% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/confint.mkinfit.R
\name{confint.mkinfit}
\alias{confint.mkinfit}
\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"),
  transformed = TRUE, backtransform = TRUE,
  cores = round(detectCores()/2), quiet = FALSE, ...)
}
\arguments{
\item{object}{An \code{\link{mkinfit}} object}

\item{parm}{A vector of names of the parameters which are to be given
confidence intervals. If missing, all parameters are considered.}

\item{level}{The confidence level required}

\item{alpha}{The allowed error probability, overrides 'level' if specified.}

\item{cutoff}{Possibility to specify an alternative cutoff for the difference
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{transformed}{If the quadratic approximation is used, should it be
applied to the likelihood based on the transformed parameters?}

\item{backtransform}{If we approximate the likelihood in terms of the
transformed parameters, should we backtransform the parameters with
their confidence intervals?}

\item{cores}{The number of cores to be used for multicore processing. This
is only used when the \code{cluster} argument is \code{NULL}. On Windows
machines, cores > 1 is not supported.}

\item{quiet}{Should we suppress the message "Profiling the likelihood"}

\item{\dots}{Not used}
}
\value{
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).
}
\examples{
f <- mkinfit("SFO", FOCUS_2006_C, quiet = TRUE)
confint(f, method = "quadratic")

\dontrun{
confint(f, method = "profile")

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))
ci_profile
ci_quadratic_transformed <- confint(f_d_1, method = "quadratic")
ci_quadratic_transformed
ci_quadratic_untransformed <- confint(f_d_1, method = "quadratic", transformed = FALSE)
ci_quadratic_untransformed
# Against the expectation based on Bates and Watts (1988), the confidence
# intervals based on the internal parameter transformation are less
# congruent with the likelihood based intervals. Note the superiority of the
# 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

# 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
ci_quadratic_transformed_ff <- confint(f_d_2, method = "quadratic")
ci_quadratic_transformed_ff
ci_quadratic_untransformed_ff <- confint(f_d_2, method = "quadratic", transformed = FALSE)
ci_quadratic_untransformed_ff
rel_diffs_transformed_ff <- abs((ci_quadratic_transformed_ff - ci_profile_ff)/ci_profile_ff)
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
# without internal parameter transformation.
rel_diffs_transformed_ff
rel_diffs_untransformed_ff

# The profiling for the following fit does not finish in a reasonable time,
# therefore we use the quadratic approximation
m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")),
  M1 = mkinsub("SFO"),
  M2 = mkinsub("SFO"),
  use_of_ff = "max", quiet = TRUE)
DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data
f_tc_2 <- mkinfit(m_synth_DFOP_par, DFOP_par_c, error_model = "tc",
  error_model_algorithm = "direct", quiet = TRUE)
confint(f_tc_2, method = "quadratic")
confint(f_tc_2, "parent_0", method = "quadratic")
}
}
\references{
Bates DM and Watts GW (1988) Nonlinear regression analysis & its applications

  Pawitan Y (2013) In all likelihood - Statistical modelling and
  inference using likelihood. Clarendon Press, Oxford.

  Venzon DJ and Moolgavkar SH (1988) A Method for Computing
  Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37,
  87–94.
}