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A Comparison of Different Approaches for Estimating Cross-Lagged Effects from a Causal Inference Perspective

Abstract This article compares different approaches for estimating cross-lagged effects with a cross-lagged panel design under a causal inference perspective. We distinguish between models that rely on no unmeasured confounding (i.e., observed covariates are sufficient to remove confounding) and latent variable-type models (e.g., random intercept cross-lagged panel model) that use parametric assumptions to adjust for unmeasured time-invariant confounding by including additional latent variables. Simulation studies confirm that the cross-lagged panel model provides biased estimates of the cross-lagged effect in the presence of unmeasured confounding. However, the simulations also show that the latent variable-type approaches strongly depend on the specific parametric assumptions, and produce biased estimates under different data-generating scenarios. Finally, we discuss the role of the longitudinal design and the limitations of assessing model fit for estimating cross-lagged effects.