binom.profile {binom} 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.

### Author(s)

Sundar Dorai-Raj (sdorairaj@gmail.com)

`binom.confint`, `binom.bayes`, `binom.cloglog`, `binom.logit`, `binom.probit`, `binom.coverage`, `confint` in package MASS, `family`, `glm`
```binom.profile(x = 0:10, n = 10)