Estimation Methods in Multilevel Structural Equation Modeling: Under Conditions of Data Nonnormality and Varied Sample Sizes

The text examines multilevel regression models in the context of multilevel structural equation modeling (SEM) in terms of accuracy of parameter estimates, standard errors, and fit indices in normal and nonnormal data under various sample sizes and differing estimators (maximum likelihood, generalized least squares, and weighted least squares). The finding revealed that the regression coefficients were estimated with little to no bias among the study design conditions investigated. However, the number of clusters (group level) appeared to have the greatest impact on bias among the parameter estimate standard errors at both level- 1 and level-2. Regarding fit statistics, negative bias was noted among each of the fit indices investigated when the number of clusters ranged from 30 to 50 and cluster size was fixed at 10. Recommendations for the substantive researcher are presented and areas of future research are discussed.