Diagnosing and correcting the effects of multicollinearity: Bayesian implications of ridge regression

Abstract

When faced with the problem of multicollinearity most tourism researchers recommend mean-centering the variables. This procedure however does not work. It is actually one of the biggest misconceptions we have in the field. We propose instead using Bayesian ridge regression and treat the biasing constant as a parameter about which inferences are to be made. It is well known that many estimates of the biasing constant have been proposed in the literature. When the coefficients in ridge regression have a conjugate prior distribution, formal selection can be based on the marginal likelihood. In the non-conjugate case, we propose a conditionally conjugate prior for the biasing constant, and show that Gibbs sampling can be employed to make inferences about ridge regression parameters as well as the biasing constant itself. We examine posterior sensitivity and apply the techniques to a tourism data set.