On Model Averaging Partial Regression Coefficients

TL;DR: The authors compare effect estimates using a small Monte-Carlo simulation and show that model-averaged and ridge estimates have increasingly better performance, relative to full model estimates, as multicollinearity increases.

Abstract: Model averaging of partial regression coefficients has been criticized for averaging over a set of models with coefficients that have different meanings from model to model. however, partial regression coefficients from different models have the same meaning if they are used to estimate the effect parameters of a causal model, which derive their meaning from the specified paths and not from the set of covariates. A multiple regression model implicitly specifies a causal model with direct, causal paths from each predictor to the response. Consequently, the partial regression coefficient for any predictor has the same meaning across all sub-models if the goal is estimation of the causal effects that generated the response. In order to clarify the effects of multicollinearity on model-averaged estimates, I compare effect estimates using a small Monte-Carlo simulation. The simulation results show that model-averaged and ridge estimates have increasingly better performance, relative to full model estimates, as multicollinearity increases.