A nonparametric framework for linear–circular regression: Applications in environmental and biological sciences

Abstract

Circular data arise in numerous scientific fields, necessitating specialized regression models to relate linear predictors to circular responses. Existing approaches often rely on restrictive parametric assumptions, limiting their flexibility in capturing complex nonlinear relationships. Here we propose a flexible nonparametric linear–circular regression framework that models circular responses as modulo transformations of latent linear variables following wrapped exponential family distributions. This leads to a finite mixture of locally weighted generalized linear models, estimated efficiently via an Expectation-Maximization algorithm. Through extensive simulations and applications to environmental and biological datasets—including droplet motion, snail movement, and wind direction—our method consistently outperforms established models in accuracy and computational efficiency. These results demonstrate the framework’s adaptability and robustness in modeling complex circular data, offering a valuable tool for diverse scientific analyses involving directional outcomes.