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

Source: R/statpsych2.R
ci.bayes.cor.Rd

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.

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

Examples

ci.bayes.cor(.05, .1, .536, 0, 50)
#>  Posterior mean         LL        UL
#>       0.1873765 0.02795441 0.3375031

# Should return:
# Posterior mean         LL        UL
#      0.1873765 0.02795441 0.3375031

ci.bayes.cor(.05, .1, .536, 0, 300)
#>  Posterior mean        LL        UL
#>       0.4195068 0.3352449 0.4971107

# Should return:
#  Posterior mean        LL        UL
#       0.4195068 0.3352449 0.4971107