Adjusting for Unequal Selection Probability in Structural Equation and Multilevel Models: Applications to Demographic Survey Data

Kim Chantala, University of North Carolina at Chapel Hill
C. M. Suchindran, University of North Carolina at Chapel Hill

Most demographic surveys collect data using complex sampling plans involving selection of both clusters and individuals with unequal probability of selection. Research in methods of using structural equation modeling (SEM) and multilevel modeling (MLM) procedures to analyze such data is relatively new. Often sampling weights based on selection probabilities of individuals are used to estimate population-based models. However, sampling weights used for estimating multilevel models need to be constructed differently than weights used for single-level (population-average) models. This paper provides guidelines for using SEM or MLM techniques with complex survey data. First, the capabilities of popular SEM and MLM analysis software for analyzing data collected with a complex sampling plan are summarized. Next, we discuss how sampling weights needed for MLM analysis differ from weights needed for analyzing population-average models. Finally, we use existing software to demonstrate SEM and MLM analysis using data from the National Longitudinal Survey of Adolescents.