Model Fit Estimation for Multilevel Structural Equation Models

Structural equation modeling (SEM) provides an extensive toolbox to analyze the multivariate interrelations of directly observed variables and latent constructs. Multilevel SEM integrates mixed effects to examine the covariances between observed and latent variables across many levels of analysis. However, while it is necessary to consider model fit, traditional indices are largely insufficient to analyze model fit at each level of analysis. The present article reviews (a) the partially saturated model fit approach first suggested by Ryu and West and (b) an alternative model parameterization that removes the multilevel data structure. We next describe the implementation of an algorithm to compute partially saturated model fit for 2-level structural equation models in the open source SEM package, OpenMx, including verification in a simulation study. Finally, an example empirical application evaluates leading theories on the structure of affect from ecological momentary assessment data collected thrice daily for two weeks from 345 participants.