A Bayesian regression framework for circular models with INLA

Abstract Regression models for circular variables constitute a class of statistical models that has received comparatively little development and attention within the general statistical framework. This is largely because constructing a linear predictor through linear combinations of covariates and random effects tends to break the circular nature of the response variable, making standard regression approaches difficult to apply. In this paper, we introduce a new approach to address this issue, resulting in well-defined regression models for circular responses when the data are concentrated. The proposed framework naturally extends to joint regression settings involving multiple circular and non-circular responses, and accommodates a combination of linear covariates, circular covariates, and various random effects. This approach provides an efficient implementation for jointly modelling the complex temporal dynamics of wind speed and direction in the presence of additional covariates. Our formulation is well suited to the integrated nested Laplace approximation (INLA), enabling fast and accurate Bayesian inference. We demonstrate the performance of the approach using several simulated and real data examples.