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Nesting and Equivalence Testing for Structural Equation Models

In this article, we discuss the nesting and equivalence testing (NET) methodology developed in Bentler and Satorra (2010). We describe how the methodology is implemented in Mplus for the general structural equation model (SEM) model with continuous variables based on the maximum-likelihood (ML) estimation as well as the general SEM model with categorical, censored and continuous dependent variables based on the weighted least squares (WLS) family of estimators. We use the NET methodology to address several model nesting questions that arise in the bi-factor CFA model and the multiple group factor analysis model.