Guidelines for a graph-theoretic implementation of structural equation modeling

By J. Grace, D. Schoolmaster, G. Guntenspergen, A. Little, B. Mitchell, K. Miller, E. W. Schweiger. Ecosphere, 2012

550 citations recorded by the source corpus.

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. 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 analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. 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 involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

Subfields: Artificial Intelligence, Ecological Modeling

View Paper: https://www.semanticscholar.org/paper/cc0b5f0ea6a81c2f9ee95e8a246733b630c11e63

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Citations in the corpus

Positive species diversity and above‐ground biomass relationships are ubiquitous across forest strata despite interference from overstorey trees (2017, methodology): “To validate the specification of SEM and aid in interpretation of the SEM results (Grace et al. 2012, 2016), we examined the bivariate relationships representing each directional causal path according to the hypotheses in Fig.”
Conditions favouring Bromus tectorum dominance of endangered sagebrush steppe ecosystems (2013, methodology): “Our modelling process considered the available observed variables to identify ‘indicator variables’ (the observed variables that will serve as proxies for conceptual variables in the meta-SEM) using procedures described in Grace et al. (2012).”
Multivariate mapping of soil with structural equation modelling (2017, background): “2 Graphical model: the conceptual model becomes more specific in a graphical model that defines the type of variables included, such as observed, latent or composite variables (Grace et al., 2012).”
Linking resource availability and heterogeneity to understorey species diversity through succession in boreal forest of Canada (2018, methodology): “To validate the specification of SEM and aid in interpretation of the SEM results (Grace et al., 2012, 2016), we examined the bivariate relationships representing each directional causal path according to the hypotheses in Figure 1, using partial regression analysis.”
Response to Leslie Hayduk’s Review of Principles and Practice of Structural Equation Modeling, 4th Edition (2018, background): “The organization just described also better supported the inclusion in the 4th edition of a new topic, Judea Pearl’s structural causal model (SCM), or a graph-theoretic approach to SEM, also called third generation SEM (Grace et al. 2012).”