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; and (3) test the goodness-of-fit of the given model.
KeywordsLinear Mixed Effect Model Saturated Model Linear Mixed Effect Model Bayesian Model Selection Unknown Model Parameter
This work was supported by National Institute on Drug Abuse Grants DA01070, DA00017, and the University of New Haven 2006 and 2007 Summer Faculty Fellowships.
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