correlationPosterior {TreeBUGS}

Posterior Distribution for Correlations

Description

Adjusts the posterior distribution of correlations for the sampling error of a population correlation according to the sample size (i.e., the number of participants; Ly, Marsman, & Wagenmakers, 2018).

Usage

correlationPosterior(
  fittedModel,
  r,
  N,
  kappa = 1,
  ci = 0.95,
  M = 1000,
  precision = 0.005,
  maxiter = 10000,
  plot = TRUE,
  nCPU = 4
)

Arguments

fittedModel

a fitted betaMPT or traitMPT model with covariates (added during fitting by the argument covData)

r

optional: a vector of posterior correlations (instead of fittedModel)

N

only if r is used: the number of participants the correlation is based on

kappa

parameter for the prior of the correlation, that is, a scaled beta distribution: Beta(1/kappa, 1/kappa). The default kappa=1 defines a uniform distribution on [-1,1], whereas kappa<1 defines a unimodal prior centered around zero.

ci

credibility interval

M

number of subsamples from the fitted model

precision

precision on the interval [-1,1] to approximate the posterior density

maxiter

maximum number of iterations in genhypergeo. Higher values might be necessary to increase numerical stability for large correlations (r>.95).

plot

whether to plot (a) the unadjusted posterior correlations (gray histogram) and (b) the corrected posterior (black line with red credibility intervals)

nCPU

number of CPUs used for parallel computation of posterior distribution

Details

This function (1) uses all posterior samples of a correlation to (2) derive the posterior of the correlation corrected for sampling error and (3) averages these densities across the posterior samples. Thereby, the method accounts for estimation uncertainty of the MPT model (due to the use of the posterior samples) and also for sampling error of the population correlation due to sample size (cf. Ly, Boehm, Heathcote, Turner, Forstmann, Marsman, & Matzke, 2016).

Author(s)

Daniel W. Heck, Alexander Ly

References

Ly, A., Marsman, M., & Wagenmakers, E.-J. (2018). Analytic posteriors for Pearson’s correlation coefficient. Statistica Neerlandica, 72, 4–13. doi:10.1111/stan.12111

Ly, A., Boehm, U., Heathcote, A., Turner, B. M. , Forstmann, B., Marsman, M., and Matzke, D. (2017). A flexible and efficient hierarchical Bayesian approach to the exploration of individual differences in cognitive-model-based neuroscience. https://osf.io/evsyv/. doi:10.1002/9781119159193

Examples

# test effect of number of participants:
set.seed(123)
cors <- rbeta(50, 100, 70)
correlationPosterior(r = cors, N = 10, nCPU = 1)
correlationPosterior(r = cors, N = 100, nCPU = 1)