Spatial Hyperspheric Models for Compositional Data

Abstract

Compositional observations 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 trans-formed compositions and directional distributions. Such distributions naturally allow for zero-valued components and positive correlations, yet they may include support outside the nonnegative orthant and are not generative for compositional data. To overcome this challenge, we truncate the elliptically symmetric angular Gaussian (ESAG) distribution to the nonnegative orthant. Additionally, we propose a spatial hyperspheric regression model that contains fixed and random multivariate spatial effects. The proposed model also contains a term that can be used to propagate uncertainty that may arise from precursory stochastic models (i.e., machine learning classification). We used our model in a simulation study and for a spatial analysis of classified bioacoustic signals of the Dryobates pubescens (downy woodpecker).