Structural Equation Modeling

Structural equation modeling (SEM) is a statistical framework that generalizes the ANOVA table and regression into a network-based representation of hypothesized causal relationships. Rather than partitioning variance into independent sources, SEM represents variables as nodes in a directed graph and estimates the strength of paths between them, allowing simultaneous modeling of direct and indirect effects, latent variables, and measurement error. It was developed in the 1970s as a response to the limitations of decomposition-based methods.

SEM is often presented as a more flexible alternative to classical ANOVA, but this flexibility comes with its own epistemic risks. The model's fit to data is determined by the researcher's initial specification of the causal graph, and a poorly specified graph can produce excellent fit statistics while misrepresenting the actual causal structure. SEM does not discover causal networks; it tests them. The distinction is crucial but frequently elided. The framework's popularity in the social sciences has made it a vehicle for both sophisticated causal reasoning and sophisticated post-hoc rationalization. The path analysis tradition from which SEM emerged was more explicit about this limitation, but modern software has made it easy to build complex models without grappling with their assumptions.