Title: Graphical Linear Regression to Combat Multicollinearity

Authors: Don van den Bergh, Eric-Jan Wagenmakers, Max Hinne

Affiliation: University of Amsterdam

Abstract:
Many statistical analyses suffer when predictors are highly correlated, a
problem commonly referred to as multicollinearity. In the context of Bayesian
linear regression, multicollinearity induces indecisiveness in the results,
that persists even as the sample size increases. Whereas correlated predictors
hamper regression approaches, other methods such as Gaussian graphical models
focus on estimating these correlations. In this presentation, we present a
hybrid form of linear regression and the Gaussian graphical model, dubbed
graphical linear regression (GLR), to address the difficulties that arise due
to multicollinearity. We showcase GLR with simulated data and an empirical
example and compare its performance to that of Bayesian linear regression and
the Gaussian graphical model. Afterward, we discuss some of the practical and
computational difficulties of inference with correlated predictors, such as
multimodal posteriors. The presentation is concluded with some future
directions on how to expand GLR to, for instance, general linear models.