binom.lrt {binom} R Documentation

## Binomial confidence intervals using the lrt likelihood

### Description

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. If `bayes` is numeric, it is assumed to be the parameters to beta distribution. `conf.adj` logical; if `TRUE` 0 or 100% successes return a one-sided 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 a `list` of plotting parameters to be passed to `xyplot`. `...` 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`. 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 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.lrt(x = 0:10, n = 10)