Small Sample SEM Estimators for (Quasi-) Experiments With Complex Structures

A core limitation of conventional SEM is the computational challenge of estimating complex models with small samples. For example, prior investigations of simple cross-classified structures (e.g., students cross-classified between schools and neighborhoods) have demonstrated that even the simplest cross-classified SEMs with just a few latent variables (e.g., mediation model) at each level are notoriously computationally challenging. To circumvent computational challenges, most SEM software limits users just two or three levels. In this study, we develop global and local method-of-moments corrected maximum likelihood estimators for n-level (any number of levels or [non-] hierarchical structure) SEMs. The estimators are well-suited to the types of experiments with complex structures because the framework and estimation method easily extends to accommodate arbitrary structures and levels of nesting (e.g., any structure or number of levels) including interactions between latent variables across levels of nesting (e.g., interactions between school and neighborhood membership that operationalize intersectionality).