Structural equation modelling with complex sampling designs and non-random attrition: A tutorial using Mplus

Complex sampling designs involving features such as stratification, cluster sampling, and unequal selection probabilities are often used in large-scale longitudinal surveys to improve cost-effectiveness and ensure adequate sampling of small or under-represented groups. However, complex sampling designs create challenges when there is a need to account for non-random attrition; a near inevitability in social science longitudinal studies. In this article we discuss these challenges and demonstrate the application of weighting approaches to simultaneously account for non-random attrition and complex design in a large UK-population representative survey. Using an auto-regressive latent trajectory model with structured residuals (ALT-SR) to model the relations between relationship satisfaction and mental health in the Understanding Society study as an example, we provide guidance on implementation of this approach in both R and Mplus is provided. Two standard error estimation approaches are illustrated: pseudo-maximum likelihood robust estimation and Bootstrap resampling. A comparison of unadjusted and design-adjusted results also highlights that ignoring the complex survey designs when fitting structural equation models can result in misleading conclusions.