The effect of estimation method and sample size in multilevel structural equation modeling
Article first published online: 30 DEC 2009
© 2009 The Authors. Journal compilation © 2009 VVS
Volume 64, Issue 2, pages 157–170, May 2010
How to Cite
Hox, J. J., Maas, C. J. M. and Brinkhuis, M. J. S. (2010), The effect of estimation method and sample size in multilevel structural equation modeling. Statistica Neerlandica, 64: 157–170. doi: 10.1111/j.1467-9574.2009.00445.x
After the online publication of this article, Cora Maas passed away on 8 February at the age of 45. We will miss her.
- Issue published online: 15 APR 2010
- Article first published online: 30 DEC 2009
- Recieived: April 2008. Revised: October 2009.
- Two-level structural equation modeling;
- estimation method;
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.