Binomial confidence intervals using the profile likelihood

Description

Uses the profile likelihood on the observed proportion to construct confidence intervals.

Usage

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binom.profile(x, n, conf.level = 0.95, maxsteps = 50,
              del = zmax/5, bayes = TRUE, plot = FALSE, ...)

Arguments

x

Vector of number of successes in the binomial experiment.

n

Vector of number of independent trials in the binomial experiment.

conf.level

The level of confidence to be used in the confidence interval.

maxsteps

The maximum number of steps to take in the profiles.

del

The size of the step to take

bayes

logical; if TRUE use a Bayesian correction at the edges.

plot

logical; if TRUE plot the profile with a spline fit.

...

ignored

Details

Confidence intervals are based on profiling the binomial deviance in the neighbourhood of the MLE. If x == 0 or x == n and bayes is TRUE, then a Bayesian adjustment is made to move the log-likelihood function away from Inf. Specifically, these values are replaced by (x + 0.5)/(n + 1), which is the posterier mode of f(p|x) using Jeffrey's prior on p. Typically, the observed mean will not be inside the estimated confidence interval. If bayes is FALSE, then the Clopper-Pearson exact method is used on the endpoints. This tends to make confidence intervals at the end too conservative, though the observed mean is guaranteed to be within the estimated confidence limits.

Value

A data.frame containing the observed proportions and the lower and upper bounds of the confidence interval.

Author(s)

Sundar Dorai-Raj (sdorairaj@gmail.com)

See Also

binom.confint, binom.bayes, binom.cloglog, binom.logit, binom.probit, binom.coverage, confint in package MASS, family, glm

Examples

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binom.profile(x = 0:10, n = 10)