A two-level group-specific curve model is such that the mean response of each member of a group is a separate smooth function of a predictor of interest. The three-level extension is such that one grouping variable is nested within another one, and higher level extensions are analogous. Streamlined variational inference for higher level group-specific curve models is a challenging problem. We confront it by systematically working through two-level and then three-level cases and making use of the higher level sparse matrix infrastructure laid down in Nolan and Wand (2018). A motivation is analysis of data from ultrasound technology for which three-level group-specific curve models are appropriate. Whilst extension to the number of levels exceeding three is not covered explicitly, the pattern established by our systematic approach sheds light on what is required for even higher level group-specific curve models.

中文翻译：

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用于更高级别组特定曲线模型的流线型变分推理

两级组特定曲线模型使得组中每个成员的平均响应是感兴趣的预测变量的单独平滑函数。三级扩展是这样的，一个分组变量嵌套在另一个分组变量中，更高级别的扩展是类似的。更高级别组特定曲线模型的流线型变分推理是一个具有挑战性的问题。我们通过系统地处理两级和三级案例来应对它，并利用 Nolan 和 Wand（2018 年）制定的更高级别的稀疏矩阵基础设施。一个动机是分析来自超声技术的数据，其中三级组特定曲线模型是合适的。虽然没有明确涵盖超过三级的扩展，