A Bayesian solution to multicollinearity through unobserved common factors

Abstract

Abstract This paper considers the unobserved common factor multicollinearity problem proposed by Kalnins (2018), who demonstrated how regression analyses with correlated regressors via a common factor can lead to Type 1 errors. The paper proposes novel Bayesian techniques to test and mitigate multicollinearity. The methods are based on Markov Chain Monte Carlo. The advantage of the proposed techniques is that they are not ad hoc, but are part of a common framework that can be used to test for and mitigate multicollinearity. In fields such as tourism and hospitality, where many variables are not observed directly, but measured through proxies, the risk of making Type 1 errors is high. These proxies are often correlated via an unobserved common factor.