Make the 'quadratic' the default for 'confint'

Also the documentation was improved here and there

5 files changed, 55 insertions, 34 deletions

diff --git a/man/AIC.mmkin.Rd b/man/AIC.mmkin.Rd
index a49b69b8..a10d0aeb 100644
--- a/man/AIC.mmkin.Rd
+++ b/man/AIC.mmkin.Rd
@@ -31,15 +31,21 @@ same dataset.
   f <- mmkin(c("SFO", "FOMC", "DFOP"),
     list("FOCUS A" = FOCUS_2006_A,
          "FOCUS C" = FOCUS_2006_C), cores = 1, quiet = TRUE)
-  AIC(f[1, "FOCUS A"]) # We get a single number for a single fit
+  # We get a warning because the FOMC model does not converge for the
+  # FOCUS A dataset, as it is well described by SFO
+
+  AIC(f["SFO", "FOCUS A"]) # We get a single number for a single fit
+  AIC(f[["SFO", "FOCUS A"]]) # or when extracting an mkinfit object
 
   # For FOCUS A, the models fit almost equally well, so the higher the number
   # of parameters, the higher (worse) the AIC
   AIC(f[, "FOCUS A"])
   AIC(f[, "FOCUS A"], k = 0) # If we do not penalize additional parameters, we get nearly the same
+  BIC(f[, "FOCUS A"])        # Comparing the BIC gives a very similar picture
 
   # For FOCUS C, the more complex models fit better
   AIC(f[, "FOCUS C"])
+  BIC(f[, "FOCUS C"])
   }
 
 }
diff --git a/man/confint.mkinfit.Rd b/man/confint.mkinfit.Rd
index ee07c9c1..e4a60556 100644
--- a/man/confint.mkinfit.Rd
+++ b/man/confint.mkinfit.Rd
@@ -5,7 +5,7 @@
 \title{Confidence intervals for parameters of mkinfit objects}
 \usage{
 \method{confint}{mkinfit}(object, parm, level = 0.95, alpha = 1 -
-  level, cutoff, method = c("profile", "quadratic"),
+  level, cutoff, method = c("quadratic", "profile"),
   transformed = TRUE, backtransform = TRUE,
   cores = round(detectCores()/2), quiet = FALSE, ...)
 }
@@ -23,11 +23,11 @@ confidence intervals. If missing, all parameters are considered.}
 in the log-likelihoods at the confidence boundary. Specifying an explicit
 cutoff value overrides arguments 'level' and 'alpha'}
 
-\item{method}{The 'profile' method searches the parameter space for the
-cutoff of the confidence intervals by means of a likelihood ratio test.
-The 'quadratic' method approximates the likelihood function at the
-optimised parameters using the second term of the Taylor expansion, using
-a second derivative (hessian) contained in the object.}
+\item{method}{The 'quadratic' method approximates the likelihood function at
+the optimised parameters using the second term of the Taylor expansion,
+using a second derivative (hessian) contained in the object.
+The 'profile' method searches the parameter space for the
+cutoff of the confidence intervals by means of a likelihood ratio test.}
 
 \item{transformed}{If the quadratic approximation is used, should it be
 applied to the likelihood based on the transformed parameters?}
@@ -49,9 +49,14 @@ A matrix with columns giving lower and upper confidence limits for
   each parameter.
 }
 \description{
-The default method 'profile' is based on the profile likelihood for each
-parameter. The method uses two nested optimisations. The speed of the method
-could likely be improved by using the method of Venzon and Moolgavkar (1988).
+The default method 'quadratic' is based on the quadratic approximation of
+the curvature of the likelihood function at the maximum likelihood parameter
+estimates.
+The alternative method 'profile' is based on the profile likelihood for each
+parameter. The method uses two nested optimisations and can take a very long
+time, even if parallelized by specifying 'cores' on unixoid platforms. The
+speed of the method could likely be improved by using the method of Venzon
+and Moolgavkar (1988).
 }
 \examples{
 f <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE)
@@ -60,19 +65,26 @@ confint(f, method = "quadratic")
 \dontrun{
 confint(f, method = "profile")
 
+# Set the number of cores for the profiling method for further examples
+if (identical(Sys.getenv("NOT_CRAN"), "true")) {
+  n_cores <- parallel::detectCores() - 1
+} else {
+ n_cores <- 1
+}
+if (Sys.getenv("TRAVIS") != "") n_cores = 1
+if (Sys.info()["sysname"] == "Windows") n_cores = 1
+
 SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"), quiet = TRUE)
 SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"),
   use_of_ff = "max", quiet = TRUE)
 f_d_1 <- mkinfit(SFO_SFO, subset(FOCUS_2006_D, value != 0), quiet = TRUE)
-system.time(ci_profile <- confint(f_d_1, cores = 1, quiet = TRUE))
-# The following does not save much time, as parent_0 takes up most of the time
-# system.time(ci_profile <- confint(f_d_1, cores = 5))
-# system.time(ci_profile <- confint(f_d_1,
-#   c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = 1))
-# If we exclude parent_0 (the confidence of which is often of minor interest), we get a nice
-# performance improvement from about 30 seconds to about 12 seconds
-# system.time(ci_profile_no_parent_0 <- confint(f_d_1, 
-#   c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = 4))
+system.time(ci_profile <- confint(f_d_1, method = "profile", cores = 1, quiet = TRUE))
+# Using more cores does not save much time here, as parent_0 takes up most of the time
+# If we additionally exclude parent_0 (the confidence of which is often of
+# minor interest), we get a nice performance improvement from about 50
+# seconds to about 12 seconds if we use at least four cores
+system.time(ci_profile_no_parent_0 <- confint(f_d_1, method = "profile",
+  c("k_parent_sink", "k_parent_m1", "k_m1_sink", "sigma"), cores = n_cores))
 ci_profile
 ci_quadratic_transformed <- confint(f_d_1, method = "quadratic")
 ci_quadratic_transformed
@@ -84,21 +96,14 @@ ci_quadratic_untransformed
 # interval based on the untransformed fit for k_m1_sink
 rel_diffs_transformed <- abs((ci_quadratic_transformed - ci_profile)/ci_profile)
 rel_diffs_untransformed <- abs((ci_quadratic_untransformed - ci_profile)/ci_profile)
-rel_diffs_transformed
-rel_diffs_untransformed
+rel_diffs_transformed < rel_diffs_untransformed
+signif(rel_diffs_transformed, 3)
+signif(rel_diffs_untransformed, 3)
 
-# Set the number of cores for further examples
-if (identical(Sys.getenv("NOT_CRAN"), "true")) {
-  n_cores <- parallel::detectCores() - 1
-} else {
- n_cores <- 1
-}
-if (Sys.getenv("TRAVIS") != "") n_cores = 1
-if (Sys.info()["sysname"] == "Windows") n_cores = 1
 
 # Investigate a case with formation fractions
 f_d_2 <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), quiet = TRUE)
-ci_profile_ff <- confint(f_d_2, cores = n_cores)
+ci_profile_ff <- confint(f_d_2, method = "profile", cores = n_cores)
 ci_profile_ff
 ci_quadratic_transformed_ff <- confint(f_d_2, method = "quadratic")
 ci_quadratic_transformed_ff
@@ -108,8 +113,9 @@ rel_diffs_transformed_ff <- abs((ci_quadratic_transformed_ff - ci_profile_ff)/ci
 rel_diffs_untransformed_ff <- abs((ci_quadratic_untransformed_ff - ci_profile_ff)/ci_profile_ff)
 # While the confidence interval for the parent rate constant is closer to
 # the profile based interval when using the internal parameter
-# transformation, the intervals for the other parameters are 'better
+# transformation, the interval for the metabolite rate constant is 'better
 # without internal parameter transformation.
+rel_diffs_transformed_ff < rel_diffs_untransformed_ff
 rel_diffs_transformed_ff
 rel_diffs_untransformed_ff
 
diff --git a/man/parms.Rd b/man/parms.Rd
index 73cb23cd..5752de0b 100644
--- a/man/parms.Rd
+++ b/man/parms.Rd
@@ -25,3 +25,8 @@ This function always returns degradation model parameters as well as error
 model parameters, in order to avoid working with a fitted model without
 considering the error structure that was assumed for the fit.
 }
+\examples{
+fit <- mkinfit("SFO", FOCUS_2006_C)
+parms(fit)
+parms(fit, transformed = TRUE)
+}
diff --git a/man/residuals.mkinfit.Rd b/man/residuals.mkinfit.Rd
index 407b89b9..aaff12c0 100644
--- a/man/residuals.mkinfit.Rd
+++ b/man/residuals.mkinfit.Rd
@@ -7,7 +7,7 @@
 \method{residuals}{mkinfit}(object, standardized = FALSE, ...)
 }
 \arguments{
-\item{object}{An \code{\link{mkinfit}} object}
+\item{object}{A \code{\link{mkinfit}} object}
 
 \item{standardized}{Should the residuals be standardized by dividing by the
 standard deviation obtained from the fitted error model?}
diff --git a/man/update.mkinfit.Rd b/man/update.mkinfit.Rd
index aae1fbb4..7054d2e6 100644
--- a/man/update.mkinfit.Rd
+++ b/man/update.mkinfit.Rd
@@ -23,7 +23,11 @@ override these starting values.
 }
 \examples{
 \dontrun{
-fit <- mkinfit("DFOP", subset(FOCUS_2006_D, value != 0), quiet = TRUE)
-update(fit, error_model = "tc")
+fit <- mkinfit("SFO", subset(FOCUS_2006_D, value != 0), quiet = TRUE)
+parms(fit)
+plot_err(fit)
+fit_2 <- update(fit, error_model = "tc")
+parms(fit_2)
+plot_err(fit_2)
 }
 }