Compositional data are an increasingly prevalent data source in spatial statistics. Analysis of such data is typically done on log-ratio transformations or via Dirichlet regression. However, these approaches often make unnecessarily strong assumptions (e.g., strictly positive components, exclusively negative correlations). An alternative approach uses square-root transformed compositions and directional distributions. Such distributions naturally allow for zero-valued components and positive correlations, yet they may include support outside the non-negative orthant and are not generative for compositional data. To overcome this challenge, we truncate the elliptically symmetric angular Gaussian (ESAG) distribution to the non-negative orthant. Additionally, we propose a spatial hyperspheric regression that contains fixed and random multivariate spatial effects. The proposed method also contains a term that can be used to propagate uncertainty that may arise from precursory stochastic models (i.e., machine learning classification). We demonstrate our method on a simulation study and on classified bioacoustic signals of the Dryobates pubescens (downy woodpecker).

翻译：成分数据在空间统计学中日益成为一种普遍的数据源。对此类数据的分析通常通过对数比变换或狄利克雷回归进行。然而，这些方法往往做出不必要的强假设（例如，严格为正的分量、完全负相关）。另一种方法使用平方根变换后的成分数据和方向分布。这类分布天然允许零值分量和正相关关系，但其支撑集可能超出非负象限，且不能生成成分数据。为克服这一挑战，我们将椭圆对称角高斯（ESAG）分布截断至非负象限。此外，我们提出了一种包含固定和随机多元空间效应的空间超球面回归方法。所提出的方法还包含一个可用于传播由前置随机模型（即机器学习分类）产生的不确定性的项。我们通过模拟研究和对Dryobates pubescens（绒啄木鸟）生物声学信号分类的实例验证了所提方法的有效性。