The effect of estimation method and sample size in multilevel structural equation modeling

Multilevel structural equation modeling (multilevel SEM) has become an established method to analyze multilevel multivariate data. The first useful estimation method was the pseudobalanced method. This method is approximate because it assumes that all groups have the same size, and ignores unbalance when it exists. In addition, full information maximum likelihood (ML) estimation is now available, which is often combined with robust chi-squares and standard errors to accommodate unmodeled heterogeneity (MLR). In addition, diagonally weighted least squares (DWLS) methods have become available as estimation methods. This article compares the pseudobalanced estimation method, ML(R), and two DWLS methods by simulating a multilevel factor model with unbalanced data. The simulations included different sample sizes at the individual and group levels and different intraclass correlation (ICC). The within-group part of the model posed no problems. In the between part of the model, the different ICC sizes had no effect. There is a clear interaction effect between number of groups and estimation method. ML reaches unbiasedness fastest, then the two DWLS methods, then MLR, and then the pseudobalanced method (which needs more than 200 groups). We conclude that both ML(R) and DWLS are genuine improvements on the pseudobalanced approximation. With small sample sizes, the robust methods are not recommended.