Residual Structural Equation Models

The residual variables in a structural equation model can be used to create a secondary structural model which we call the residual structural equation model (RSEM). We describe the maximum-likelihood, weighted least squares and Bayesian estimations for RSEM. The methodology is illustrated with several examples and simulation studies. We discuss the implementation of RSEM in the Mplus software package and provide scripts for the simulation studies. The RSEM framework is utilized to estimate and simplify popular models such as the random intercept cross-lagged panel model (RI-CLPM) and the latent curve model with structured residuals (LCM-SR). We discuss in details RSEM models with categorical observed variables as well as categorical latent variables in the context of mixture modeling.

Automated summary

This article introduces the estimation methods for the residual structural equation model (RSEM) and validates them through examples and simulation studies. The implementation of RSEM in the Mplus software package is discussed, and scripts for simulation studies are provided. The RSEM framework can be applied to estimate and simplify popular models, and can also handle cases with categorical observed variables and latent variables.