Year: 2026
Type: article
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.
Source: Statistics and Computing
Institution: University of Florence
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W7162781671