proportionBF | R Documentation |

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

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

`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 |

`callback` |
callback function for third-party interfaces |

`...` |
further arguments to be passed to or from methods. |

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

`\lambda~logistic(\lambda_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.

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 `p_0`

, 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.

Richard D. Morey (richarddmorey@gmail.com)

`prop.test`

```
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"])
```

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