Bayesian credible interval for a semipartial correlation with a skeptical prior

Computes an approximate Bayesian credible interval for a semipartial 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 semipartial 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 semipartial 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 semipartial correlation value that is considered to be small will depend on the application. This function requires the standard error of the estimated semipartial correlation which can be obtained from the ci.spcor function.

Usage

ci.bayes.spcor(alpha, prior_sd, cor, se)

Arguments

alpha: alpha level for 1-alpha credibility interval
prior_sd: standard deviation of skeptical prior distribution
cor: estimated semipartial partial correlation
se: standard error of estimated semipartial correlation

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

Examples

ci.bayes.spcor(.05, .1, .582, .137)
#>  Posterior mean         LL        UL
#>       0.2272797 0.07288039 0.3710398

# Should return:
#  Posterior mean        LL        UL
#       0.2272797 0.07288039 0.3710398