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

Abstract

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.

Keywords:

• Multilevel CFA
• Categorical data
• WLSMV
• ULSMV
• Bias
• Efficiency

Data availability statement

The data that support the findings of this study are openly available in Texas Data Repository at http://doi.org/10.18738/T8/VPAH7O (Padgett 2019). Additional results are available in the online supplemental material as well (Padgett and Morgan 2019).