Statisticians use covariance structure modeling as a versatile tool fo
r modeling and testing theory. The models that result provide explicit
and detailed descriptions of stochastic systems. We show how covarian
ce structure models are related-mathematically, conceptually, philosop
hically 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 prescrip
tive domain of decision analysis. The paper includes an example concer
ning the management of hazardous materials, in which a covariance stru
cture model is converted to an influence diagram for use in a prescrip
tive analysis.