A third generation of structural equation modeling: From theories to queries

Background/Question/Methods

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of systems. New ideas and methods emerging from the study of causality, influences from graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of the enterprise. In this paper we describe new developments in SEM that constitute a third-generation of the methodology (3GSEM). Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than on properties of matrices (which has characterized the first and second generations of SEM). Also new devices, such as metamodels and causal diagrams, as well as an increased emphasis on queries, are included in the updated procedures.

Results/Conclusions

The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process, starting with theory translation, proceeding through model evaluation and inference, and ending with prospective analyses based on the prediction equations. Results obtained show how these wetlands are sensitive to eutrophication, invasion by cattails, and degradation of characteristic Sphagnum bog communities. We further illustrate how the SE model can be queried to explore how interventions might take advantage of an environmental threshold to limit cattail invasions. 3GSEM subsumes the historical matrix approach under a graph-theory implementation. It also fills certain procedural gaps in the science process, including in model formulation, exposition of the assumptions/implications behind models, and supports a more rigorous consideration of the requirements for drawing causal inferences. It is also designed to permit complex specifications and to be compatible with Bayesian and likelihood estimation methods. Finally, 3GSEM fosters the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.