We introduce generalized partially linear models with covariates on Riemannian manifolds. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for scalar response variables with error distribution models other than a normal distribution. Partially linear models are particularly useful when some of the covariates of the model are elements of a Riemannian manifold, because the curvature of these spaces makes it difficult to define parametric models. The model was developed to address an interesting application: the prediction of children's garment fit based on three‐dimensional scanning of their bodies. For this reason, we focus on logistic and ordinal models and on the important and difficult case where the Riemannian manifold is the three‐dimensional case of Kendall's shape space. An experimental study with a well‐known three‐dimensional database is carried out to check the goodness of the procedure. Finally, it is applied to a three‐dimensional database obtained from an anthropometric survey of the Spanish child population. A comparative study with related techniques is carried out.

中文翻译：

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黎曼流形上的广义部分线性模型

我们介绍在黎曼流形上带有协变量的广义部分线性模型。这些模型与普通的广义线性模型一样，是黎曼流形上部分线性模型的泛化，它允许标量响应变量具有非正态分布的误差分布模型。当模型的某些协变量是黎曼流形的元素时，部分线性模型特别有用，因为这些空间的曲率使其很难定义参数模型。该模型的开发是为了解决一个有趣的应用：基于对儿童身体的三维扫描来预测儿童服装的合身性。为此原因，我们关注逻辑模型和序数模型，以及黎曼流形是肯德尔形状空间的三维情况的重要和困难情况。使用著名的三维数据库进行了一项实验研究，以检查该程序的有效性。最后，将其应用于从西班牙儿童人口的人体测量调查中获得的三维数据库。与相关技术进行了比较研究。