Structural equation models (SEMs) are becoming increasingly popular in health research. This modeling framework is useful in analyzing data from studies where multivariate outcomes or multiple, highly correlated surrogates of exposure have been collected. SEMs succinctly describe associations between exposure surrogates and outcomes, reduce collinearity problems, and alleviate multiple comparison concerns. However, classical fitting methods for these models typically make covariance structure, distributional, and linearity assumptions that are often suspect and difficult to verify.; In Chapter 1 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 as compared to traditional regressions. A detailed example underscores the critical role of subject matter knowledge in the successful implementation of SEMs.; In Chapter 2 we propose an estimating equations approach for estimating latent exposure models with longitudinal outcomes. Our proposed method is robust to misspecification of the outcome variance, and, compared to maximum likelihood, the loss of efficiency of the proposed method is relatively small. The proposed estimation approach is similar to regression calibration and regression on factor scores, but often renders more efficient estimators compared to regression calibration. We apply this method to a study of the effects of in-utero lead exposure on child development.; In Chapter 3 we apply recently developed residual-based diagnostic methodology for correlated data to structural equation models with latent variables. Residual-based diagnostics are of interest in structural equation modeling because the majority the currently available tools are based on aggregate forms of the data and are not sufficient for detecting certain departures from model assumptions, for example incorrectly specified error distributions, or nonlinearities. We evaluate the use of the rotated residuals for outlier detection and for covariate selection. These methods are applied to an example of in-utero lead exposure.
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