binom.lrt
Binomial confidence intervals using the lrt likelihood
Uses the lrt likelihood on the observed proportion to construct confidence intervals.
Usage
binom.lrt(x, n, conf.level = 0.95, bayes = FALSE, conf.adj = FALSE, 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.
 bayes
 logical; if
TRUE
use a Bayesian correction at the edges. Specfically, a beta prior with shape parameters 0.5 is used. Ifbayes
is numeric, it is assumed to be the parameters to beta distribution.  conf.adj
 logical; if
TRUE
0 or 100% successes return a onesided confidence interval  plot
 logical; if
TRUE
a plot showing the the square root of the binomial deviance with reference lines for mean, lower, and upper bounds. This argument can also be alist
of plotting parameters to be passed toxyplot
.  ...
 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
. Furthermore, if
conf.adj
is TRUE
, then the upper (or lower) bound uses
a 1  alpha
confidence level. 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.lrt(x = 0:10, n = 10)