The Impact of Non-Normality on Causal Effect Estimates in Structural Equation Models with Ordered Categorical Variables

Multilevel structural equation models (SEM) are widely used for estimating causal effects in social and behavioral sciences. However, the impact of non-normality on these estimates, particularly with ordered categorical variables, remains unclear. This study investigates how non-normality affects causal effect estimation in path and multigroup SEMs with ordered categorical variables. Using the Vine-to-Anything approach, we simulated multivariate distributions by independently varying marginals and copulas. We compared maximum likelihood (ML), robust ML, and diagonally weighted least squares (DWLS) estimators across various non-normal conditions in three simulation studies. Results show that bias in effect estimates critically depends on the combination of copulas and marginal distributions in treatment and control groups. DWLS generally outperformed ML, especially for average treatment effects and interaction effects. However, all methods were sensitive to distributional misspecifications. These findings highlight the importance of considering distributional assumptions when using ordered categorical data in causal inference studies.