Direction of Dependence in Non-linear Models via Linearization

Statistical methods of causal learning and direction of dependence are designed to identify the direction of causation of variable associations from observational data. In the linear case, identification of the causal direction of effect relies on non-normality of variables. The reason for this is that under non-normality, asymmetry in variable distributions, error distributions, and independence structures of cause and error exist that allow one to probe whether a causal model of the from x → y or the reverse causation model y → x better approximates the underlying causal mechanism. In contrast, for non-linear variable relations, no distributional assumptions are required, and causal model identification relies on asymmetry of the independence structure of predictors and of competing models, provided that errors are additive. However, in practice, variables may be non-normal and non-linearly related to each other, and errors may be multiplicative. Thus, the present chapter discusses linearizable non-linear models for which distributional and independence-based direction dependence measures are applicable. Simulation results suggest that direction of dependence properties of linearized models allows one to identify the direction of causation for a variety of non-linear functional forms. An empirical example is given, and assumptions for model identification and extensions are discussed.