A Comparison of Scaled Difference Tests for Forming Confidence Intervals in SEM

Likelihood-based confidence intervals often perform better than Wald-based intervals in structural equation modeling. One challenge involves their robustness to nonnormality. While prior research has implemented a “robust” variant based on one scaled test, other scaled difference tests are available. In addition, lavaan-based software implementations are challenging and several solutions, including the semlbci package, have not been compared. We report two simulations evaluating three scaled difference tests and two software implementations; we also include bootstrapping, Bayesian estimation, and Wald-based intervals based on a sandwich covariance matrix with observed information (Huber-White or “MLR”). We vary nonnormality and examined a behavioral genetics model and a cross-lagged panel model with an indirect effect. The originally used scaled test outperformed other scaled tests, was comparable to bootstrapping, and slightly outperformed MLR under certain nonnormality conditions with the behavioral genetics model. We document challenges in estimation of these intervals with lavaan.