Bayesian Model Averaging Over Directed Acyclic Graphs with Implications for Prediction with Structural Equation Models

David Kaplan, Ph.D.Patricia Busk Professor of Quantitative Methods, University of Wisconsin-Madison

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The Spring 2015 Nebraska Methodology Workshop concluded with Kaplan’s keynote address titled, "Bayesian Model Averaging Over Directed Acyclic Graphs With Implications for Improving the Predictive Performance of Structural Equation Models."

This keynote examines Bayesian model averaging as a means of improving the predictive performance of structural equation models. Structural equation modeling from a Bayesian perspective addresses the problem of parameter uncertainty through the specification of prior distributions on all model parameters. 

In addition to parameter uncertainty, it is recognized that there is uncertainty in the choice of models themselves, insofar as a particular model is chosen based on prior knowledge of the problem at hand. This form of uncertainty is not accounted for in frequentist structural equation modeling and neither has it been directly addressed in Bayesian structural equation modeling. An internally consistent Bayesian framework for structural equation modeling estimation must also account for model uncertainty. 

The current approach to addressing the problem of model uncertainty lies in the method of Bayesian model averaging. We expand the framework of Madigan and his colleagues as well as Pearl by considering a structural equation model as a special case of a directed acyclic graph. We then provide an algorithm that searches the model space for sub-models that satisfy the conditions of Occam's razor and Occam's window and obtains a weighted average of the sub-models using posterior model probabilities as weights. 

Our simulation studies indicate that the model-averaged sub-models provided better posterior predictive performance compared to the estimation of the initially specified model, as measured by the log-scoring rule.