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.

Keywords:

• Causal inference
• cross-lagged effect
• cross-lagged panel model
• longitudinal data
• random intercept cross-lagged panel model

Notes

1 Usually, a second assumption is added (positivity assumption) which states that in the population, the density of observing any exposure level given the covariates is positive. This assumption implies that there exists sufficient overlap in the covariate distributions between the different exposure levels under consideration.

2 Allison et al. (2017, p. 3) write: “And not having to specifiy the functional form of the dependence of x on y both simplifies the estimation problem and reduces the danger of misspecification. If you are interested in the dependence of x on y, you can always specify a second dynamic panel model for y and estimate that separately.”

3 Note that this is different from multilevel structural equation modelling where the level-1 units are treated as exchangeable, and separate saturated covariance structures exist at level 1 and level 2. In this case, the number of estimated parameters at one level (e.g., level 2) does not affect the number of estimable parameters at the other level (e.g., level 1), and level-specific evaluations for ${\mathbf{\Sigma }}_B$ and ${\mathbf{\Sigma }}_W$ are possible and recommended (Ryu & West, 2009).