Does X at Time 1 Cause Y at Time 2? Longitudinal Causal Learning with Hidden Confounders

In this study, we develop statistical methods for bivariate causal learning using higher-order moment information from two-wave longitudinal data. Within the framework of linear non-Gaussian models, we derive tests based on joint cumulants and propose a multiple-testing algorithm to detect the existence of a longitudinal causal path in the presence of hidden confounders. By combining temporal information from longitudinal designs with higher-order distributional properties of the observed data, the proposed method allows researchers to draw valid causal conclusions under realistic scenarios commonly encountered in psychological studies. The performance of the proposed algorithm is evaluated through simulation studies. As expected for higher-moment methods, the proposed algorithm may require larger sample sizes than typically needed for second-moment methods to achieve high statistical power. Results demonstrate that the proposed algorithm provides sufficient evidence to establish the existence of a longitudinal causal path, particularly in large-scale data analysis. We then present two real-world data examples to illustrate the application of the causal learning algorithm in psychological research. Finally, we discuss practical implications and potential future research directions.