Evaluating Predictors’ Relative Importance Using Bayes Factors in Regression Models

This study presents a Bayesian inference approach to evaluate the relative importance of predictors in regression models. Depending on the interpretation of importance, a number of indices are introduced, such as the standardized regression coefficient, the average squared semipartial correlation, and the dominance analysis measure. Researchers’ theories about relative importance are represented by order constrained hypotheses. Support for or against the hypothesis is quantified by the Bayes factor, which can be computed from the prior and posterior distributions of the importance index. As the distributions of the indices are often unknown, we specify prior and posterior distributions for the covariance matrix of all variables in the regression model. The prior and posterior distributions of each importance index can be obtained from the prior and posterior samples of the covariance matrix. Simulation studies are conducted to show different inferences resulting from various importance indices and to investigate the performance of the proposed Bayesian testing approach. The procedure of evaluating relative importance using Bayes factors is illustrated using two real data examples.