Circular data is different from linear data and its analysis also requires methods different from conventional methods. In this study a Bayesian embedding approach to estimating circular regression models is investigated, by means of simulation studies, in terms of performance, efficiency, and flexibility. A new Markov chain Monte Carlo (MCMC) sampling method is proposed and contrasted to an existing method. An empirical example of a regression model predicting teachers’ scores on the interpersonal circumplex will be used throughout. Performance and efficiency are better for the newly proposed sampler and reasonable to good in most situations. Furthermore, the method in general is deemed very flexible. Additional research should be done that provides an overview of what circular data looks like in practice, investigates the interpretation of the circular effects and examines how we might conduct a way of hypothesis testing or model checking for the embedding approach.

中文翻译：

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评估圆形回归模型的贝叶斯嵌入方法

循环数据不同于线性数据，其分析还需要与常规方法不同的方法。在这项研究中，通过性能研究，性能，效率和灵活性，研究了贝叶斯嵌入方法来估计循环回归模型。提出了一种新的马尔可夫链蒙特卡洛（MCMC）采样方法，并将其与现有方法进行了对比。贯穿整个过程，将使用回归模型的经验示例来预测教师在人际交往方面的得分。对于新提出的采样器，性能和效率更高，并且在大多数情况下是合理的。此外，通常认为该方法非常灵活。应该进行其他研究，以概述实际中的循环数据，