R: Function for Bayesian analysis of proportions

proportionBF {BayesFactor} | R Documentation

## Function for Bayesian analysis of proportions

### Description

Bayes factors or posterior samples for binomial, geometric, or neg. binomial data.

### Usage

    proportionBF(y, N, p, rscale = "medium", nullInterval = NULL,
      posterior = FALSE, callback = function(...) as.integer(0), ...)

### Arguments

`y` | a vector of successes
`N` | a vector of total number of observations
`p` | the null value for the probability of a success to be tested against
`rscale` | prior scale. A number of preset values can be given as strings; see Details.
`nullInterval` | optional vector of length 2 containing lower and upper bounds of an interval hypothesis to test, in probability units
`posterior` | if `TRUE`, return samples from the posterior instead of Bayes factor
`callback` | callback function for third-party interfaces
`...` | further arguments to be passed to or from methods.

### Details

Given count data modeled as a binomial, geometric, or negative binomial random variable, the Bayes factor provided by `proportionBF` tests the null hypothesis that the probability of a success is p_0 (argument `p`). Specifically, the Bayes factor compares two hypotheses: that the probability is p_0, or probability is not p_0. Currently, the default alternative is that

λ~logistic(λ_0,r)

where lambda_0=logit(p_0) and lambda=logit(p). r serves as a prior scale parameter.

For the `rscale` argument, several named values are recognized: "medium", "wide", and "ultrawide". These correspond to r scale values of 1/2, sqrt(2)/2, and 1, respectively.

The Bayes factor is computed via Gaussian quadrature, and posterior samples are drawn via independence Metropolis-Hastings.

### Value

If `posterior` is `FALSE`, an object of class `BFBayesFactor` containing the computed model comparisons is returned. If `nullInterval` is defined, then two Bayes factors will be computed: The Bayes factor for the interval against the null hypothesis that the probability is p0, and the corresponding Bayes factor for the compliment of the interval.

If `posterior` is `TRUE`, an object of class `BFmcmc`, containing MCMC samples from the posterior is returned.

### Author(s)

Richard D. Morey (richarddmorey@gmail.com)

### See Also

`prop.test`

### Examples

    bf = proportionBF(y = 15, N = 25, p = .5)
    bf
    ## Sample from the corresponding posterior distribution
    samples =proportionBF(y = 15, N = 25, p = .5, posterior = TRUE, iterations = 10000)
    plot(samples[,"p"])

[Package BayesFactor version 0.9.12-4.2 Index]