Using n-Level Structural Equation Models for Causal Modeling in Fully Nested, Partially Nested, and Cross-Classified Randomized Controlled Trials.

Complex data structures are ubiquitous in psychological research, especially in educational settings. In the context of randomized controlled trials, students are nested in classrooms but may be cross-classified by other units, such as small groups. Furthermore, in many cases only some students may be nested within a unit while other students may not. Such instances of partial nesting requires a more flexible framework for estimating treatment effects so that the model coefficients are correctly estimated. Although several recommendations have been offered to the field on handling partially nested data, few are comprehensive in their treatment of manifest and latent variables in the context of partial nesting, full nesting, and cross-classification. The present study introduces n-level structural equation modeling (SEM) as a flexible measurement and analytic framework for the estimation of treatment effects for complex data structures that frequently present in randomized controlled trials. In this tutorial, we explore how the notation of n-level SEM allows for parsimonious model specification whether data are observed or latent and in the presence of partial nested or cross-classified designs. By using the xxm package in R, the advantage of using n-level SEM framework is demonstrated through five examples for single outcome manifest variables, as in the traditional multilevel model, as well as latent applications as in multilevel SEM.