Structural equation models:: A review with applications to environmental epidemiology

Structural equation models (SEMs) have been discussed extensively in the psychometrics and quantitative behavioral sciences literature. However, many statisticians and researchers in other areas of application are relatively unfamiliar with their implementation. Here we review some of the SEM literature and describe basic methods, using examples from environmental epidemiology. We make connections to recent work on latent variable models for multivariate outcomes and to measurement error methods, and discuss advantages and disadvantages of SEMs compared with traditional regressions. We give a detailed example in which two models fit the same data well, yet one is physiologically implausible. This underscores the critical role of subject matter knowledge in the successful implementation of SEMs. A brief discussion on open research areas is included.