Using SEM to Analyze Complex Survey Data: A Comparison between Design-Based Single-Level and Model-Based Multilevel Approaches

Both ad-hoc robust sandwich standard error estimators (design-based approach) and multilevel analysis (model-based approach) are commonly used for analyzing complex survey data with nonindependent observations. Although these 2 approaches perform equally well on analyzing complex survey data with equal between- and within-level model structures (B. O. Muthén & Satorra, 1995), the performances of these 2 approaches for analyzing multilevel data with unequal between- and within-level structures have not yet been systematically examined. In this study, we extended B. O. Muthén and Satorra's (1995) study by comparing these 2 approaches and an additional model-based maximum model for analyzing multilevel data considering number of clusters, cluster size, intraclass correlation, and the equality of different level structures. The simulation results showed the model-based maximum model generally performed well across conditions. This model is also recommended as an alternative for analyzing nonindependent survey data, especially when the information of the higher level model structure is not known.