Croon's Bias-Corrected Estimation for Multilevel Structural Equation Models with Non-Normal Indicators and Model Misspecifications.

Multilevel structural equation models (MSEMs) are well suited for educational research because they accommodate complex systems involving latent variables in multilevel settings. Estimation using Croon's bias-corrected factor score (BCFS) path estimation has recently been extended to MSEMs and demonstrated promise with limited sample sizes. This makes it well suited for planned educational research which often involves sample sizes constrained by logistical and financial factors. However, the performance of BCFS estimation with MSEMs has yet to be thoroughly explored under common but difficult conditions including in the presence of non-normal indicators and model misspecifications. We conducted two simulation studies to evaluate the accuracy and efficiency of the estimator under these conditions. Results suggest that BCFS estimation of MSEMs is often more dependable, more efficient, and less biased than other estimation approaches when sample sizes are limited or model misspecifications are present but is more susceptible to indicator non-normality. These results support, supplement, and elucidate previous literature describing the effective performance of BCFS estimation encouraging its utilization as an alternative or supplemental estimator for MSEMs.