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Abstract:
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A way to address problems of causality is applying cyclic Structural Equation Models (SEMs). Cyclic SEMs, however, are known for the difficulty of identifaibility, i.e., any cyclic linear SEMs with normal errors are not identifiable (Nagase and Kano 2017). One approach to get rid of the difficulty is to adopt models with non-normal error terms (Kano and Shimizu 2003). In this talk, we consider non-linear SEMs with normal error terms and show that such models are identified under some conditions. One advantage of the models is that it can allow for the covariance between errors that are generally considered to imply the existence of unobserved confounders. We both numerically and analytically have addressed the models and we provided through proofs on their identifiability, a certain condition for non-linear functions needed to reach stable equilibrium state and so forth. Key findings are that, under a certain conditions, the model can accurately depict not only its causal direction but also their significance and affection of unobserved confounder as well. Details will be delivered at our presentation.
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