Supplemental material for A Simple Solution to Heteroscedasticity in Multilevel Nonlinear Structural Equation Modeling

In multilevel nonlinear structural equation modeling via latent moderated structural equations, the homoscedasticity assumption is typically made; that is, it is assumed that the variances within higher-level units are equal across these units. However, this assumption is frequently violated in research, potentially leading to inaccuracies in standard errors and inferences. In this article, we present an extensive Monte Carlo simulation study that provides evidence that the robust standard errors for moderation effects as obtained from the commonly employed sandwich estimator in Mplus can perform poorly under realistic conditions. This outcome holds true not only in scenarios characterized by substantial heteroscedasticity but also, albeit to a lesser degree, when homoscedasticity is upheld. As a remedy, we propose a computationally efficient delete-d type jackknife and a variant thereof. The two jackknife techniques outperformed the sandwich estimator in small to medium-sized samples. Therefore, we caution users not to apply the sandwich estimator and suggest that a jackknife technique should be preferred.