The incorporation of sample weights into multilevel structural equation models

Over the past decade and a half, methodologists working with structural equation modeling (SEM) have developed approaches for accommodating multilevel data. These approaches are particularly helpful when modeling data that come from complex sampling designs. However, most data sets that are associated with complex sampling designs also include observation weights, and methods to incorporate these sampling weights into multilevel SEM analyses have not been addressed. This article investigates the use of different weighting techniques and finds, through a simulation study, that the use of an effective sample size weight provides unbiased estimates of key parameters and their sampling variances. Also, a popular normalization technique of scaling weights to reflect the actual sample size is shown to produce negatively biased sampling variance estimates, as well as negatively biased within-group variance parameter estimates in the small group size case.