Evaluation of Two Methods for Modeling Measurement Errors When Testing Interaction Effects With Observed Composite Scores

Path models with observed composites based on multiple items (e.g., mean or sum score of the items) are commonly used to test interaction effects. Under this practice, researchers generally assume that the observed composites are measured without errors. In this study, we reviewed and evaluated two alternative methods within the structural equation modeling (SEM) framework, namely, the reliability-adjusted product indicator (RAPI) method and the latent moderated structural equations (LMS) method, which can both flexibly take into account measurement errors. Results showed that both these methods generally produced unbiased estimates of the interaction effects. On the other hand, the path modelwithout considering measurement errorsled to substantial bias and a low confidence interval coverage rate of nonzero interaction effects. Other findings and implications for future studies are discussed.