Testing for Collinearity using Bayesian Analysis

Testing for collinearity continues to be a controversial issue in the literature. Multicollinearity detection criteria, such as the variance inflation factor, often fail to detect the true extent of multicollinearity. In this article, we propose utilizing the Bayesian approach as an attractive alternative. Under the Bayesian approach, we recommend comparing the marginal posterior of regression parameters under two different priors. If the difference in the posterior under these two priors is pronounced, one can surmise that collinearity is harmful. The Kolmogorov–Smirnov test can also be used as further evidence to confirm whether the posterior difference is significant.