Integration of Moderation and Mediation in a Latent Variable Framework: A Comparison of Estimation Approaches for the Second-Stage Moderated Mediation Model

An increasing number of studies have focused on models that integrate moderation and mediation. Four approaches can be used to test integrated mediation and moderation models: path analysis (PA), product indicator analysis (PI, constrained approach and unconstrained approach), and latent moderated structural equations (LMS). To the best of our knowledge, few studies have compared the performances of PA, PI, and LMS in evaluating integrated mediation and moderation models. As a result, it is difficult for applied researchers to choose an appropriate method in their data analysis. This study investigates the performance of different approaches in analyzing the models, using the second-stage moderated mediation model as a representative model to be evaluated. Four approaches with bootstrapped standard errors are compared under different conditions. Moreover, LMS with robust standard errors and Bayesian estimation of LMS and PA were also considered. Results indicated that LMS with robust standard errors is the superior evaluation method in all study settings. And PA estimates could be severely underestimated as they ignore measurement errors. Furthermore, it is found that the constrained PI and unconstrained PI only provide acceptable estimates when the multivariate normal distribution assumption is satisfied. The practical guidelines were also provided to illustrate the implementation of LMS. This study could help to extend the application of LMS in psychology and social science research.