Regression models for circular data based on nonnegative trigonometric sums

The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is the surface of a hypersphere; thus, constructing regression models for a circular-dependent variable using NNTS models can comprise fitting great (small) circles on the parameter hypersphere that can identify different regions (rotations) along the great (small) circle. We propose regression models for circular- (angular-) dependent random variables in which the original circular random variable, which is assumed to be distributed (marginally) as an NNTS model, is transformed into a linear random variable such that common methods for linear regression can be applied. The usefulness of NNTS models with skewness and multimodality is shown in examples with simulated and real data. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper presents the application of nonnegative trigonometric sums (NNTS) models in circular data analysis. Regression models for circular-dependent variables are constructed by fitting great circles on the parameter hypersphere, enabling the identification of different regions along the circle. The transformation of the original circular variable into a linear variable allows for the application of common linear regression methods in circular data analysis.