This article considers a circular regression model for clustered data, where both the cluster effects and the regression errors have von Mises distributions. It involves β, a vector of parameters for the fixed effects, and two concentration parameters for the error distribution. A measure of intra‐cluster circular correlation and a predictor for an unobserved cluster random effect are studied. Preliminary estimators for the vector β and the two concentration parameters are proposed, and their performance is compared with that of the maximum likelihood estimators in a simulation study. A numerical example investigating the factors impacting the orientation taken by a sand hopper when released is presented. The Canadian Journal of Statistics 47: 712–728; 2019 © 2019 Statistical Society of Canada

中文翻译：

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聚类循环数据的随机效应模型

本文考虑了针对聚类数据的循环回归模型，其中聚类效应和回归误差均具有冯·米塞斯分布。它涉及β，固定效果的参数向量和两个误差分布的浓度参数。研究了集群内循环相关性的度量和未观察到的集群随机效应的预测因子。提出了向量β和两个浓度参数的初步估计量，并在模拟研究中将它们的性能与最大似然估计量进行了比较。给出了一个数值示例，研究了释放沙漏斗时影响方位的因素。加拿大统计杂志47：712-728；2019©2019加拿大统计学会