Assessing Direct and Indirect Effects in Multilevel Designs with Latent Variables

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Abstract
Researchers commonly ask whether relationships between exogenous predictors, X, and outcomes, Y, are mediated by a third set of variables, Z. Simultaneous equations decompose the relationship between X and Y into an indirect component, operating through Z, and a direct component, the relationship between X and Y given Z. Often, X, Y, and/or Z are measured with error. Structural equation modeling is widely used in this scenario. However, sociological data commonly have a nested structure (students within schools, residents within local areas). Hierarchical linear models represent such multilevel data well and can handle errors of measurement, but have not incorporated simultaneous equations for direct and indirect effects. This article incorporates the study of such mediated effects into the hierarchical linear model, naturally extending the analysis to include unbalanced, multilevel designs and missing data. The authors illustrate the approach by examining the extent to which neighborhood social control mediates the relationship between neighborhood social composition and violence in Chicago.