Interaction Effects in Cross-Lagged Panel Models: SEM with Latent Interactions Applied to Work-Family Conflict, Job Satisfaction, and Gender

Researchers often combine longitudinal panel data analysis with tests of interactions (i.e., moderation). A popular example is the cross-lagged panel model (CLPM). However, interaction tests in CLPMs and related models require caution because stable (i.e., between-level, B) and dynamic (i.e., within-level, W) sources of variation are present in longitudinal data, which can conflate estimates of interaction effects. We address this by integrating literature on CLPMs, multilevel moderation, and latent interactions. Distinguishing stable B and dynamic W parts, we describe three types of interactions that are of interest to researchers: 1) purely dynamic or WxW; 2) cross-level or BxW; and 3) purely stable or BxB. We demonstrate estimating latent interaction effects in a CLPM using a Bayesian SEM in Mplus to apply relationships among work-family conflict and job satisfaction, using gender as a stable B variable. We support our approach via simulations, demonstrating that our proposed CLPM approach is superior to a traditional CLPMs that conflate B and W sources of variation. We describe higher-order nonlinearities as a possible extension, and we discuss limitations and future research directions.