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

Many statistical models have been proposed to examine reciprocal cross-lagged causal effects from panel data. The present article aims to clarify how these various statistical models control for unmeasured time-invariant confounders, helping researchers understand the differences in the statistical models from a causal inference perspective. Assuming that the true data generation model (i.e., causal model) has time-invariant confounders that were not measured, we compared different statistical models (e.g., dynamic panel model and random-intercept cross-lagged panel model) in terms of the conditions under which they can provide a relatively accurate estimate of the target causal estimand. Based on the comparisons and realistic plausibility of these conditions, we made some practical suggestions for researchers to select a statistical model when they are interested in causal inference.