Latent Interactions with Ordinal Categorical Indicators and Non-Gaussian Bivariate Copulas

Latent interaction modeling is an important tool for educational and psychological research, yet its performance in the presence of non-normality and categorical ordinal indicators is not well understood. This study evaluates the performance of latent interaction modeling approaches under various conditions. The most notable condition is the non-Gaussian copula. Typically, latent interaction approaches have been evaluated with the assumption of a Gaussian copula. Including the non-Gaussian copula in this study allowed for a more accurate evaluation of the performance of the latent interaction modeling approaches under broader definitions of non-normality. The unconstrained product indicator approach was found to be more robust to non-normality but less precise and powered than Latent Moderated Structural equations. The treatment of categorical indicators as continuous resulted in biased estimates, emphasizing the need to treat categorical indicators as categorical. Future research should explore selecting the appropriate copula for non-normality and improving the computational efficiency of Bayesian analyses. This study provides insights into the limitations and opportunities for applied researchers dealing with categorical data