A Solution to Modeling Multilevel Confirmatory Factor Analysis with Data Obtained from Complex Survey Sampling to Avoid Conflated Parameter Estimates.

The issue of equality in the between-and within-level structures in Multilevel Confirmatory Factor Analysis (MCFA) models has been influential for obtaining unbiased parameter estimates and statistical inferences. A commonly seen condition is the inequality of factor loadings under equal level-varying structures. With mathematical investigation and Monte Carlo simulation, this study compared the robustness of five statistical models including two model-based (a true and a mis-specified models), one design-based, and two maximum models (two models where the full rank of variance-covariance matrix is estimated in between level and within level, respectively) in analyzing complex survey measurement data with level-varying factor loadings.