Function for Bayesian analysis of proportions
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
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.
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.
Richard D. Morey (richarddmorey@gmail.com)
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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