Structural Equation Models

Ecological data sets tend to present a tangled web of correlations among variables. Structural equation modeling (SEM) is a method for explicitly analyzing this web of correlations, by declaring why the variables should be correlated. A structural equation model is based on a path diagram that poses causal interactions among variables, which might include indirect effects mediated by several variables. A SEM also poses a measurement model, which might include latent variables representing concepts that can be measured only indirectly via indicator variables (e.g., the concept of water quality as indicated by sediment or contaminant loadings). The path model implies a pattern of covariation among variables; this implied covariance provides the basis for testing both the path and measurement model. The process of SEM is an iterative workflow from an initial conceptual model, though estimating and evaluating a formal SE model (or perhaps several of these), to post-processing that summarizes all of the direct and indirect effects in the model. As ecologists increasingly deal with targets such as water quality, environmental health, and other latent concepts, SEM should be a valuable part of the ecological toolkit.