Crossing Borders: Merging multilevel and structural equation

Crossing Borders: Merging multilevel and structural equation modeling
Joop Hox
Utrecht University, the Netherlands
Structural equation modeling (SEM) is a very general analysis technique, which is widely
used in the social and behavioral sciences. It is a combination of factor analysis and
regression analysis, and includes as special cases several traditional multivariate techniques,
such factor analysis, regression analysis, Manova, and others. The interest in SEM is often on
theoretical constructs that are represented by latent factors. The relationships between the
theoretical constructs are represented by regression or path coefficients between the factors.
Multilevel Modeling (MLM) is an analysis technique developed for hierarchically nested
data. Examples are pupils who are nested within classes and schools, family members who
are nested in families, and residents who are nested within neighborhoods. Researchers are
often interested in the question how individual characteristics and characteristics of the
context (class, family, neighborhood) interact and influence important individual outcome
variables. Multilevel regression analysis offers a tool to analyze hierarchical data and provide
answers to this question.
An ongoing development is that multilevel models and structural equation models are
merging. Theoretical work has shown that from an abstract statistical view multilevel models
can be looked at as a special structural equation model. In addition, most important SEM
software now allows for multilevel structures. As a result, we can now analyze multilevel
factor models and multilevel path models, for example multilevel models for mediation