Covariance Structure Models and Influence Diagrams

Statisticians use covariance structure modeling as a versatile tool for modeling and testing theory. The models that result provide explicit and detailed descriptions of stochastic systems. We show how covariance structure models are related---mathematically, conceptually, philosophically and practically---to Gaussian influence diagrams as described by Shachter and Kenley (1989). This relationship suggests ways in which covariance structure modeling can be used to advantage in the prescriptive domain of decision analysis. The paper includes an example concerning the management of hazardous materials, in which a covariance structure model is converted to an influence diagram for use in a prescriptive analysis.