A comparison of scaled difference tests for forming confidence intervals in SEM

Likelihood-based confidence intervals often perform better than Wald-based intervals instructural equation modelling, but one challenge involves their robustness to distributionalassumption violations. While Falk (2018) implemented a “robust” variant based on invertinga test by Satorra (2000), other scaled difference tests are available. These approaches havenot been compared to Wald-based intervals based on a sandwich covariance matrix withobserved information (Huber-White or “MLR”). In addition, lavaan-based softwareimplementations are challenging and several solutions, including the new semlbci package(Cheung Pesigan, 2023), have not been compared. We report two simulations evaluatingthree scaled difference tests, Huber-White standard errors, and two softwareimplementations. Under several nonnormality conditions, we examine a classic behavioralgenetics model and a cross-lagged panel model with an indirect effect. Satorra’s (2000)difference test worked best and sometimes outperformed Huber-White standard errors. Wedocument challenges in estimation of these intervals if lavaan (Rosseel, 2012) is used.