Version:	0.42.2
Date:	2023-04-26
Author:	Samuel Pawel [aut, cre]
Maintainer:	Samuel Pawel <samuel.pawel@uzh.ch>
Title:	Calibration of Confidence Intervals to Support Intervals
Description:	Provides functionality for computing support intervals for univariate parameters based on confidence intervals or parameter estimates with standard errors (Pawel et al., 2022) <doi:10.48550/arXiv.2206.12290>.
License:	GPL-3
Encoding:	UTF-8
Imports:	lamW
Suggests:	roxygen2, testthat
NeedsCompilation:	no
RoxygenNote:	7.2.3
URL:	https://github.com/SamCH93/ciCalibrate
BugReports:	https://github.com/SamCH93/ciCalibrate/issues
Packaged:	2023-04-26 06:38:28 UTC; sam
Repository:	CRAN
Date/Publication:	2023-04-26 07:52:31 UTC

Calibrate confidence intervals to support intervals

Description

This function computes a support interval for an unknown parameter based on either a confidence interval for the parameter or a parameter estimate with standard error.

Usage

ciCalibrate(
  ci = NULL,
  ciLevel = 0.95,
  estimate = mean(ci),
  se = diff(ci) * 0.5/stats::qnorm(p = 0.5 * (1 + ciLevel)),
  siLevel = 1,
  method = c("SI-normal", "SI-normal-local", "SI-normal-nonlocal", "mSI-all",
    "mSI-normal-local", "mSI-eplogp"),
  priorMean,
  priorSD
)

Arguments

Details

A support interval with support level k is defined by the parameter values \theta_0 for which the Bayes factor contrasting H_0\colon \theta = \theta_0 to H_1\colon \theta \neq \theta_0 is larger or equal than k, i.e., the parameter values for which the data are at least k times more likely than under the alternative. Different prior distributions for the parameter \theta under the alternative H_1 are available:

• method = "SI-normal": a normal prior centered around priorMean with standard deviation priorSD, i.e., \theta \,|\, H_1 \sim N(\code{priorMean}, \code{priorSD}^2)

• method = "SI-normal-local": a local normal prior with standard deviation priorSD, i.e., \theta \,|\, H_1 \sim N(\theta_0, \code{priorSD}^2)

• method = "SI-normal-nonlocal": a nonlocal normal moment prior with spread parameter priorSD, i.e., a prior with density f(\theta \,|\, H_1) = N(\theta \,|\, \theta_0, \code{priorSD}^2) \times (\theta - \theta_0)^2/\code{priorSD}^2

The function also allows to compute minimum support intervals which require to only specify a class of priors for the parameter under the alternative and then compute the minimum Bayes factor over the class of alternatives. The following classes of prior distribution are available:

• method = "mSI-all": the class of all prior distributions under the alternative, this leads to the narrowest support interval possible

• method = "mSI-normal-local": the class of local normal prior distributions under the alternative, i.e., \theta \,|\, H_1 \sim N(\theta_0, v) with v \geq 0

• method = "mSI-eplogp": the class of monotonically decreasing beta prior distributions on the p-value of the data p = 2(1 - \Phi(|\code{estimate} - \theta_0|/\code{se})), i.e. p \,|\, H_1 \sim \mbox{Be}(\xi, 1) with \xi \geq 1

Value

Returns an object of class "supInt" which is a list containing:

Author(s)

Samuel Pawel

References

Pawel, S., Ly, A., and Wagenmakers, E.-J. (2022). Evidential calibration of confidence intervals. arXiv preprint. doi:10.48550/arXiv.2206.12290

Wagenmakers, E.-J., Gronau, Q. F., Dablander, F., and Etz, A. (2020). The support interval. Erkenntnis. doi:10.1007/s10670-019-00209-z

Examples

## confidence interval of hazard ratio needs to be transformed to log-scale
ciHR <- c(0.75, 0.93)
ci <- log(ciHR)

## normal prior under the alternative hypothesis H1
m <- log(0.8) # prior mean
s <- 2 # prior sd

## compute 10 support interval
si <- ciCalibrate(ci = ci, method = "SI-normal", priorMean = m,
                  priorSD = s, siLevel = 10)
si # on logHR scale
exp(si$si) # on HR scale

## plot Bayes factor function and support interval
plot(si)

## minimum support interval based on local normal priors
msi <- ciCalibrate(ci = ci, method = "mSI-normal-local")
plot(msi)

Plot method for class "supInt"

Description

Plots Bayes factor function and support interval at the specified support level.

Usage

## S3 method for class 'supInt'
plot(x, xlim = x$estimate + c(-1, 1) * 3 * x$se, ...)

Arguments

Value

Generates a plot of the Bayes factor function with support interval

Author(s)

Samuel Pawel

Examples

## compute 3 support interval
si3 <- ciCalibrate(ci = c(0.3, 1.5), method = "SI-normal", priorMean = 0,
                   priorSD = 2, siLevel = 3)

## plot Bayes factor function and support interval
plot(si3, xlim = c(0, 1.75))

Print method for class "supInt"

Description

Prints parameter estimate, confidence interval, and support interval.

Usage

## S3 method for class 'supInt'
print(x, ...)

Arguments

Value

Prints text summary in the console and invisibly returns the "supInt" object

Author(s)

Samuel Pawel

Examples

## compute and print 5 support interval
si5 <- ciCalibrate(ci = c(-2, -0.5), method = "SI-normal", priorMean = -0.3,
                   priorSD = 2, siLevel = 5)
print(si5)