A Unified Approach to Two-Level Structural Equation Models and Linear Mixed Effects Models

Two-level structural equation models (two-level SEM for simplicity) are widely used to analyze correlated clustered data (or two-level data) such as data collected from students (level-1 units) nested in different schools (level-2 units), or data collected from siblings (level-1 units) nested in different families (level-2 units). These data are usually collected by two sampling steps: randomly choosing some level-2 units; and then, randomly choosing some level-1 units from each chosen level-2 unit. Data collected in this way can be considered to be affected by two different random sources or random effects, namely, level-1 effects and level-2 effects. The substantive goal with such two-level data is to obtain theoretically meaningful and statistically adequate submodels for both the level-1 and level-2 effects. Realization of this main task consists of three steps:

• (1) set up an initial model with both level-1 and level-2 effects;
• (2) estimate the unknown model parameters;
• (3) test the goodness-of-fit of the given model.
  

http://link.springer.com/chapter/10.1007%2F978-0-387-76721-5_5