correlationBF: Function for Bayesian analysis of correlations

In BayesFactor: Computation of Bayes Factors for Common Designs

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

y	first continuous variable
x	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.

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.

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.

Author(s)

Richard D. Morey ([e-mail])

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, https://dx.doi.org/10.1016/j.jmp.2015.06.004.

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

See Also

cor.test

Examples

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"])

BayesFactor documentation built on Sept. 22, 2023, 1:06 a.m.