Non-linear regression for causal inference

Regression’s capability extends beyond linear associations by leveraging parameter linearity rather than necessitating linearity in the data itself. Parameter linearity in regression means that the model is linear in its coefficients (parameters), regardless of whether the relationship between variables is linear or non-linear.

This flexibility allows the modeling of non-linear relationships through data transformations and the inclusion of polynomial or interaction terms. Specifically, interaction terms, which model the multiplicative effects between variables, are incorporated by adding a product term to the regression equation. For example, to model the interaction between variables and , we introduce the term into the model. Additionally, non-linear dependencies can be quantitatively assessed using entropy-based metrics such as mutual information, providing a robust framework for understanding complex variable relationships...