binom.profile
Binomial confidence intervals using the profile likelihood
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 aspline
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 loglikelihood function away from Inf
. Specifically, these
values are replaced by (x + 0.5)/(n + 1)
, which is the posterier
mode of f(px)
using Jeffrey's prior on p
. Typically, the
observed mean will not be inside the estimated confidence interval.
If bayes
is FALSE
, then the ClopperPearson 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.
See Also
binom.confint
, binom.bayes
, binom.cloglog
,
binom.logit
, binom.probit
, binom.coverage
,
confint
in package MASS,
family
, glm
Examples
binom.profile(x = 0:10, n = 10)