Cyclic structural causal model with unobserved confounder effect

This study examined cyclic non linear structural equation models (SEMs) with an unobserved confounder. The determination of causal direction, identifying whether X causes Y, Y causes X, or X and Y affect each other, is a fundamental issue in science and technology. Unobserved confounding factors are so-called third variables which influence both X and Y. Inclusion of unobserved confounding factors in the model, if they exist, is highly important, as unnoticed confounding variables can result not only in biased estimates but in pseudo-correlation between X and Y, which can distort causal inference. In this article, a cyclic non linear SEM with confounding factors was developed and the causal graph identifiability of the model was proved. The model’s identifiability was confirmed by simulation studies involving synthetic datasets and by application to a real dataset, namely, a Census Income (KDD) dataset containing weighted census data extracted from the 1994 and 1995 current population surveys conducted by the U.S. Census Bureau. The model effectively described the relationship between the variables age and wages, and no strong confounding factors effect was detected.