Bayesian hierarchical moderated factor analysis for testing measurement invariance in multilevel data: Model development, simulation studies, and experience sampling application

Moderated Nonlinear Latent Factor Analysis (MNLFA) has been introduced as a flexible approach for testing measurement invariance among categorical and continuous covariates. Equipped with Bayesian shrinkage priors, MNLFA can handle large numbers of covariates and potentially invariant item parameters. The present study extends the capabilities of the Bayesian MNLFA to multilevel and longitudinal confirmatory factor analysis. We show how a Bayesian hierarchical MNLFA (BH-MNLFA) can be implemented and provide two simulation studies to demonstrate its functionality. Focusing on invariance explorations in experience sampling data as a potential use case in the context of longitudinal data analysis, we showcase the utility of BH-MNLFA with data from educational psychology, and test invariance of state self-concepts measures across time and school subjects.