Evaluating the relative efficiency among robust estimation methods for multilevel factor analysis with categorical data

Multilevel measurement models are more frequently applied to help answer questions when data arise from hierarchically structured multivariate data. In this simulation study of multilevel factor models, we evaluated the relative efficiency among three estimation methods: robust maximum likelihood, unweighted least squares, and weighted least squares. We found that weighted least squares yielded more or equally efficient parameter estimates under all sample size conditions for all model parameters. The relative efficiency of standard errors was less straightforward where maximum likelihood was more efficient for loadings and residual variances, but weighted least squares was more efficient for the factor covariance matrices. Finally, we give recommendations for estimating multilevel confirmatory factor analysis models and directions for future research.

Automated summary

The study found that weighted least squares produced more or equally efficient parameter estimates under all sample size conditions in the simulation study of multilevel factor models. The relative efficiency of standard errors was more complex, with maximum likelihood being more efficient for loadings and residual variances, while weighted least squares was more efficient for factor covariance matrices. Recommendations for estimating multilevel confirmatory factor analysis models and directions for future research were provided.