Factored Structural Equation Modeling in Blimp

This tutorial introduces Factored Structural Equation Modeling (FSEM), an alternative to classic multivariate SEM, and demonstrates its implementation in the Blimp software and the rblimp R package. FSEM reconceptualizes the joint distribution of observed and latent variables as a set of univariate and multivariate submodels—each specified via simple regression equations—and treats latent variables as missing data to be imputed via Bayesian data augmentation. This approach seamlessly accommodates combinations of continuous (normal and nonnormal), binary, ordinal, nominal, count, and two-part variables; interactions; nonlinear effects; heteroscedasticity; and multilevel data structures without violating distributional assumptions. We first outline the theoretical foundations of factored regression specification and its connection to the probability chain rule. We then describe the Markov chain Monte Carlo estimation and missing-data imputation algorithms that underlie FSEM. Next, we present a series of illustrative models—ranging from basic confirmatory factor analysis to complex dynamic, multilevel, and hybrid generalized-linear-SEM applications—providing Blimp syntax excerpts and a real-data example. We conclude by discussing practical considerations, limitations, and directions for future methodological research. This tutorial aims to equip researchers with a flexible, user-friendly framework for modeling complex data in behavioral and social sciences.