R: Binomial confidence intervals using the profile likelihood
binom.profile
R Documentation
Binomial confidence intervals using the profile likelihood
Description
Uses the profile likelihood on the observed
proportion to construct confidence intervals.
Usage
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.