Comparing Empirical Power of Multilevel Structural Equation Models and Hierarchical Linear Models: Understanding Cross-Level Interactions

Both structural equation models and hierarchical linear models (HLMs) have been commonly used in multilevel analysis. This study utilized simulated data to investigate the power difference among 3 multilevel models: HLM, deviation structural equation models, and a hybrid approach of HLM and structural equation models. Two factors were examined: sample size and the second-level regression coefficient, each of which was varied independently to evaluate the empirical power of the 3 models. Results showed that large samples were crucial for HLM to perform well. The power of the other 2 methods was similar and generally higher than HLM, although the deviation structural equation model had the best overall performance. In addition, power did not always increase with larger second-level regression coefficient values. First-level unit size was an important component with an asymptotic efficiency at about n = 35. HLM power was more susceptible to change in second-level regression coefficient values than the other 2 methods.