Latent Variable Interactions with Categorical Indicators: Continuous and Categorical Latent Moderated Structural Equations Approaches

Social science phenomena are often predicted by interactions between variables. When these variables cannot be directly observed, one option is to model them as latent variables that are measured by multiple indicators. When indicators are continuous, latent interactions can be modeled and estimated using the latent moderated structural equations (LMS) approach. A categorical LMS (LMS-cat) approach with full information estimation was more recently developed. While previous research suggests that ordered categorical indicators can sometimes be treated as continuous, LMS and LMS-cat have not yet been directly compared. In this study, we evaluate continuous and categorical LMS for the estimation of latent interactions under ordinal indicators with 2, 3, 5, and 7 categories. Further, we compared the performance of frequentist and Bayesian estimation for both LMS models. Results suggest that categorical approaches are a safer choice, and that frequentist and non-informative Bayesian estimation approaches perform similarly.