Appropriate modeling of endogeneity in cross-lagged models: Efficacy of auxiliary and model-implied instrumental variables.

Endogeneity is a critical concern in research methodologies, yet it has been insufficiently addressed in longitudinal cross-lagged models, leading to potentially biased outcomes. This study scrutinized the endogeneity inherent in the cross-lagged panel model (CLPM), a prevalent and representative framework in longitudinal studies. We evaluated the efficacy of the instrumental variables (IV) methods, specifically focusing on both the auxiliary IVs (AIVs) and the model-implied IVs (MIIVs), in mitigating endogeneity issues. Simulation results indicated that endogeneity induced bias in CLPM, notably overestimating cross-lagged effects and thereby amplifying the apparent causal relationships. AIV-CLPM showed a smaller, yet still unacceptably high bias, along with low robustness and elevated type I error rates. In contrast, the MIIV-CLPM produced more accurate estimates with fewer type I errors, and, given sufficient observations, it achieved moderate statistical power. An extended simulation incorporating the random-intercept CLPM supported these findings, highlighting the generalizability of this approach. Furthermore, an empirical illustration demonstrated the practicality and feasibility of the MIIV-CLPM. Overall, MIIV is proven to be a superior modeling option within cross-lagged frameworks, effectively mitigating biases caused by endogeneity.