An interpretable varying coefficients approach to non-linear regression

Abstract Non-linear regression models are flexible approaches used to model complex associations. In many recent proposals, additional flexibility comes at the cost of loss of interpretability of the model’s parameters and, consequently, of the data analysis results. This paper introduces a flexible model whose parameters are easily interpretable. In particular, the model incorporates non-linear effects through a semi-parametric spline-based representation that separates linear and non-linear effects via an orthogonal basis decomposition. We introduce a covariate-dependent regression coefficient to enhance flexibility and show the proposed approach’s equivalence with a non-linear interaction model. In the proposed approach, the order of the covariates is relevant; however, we demonstrate that the model is invariant to this ordering. The proposed model performs comparatively well in simulation studies compared to state-of-the-art approaches. Finally, we illustrate the practical utility of the proposed approach through two applications that show a varying degree of non-linear associations.