Thinking clearly about time-invariant confounders in cross-lagged panel models: A guide for choosing a statistical model from a causal inference perspective

Abstract

Many models have been proposed to examine the reciprocal cross-lagged causal effects from panel data. The purpose of the current article is to clarify how these various models control for unmeasured time-invariant confounders, helping researchers understand the differences of the models from causal inference perspective. We showed that cross-lagged panel model controls for time-invariant confounders that indirectly influence the relationships from prior time points. We also showed that there are other models (e.g., dynamic panel model, random-intercept cross-lagged panel model) that directly control for time-invariant confounders using time-invariant latent factor(s). These models vary in terms of the type of time-invariant confounders that are controlled as well whether the model assumes simple or complex individual trajectories over time. Based on the comparisons, we made some practical suggestions for researchers to select a model. We close the discussion by noting that those models that directly incorporate unmeasured time-invariant confounders rest on some critical and often unrealistic assumptions, providing a caution to over-trust causal estimates.

Why the Cross-Lagged Panel Model Is Almost Never the Right Choice

“…Models like the RI-CLPM and STARTS model would not be able to capture the causal effect of the stable trait on changes at each wave. There are, however, alternatives that attempt do so while still accounting for the betweenpersons associations that models like the RI-CLPM are meant to address (see e.g., Dishop & DeShon, 2022;Gische et al, 2021;Lüdtke & Robitzsch, 2022;Murayama & Gfrörer, 2022;Usami, 2021;Zyphur et al, 2020).…”

“…Figure 3 illustrates one version of a dynamic panel model (for an accessible introduction, see Dishop & DeShon, 2022; for a comparison of dynamic panel models to alternatives like the RI-CLPM, see Lüdtke & Robitzsch, 2022;Murayama & Gfrörer, 2022). These models are designed to capture dynamic processes over time while accounting for unobserved heterogeneity (i.e., the unmeasured stable individual difference factors that bias estimates in simpler models).…”

“…This term reflects the fact that influence of the timeinvariant factor accumulates over time: It affects observations at each wave directly and indirectly through all prior waves. The inclusion of an accumulating factor means that the dynamic panel model is not a multilevel model that cleanly separates between-and withinpersons levels (Murayama & Gfrörer, 2022). Like the RI-CLPM, however, the model can still account for personlevel factors that might bias the cross-lagged associations (Dishop & DeShon, 2022).…”

“…I occasionally discuss "time-invariant confounders" because the random-intercepts in the RI-CLPM were initially proposed to control for such confounders (Hamaker et al, 2015). However, recent technical discussions of various panel models have led to a more nuanced consideration of whether the RI-CLPM works by controlling for time-invariant confounds (e.g., Gische et al, 2021;Murayama & Gfrörer, 2022;Usami, 2022). The nuances of this distinction are beyond the scope of this article, and readers are referred to these articles for more technical discussion.…”

These Are Not the Effects You Are Looking for: Causality and the Within-/Between-Persons Distinction in Longitudinal Data Analysis

“…Whether these modified approaches are sufficient to adjust for all time-invariant confounders still depends on additional assumptions about the precise nature of the confounding (e.g., Lüdtke & Robitzsch, 2022;Murayama & Gfrörer, 2022). Furthermore, models are usually unable to identify both contemporaneous and lagged effects simultaneously.…”