFrom(stats,update)
 importFrom(stats,var)
 importFrom(utils,getFromNamespace)
diff --git a/NEWS.md b/NEWS.md
index 0d5c93d3..4a923f09 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -10,6 +10,8 @@
 
 - 'mkinfit': Make 'use_of_ff' = "max" also the default for models specified using short names like "SFO" or "FOMC"
 
+- 'mkinfit': Run 'stats::shapiro.test()' on standardized residuals and warn if p < 0.05
+
 # mkin 0.9.50.2 (2020-05-12)
 
 - Increase tolerance for a platform specific test results on the Solaris test machine on CRAN
diff --git a/R/mkinfit.R b/R/mkinfit.R
index f9cb3304..d7b1b7f4 100644
--- a/R/mkinfit.R
+++ b/R/mkinfit.R
@@ -98,7 +98,7 @@ if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "time", "value"))
 #' @param quiet Suppress printing out the current value of the negative
 #'   log-likelihood after each improvement?
 #' @param atol Absolute error tolerance, passed to [deSolve::ode()]. Default
-#'   is 1e-8, which is lower than the default in the [deSolve::lsoda()] 
+#'   is 1e-8, which is lower than the default in the [deSolve::lsoda()]
 #'   function which is used per default.
 #' @param rtol Absolute error tolerance, passed to [deSolve::ode()]. Default
 #'   is 1e-10, much lower than in [deSolve::lsoda()].
@@ -119,7 +119,7 @@ if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "time", "value"))
 #'   least squares fitting ("OLS") is selected. If the error model is "obs", or
 #'   "tc", the "d_3" algorithm is selected.
 #'
-#'   The algorithm "d_3" will directly minimize the negative log-likelihood 
+#'   The algorithm "d_3" will directly minimize the negative log-likelihood
 #'   and independently also use the three step algorithm described below.
 #'   The fit with the higher likelihood is returned.
 #'
@@ -150,7 +150,7 @@ if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "time", "value"))
 #' @param trace_parms Should a trace of the parameter values be listed?
 #' @param \dots Further arguments that will be passed on to
 #'   [deSolve::ode()].
-#' @importFrom stats nlminb aggregate dist
+#' @importFrom stats nlminb aggregate dist shapiro.test
 #' @return A list with "mkinfit" in the class attribute.
 #' @note When using the "IORE" submodel for metabolites, fitting with
 #'   "transform_rates = TRUE" (the default) often leads to failures of the
@@ -168,7 +168,7 @@ if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "time", "value"))
 #'   for measurement error in analytical chemistry. *Technometrics* 37(2), 176-184.
 #'
 #'   Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical
-#'   Degradation Data. *Environments* 6(12) 124 
+#'   Degradation Data. *Environments* 6(12) 124
 #'   [doi:10.3390/environments6120124](https://doi.org/10.3390/environments6120124).
 #' @examples
 #'
@@ -177,60 +177,62 @@ if(getRversion() >= '2.15.1') utils::globalVariables(c("name", "time", "value"))
 #' summary(fit)
 #'
 #' # One parent compound, one metabolite, both single first order.
+#' # We remove zero values from FOCUS dataset D in order to avoid warnings
+#' FOCUS_D <- subset(FOCUS_2006_D, value != 0)
 #' # Use mkinsub for convenience in model formulation. Pathway to sink included per default.
 #' SFO_SFO <- mkinmod(
 #'   parent = mkinsub("SFO", "m1"),
 #'   m1 = mkinsub("SFO"))
-#' # Fit the model to the FOCUS example dataset D using defaults
-#' print(system.time(fit <- mkinfit(SFO_SFO, FOCUS_2006_D,
-#'                            solution_type = "eigen", quiet = TRUE)))
-#' parms(fit)
-#' endpoints(fit)
+#'
+#' # Fit the model quietly to the FOCUS example dataset D using defaults
+#' fit <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE)
+#' # Since mkin 0.9.50.3, we get a warning about non-normality of residuals,
+#' # so we try an alternative error model
+#' fit.tc <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE, error_model = "tc")
+#' # This avoids the warning, and the likelihood ratio test confirms it is preferable
+#' lrtest(fit.tc, fit)
+#' # We can also allow for different variances of parent and metabolite as error model
+#' fit.obs <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE, error_model = "obs")
+#' # This also avoids the warning about non-normality, but the two-component error model
+#' # has significantly higher likelihood
+#' lrtest(fit.obs, fit.tc)
+#' parms(fit.tc)
+#' endpoints(fit.tc)
+#'
+#' # We can show a quick (only one replication) benchmark for this case, as we
+#' # have several alternative solution methods for the model. We skip
+#' # uncompiled deSolve, as it is so slow. More benchmarks are found in the
+#' # benchmark vignette
 #' \dontrun{
-#' # deSolve is slower when no C compiler (gcc) was available during model generation
-#' print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D,
-#'                            solution_type = "deSolve")))
-#' parms(fit.deSolve)
-#' endpoints(fit.deSolve)
+#' if(require(rbenchmark)) {
+#'   benchmark(replications = 1, order = "relative", columns = c("test", "relative", "elapsed"),
+#'     deSolve_compiled = mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE, error_model = "tc",
+#'       solution_type = "deSolve", use_compiled = TRUE),
+#'     eigen = mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE, error_model = "tc",
+#'       solution_type = "eigen"),
+#'     analytical = mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE, error_model = "tc",
+#'       solution_type = "analytical"))
+#' }
 #' }
 #'
-#' # Use stepwise fitting, using optimised parameters from parent only fit, FOMC
+#' # Use stepwise fitting, using optimised parameters from parent only fit, FOMC-SFO
 #' \dontrun{
 #' FOMC_SFO <- mkinmod(
 #'   parent = mkinsub("FOMC", "m1"),
 #'   m1 = mkinsub("SFO"))
-#' # Fit the model to the FOCUS example dataset D using defaults
-#' fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE)
-#' # Use starting parameters from parent only FOMC fit
-#' fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE)
-#' fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE,
-#'   parms.ini = fit.FOMC$bparms.ode)
-#'
-#' # Use stepwise fitting, using optimised parameters from parent only fit, SFORB
-#' SFORB_SFO <- mkinmod(
-#'   parent = list(type = "SFORB", to = "m1", sink = TRUE),
-#'   m1 = list(type = "SFO"))
-#' # Fit the model to the FOCUS example dataset D using defaults
-#' fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, quiet = TRUE)
-#' fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve",
-#'                                  quiet = TRUE)
-#' # Use starting parameters from parent only SFORB fit (not really needed in this case)
-#' fit.SFORB = mkinfit("SFORB", FOCUS_2006_D, quiet = TRUE)
-#' fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode, quiet = TRUE)
-#' }
-#'
-#' \dontrun{
-#' # Weighted fits, including IRLS (error_model = "obs")
-#' SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"),
-#'                       m1 = mkinsub("SFO"), use_of_ff = "max")
-#' f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
-#' summary(f.noweight)
-#' f.obs <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "obs", quiet = TRUE)
-#' summary(f.obs)
-#' f.tc <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "tc", quiet = TRUE)
-#' summary(f.tc)
-#' }
+#' fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE)
+#' # Again, we get a warning and try a more sophisticated error model
+#' fit.FOMC_SFO.tc <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE, error_model = "tc")
+#' # This model has a higher likelihood, but not significantly so
+#' lrtest(fit.tc, fit.FOMC_SFO.tc)
+#' # Also, the missing standard error for log_beta and the t-tests for alpha
+#' # and beta indicate overparameterisation
+#' summary(fit.FOMC_SFO.tc, data = FALSE)
 #'
+#' # We can easily use starting parameters from the parent only fit (only for illustration)
+#' fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE, error_model = "tc")
+#' fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_D, quiet = TRUE,
+#'   parms.ini = fit.FOMC$bparms.ode, error_model = "tc")
 #'
 #' @export
 mkinfit <- function(mkinmod, observed,
@@ -716,6 +718,7 @@ mkinfit <- function(mkinmod, observed,
         errparms <- fit_direct$par[errparms_index]
       } else {
         cost.current <- Inf # reset to avoid conflict with the OLS step
+        data_direct <- current_data # We need this later if it was better
       }
     }
     if (error_model_algorithm != "direct") {
@@ -785,6 +788,7 @@ mkinfit <- function(mkinmod, observed,
             fit$d_3_message <- d_3_messages["direct"]
             degparms <- fit$par[degparms_index]
             errparms <- fit$par[errparms_index]
+            current_data  <- data_direct
           }
         }
       }
@@ -914,6 +918,10 @@ mkinfit <- function(mkinmod, observed,
   fit$errparms <- errparms
   fit$df.residual <- n_observed - length(c(degparms, errparms))
 
+  # Check for normal distribution of residuals
+  fit$shapiro.p <- shapiro.test(residuals.mkinfit(fit, standardized = TRUE))$p.value
+  if (fit$shapiro.p < 0.05) warning("The p-value for the Shapiro-Wilk test of normality on standardized residuals is < 0.05")
+
   fit$date <- date()
   fit$version <- as.character(utils::packageVersion("mkin"))
   fit$Rversion <- paste(R.version$major, R.version$minor, sep=".")
diff --git a/R/summary.mkinfit.R b/R/summary.mkinfit.R
index 2dc74bd7..2c291ffd 100644
--- a/R/summary.mkinfit.R
+++ b/R/summary.mkinfit.R
@@ -165,6 +165,7 @@ summary.mkinfit <- function(object, data = TRUE, distimes = TRUE, alpha = 0.05,
   }
 
   ans$bparms.ode <- object$bparms.ode
+  ans$shapiro.p <- object$shapiro.p
   ep <- endpoints(object)
   if (length(ep$ff) != 0)
     ans$ff <- ep$ff
@@ -228,6 +229,10 @@ print.summary.mkinfit <- function(x, digits = max(3, getOption("digits") - 3), .
       row.names = " "))
   }
 
+  if (!is.null(x$shapiro.p) && x$shapiro.p < 0.05) {
+    warning("The p-value for the Shapiro-Wilk test of normality on standardized residuals is < 0.05")
+  }
+
   cat("\nOptimised, transformed parameters with symmetric confidence intervals:\n")
   print(signif(x$par, digits = digits))
 
diff --git a/man/mkinfit.Rd b/man/mkinfit.Rd
index 5e6b242e..748dcb50 100644
--- a/man/mkinfit.Rd
+++ b/man/mkinfit.Rd
@@ -214,69 +214,6 @@ When using the "IORE" submodel for metabolites, fitting with
 numerical ODE solver. In this situation it may help to switch off the
 internal rate transformation.
 }
-\examples{
-
-# Use shorthand notation for parent only degradation
-fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
-summary(fit)
-
-# One parent compound, one metabolite, both single first order.
-# Use mkinsub for convenience in model formulation. Pathway to sink included per default.
-SFO_SFO <- mkinmod(
-  parent = mkinsub("SFO", "m1"),
-  m1 = mkinsub("SFO"))
-# Fit the model to the FOCUS example dataset D using defaults
-print(system.time(fit <- mkinfit(SFO_SFO, FOCUS_2006_D,
-                           solution_type = "eigen", quiet = TRUE)))
-parms(fit)
-endpoints(fit)
-\dontrun{
-# deSolve is slower when no C compiler (gcc) was available during model generation
-print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D,
-                           solution_type = "deSolve")))
-parms(fit.deSolve)
-endpoints(fit.deSolve)
-}
-
-# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
-\dontrun{
-FOMC_SFO <- mkinmod(
-  parent = mkinsub("FOMC", "m1"),
-  m1 = mkinsub("SFO"))
-# Fit the model to the FOCUS example dataset D using defaults
-fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE)
-# Use starting parameters from parent only FOMC fit
-fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE)
-fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE,
-  parms.ini = fit.FOMC$bparms.ode)
-
-# Use stepwise fitting, using optimised parameters from parent only fit, SFORB
-SFORB_SFO <- mkinmod(
-  parent = list(type = "SFORB", to = "m1", sink = TRUE),
-  m1 = list(type = "SFO"))
-# Fit the model to the FOCUS example dataset D using defaults
-fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, quiet = TRUE)
-fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve",
-                                 quiet = TRUE)
-# Use starting parameters from parent only SFORB fit (not really needed in this case)
-fit.SFORB = mkinfit("SFORB", FOCUS_2006_D, quiet = TRUE)
-fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode, quiet = TRUE)
-}
-
-\dontrun{
-# Weighted fits, including IRLS (error_model = "obs")
-SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"),
-                      m1 = mkinsub("SFO"), use_of_ff = "max")
-f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
-summary(f.noweight)
-f.obs <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "obs", quiet = TRUE)
-summary(f.obs)
-f.tc <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "tc", quiet = TRUE)
-summary(f.tc)
-}
-
-
-}
 \references{
 Rocke DM and Lorenzato S (1995) A two-component model
 for measurement error in analytical chemistry. \emph{Technometrics} 37(2), 176-184.
diff --git a/test.log b/test.log
index e026e559..a1fa7dfb 100644
--- a/test.log
+++ b/test.log
@@ -2,10 +2,10 @@ Loading mkin
 Testing mkin
 ✔ |  OK F W S | Context
 ✔ |   2       | Export dataset for reading into CAKE
-✔ |  13       | Results for FOCUS D established in expertise for UBA (Ranke 2014) [1.1 s]
+✔ |  14       | Results for FOCUS D established in expertise for UBA (Ranke 2014) [0.9 s]
 ✔ |   4       | Calculation of FOCUS chi2 error levels [0.4 s]
 ✔ |   7       | Fitting the SFORB model [3.3 s]
-✔ |   5       | Analytical solutions for coupled models [3.1 s]
+✔ |   5       | Analytical solutions for coupled models [3.2 s]
 ✔ |   5       | Calculation of Akaike weights
 ✔ |  10       | Confidence intervals and p-values [1.1 s]
 ✔ |  14       | Error model fitting [4.0 s]
@@ -15,22 +15,29 @@ Testing mkin
 ✔ |  12       | Special cases of mkinfit calls [0.6 s]
 ✔ |   8       | mkinmod model generation and printing [0.2 s]
 ✔ |   3       | Model predictions with mkinpredict [0.4 s]
-✔ |  16       | Evaluations according to 2015 NAFTA guidance [1.6 s]
-✔ |   9       | Nonlinear mixed-effects models [7.7 s]
+✔ |  16       | Evaluations according to 2015 NAFTA guidance [1.5 s]
+✔ |   9       | Nonlinear mixed-effects models [7.8 s]
 ✔ |   4       | Calculation of maximum time weighted average concentrations (TWAs) [2.4 s]
-✔ |   3       | Summary
-✔ |  14       | Plotting [1.5 s]
+✔ |   3   2   | Summary
+────────────────────────────────────────────────────────────────────────────────
+test_plots_summary_twa.R:59: warning: Summaries are reproducible
+The p-value for the Shapiro-Wilk test of normality on standardized residuals is < 0.05
+
+test_plots_summary_twa.R:72: warning: Summaries are reproducible
+The p-value for the Shapiro-Wilk test of normality on standardized residuals is < 0.05
+────────────────────────────────────────────────────────────────────────────────
+✔ |  14       | Plotting [1.4 s]
 ✔ |   4       | AIC calculation
 ✔ |   4       | Residuals extracted from mkinfit models
-✔ |   2       | Complex test case from Schaefer et al. (2007) Piacenza paper [1.4 s]
+✔ |   2       | Complex test case from Schaefer et al. (2007) Piacenza paper [1.5 s]
 ✔ |   1       | Summaries of old mkinfit objects
-✔ |   4       | Results for synthetic data established in expertise for UBA (Ranke 2014) [2.3 s]
+✔ |   4       | Results for synthetic data established in expertise for UBA (Ranke 2014) [2.1 s]
 ✔ |   9       | Hypothesis tests [6.6 s]
 
 ══ Results ═════════════════════════════════════════════════════════════════════
-Duration: 38.5 s
+Duration: 38.3 s
 
-OK:       159
+OK:       160
 Failed:   0
-Warnings: 0
+Warnings: 2
 Skipped:  0
diff --git a/tests/testthat/FOCUS_2006_D.csf b/tests/testthat/FOCUS_2006_D.csf
index f845cc1d..7c8340cd 100644
--- a/tests/testthat/FOCUS_2006_D.csf
+++ b/tests/testthat/FOCUS_2006_D.csf
@@ -5,7 +5,7 @@ Description:
 MeasurementUnits: % AR
 TimeUnits: days
 Comments: Created using mkin::CAKE_export
-Date: 2020-05-28
+Date: 2020-05-29
 Optimiser: IRLS
 
 [Data]
diff --git a/tests/testthat/setup_script.R b/tests/testthat/setup_script.R
index def52697..8d8ba3e9 100644
--- a/tests/testthat/setup_script.R
+++ b/tests/testthat/setup_script.R
@@ -57,18 +57,26 @@ DFOP_SFO <- mkinmod(parent = mkinsub("DFOP", to = "m1"),
 # Avoid warning when fitting a dataset where zero value is removed
 FOCUS_D <- subset(FOCUS_2006_D, value != 0)
 
+# We do not want warnings about non-normality of residuals here
+suppressWarnings(
 f_sfo_sfo_desolve <- mkinfit(SFO_SFO, FOCUS_D,
   solution_type = "deSolve", quiet = TRUE)
+)
+suppressWarnings(
 f_sfo_sfo_eigen <- mkinfit(SFO_SFO, FOCUS_D,
   solution_type = "eigen", quiet = TRUE)
-
+)
+suppressWarnings(
 f_sfo_sfo.ff <- mkinfit(SFO_SFO.ff, FOCUS_D,
   quiet = TRUE)
+)
 
 SFO_lin_a <- synthetic_data_for_UBA_2014[[1]]$data
 DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
 
-f_2_mkin <- mkinfit("DFOP", DFOP_par_c, quiet = TRUE)
+# We also suppress the warning about non-normality of residuals here, the data
+# were generated with a different error model, so no wonder!
+f_2_mkin <- suppressWarnings(mkinfit("DFOP", DFOP_par_c, quiet = TRUE))
 f_2_nls <- nls(value ~ SSbiexp(time, A1, lrc1, A2, lrc2), data = subset(DFOP_par_c, name == "parent"))
 f_2_anova <- lm(value ~ as.factor(time), data = subset(DFOP_par_c, name == "parent"))
 
@@ -86,9 +94,9 @@ m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
 
 fit_nw_1 <- mkinfit(m_synth_SFO_lin, SFO_lin_a, quiet = TRUE)
 
-# We know direct optimization is OK and direct needs 4 sec versus 5.5 for threestep and 6 for IRLS
+# We know direct optimization is OK and direct is faster than the default d_3
 fit_obs_1 <- mkinfit(m_synth_SFO_lin, SFO_lin_a, error_model = "obs", quiet = TRUE,
   error_model_algorithm = "direct")
-# We know threestep is OK, and threestep (and IRLS) need 4.8 se versus 5.6 for direct
+# We know threestep is OK, and threestep (and IRLS) is faster here
 fit_tc_1 <- mkinfit(m_synth_SFO_lin, SFO_lin_a, error_model = "tc", quiet = TRUE,
   error_model_algorithm = "threestep")
diff --git a/tests/testthat/test_FOCUS_D_UBA_expertise.R b/tests/testthat/test_FOCUS_D_UBA_expertise.R
index be2806de..101c8e15 100644
--- a/tests/testthat/test_FOCUS_D_UBA_expertise.R
+++ b/tests/testthat/test_FOCUS_D_UBA_expertise.R
@@ -2,11 +2,10 @@ context("Results for FOCUS D established in expertise for UBA (Ranke 2014)")
 
 # Results are from p. 40
 
-# Avoid warnings due to the zero value in the data for m1 at time zero
-FOCUS_D <- subset(FOCUS_2006_D, value != 0)
-
 test_that("Fits without formation fractions are correct for FOCUS D", {
-  fit.noff <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE)
+  expect_warning(
+    fit.noff <- mkinfit(SFO_SFO, FOCUS_D, quiet = TRUE),
+    "p-value.*Shapiro-Wilk")
 
   expect_equal(round(as.numeric(endpoints(fit.noff)$distimes["parent", ]), 2),
                c(7.02, 23.33))
@@ -16,8 +15,7 @@ test_that("Fits without formation fractions are correct for FOCUS D", {
 })
 
 test_that("Fits with formation fractions are correct for FOCUS D", {
-  skip_on_cran()
-  fit.ff <- mkinfit(SFO_SFO.ff, FOCUS_D, quiet = TRUE)
+  fit.ff <- f_sfo_sfo.ff
   expect_equivalent(round(fit.ff$bparms.optim, c(2, 4, 4, 4)),
                     c(99.60, 0.0987, 0.0053, 0.5145))
 
diff --git a/tests/testthat/test_SFORB.R b/tests/testthat/test_SFORB.R
index 4fb736ec..91c8f2fb 100644
--- a/tests/testthat/test_SFORB.R
+++ b/tests/testthat/test_SFORB.R
@@ -1,5 +1,8 @@
 context("Fitting the SFORB model")
 
+# We do not want the warnings due to non-normality of residuals here
+warn_option <- options(warn=-1)
+
 test_that("Fitting the SFORB model is equivalent to fitting DFOP", {
   f_sforb <- mkinfit("SFORB", FOCUS_2006_C, quiet = TRUE)
   f_dfop <- mkinfit("DFOP", FOCUS_2006_C, quiet = TRUE)
@@ -32,3 +35,5 @@ test_that("Fitting the SFORB model is equivalent to fitting DFOP", {
   expect_equivalent(endpoints(f_sforb_sfo_eigen)$distimes, endpoints(f_dfop_sfo)$distimes,
     tolerance = 1e-6)
 })
+
+options(warn = warn_option$warn)
diff --git a/tests/testthat/test_analytical.R b/tests/testthat/test_analytical.R
index a34fa2cd..66fb1ace 100644
--- a/tests/testthat/test_analytical.R
+++ b/tests/testthat/test_analytical.R
@@ -1,5 +1,8 @@
 context("Analytical solutions for coupled models")
 
+# We do not want the warnings due to non-normality of residuals here
+warn_option <- options(warn=-1)
+
 test_that("The analytical solutions for SFO-SFO are correct", {
   # No sink, no formation fractions
   SFO_SFO_nosink <- mkinmod(
@@ -58,3 +61,5 @@ test_that("The analytical solution for DFOP-SFO are correct", {
     tolerance = 5e-6
   )
 })
+
+options(warn = warn_option$warn)
diff --git a/tests/testthat/test_error_models.R b/tests/testthat/test_error_models.R
index 2dfb2e37..169001f1 100644
--- a/tests/testthat/test_error_models.R
+++ b/tests/testthat/test_error_models.R
@@ -15,36 +15,37 @@ test_that("Error model 'tc' works", {
 test_that("The different error model fitting methods work for parent fits", {
   skip_on_cran()
 
-  f_9_OLS <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
-                     quiet = TRUE)
+  test_9 <- experimental_data_for_UBA_2019[[9]]$data
+
+  f_9_OLS <- mkinfit("SFO", test_9, quiet = TRUE)
   expect_equivalent(round(AIC(f_9_OLS), 2), 137.43)
   f_9_parms_const <- parms(f_9_OLS)
 
-  f_9_direct <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
+  f_9_direct <- mkinfit("SFO", test_9,
     error_model = "tc", error_model_algorithm = "direct", quiet = TRUE)
   expect_equivalent(round(AIC(f_9_direct), 2), 134.94)
   f_9_parms_tc_direct <- parms(f_9_direct)
 
-  f_9_twostep <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
+  f_9_twostep <- mkinfit("SFO", test_9,
     error_model = "tc", error_model_algorithm = "twostep", quiet = TRUE)
   expect_equivalent(parms(f_9_twostep), f_9_parms_tc_direct, tolerance = 1e-5)
 
-  f_9_threestep <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
+  f_9_threestep <- mkinfit("SFO", test_9,
     error_model = "tc", error_model_algorithm = "threestep", quiet = TRUE)
   expect_equivalent(round(AIC(f_9_threestep), 2), 139.43)
   expect_equivalent(parms(f_9_threestep)[1:3], f_9_parms_const)
 
-  f_9_fourstep <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
+  f_9_fourstep <- mkinfit("SFO", test_9,
     error_model = "tc", error_model_algorithm = "fourstep", quiet = TRUE)
   expect_equivalent(round(AIC(f_9_fourstep), 2), 139.43)
   expect_equivalent(parms(f_9_fourstep)[1:3], f_9_parms_const)
 
-  f_9_IRLS <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
+  f_9_IRLS <- mkinfit("SFO", test_9,
     error_model = "tc", error_model_algorithm = "IRLS", quiet = TRUE)
   expect_equivalent(round(AIC(f_9_IRLS), 2), 139.43)
   expect_equivalent(parms(f_9_IRLS)[1:3], f_9_parms_const)
 
-  f_9_d_3 <- mkinfit("SFO", experimental_data_for_UBA_2019[[9]]$data,
+  f_9_d_3 <- mkinfit("SFO", test_9,
     error_model = "tc", error_model_algorithm = "d_3", quiet = TRUE)
   expect_equivalent(round(AIC(f_9_d_3), 2), 134.94)
   expect_equivalent(parms(f_9_d_3), f_9_parms_tc_direct)
diff --git a/tests/testthat/test_nafta.R b/tests/testthat/test_nafta.R
index 2cc25f82..595db999 100644
--- a/tests/testthat/test_nafta.R
+++ b/tests/testthat/test_nafta.R
@@ -28,8 +28,11 @@ test_that("Test data from Appendix B are correctly evaluated", {
 })
 
 test_that("Test data from Appendix D are correctly evaluated", {
+  # We are not interested in the warnings about non-normal residuals here
+  suppressWarnings(
   res <- nafta(NAFTA_SOP_Appendix_D, "MRID 555555", 
-                              cores = 1, quiet = TRUE)
+    cores = 1, quiet = TRUE)
+  )
 
   # From Figure D.1
   dtx_sop <- matrix(c(407, 541, 429, 1352, 5192066, 2383), nrow = 3, ncol = 2)
diff --git a/tests/testthat/test_synthetic_data_for_UBA_2014.R b/tests/testthat/test_synthetic_data_for_UBA_2014.R
index 4bff1b5a..989f963a 100644
--- a/tests/testthat/test_synthetic_data_for_UBA_2014.R
+++ b/tests/testthat/test_synthetic_data_for_UBA_2014.R
@@ -7,8 +7,8 @@ test_that("Results are correct for SFO_lin_a", {
                              M1 = mkinsub("SFO", "M2"),
                              M2 = mkinsub("SFO"),
                              use_of_ff = "max", quiet = TRUE)
-  fit_SFO_lin_a <- mkinfit(m_synth_SFO_lin, 
-                           synthetic_data_for_UBA_2014[[1]]$data, 
+  fit_SFO_lin_a <- mkinfit(m_synth_SFO_lin,
+                           synthetic_data_for_UBA_2014[[1]]$data,
                            quiet = TRUE)
   # Results for SFO_lin_a from p. 48
 
@@ -21,19 +21,18 @@ test_that("Results are correct for SFO_lin_a", {
 # Results for DFOP_par_c from p. 54
 
 test_that("Results are correct for DFOP_par_c", {
-  skip_on_cran()          
-  m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
-                             M1 = mkinsub("SFO"),
-                             M2 = mkinsub("SFO"),
-                             use_of_ff = "max", quiet = TRUE)
-
+  skip_on_cran()
 
-  fit_DFOP_par_c <- mkinfit(m_synth_DFOP_par, 
-                            synthetic_data_for_UBA_2014[[12]]$data,
-                            quiet = TRUE)
+  # Supress warning about non-normal residuals, the data were generated
+  # using a different error model, so no wonder
+  suppressWarnings(
+    fit_DFOP_par_c <- mkinfit(m_synth_DFOP_par,
+      synthetic_data_for_UBA_2014[[12]]$data,
+      quiet = TRUE)
+  )
 
   parms <- round(fit_DFOP_par_c$bparms.optim, c(1, 4, 4, 4, 4, 4, 4, 4))
-  expect_equal(parms, c(parent_0 = 103.0, 
+  expect_equal(parms, c(parent_0 = 103.0,
                         k_M1 = 0.0389, k_M2 = 0.0095,
                         f_parent_to_M1 = 0.5565, f_parent_to_M2 = 0.3784,
                         k1 = 0.3263, k2 = 0.0202, g = 0.7130))