correlationBF: Function for Bayesian analysis of correlations

Description

Bayes factors or posterior samples for correlations.

Usage

correlationBF(y, x, rscale = "medium", nullInterval = NULL,
  posterior = FALSE, callback = function(...) as.integer(0), ...)

Arguments

first continuous variable

second continuous variable

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 correlation 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.

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 0, and the corresponding Bayes factor for the complement of the interval.

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

Details

The Bayes factor provided by ttestBF tests the null hypothesis that the true linear correlation \(\rho\) between two samples (\(y\) and \(x\)) of size \(n\) from normal populations is equal to 0. The Bayes factor is based on Jeffreys (1961) test for linear correlation. Noninformative priors are assumed for the population means and variances of the two population; a shifted, scaled beta(1/rscale,1/rscale) prior distribution is assumed for \(\rho\) (note that rscale is called \(\kappa\) by Ly et al. 2015; we call it rscale for consistency with other BayesFactor functions).

For the rscale argument, several named values are recognized: "medium.narrow", "medium", "wide", and "ultrawide". These correspond to \(r\) scale values of \(1/\sqrt(27)\), \(1/3\), \(1/\sqrt(3)\) and 1, respectively.

The Bayes factor is computed via several different methods.

References

Ly, A., Verhagen, A. J. & Wagenmakers, E.-J. (2015). Harold Jeffreys's Default Bayes Factor Hypothesis Tests: Explanation, Extension, and Application in Psychology. Journal of Mathematical Psychology, Available online 28 August 2015, http://dx.doi.org/10.1016/j.jmp.2015.06.004.

Jeffreys, H. (1961). Theory of probability, 3rd edn. Oxford, UK: Oxford University Press.

Examples

Run this code

# NOT RUN {
bf = correlationBF(y = iris$Sepal.Length, x = iris$Sepal.Width)
bf
## Sample from the corresponding posterior distribution
samples = correlationBF(y = iris$Sepal.Length, x = iris$Sepal.Width,
          posterior = TRUE, iterations = 10000)
plot(samples[,"rho"])
# }

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