confint.SLik: Compute confidence intervals by (profile) summary likelihood

Description

confint takes an SLik object (as produced by MSL) and deduces confidence bounds for each parameter, using a (profile, if relevant) likelihood ratio method, and optionally a bootstrap method.

allCIs calls confint for all fitted parameters and re-structure the results.

Usage

allCIs(object, level=0.95, verbose=TRUE, ...)
# S3 method for SLik_j
confint(object, parm, level=0.95, verbose=interactive(), fixed=NULL,
                         which=c(TRUE,TRUE), nsim=0L, reset=TRUE, 
                         cluster_args=NULL, nb_cores=NULL, type="perc",...)
# S3 method for SLik
confint(object, parm, level=0.95, verbose=interactive(), fixed=NULL, 
                       which=c(TRUE,TRUE), ...)

Value

Both functions modify the fit object as a side effect (see Details).

confint returns a list with sublists for each parameter, each sublist containing: the bounds of the one-dimensional confidence interval (element interval, a vector); the parameter point for the lower bound (element lowerpar, a vector including all parameters fitted in the SLik object), the full parameter point for the upper bound (element upperpar, formatted as lowerpar), and optionally if a bootstrap was run, the return value of a boot::boot.ci call (element bootCI) and the simulated distribution of parameter estimates (element booreps, 1-column matrix).

allCIs returns invisibly a list with elements including CIs (itself a list of confint results), bounds (a matrix made of bound points for all parameters), and some other elements.

Arguments

object: an SLik or SLik_j object
parm: The parameter which confidence bounds are to be computed
level: The desired coverage of the interval
verbose: Whether to print some information or not
fixed: When this is NULL the computed interval is a profile confidence interval over all parameters excluding parm. fixed allows one to set fixed values to some of these parameters.
which: A pair of booleans, controlling whether to compute respectively the lower and the upper CI bounds.
nsim: Integer: number of bootstrap replicates. If >1, bootstrap interval(s) are computed as further controlled by the type argument. Note that this will be ignored if the bootstrap has previously been run and reset=FALSE.
reset: Boolean: Whether to use any previously computed distribution (see Details) or not.
cluster_args, nb_cores: Passed to parallelization wrappers such as dopar.
type: Character vector, ignored if nsim = 0: bootstrap CI type(s). Possible types are "norm", "basic", "perc" (as handled by boot.ci), and "Bartlett" (where the interval bounds are defined by threshold values of the likelihood ratio statistics modified using a Bartlett correction).
...: further arguments passed to or from other methods. allCIs passes them to confint, so that, e.g., nsim can be passed through the .... confint passes them to parallelization wrappers such as dopar.

Details

confint.SLik_j results are stored in the object (until the next refine), including the result of the bootstrap simulations if it was performed. This distribution may then be reused by a next call to confint for the same parm if reset=FALSE. The default is however to recompute the distribution (reset=TRUE).

Bootstrap CIs computed using boot.ci are stored as distinct elements of the return list (see Value). However, for the "Bartlett" type of CI, the interval element of the return value is modified.

Examples

Run this code

if (Infusion.getOption("example_maxtime")>3) {
#### Provide fit for minimal toy example: 
myrnorm <- function(mu,s2,sample.size) {
  s <- rnorm(n=sample.size,mean=mu,sd=sqrt(s2))
  return(c(mean=mean(s),var=var(s)))
} # simulate means and variances of normal samples of size 'sample.size'
set.seed(123)
# simulated data with stands for the actual data to be analyzed:  
ssize <- 40L
(Sobs <- myrnorm(mu=4,s2=1,sample.size=ssize) )
## Construct initial reference table:
# Uniform sampling in parameter space:
parsp <- init_reftable(lower=c(mu=2.8, s2=0.4, sample.size=ssize), 
                         upper=c(mu=5.2, s2=2.4, sample.size=ssize))
# Build simulation table:
# set.seed(456) 
simuls <- add_reftable(Simulate="myrnorm", parsTable=parsp)

# Infer surface:
densv <- infer_SLik_joint(simuls,stat.obs=Sobs)
# Usual workflow using inferred surface:
slik_1 <- MSL(densv) ## find the maximum of the log-likelihood surface

####  Confidence interval calculations:
(ci1 <- confint(slik_1,"mu")) # basic likelihood ratio interval
(ci2 <- confint(slik_1,"mu", nsim=199L)) # Percentile interval added
(ci3 <- confint(slik_1,"mu", nsim=199L, type="Bartlett")) # 'interval' corrected

# Previous bootstrap computations are stored in the fit object,  
# and recycled if reset=FALSE *and* nsim > 0:
(ci4 <- confint(slik_1,"mu", nsim=199L, type= "Bartlett", reset=FALSE)) # = ci3
(ci5 <- confint(slik_1,"mu", nsim=199L, type= "perc", reset=FALSE)) # = ci2
}