Bayesian Bootstrapped Correlation Coefficients

Abstract

We propose the Bayesian bootstrap (BB) as a generic, simple, and accessible method for sampling from the posterior distribution of various correlation coefficients that are commonly used in the social-behavioral sciences. In a series of examples, we demonstrate how the BB can be used to estimate Pearson's, Spearman's, Gaussian rank, Kendall's $\tau $, and polychoric correlations. We also describe an approach based on a region of practical equivalence to evaluate differences and null associations among the estimated correlations. In addition, we have implemented the methodology in the R package BBcor (https://cran.r-project.org/web/packages/BBcor/index.html). Example code and key advantages of the proposed methods are illustrated in an applied example.

Keywords

• bayesian bootstrap
• correlation
• ordinal
• credible interval