Latent Moderation Analysis: A Factor Score Approach

Moderation analysis with latent variables is an important topic in social science research. Although different methods have been proposed for latent moderation analysis in the past three decades, these methods have weaknesses in certain circumstances. We therefore propose the factor score approach as a straightforward and implementation-friendly alternative in latent moderation analysis. This approach has several advantages over other existing methods, such as being able to test higher-order interaction models and interaction-as-outcome models. We compared the empirical performance of the factor score approach and other commonly used methods, namely the unconstrained product indicator approach and the latent moderated structural equation approach, by conducting a simulation study. Results indicated that the factor score approach worked satisfactorily under a range of model conditions. Using these results, we can offer applied researchers some practical guidelines of use for the factor score approach with regard to the subject variable (N/P) ratio and reliability level.