Using structural equation modeling to investigate relationships among ecological variables

Structural equation modeling is an advanced multivariate statistical process with which a researcher can construct theoretical concepts, test their measurement reliability, hypothesize and test a theory about their relationships, take into account measurement errors, and consider both direct and indirect effects of variables on one another. Latent variables are theoretical concepts that unite phenomena under a single term, e.g., ecosystem health, environmental condition, and pollution (Bollen, 1989). Latent variables are not measured directly but can be expressed in terms of one or more directly measurable variables called indicators. For some researchers, defining, constructing, and examining the validity of latent variables may be the end task of itself. For others, testing hypothesized relationships of latent variables may be of interest. We analyzed the correlation matrix of eleven environmental variables from the U.S. Environmental Protection Agency's (USEPA) Environmental Monitoring and Assessment Program for Estuaries (EMAP-E) using methods of structural equation modeling. We hypothesized and tested a conceptual model to characterize the interdependencies between four latent variables-sediment contamination, natural variability, biodiversity, and growth potential. In particular, we were interested in measuring the direct, indirect, and total effects of sediment contamination and natural variability on biodiversity and growth potential. The model fit the data well and accounted for 81% of the variability in biodiversity and 69% of the variability in growth potential. It revealed a positive total effect of natural variability on growth potential that otherwise would have been judged negative had we not considered indirect effects. That is, natural variability had a negative direct effect on growth potential of magnitude -0.3251 and a positive indirect effect mediated through biodiversity of magnitude 0.4509, yielding a net positive total effect of 0.1258. Natural variability had a positive direct effect on biodiversity of magnitude 0.5347 and a negative indirect effect mediated through growth potential of magnitude -0.1105 yielding a positive total effects of magnitude 0.4242. Sediment contamination had a negative direct effect on biodiversity of magnitude -0.1956 and a negative indirect effect on growth potential via biodiversity of magnitude -0.067. Biodiversity had a positive effect on growth potential of magnitude 0.8432, and growth potential had a positive effect on biodiversity of magnitude 0.3398. The correlation between biodiversity and growth potential was estimated at 0.7658 and that between sediment contamination and natural variability at -0.3769.