A Bayesian regression framework for circular models with INLA

TL;DR

This paper introduces a Bayesian regression framework for circular data using INLA, enabling efficient modeling of circular responses with mixed covariates and random effects, demonstrated through simulations and real data.

Contribution

The paper develops a novel Bayesian regression approach for circular variables that integrates seamlessly with INLA, extending to joint models with multiple response types.

Findings

Effective modeling of circular responses with INLA

Applicable to joint models with mixed responses

Validated through simulations and real data examples

Abstract

Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we introduce a new approach to rectify this issue, leading to well-defined regression models for circular responses when the data are concentrated. Our approach extends naturally to joint regression models where we can have several circular and non-circular responses, and allow us to handle a mix of linear covariates, circular covariates and various random effects. Our formulation aligns naturally with the integrated nested Laplace approximation (INLA), which provides fast and accurate Bayesian inference. We illustrate our approach through several simulated and real examples.