A linear structural equation model (SEM) without free parameters has two parts: a probability distribution and an associated path diagram corresponding to the causal relations among variables specified by the structural equations and the correlations among the error terms. This article shows how path diagrams can be used to solve a number of important problems in structural equation modeling; for example, How much do sample data underdetermine the correct model specification? Given that there are equivalent models, is it possible to extract the features common to those models? When a modeler draws conclusions about coefficients in an unknown underlying SEM from a multivariate regression, precisely what assumptions are being made about the SEM? The authors explain how the path diagram provides much more than heuristics for special cases; the theory of path diagrams helps to clarify several of the issues just noted.
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