A linear-circular regression using a finite mixture of the generalized linear regression models

Abstract This paper introduces a novel and extensive framework for addressing linear-circular regression problems, where linear predictors are related to a circular (angular) response variable. The proposed methodology depends on the wrapped technique, a well-established technique for transforming any linear distribution into a circular distribution, to facilitate linear-circular regression analysis. The core of our methodology is the treatment of circular responses as the outcome of a modulo operation applied to unobserved linear responses. This conceptualization leads to a flexible mixture model that combines multiple linear-linear regression models, allowing for the detection of complex relationships between circular outcomes and linear predictors. To estimate the parameters of the proposed mixture model, we use the Expectation–Maximization algorithm for maximum likelihood estimation. We use four numerical examples to evaluate the performance of the suggested models and show how well they handle different types of data. To demonstrate the real-world effectiveness of our approach, we apply it to two challenging problems: estimating wind directions and tracking the movement patterns of blue periwinkles both of which exhibit complex, highly variable behavior.