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.

翻译：针对圆形变量的回归模型发展相对不足，因为通过协变量与各类随机效应的线性组合构建线性预测因子的概念会破坏变量的圆形特性。本文提出一种新方法以修正此问题，当数据呈集中分布时，该方法可为圆形响应变量构建定义明确的回归模型。我们的方法可自然扩展至联合回归模型，其中可包含多个圆形与非圆形响应变量，并能同时处理线性协变量、圆形协变量及各类随机效应。该建模框架与集成嵌套拉普拉斯近似（INLA）方法天然契合，后者能够提供快速精确的贝叶斯推断。我们通过多个模拟与真实案例展示了所提方法的有效性。