Bayesian credible interval for a Pearson or partial correlation with a skeptical prior

Computes an approximate Bayesian credible interval for a Pearson or partial correlation with a skeptical prior. The skeptical prior distribution is Normal with a mean of 0 and a small standard deviation. A skeptical prior assumes that the population correlation is within a range of small values (-r to r). If the skeptic is 95% confident that the population correlation is between -r and r, then the prior standard deviation can be set to r/1.96. A correlation that is less than .2 in absolute value is typically considered to be "small", and the prior standard deviation could then be set to .2/1.96. A correlation value that is considered to be small will depend on the application. Set s = 0 for a Pearson correlation.

For more details, see Section 1.33 of Bonett (2021, Volume 2)

Usage

ci.bayes.cor(alpha, prior_sd, cor, s, n)

Arguments

alpha: alpha level for 1-alpha credibility interval
prior_sd: standard deviation of skeptical prior distribution
cor: estimated Pearson or partial correlation
s: number of control variables
n: sample size

Value

Returns a 1-row matrix. The columns are:

Posterior mean - posterior mean (Bayesian estimate of correlation)
LL - lower limit of the credible interval
UL - upper limit of the credible interval

References

Bonett DG (2021). Statistical Methods for Psychologists https://dgbonett.sites.ucsc.edu/.

Examples

ci.bayes.cor(.05, .1, .536, 0, 50)
#>  Posterior mean    LL     UL
#>          0.1874 0.028 0.3375

# Should return:
# Posterior mean     LL     UL
#         0.1874  0.028 0.3375

ci.bayes.cor(.05, .1, .536, 0, 300)
#>  Posterior mean     LL     UL
#>          0.4195 0.3352 0.4971

# Should return:
# Posterior mean     LL     UL
#         0.4195 0.3352 0.4971