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

Abstract

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.

Comparing revised latent state–trait models including autoregressive effects.

“…Therefore, revisiting the arguments from the new perspective certainly would be interesting. Further interesting topics that are worth investigating in view of LST-R theory are the inclusion of short- and long-term intervention effects (Shamsollahi et al, 2021), latent moderation (Ozkok et al, 2021), and continuous time models (Voelkle et al, 2018). A particular advantage of LST-R theory is that it is very explicit in the random experiment considered and includes model-free definitions of latent variables.…”

Temporal exploration of the interpersonal theory of suicide among adolescents during treatment.

“…Third, the ITS specifies that suicidal ideation is the result of the three-way interaction between thwarted belongingness, burdensomeness, and hopelessness. However, due to the limitations of the software we used (Ozkok et al, 2021), we were not able to test this interaction. Fourth, there may have been issues related to psychometric measurement that contributed to these findings.…”

Testing for Within × Within and Between × Within Moderation Using Random Intercept Cross-Lagged Panel Models

“…Second, we have the between-person components (i.e. random intercepts, x Bi , y Bi ), which capture the (stable) within person deviations from these group means, thus representing an individual's time-invariant deviations from the time-specific mean, using similar notation as in Ozkok et al (2021). In SEM software such as Mplus, the person-specific intercepts are specified using latent variables composed of repeated measures with factor loadings fixed to 1.…”

“…Analyses were implemented in the structural equation modelling (SEM) software Mplus (L. K. . This is the only software that can currently effectively deal with multiple latent variable interactions (Ozkok et al, 2021). To date, only one previous study has implemented continuous interaction terms within a RI-CLPM framework.…”

“…To date, only one previous study has implemented continuous interaction terms within a RI-CLPM framework. Ozkok et al (2021) illustrated latent variable interactions within the context of the relations between work conflict and job satisfaction, comparing results from Between  Within, and Within  Within interactions in a standard CLPM to results from a model controlling for stable between-person effects. Here we move beyond this by making the important distinction between Between  Within interactions using a time-invariant moderator vs Between  Within interactions using the between-person component of a time-varying moderator, as well as developing a Within  Within interaction involving two time-varying dependent variables.…”